Wages, Employment Not Determined By Supply, Demand
Robert Vienneau
This long post presents an example in which higher wages are
associated with firms choosing to employ more workers per unit output
produced. The exact numeric values used are obviously unreasonable. The
example, though, is used to make a point.
I assume a reader willing to follow tedious arithmetic. Skip down
to the conclusions at the end if you're curious about my point.
2.0 DATA ON TECHNOLOGY
Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, steel, and (seed)
corn. All production processes in this example require a year to
complete. Only one production process is known for producing corn. This
process requires the following inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year:
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Steel is also produced by this firm. Two processes are known for
producing steel:
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
Apparently, inputs of corn and steel can be traded off in producing
steel. The process that uses less corn and more steel, however, also
requires a greater quantity of labor input.
3.0 QUANTITY FLOWS
I want to consider a couple of different levels at which this
firm can operate the corn-producing process and each steel-producing
process. First, suppose the corn-producing process is used to
produce 1.208 Bushels corn and the Alpha process is used to produce
0.3717 Tons steel. The quantity flows shown in Table 3 result.
TABLE 3: THE CORN-PRODUCING TECHNIQUE USING THE
ALPHA STEEL-PRODUCING PROCESS
0.07182 Person-Years 1.0000 Person-Years
0.1301 Tons Steel 0.2416 Tons Steel
0.003552 Bushels Corn 0.2040 Bushels Corn
0.3717 Tons Steel 1.208 Bushels Corn
When the firm operates these processes in parallel, it requires
a total of 0.208 Bushels corn as input. The output of the
corn-producing process can replace this input, leaving a net
output of one Bushel corn. Notice that the total inputs of
steel is 0.1301 + 0.2416 = 0.3717 Tons steel, which is exactly
replaced by the output of the Alpha process. So Table 3 shows
a technique in which 1.072 Person-Years labor is used to produce
a net output of one Bushel corn. The firm, when operating this
technique can produce any desired output of corn by scaling
both processes equally.
Next, suppose the corn-producing process is used to produce
1.258 Bushels corn, and the Beta process is used to produce 0.2903
Tons steel. Table 4 results.
TABLE 4: THE CORN-PRODUCING TECHNIQUE USING THE
BETA STEEL-PRODUCING PROCESS
0.009752 Person-Years 1.042 Person-Years
0.03869 Tons Steel 0.2516 Tons Steel
0.04526 Bushels Corn 0.2125 Bushels Corn
The same sort of arithmetic shows that this technique uses
1.0516 Person-Years to produce one Bushel corn.
4.0 PRICES
Which technique will the firm adopt, if any? The answer
depends, in this analysis, on which is more profitable. So one
has to consider prices. I assume throughout that inputs of steel,
corn, and labor are charged at the start of the year. The price
of corn is assumed constant at $10,000 per Bushel. Two different
levels of wages are considered.
4.1 PRICES WITH LOW WAGES
Accordingly, assume wages are initially $1,338.8 per Person-Year.
By assumption, the firm neither buys nor sells steel on the market.
The firm produces steel solely for its own use. Still, the firm
must enter a price of steel on its books. I assume that the firm
sets this price so that it is making the same rate of profits in
both processes it uses.
The initial price of steel, by this criterion, is $6,013 per
Ton. Table 5 illustrates. Note that the cost of operating the
Beta process is less than the Alpha process. Because of this
cheapness, this firm will produce steel only with the Beta
process; the quantity flows shown above in Table 4 will apply.
Also notice that the rate of profits is the same in producing
corn and in producing steel, as desired. This firm is content.
TABLE 5: COSTS, WAGE $1,338.8 PER PERSON-YEAR,
PRICE OF STEEL $6,013 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$1,338.8 = $4,000 150%
Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
+ 0.19321*$1,338.8 = $2,459
Steel Beta 0.13329*$6,013 + 0.15590*$10,000
+ 0.033594*$1,338.8 = $2,405 150%
4.2 ONE SET OF PRICES WITH HIGH WAGES
Suppose this firm faces a higher wage, namely $2,932 per
Person-Year. Consider what happens if the firm doesn't
revalue the price of steel on its books. Table 6 shows this
case.
TABLE 6: COSTS, WAGE $2,932 PER PERSON-YEAR,
PRICE OF STEEL $6,013 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$2,932 = $5,320 88%
Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
+ 0.19321*$2,932 = $2,767
Steel Beta 0.13329*$6,013 + 0.15590*$10,000
+ 0.033594*$2,932 = $2,459 145%
This firm cannot continue with production with this set of
books. Why would the firm produce any corn when it can make a
greater return by producing only steel? But if nobody is
producing corn, where will the firm get the corn inputs needed
to continue production? Something must change.
4.3 ANOTHER SET OF PRICES
Perhaps all that is needed is to re-evaluate steel on the
firm's books. Higher wages have made steel less valuable. Table
7 shows costs and the rate of profits when steel is
evaluated at an accounting price of $4,499 per Ton.
TABLE 7: COSTS, WAGE $2,932 PER PERSON-YEAR,
PRICE OF STEEL $4,499 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$4,499 + 0.16889*$10,000
+ 0.82816*$2,932 = $5,017 99%
Steel Alpha 0.35*$4,499 + 0.0095553*$10,000
+ 0.19321*$2,932 = $2,237
Steel Beta 0.13329*$4,499 + 0.15590*$10,000
+ 0.033594*$2,932 = $2,257 99%
If the firm were to continue using the Beta process to
produce steel, this firm would be making the same rate of
profit in producing corn and in producing its input of
steel. But the manager of the steel-process would soon
notice that the cost of operating the Alpha process is
cheaper.
4.4 FINAL EQUILIBRIUM PRICES
So the firm would ultimately switch to using the Alpha
process to produce steel. The price the firm would enter
on its books would fall even more. Table 8 shows the accounting
with a price of steel of $4,414 per ton. The firm has adopted
the cheapest process for producing steel, and the rate of profits
is the same in both corn-production and steel-production. The
accounting for this vertically-integrated firm is internally
consistent.
TABLE 8: COSTS, WAGE $2,932 PER PERSON-YEAR,
PRICE OF STEEL $4,414 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$4,414 + 0.16889*$10,000
+ 0.82816*$2,932 = $5,000 100%
Steel Alpha 0.35*$4,414 + 0.0095553*$10,000
+ 0.19321*$2,932 = $2,207 100%
Steel Beta 0.13329*$4,414 + 0.15590*$10,000
+ 0.033594*$2,932 = $2,246
5.0 CONCLUSIONS
Table 9 summarizes these calculations. The ultimate result of
a higher wage is the adoption of a more labor-intensive technique.
If this firm continues to produce the same level of net output
and maximizes profits, its managers will want to employ more workers
at the higher of the two wages considered.
TABLE 9: PROFIT-MAXIMIZING FIRM ADOPTS MORE LABOR-INTENSIVE
TECHNIQUE AT HIGHER WAGE
STEEL-PRODUCING LABOR-INTENSITY OF
WAGE PROCESS CORN-PRODUCING TECHNIQUE
$1,338.8 Per Person-Year Beta 1.0516 Person-Years Per Bushel
$2,932 Per Person-Year Alpha 1.072 Person-Years Per Bushel
So much for the theory that wages and employment are determined
by the interaction of well-behaved supply and demand curves on the
labor market.
--
Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html
To solve Linear Programs: .../LPSolver.html
r c A game: .../Keynes.html
v s a Whether strength of body or of mind, or wisdom, or
i m p virtue, are found in proportion to the power or wealth
e a e of a man is a question fit perhaps to be discussed by
n e . slaves in the hearing of their masters, but highly
@ r c m unbecoming to reasonable and free men in search of
d o the truth. -- Rousseau
John Weatherby
theory or refutation of theory. The process are just numbers there is no
substance nor a model.
> 2.0 DATA ON TECHNOLOGY
>
Data? I don't see any data just some cooked up numbers.
> TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
>
> 0.82816 Person-years
> 0.2 Tons steel
> 0.16889 Bushels corn
>
What sort of function is driving this? Is there a function or just some
made up numbers?
> Steel is also produced by this firm. Two processes are known for
> producing steel:
>
> TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
>
> Process Alpha Process Beta
>
> 0.19321 Person-Years 0.033594 Person-Years
> 0.35 Tons Steel 0.13329 Tons Steel
> 0.0095553 Bushels Corn 0.15590 Bushels Corn
>
So here you have two choices you user more labor and steel and less corn
or less labor less steel and more corn. Part of what drives your result here
is the fact the final good is also a capital good. The less labor intensive
process is going to be much more costly giving the wages and price of corn.
Hmmm doesn't make the results interesting or surprising.
> 5.0 CONCLUSIONS
>
> Table 9 summarizes these calculations. The ultimate result of
> a higher wage is the adoption of a more labor-intensive technique.
> If this firm continues to produce the same level of net output
> and maximizes profits, its managers will want to employ more workers
> at the higher of the two wages considered.
>
Part of the problem with this analysis is the price of corn is constant.
This is the downfall. The less labor intensive process also uses more corn.
For a firm to use this process would also mean bidding up the price for
corn, there is a higher demand for corn. Not taking this into account is the
fatal flaw of the model. Yes the less labor intensive process may be more
costly under these assumption however corn also sells for a higher price
raising the profits of making corn. It is unclear when this is taken into
account which process is chosen.
> So much for the theory that wages and employment are determined
> by the interaction of well-behaved supply and demand curves on the
> labor market.
>
Well if you would try putting supply and demand in the model rather than
holding prices of corn constant you would get a much different result. This
is like trying to prove that gas consumption will not increase as a car
engine goes faster while assuming that gas consumption is equal for all
speeds.
John
Robert Vienneau
"John Weatherby" <jjwea...@earthlink.net> wrote:
> How long did it take to cook up numbers to find this result. This is no
> theory or refutation of theory. The process are just numbers there is no
> substance nor a model.
Mr. Weatherby's incomprehension is no refutation. He also doesn't seem
to understand how to relate examples to theory. As for models, my
presentation is an attempt to convey a point of models like this one:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LaborDemand.pdf>
The example relates to standard models. It is particularly ironic when
a supposed specialist in growth theory does not recognize an example
consistent with (generalizations of) the givens of the Von Neumann
model of endogeneous growth.
> > 2.0 DATA ON TECHNOLOGY
> Data? I don't see any data just some cooked up numbers.
In neoclassical economic theory, prices in competitive markets are
supposed to be determined by the interaction of supply and demand
curves. The givens in neoclassical theory are technology, tastes,
and endowments. Another term for the "givens" is the "data".
If the theory were correct, one would not be able to construct ("cooked
up numbers" in one incomprehension-revealing formulation) a specific
numeric example which meets the assumptions of the theory but has
contradictory conclusions. This is a matter of logic, not one of
running regressions on empirical data.
For example, if the theory stated that labor-demand curves never
slope up, one would be able to construct non-upward-sloping labor
demand curves for the example. (It would be acceptable in such a
construction to include assumptions on aspects of a model not
specified in the example but consistent with the example.) Or one
would be able to specify exactly what assumptions of the theory
are violated by the example.
I don't imagine my conclusion is not a matter of standard price
theory, at least as that theory is understood among good economic
theoreticians:
"But, as economic theory has learned since the 1930s, the
pattern of activities adopted in the face of long-run
factor-price changes can be complicated and counterintuitive.
Consequently, the long-run demand for factors can be badly
behaved functions of factor prices... The principle of
variation works as an argument for long-run determinancy insofar
as the set of zero-profit activities shift in response to factor
price changes; it is not necessary that newly adopted activities
use cheaper factors more intensively or that production is more
capital intensive when r falls."
-- Michael Mandler, _Dilemmas In Economic Theory: Persisting
Foundational Problems Of Microeconomics_. Oxford, 1999.
p. 34.
This newsgroup has shown that many doctoral candidates in economics
and many professors of economics do not understand these standard
conclusions of price theory.
This lack of understanding has implications for empirical work. If
one wants to use models in which "the long-run demand for factors"
cannot "be badly behaved functions of factor prices", one should
recognize one is using, at best, special cases. Suppose one adopts
the mainstream view of the necessity for mathematical models. Then
one should be able to specify the assumptions, e.g., on technology, of
such special cases.
> > TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
> >
> > 0.82816 Person-years
> > 0.2 Tons steel
> > 0.16889 Bushels corn
> What sort of function is driving this? Is there a function or just
> some made up numbers?
False dichotomy.
Mr. Weatherby should recognize that, if this is the only process known
for producing corn, the following production function applies here:
X = min( L/0.82816, Q1/0.2, Q2/0.16889 )
where X is bushels corn produced, L is labor input, Q1 is input of
steel, and Q2 is input of corn.
This is an example of a frequently used production function. There
are specific numeric values for the parameters (number of inputs,
coefficients of production) of the function.
> > Steel is also produced by this firm. Two processes are known for
> > producing steel:
> >
> > TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
> >
> > Process Alpha Process Beta
> >
> > 0.19321 Person-Years 0.033594 Person-Years
> > 0.35 Tons Steel 0.13329 Tons Steel
> > 0.0095553 Bushels Corn 0.15590 Bushels Corn
> So here you have two choices you user more labor and steel and less
> corn
> or less labor less steel and more corn. Part of what drives your result
> here
> is the fact the final good is also a capital good.
No. In the example, the final good is also a capital good, in some
sense. However, examples can be constructed with the same conclusion,
but without this property (e.g., Samuelson's example in his article
"summing up" one aspect of the Cambridge Capital Controversy).
So this property does not drive my result.
> The less labor intensive
> process is going to be much more costly giving the wages and price of
> corn.
I am not at all sure that that is a standard use of the phrase
"labor-intensive". Mr. Weatherby seems to be saying that my
results, at least qualitatively, do not depend on the specific
numeric values defining the one process known for producing
corn. I think Mr. Weatherby clearly mistaken.
(Consider prices in the example for each technique when r = 0%.
One could compare the ratio, for each process, of labor inputs
to the sum of the value of the inputs of corn and steel. Then
one could talk about one process as being more or less labor-
intensive than the other. I doubt Mr. Weatherby has done these
calculations.)
> Hmmm doesn't make the results interesting or surprising.
Well, Samuelson has said repeatedly that this result is interesting,
and that he found it surprising. Of course, all the evidence is
that Mr. Weatherby does not understand the result and its implications.
> > 5.0 CONCLUSIONS
> > Table 9 summarizes these calculations. The ultimate result of
> > a higher wage is the adoption of a more labor-intensive technique.
> > If this firm continues to produce the same level of net output
> > and maximizes profits, its managers will want to employ more workers
> > at the higher of the two wages considered.
> Part of the problem with this analysis is the price of corn is
> constant.
(A small quantity of) corn is the numeraire.
> This is the downfall. The less labor intensive process also uses more
> corn.
The above is a matter of Mr. Weatherby using equivocation. I used
"labor-intensive" in one fashion. He's using it in another.
> For a firm to use this process would also mean bidding up the price for
> corn, there is a higher demand for corn.
The price of corn would be bid up relative to what numeraire? And
what about the non-substitution theorem?
> Not taking this into account is
> the fatal flaw of the model...
Nope. Mr. Weatherby has presented no argument whatsoever that examples
cannot be constructed with my result and the inputs of processes not
connected like in my specific example.
> Yes the less labor intensive process may be more
> costly under these assumption however corn also sells for a higher price
> raising the profits of making corn. It is unclear when this is taken into
> account which process is chosen.
I read the above as a recognition that Mr. Weatherby doesn't have
an argument.
> > So much for the theory that wages and employment are determined
> > by the interaction of well-behaved supply and demand curves on the
> > labor market.
--
John J. Weatherby
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-EE4968....@news.dreamscape.com...
> In article <r_Ly8.10112$iU4.8...@newsread2.prod.itd.earthlink.net>,
> Mr. Weatherby's incomprehension is no refutation. He also doesn't seem
> to understand how to relate examples to theory. As for models, my
> presentation is an attempt to convey a point of models like this one:
>
you showed what that function was. Even in early game theory where the
payoffs were sort of cooked up, they still explained how and why the numbers
got there. There is no explanation here. Anyone with any idea about how
theory and data work will ask you how you got the numbers.
> The example relates to standard models.
Such as? As usually you usually loose a term standard models to imply you
are bringing down every economic model. Can you even name a model that is in
use to today that this applies to? I highly doubt it. Again I challenge you
which standard model are you trying to refute?
> In neoclassical economic theory, prices in competitive markets are
> supposed to be determined by the interaction of supply and demand
> curves. The givens in neoclassical theory are technology, tastes,
> and endowments. Another term for the "givens" is the "data".
>
Right but I see no utility functions giving preferences. I see no
functions for production. Without these you can find supply nor demand
curves for a competitive market. To have demand you have to start with
preferences and for factor demands you need production functions. There are
no utility nor production functions here just cooked up numbers that are
completely unclear how they can about. If these represent functions I highly
doubt anyone would take a linear production function seriously.
> If the theory were correct, one would not be able to construct ("cooked
> up numbers" in one incomprehension-revealing formulation) a specific
> numeric example which meets the assumptions of the theory but has
> contradictory conclusions. This is a matter of logic, not one of
> running regressions on empirical data.
>
To run a numerical simulation you have to have functions. You need to
specify the assumptions in some form instead of putting down a lot of
numbers. Again what sort of production functions allow these numbers. From
the table you gave it seems you assume a linear production function which is
absurd.
> For example, if the theory stated that labor-demand curves never
> slope up, one would be able to construct non-upward-sloping labor
> demand curves for the example. (It would be acceptable in such a
> construction to include assumptions on aspects of a model not
> specified in the example but consistent with the >example.)
Again just placing a bunch numbers is equivalent to drawing an upward
sloping demand curve and claiming it exist because I can draw it.
> This newsgroup has shown that many doctoral candidates in economics
> and many professors of economics do not understand these standard
> conclusions of price theory.
>
No I think it is you who do not understand
A. the flaws in the argument
B. The fact that these are not applicable to most modern methods.
C. What standard price theory actually concludes. This has been the biggest
problem you have read a majority of critiques and never stop to find out
what mainstream does say. You have taken the critics word for it a dangerous
thing to do.
> Mr. Weatherby should recognize that, if this is the only process known
> for producing corn, the following production function applies here:
>
> X = min( L/0.82816, Q1/0.2, Q2/0.16889 )
>
> where X is bushels corn produced, L is labor input, Q1 is input of
> steel, and Q2 is input of corn.
>
Leontif that is the problem. Again you are going back to Harrod-Domar
and the associated problems with that model. The Leontif production is not
commonly used in modern theory. It is sort of a trick question put on comps
to see if you can work out a problem when you can't use calculus. It is sort
of a test to see if you know the concept or only the math.
> > Yes the less labor intensive process may be more
> > costly under these assumption however corn also sells for a higher price
> > raising the profits of making corn. It is unclear when this is taken
into
> > account which process is chosen.
>
> I read the above as a recognition that Mr. Weatherby doesn't have
> an argument.
You mention profit maximizing at several points but fail to take into
account that a process that uses more corn will drive up the price of corn.
This means the profit function changes. You calculate profits for both
techniques assuming that corn has the same price. Corn will not have the
same price under both techniques. One technique will mean higher prices for
corn. This means that the profit calculations are different for each
technique. Without a theory of consumer demand for corn you can not
calculate what the difference in price will be. In short your calculations
are flawed because you don't take into account supply and demand. Supply and
Demand does not seem to have effect because you have not analyzed the corn
market.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-EE4968....@news.dreamscape.com...
> > In article <r_Ly8.10112$iU4.8...@newsread2.prod.itd.earthlink.net>,
> > Mr. Weatherby's incomprehension is no refutation. He also doesn't seem
> > to understand how to relate examples to theory. As for models, my
> > presentation is an attempt to convey a point of models like this one:
> Well if the numbers are driven by some sort of function it would be nice
> if
> you showed what that function was. Even in early game theory where the
> payoffs were sort of cooked up, they still explained how and why the
> numbers
> got there. There is no explanation here. Anyone with any idea about how
> theory and data work will ask you how you got the numbers.
Actually, that is the closest anybody has come in years to asking
how I made up these numbers. If one actually read the first post
on this thread, one might note the coefficients of production
are ugly, but I end up with "nice" numbers for interest rates
(100%, 150%) and some costs ($4,000, $5,000). Obviously, I
solved the model - and there is a model - backwards and played
around with the equations.
Where is this model? Well, there was the URL in the post Mr. Weatherby
is pretending to respond to:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LaborDemand.pdf>
There's also:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
The Appendices in the latter and up through Figure 7 are standard models.
> > The example relates to standard models.
[>> It is particularly ironic when ]
[>> a supposed specialist in growth theory does not recognize an example]
[>> consistent with (generalizations of) the givens of the Von Neumann ]
[>> model of endogeneous growth. ]
> Such as?
Such as the model mentioned in the text Mr. Weatherby deleted
immediately following the sentence he is pretending to respond to.
> As usually you usually loose a term standard models to imply you
> are bringing down every economic model.
Mr. Weatherby reads as well as he writes. I am explaining rigorous
price theory, not the outdated mystical mush that some economists
seem to believe and teach.
> Can you even name a model that is
> in use to today that this applies to?
References are provided in those URLs. Some are textbooks. I consider
1995 to be the date of a contemporary reference, for example.
> I highly doubt it. Again I
> challenge you
> which standard model are you trying to refute?
See above.
> > In neoclassical economic theory, prices in competitive markets are
> > supposed to be determined by the interaction of supply and demand
> > curves. The givens in neoclassical theory are technology, tastes,
> > and endowments. Another term for the "givens" is the "data".
> Right but I see no utility functions giving preferences.
I don't need utility functions for my point. But because I am used
to this sort of incomprehension, I provided utility functions in
Section 2.4 of Sraffa3.pdf at the URL given above.
> I see no functions for production.
I gave one below for the corn process. In the other
thread "Maximize Production", I describe how to construct a
production function out of the steel processes.
> Without these you can find supply nor demand
> curves for a competitive market. To have demand you have to start with
> preferences and for factor demands you need production functions. There
> are
> no utility nor production functions here just cooked up numbers that are
> completely unclear how they can about. If these represent functions I
> highly
> doubt anyone would take a linear production function seriously.
The "cooked-up numbers" yield production functions. Production
functions for my example exhibit common assumptions, e.g., constant
returns to scale and diminishing marginal returns. (No, I am not
interested here in discussing increasing returns to scale in the
endogeneous growth models Mr. Weatherby is familiar with.)
> > If the theory were correct, one would not be able to construct ("cooked
> > up numbers" in one incomprehension-revealing formulation) a specific
> > numeric example which meets the assumptions of the theory but has
> > contradictory conclusions. This is a matter of logic, not one of
> > running regressions on empirical data.
> To run a numerical simulation you have to have functions. You need to
> specify the assumptions in some form instead of putting down a lot of
> numbers.
To construct and solve a numerical example, you need to have some
understanding of what you are talking about.
> Again what sort of production functions allow these numbers.
> From
> the table you gave it seems you assume a linear production function which
> is absurd.
I make standard assumptions. Mr. Weatherby, of course, is free to
reject the assumptions of some versions of mainstream theory.
> > For example, if the theory stated that labor-demand curves never
> > slope up, one would be able to construct non-upward-sloping labor
> > demand curves for the example. (It would be acceptable in such a
> > construction to include assumptions on aspects of a model not
> > specified in the example but consistent with the example.)
> Again just placing a bunch numbers is equivalent to drawing an upward
> sloping demand curve and claiming it exist because I can draw it.
Nope. That's not what I did.
> > This newsgroup has shown that many doctoral candidates in economics
> > and many professors of economics do not understand these standard
> > conclusions of price theory.
> No I think it is you who do not understand
> A. the flaws in the argument
There are none in the initial post in this thread. Responses, such as
Mr. Weatherby's, merely say something about the sociology of economics.
"Modern-day economics students...are insufficiently numerate
because the material which establishes the intellectual
weaknesses of economics is complex. Understanding this
literature in its raw form requires an appreciation of some
quite difficult areas of mathematics - concepts which require
up to two years of undergraduate mathematical training to
understand.
Curiously, though economists like to intimidate other social
scientists with the mathematical rigour of their discipline,
most economists do NOT have this level of mathematical
education."
-- Steve Keen
Has any mainstream economist acknowledged here that the example in
my first post is correct?
> B. The fact that these are not applicable to most modern methods.
See below after Mr. Weatherby's comment about the Harrod-Domar
model.
> C. What standard price theory actually concludes.
What economists like Paul Samuelson, Edwin Burmeister, Michael Mandler,
Franklin Fisher, and Frank Hahn says it says, for example. Which
is what I have been saying.
Notice whenever I quote some economist saying what I am saying
about price theory, many respondents delete such quotes without
ever commenting on why they disagree with this economist, or why
that quote is saying something different than I am saying. Of
course, when Mr. Weatherby comments on Samuelson, say, he makes
a hash of it.
> This has been the biggest
> problem you have read a majority of critiques and never stop to find out
> what mainstream does say. You have taken the critics word for it a
> dangerous thing to do.
The above is simply untrue. I was TAUGHT mainstream theory at an
institution where every student is assumed to understand, at least,
calculus after their frosh year. Furthermore, I have obviously read
the responses of mainstream economists to my favorite critique. For
that matter, I don't know why Mr. Weatherby assumes Michael Mandler,
for example, is not mainstream or an internal critic. I don't know,
though I know he is insightful.
> > Mr. Weatherby should recognize that, if this is the only process known
> > for producing corn, the following production function applies here:
> >
> > X = min( L/0.82816, Q1/0.2, Q2/0.16889 )
> >
> > where X is bushels corn produced, L is labor input, Q1 is input of
> > steel, and Q2 is input of corn.
> Leontif that is the problem.
Hogswallop. The above production function is, indeed, Leontief. But
that does not drive the results.
Consider Figure 1 in LaborDemand.pdf, which was drawn for the
numerical example with which I began this thread. Look at the
boundary around the region in which X1( alpha ) is positive.
I am considering the rightmost intersection of this boundary
with the boundaries of the regions in which X1( beta ) and X2 are
positive. Suppose other processes were known for producing corn.
They would result in straight lines dividing the region in which
X2 is positive. Obviously, lots of lines can be drawn, and the
point which I am considering would still, by construction, appear
on the relevant locus. Likewise, we could divide up the region
above the piecewise curved locus with a lot more straight lines.
(These divisions would replace pieces of the curved locus with
different curves.)
When there are choices of processes for producing corn and steel,
the production functions are not Leontief. Furthermore, they are
variable-coefficient, not fixed coefficient production functions.
Apparently Mr. Weatherby is asserting that the special case of
non-Leontief production functions will rule out the results I
am highlighting. The above shows he is clearly wrong.
Is there a theorem asserting the special case assumption of
production functions differentiable everywhere (and not
merely non-differentiable only on a set of measure zero) will
rule out these results? If there were such a theorem in the
literature, I think I would know about it. And I don't think
there is any such theorem. Furthermore, several economists
say otherwise. In fact, Steedman provides a proof showing
how to construct reswitching with "smooth" production functions.
Since he presumes certain knowledge of price theory, I won't even
bother giving the URL here.
> Again you are going back to Harrod-Domar
> and the associated problems with that model. The Leontif production is
> not
> commonly used in modern theory. It is sort of a trick question put on
> comps
> to see if you can work out a problem when you can't use calculus. It is
> sort
> of a test to see if you know the concept or only the math.
Early neoclassical theory after the development of marginal
productivity theory tended to assume differentiability. The
post-war (WWII) western economists, however, turned toward
topological models. These topological arguments, as in canonical
presentations of the Arrow-Debreu model, are supposed to
apply indifferently to Leontief production functions, other
production functions that are not differentiable everywhere,
and "smooth" production function. There may have been a turn
lately back to calculus-based arguments. I wonder if mainstream
economists think that they have lost the supposed rigor of
this postwar turn.
Anyway, Mr. Weatherby acknowledges above that my example is
logically consistent with the assumptions of mainstream theory.
He's seems to be making a mistaken assertion that the result
I highlight is not possible under the special-case assumption
of production functions differentiable everywhere.
> > > Yes the less labor intensive process may be more
> > > costly under these assumption however corn also sells for a higher
> > > price
> > > raising the profits of making corn. It is unclear when this is taken
> > > into
> > > account which process is chosen.
> > I read the above as a recognition that Mr. Weatherby doesn't have
> > an argument.
> You mention profit maximizing at several points but fail to take into
> account that a process that uses more corn will drive up the price of
> corn.
[ >> (A small quantity of) corn is the numeraire. ]
So the following has already been shown to be nonsense:
> This means the profit function changes. You calculate profits for both
> techniques assuming that corn has the same price. Corn will not have the
> same price under both techniques. One technique will mean higher prices
> for
> corn. This means that the profit calculations are different for each
> technique. Without a theory of consumer demand for corn you can not
> calculate what the difference in price will be.
This here is nonsense for other reasons as well:
> In short your
> calculations
> are flawed because you don't take into account supply and demand. Supply
> and
> Demand does not seem to have effect because you have not analyzed the
> corn
> market.
My assertion was about the (absence of) well-behaved supply and
demand functions in the labor market, particularly a demand
function for labor.
If Mr. Weatherby actually wanted to construct an argument, he is
always free to append additional assumptions and show how to construct
a (well-behaved) labor demand function in my example.
Of course, I construct a complete equilibrium in Sraffa3.pdf.
maximus
post).
Even though I may accept the *point* and the case, or even
thousands of the points, altogether they can not make a rejection
of a theory.
max
-------
"John J. Weatherby" <jjwea...@earthlink.net> wrote in message
news:bpXy8.11665$8p3.9...@newsread1.prod.itd.earthlink.net...
John J. Weatherby
>(No, I am not
> interested here in discussing increasing returns to scale in the
> endogeneous growth models Mr. Weatherby is familiar with.)
>
these models. If you did you realize the scale effect deals with the effect
of population on growth not the standard idea of size of the firm affecting
output.
> There are none in the initial post in this thread. Responses, such as
> Mr. Weatherby's, merely say something about the sociology of economics.
>
Yes there are you hold the price of corn constant. You use this constant
price to calculate profits for each process. This is clearly wrong. I do not
know what the results would be if you fixed nor do I have time to work them
out. I am after all working on things to be published and not just bitching
on some newsgroup.
> "Modern-day economics students...are insufficiently numerate
> because the material which establishes the intellectual
> weaknesses of economics is complex. Understanding this
> literature in its raw form requires an appreciation of some
> quite difficult areas of mathematics - concepts which require
> up to two years of undergraduate mathematical training to
> understand.
>
> Curiously, though economists like to intimidate other social
> scientists with the mathematical rigour of their discipline,
> most economists do NOT have this level of mathematical
> education."
> -- Steve Keen
>
Hogwash. A good number of people in this field hold undergraduate Math
degrees. Many studied physics and other sciences as an undergraduate. Some
of the nobel prize winners have even thought physics in their spare time. I
have not had many professors that did not at least have a minor in math.
That is part of the reason they got in a top ten school in the first place.
> Has any mainstream economist acknowledged here that the example in
> my first post is correct?
>
I don't think too many care much about a Leontif function with two
production processes. Rarely is more than one production process used in any
model.
> > B. The fact that these are not applicable to most modern methods.
>
> See below after Mr. Weatherby's comment about the Harrod-Domar
> model.
>
Harrod-Domar is pre-modern. It is a terrible model that has a fatal flaw
of assuming that the average product of capital is constant for every level
of capital. Much like your assumption that the price of corn is constant for
every level of corn production.
> When there are choices of processes for producing corn and steel,
> the production functions are not Leontief. Furthermore, they are
> variable-coefficient, not fixed coefficient production functions.
>
Well again this is far from standard assumptions that the coefficents in
a production function change. This is like saying the Solow model is
completely wrong because I can write down an endogenous growth model. The
Solow model is wrong because it lacks micro foundations and does not match
the data well on certain points like speed of convergence.
> [ >> (A small quantity of) corn is the numeraire. ]
>
> So the following has already been shown to be nonsense:
>
Look at this table:
TABLE 5: COSTS, WAGE $1,338.8 PER PERSON-YEAR,
PRICE OF STEEL $6,013 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$1,338.8 = $4,000 150%
Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
+ 0.19321*$1,338.8 = $2,459
Steel Beta 0.13329*$6,013 + 0.15590*$10,000
+ 0.033594*$1,338.8 = $2,405 150%
Under both process you calculate the cost using the same price for corn.
Under process Beta the corn used is about 17 times as much as the corn used
in process alpha. You can not convince me that the price of corn will be the
same under each process when process beta uses 17 more of the input!!! The
prices will be different under the two processes meaning different cost and
different profits for corn produced. If the factor demand of corn is
increasing by a factor of 17 you can not convince me that this will not a
significant impact on :
A. the price of corn
and
B. the production of corn.
Without taking this into account you can not see which process the firm
will use period. That is the flaw of the model. If you rerun with the
numbers with some sort of demand for corn and see what will the difference
in prices and how that affects production decisions for corn when process
Beta is used and then compare the profits you might have something. Until
you do that this analysis is meaningless. Your cost functions are wrong
because they assume the same price on corn even when its demand as been
multiplied by a factor of 17. This is clearly wrong.
> This here is nonsense for other reasons as well:
>
Really, you mean the supply of corn and the price of corn are completely
unresponsive to the demand for corn. So if I am a firm and the demand for my
production is 17 times more I still charge the same price?
I do not think this is nonsense. It is something that needs to be fixed.
You find that supply and demand do not affect the model simply because left
out the supply and demand for a key input.
> If Mr. Weatherby actually wanted to construct an argument, he is
> always free to append additional assumptions and show how to construct
> a (well-behaved) labor demand function in my example.
>
The argument has nothing to do with the labor demand function. The
argument is that you hold prices for a small quantity of corn constant even
though process B demands 17 times the amount of corn of process alpha. This
is why the model is wrong. The increase in price from process B will have
significant implications for the production of corn and also the cost
function you state. In fact the process B will be much more costly. However,
the price of corn has risen. One would expect under process B the production
of steel drops and the production of corn rises.
I did not run the numbers to see if profits were higher under this
choice of technique. It may be that you don't find more labor hired to make
steel when wages rise. Instead production of steel drops and production of
corn rises. Again these results come from the fact you have an integrated
firm. It may be different if the corn industry and steel industry are
seperate. Your cost and profit calculations are way off. Honestly I haven't
looked further that so I can't comment on the rest of the model. Fix the
first part and maybe we can talk.
John
Robert Vienneau
<madv...@about.com> wrote:
> I am afraid that I agree more with John than with Robert (author of the
> post).
>
> Even though I may accept the *point* and the case, or even
> thousands of the points, altogether they can not make a rejection
> of a theory.
You, of course, are free to reject logic.
In Euclidean geometry, one can show that the sum of the angles
of a triangle add up to 180 degrees. If I were to correctly show how
to construct a triangle with compass and straightedge, such that
the angles of the triangle add up to something different from
180 degrees, one with a command of logic would have to
reject Euclidean geometry or realize that it needs modification.
But am I arguing for a rejection of mainstream theory?
"But, as economic theory has learned since the 1930s, the
pattern of activities adopted in the face of long-run
factor-price changes can be complicated and counterintuitive.
Consequently, the long-run demand for factors can be badly
behaved functions of factor prices... The principle of
variation works as an argument for long-run determinancy insofar
as the set of zero-profit activities shift in response to factor
price changes; it is not necessary that newly adopted activities
use cheaper factors more intensively or that production is more
capital intensive when r falls."
-- Michael Mandler, _Dilemmas In Economic Theory: Persisting
Foundational Problems Of Microeconomics_. Oxford, 1999.
p. 34.
My assertion was about the (absence of) well-behaved supply and
demand functions in the labor market, particularly a demand
function for labor.
--
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-FF5CB0....@news.dreamscape.com...
> >(No, I am not
> > interested here in discussing increasing returns to scale in the
> > endogeneous growth models Mr. Weatherby is familiar with.)
> Of course not you still do not know what a scale effect refers to in
> these models. If you did you realize the scale effect deals with the
> effect
> of population on growth not the standard idea of size of the firm
> affecting
> output.
The above is irrelevant. So, then, is the following quote:
"If A is productive as well, it follows that F cannot be a
concave production function because
F(lambda A, lambda X) > lambda F( A, X )."
-- Paul Romer (1990), p. S 76.
Though, of course, it is relevant to Mr. Weatherby's irrelevancy.
> > There are none in the initial post in this thread. Responses, such as
> > Mr. Weatherby's, merely say something about the sociology of economics.
> Yes there are you hold the price of corn constant. You use this
> constant
> price to calculate profits for each process. This is clearly wrong.
Mr. Weatherby is being silly. 1/10,000 bushel corn is the numeraire
in the model. By definition of a numeraire, its price is constant
(unity).
> > Has any mainstream economist acknowledged here that the example in
> > my first post is correct?
> I don't think too many care much about a Leontif function with two
> production processes. Rarely is more than one production process used in
> any model.
Mr. Weatherby's response is silly. If there is only one production
process, the production function is Leontief. He told us in a
previous post (with a comment directed to no cognitive values)
that the modern economists he is familiar with are not interested
in Leontief functions. In the above comment (which is also
directed to no cognitive values), he tells us that economists
do not care about models with more than one production process.
So he contradicts himself. With two production processes available,
the production function is not Leontief. So he also makes a
mistake in his comment.
But, of course, I explained how to increase the number of processes
available in the model to any number you like. Mr. Weatherby
snipped that part without comment.
Has any mainstream economist acknowledged here that the example in my
first post is correct?
> > > B. The fact that these are not applicable to most modern methods.
> > See below after Mr. Weatherby's comment about the Harrod-Domar
> > model.
> Harrod-Domar is pre-modern. It is a terrible model that has a fatal
> flaw
> of assuming that the average product of capital is constant for every
> level
> of capital.
Mr. Weatherby's comment is a non-sequitur. I have made no comment
in this thread whatsoever on the Harrod-Domar model.
> > When there are choices of processes for producing corn and steel,
> > the production functions are not Leontief. Furthermore, they are
> > variable-coefficient, not fixed coefficient production functions.
> Well again this is far from standard assumptions that the coefficents
> in a production function change.
> [ Irrelevancy about the Solow model - deleted. ]
Consider the following URL:
<http://homepage.newschool.edu/~foleyd/GECO6200/ps1.html>
Apparently, this is the first problem set in a course that Duncan
Foley, a well-known contemporary economist, is teaching this Spring.
Consider problem 1-2:
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two techniques
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two techniques for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these techniques that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
(Foley uses "technique" to mean what I call a "process".)
So much for Mr. Weatherby's knowledge of what are standard assumptions.
> You can not convince me that the price of corn will be
> the
> same under each process when process beta uses 17 more of the input!!!
"You cannot convince me" is argument from ignorance.
The price of a numeraire is set to a constant. That's what it means
to be a numeraire.
> > If Mr. Weatherby actually wanted to construct an argument, he is
> > always free to append additional assumptions and show how to construct
> > a (well-behaved) labor demand function in my example.
[>>Of course, I construct a complete equilibrium in Sraffa3.pdf.]
[ More nonsense already addressed - deleted. ]
> It may be different if the corn industry and steel industry are
> seperate. Your cost and profit calculations are way off. Honestly I
> haven't
> looked further that so I can't comment on the rest of the model. Fix the
> first part and maybe we can talk.
Let's see. I've addressed this issue in the referenced PDF files.
Mr. Weatherby deleted all references to such files and arguments. Why
would he think I would want to talk to him, given his behavior?
maximus
I can assume that the functions you use are arbitrary, as well as all
parameters.
But there are many functions that are not well-behaved, in whatever meaning
you
may mean here.
As long as you do not show the functions you use, an example cannot make the
case here.
In addition, since you want to show the higher-wage is associated with
higher employment
per unit produced, or higher L/Y, simply speaking so. This means high wage
is associated
with lower Y/L. This is opposite to observed data and casual observation.
You setting up the mechanism of price, especially for steel, is unrealistic.
If firms can set up
their prices as they like, why don't they set up a price that they can show
higher profit ?
This profit may be infinite even, in your case.
If you can find two prices that one gives profit, another shows loss, then
how firms will
decide ?
Probably you can use your time better.
I am afraid that I will not continue to follow this issue, since I am too
busy with some
paper lying around to be finished.
Good luck
max
John Weatherby
> The above is irrelevant. So, then, is the following quote:
>
> "If A is productive as well, it follows that F cannot be a
> concave production function because
> F(lambda A, lambda X) > lambda F( A, X )."
> -- Paul Romer (1990), p. S 76.
>
> Though, of course, it is relevant to Mr. Weatherby's irrelevancy.
>
models used population. The scale effect is that countries with higher
populations have bigger growth rates. Not the scale effect you are trying to
portray it to be.
> Mr. Weatherby is being silly. 1/10,000 bushel corn is the numeraire
> in the model. By definition of a numeraire, its price is constant
> (unity).
>
Then why do you set the price of corn to $10,000.
"I assume throughout that inputs of steel,
corn, and labor are charged at the start of the year. The price
of corn is assumed constant at $10,000 per Bushel. Two different
levels of wages are considered."
I don't care if you make 1/10,000 of a bushel of corn the numeraire this
price is not constant when talk about increasing factor demands by 1,700
percent. Even a normal factor demand function derived from Cobb Douglas will
not be able to handle a change this big easily. You can not increase the
demand for any good 1700 percent and expect prices to stay constant. There
is no getting around this.
> > > Has any mainstream economist acknowledged here that the example in
> > > my first post is correct?
>
> Mr. Weatherby's response is silly. If there is only one production
> process, the production function is Leontief.
No a fixed coefficent Cobb Douglas does not assume several discrete
processes.
> capital model where wages are paid at the beginning of the period
> calculate the wage-profit rate relation, assuming that the wage
> consists only of corn."
>
> (Foley uses "technique" to mean what I call a "process".)
>
Also in his model the price of corn changes. Read carefully.
> So much for Mr. Weatherby's knowledge of what are standard assumptions.
>
Really do think someone from the new school whose faculty were
presenting Post-Keynesian papers at the AEA is representive of mainstream
economics or standard assumptions.
> > You can not convince me that the price of corn will be
> > the
> > same under each process when process beta uses 17 more of the input!!!
>
> "You cannot convince me" is argument from ignorance.
>
Well then excuse me for answering ignorance with ignorance. The point is
the same you can not increase fact demands by a factor of 17 and not have an
effect on the price of the factor.
> The price of a numeraire is set to a constant. That's what it means
> to be a numeraire.
>
This is the error. You can not have a constant price when demand will
increase by a factor of 17 from one process to another. Choosing this as a
numeraire is bad choice unless you scale wages according to the price of
corn, if you do that it changes your results.
> Let's see. I've addressed this issue in the referenced PDF files.
> Mr. Weatherby deleted all references to such files and arguments. Why
> would he think I would want to talk to him, given his behavior?
>
Again when you are proven wrong it suddenly the other guy is not playing
right. If you can not answer the questions here I need not look at the
documents. If these did answer the question you would explain it here rather
than posting a URL. You did construct this site did you not? Then why can't
you explain what is on it?
John
Robert Vienneau
<mad...@about.com> wrote:
> > "But, as economic theory has learned since the 1930s, the
> > pattern of activities adopted in the face of long-run
> > factor-price changes can be complicated and counterintuitive.
> > Consequently, the long-run demand for factors can be badly
> > behaved functions of factor prices... The principle of
> > variation works as an argument for long-run determinancy insofar
> > as the set of zero-profit activities shift in response to factor
> > price changes; it is not necessary that newly adopted activities
> > use cheaper factors more intensively or that production is more
> > capital intensive when r falls."
> > -- Michael Mandler, _Dilemmas In Economic Theory: Persisting
> > Foundational Problems Of Microeconomics_. Oxford, 1999.
> > p. 34.
> > My assertion was about the (absence of) well-behaved supply and
> > demand functions in the labor market, particularly a demand
> > function for labor.
> I can assume that the functions you use are arbitrary, as well as all
> parameters.
This is silly. Suppose the theory stated that, given
o Technology as represented by a production function with constant
returns to scale and diminishing marginal returns to each factor
o Profit-maximizing firms
Firms adopt a no more labor-intensive technique at a higher wage.
If the theory stated this and were logically consistent, I would
not be able to describe a technology, no matter how arbitrary,
in which the assumptions are met and the conclusion wasn't.
> But there are many functions that are not well-behaved, in whatever
> meaning you may mean here.
>
> As long as you do not show the functions you use, an example cannot make
> the case here.
There are no functions I use that I haven't shown, e.g., in PDF
files whose URL I have already given.
> In addition, since you want to show the higher-wage is associated with
> higher employment
> per unit produced, or higher L/Y, simply speaking so. This means high
> wage is associated
> with lower Y/L. This is opposite to observed data and casual observation.
If you think that, you have identified a problem for theory. State
special-case assumptions on technology that rules out the effect
illustrated by my example.
The claim about supposed data is irrelevant to the logical flaw I
have identified in certain beliefs. It also reveals an ignorance about
what is being claimed. See the fifth footnote in:
<http://www.econ.usyd.edu.au/drawingboard/journal/0111/white.pdf>
I can provide a list of case studies illustrating the relevant
effect in my example. I have not read all of the papers I would
list, since I think such studies irrelevant to the logical point.
> You setting up the mechanism of price, especially for steel, is
> unrealistic.
> If firms can set up
> their prices as they like, why don't they set up a price that they can
> show
> higher profit ?
> This profit may be infinite even, in your case.
Nonsense. The firm needs, by assumption, to adopt both a corn-producing
process and one of the steel-producing processes in my example. That
constrains the price of steel to be as shown.
> Probably you can use your time better.
I'm free to choose to give certain people a platform with which to
amuse our readers, if there are any.
> I am afraid that I will not continue to follow this issue, since I am too
> busy with some paper lying around to be finished.
You, of course, are free to remain ignorant of textbook results in
price theory.
Robert Vienneau
"John Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-6AE0AC....@news.dreamscape.com...
> > The above is irrelevant...
> > Mr. Weatherby is being silly. 1/10,000 bushel corn is the numeraire
> > in the model. By definition of a numeraire, its price is constant
> > (unity).
> Then why do you set the price of corn to $10,000.
> "I assume throughout that inputs of steel,
> corn, and labor are charged at the start of the year. The price
> of corn is assumed constant at $10,000 per Bushel. Two different
> levels of wages are considered."
price of 1/10,000 bushel corn = 1
Multiply both sides by 10,000.
price of 1 bushel corn = 10,0000
What is Mr. Weatherby's question?
> I don't care if you make 1/10,000 of a bushel of corn the numeraire
> this
> price is not constant when talk about increasing factor demands by 1,700
> percent.
Mr. Weatherby apparently doesn't know the meaning of the term
"numeraire".
> Even a normal factor demand function derived from Cobb Douglas
> will
> not be able to handle a change this big easily. You can not increase the
> demand for any good 1700 percent and expect prices to stay constant.
> There
> is no getting around this.
Apparently Mr. Weatherby has never seen the non-substitution theorem
explained.
> > > > Has any mainstream economist acknowledged here that the example in
> > > > my first post is correct?
Has any mainstream economist acknowledged here that the example in
my first post is correct?
> > Mr. Weatherby's response is silly. If there is only one production
> > process, the production function is Leontief.
> No a fixed coefficent Cobb Douglas does not assume several discrete
> processes.
I think an uncountably infinite number is more than several. A
Cobb-Douglas production function assumes an infinite number of
production processes. (Each process is characterized by definite
values for coefficients of production.) A Cobb-Douglas is not
fixed coefficient.
1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In
an economy with two commodities, corn and iron, there are
two techniques for producing a unit of corn, (0, 1/2, 1) and
(3/8, 1/9,1) (where the first number indicates the corn input,
the second the iron input, and the third the labor input), and
two techniques for producing iron, (1/4, 0, 2) and (1/4, 1/4, 2).
For each of the four possible combinations of these techniques
that will define a simple circulating
> > capital model where wages are paid at the beginning of the period
> > calculate the wage-profit rate relation, assuming that the wage
> > consists only of corn."
> >
> > (Foley uses "technique" to mean what I call a "process".)
> Also in his model the price of corn changes. Read carefully.
Mr. Weatherby's interpretation is highly idiosyncratic, to say
the least. I think it convenient to use corn as numeraire in
solving the above problem. Since Foley knows what he is talking
about, he would agree.
Appendix A, for example, of Sraffa3.pdf explains analytical tools
for solving the above problem.
> > So much for Mr. Weatherby's knowledge of what are standard assumptions.
> Really do think someone from the new school whose faculty were
> presenting Post-Keynesian papers at the AEA is representive of mainstream
> economics or standard assumptions.
Foley used to teach at Stanford and Columbia.
I think there is no disagreement among competent economists
o On how to solve the problems in that problem set
o That the assumptions on technology are standard.
I think the set of competent economists relevant here
includes many mainstream economists.
"The Kurz-Salvadori 'Theory of Production' is a tour de force
that provides a needed authoritative survey of modern
competitive theory on technology and prices. It seems a golden
mean between mathematical complexities, policy alternatives,
and historical geneses. I expect to wear out a copy every two
years from extensive use."
-- Paul A. Samuelson (obviously, an extremely heterodox
economist)
> > The price of a numeraire is set to a constant. That's what it means
> > to be a numeraire.
> This is the error. You can not have a constant price when demand will
> increase by a factor of 17 from one process to another. Choosing this as
> a
> numeraire is bad choice unless you scale wages according to the price of
> corn, if you do that it changes your results.
I hope some are amused by such nonsense.
Since 1/10,000 bushel of corn is the numeraire in the example, wages
in the example ARE scaled by the price of 1/10,000 bushel corn.
> > Let's see. I've addressed this issue in the referenced PDF files.
> > Mr. Weatherby deleted all references to such files and arguments. Why
> > would he think I would want to talk to him, given his behavior?
> Again when you are proven wrong
Only in Mr. Weatherby's uncomprehending mind.
> it suddenly the other guy is not playing
> right. If you can not answer the questions here I need not look at the
> documents. If these did answer the question you would explain it here
> rather
> than posting a URL. You did construct this site did you not? Then why
> can't
> you explain what is on it?
Mr. Weatherby's incomprehension is not my problem.
John J. Weatherby
> In article <lnnz8.687$Wd5....@newsread1.prod.itd.earthlink.net>,
> Mr. Weatherby's interpretation is highly idiosyncratic, to say
> the least. I think it convenient to use corn as numeraire in
> solving the above problem. Since Foley knows what he is talking
> about, he would agree.
>
It is not convenient to use corn as the numeraire it is wrong. You
completely ignored the demand for corn and its effect on price. The
difference in prices of corn under the two processes will marked change your
results. It has significant effects on cost and profits. Your choice of
technique hinges on the price of corn being the same. The profit functions
will be different under the different processes becuase they are different
prices to the input. This will also effect the profit maximizing level of
corn production.
You can not assume that prices are unchanging. Even if you adjust wages
for the price of corn all other prices are affected by this as well. The
problem is you have not taking into account the change in price and how that
will affect the profit maximizing level of corn. Your assumption is that the
level of corn production is the same under both processes this is completely
wrong and I don't care who cite to try to prove differently. Any competent
economist will realize this is a short coming in the analysis even if they
still use the model to try to prove a point. When you increase demand for
corn by a factor of 17 prices will rise and production of corn will rise as
well.
Regardless it is pretty obvious from the numbers posted that you had to
spend months finding an example that actually worked. You use these numbers
only because they are the only numbers you could find to make this work.
Lets face it here you have to show extremely large differences in technique
to make the theory work. You have to require 1/6 of the labor in the B
process and 17 times the corn before you even get a slightly higher amount
of profit under alpha when wages rise.
This is just ridiculous to think that 2 process may be this divergent.
Is it somewhat interesting to show what happens when you have a choice of
technique? Perhaps. Samuelson say that these cases were different from
mainstream theory and it might be interesting to look at different cases.
Does this extreme case disprove that factor demands are downward sloping or
horizontal? No. It is a special case that has very extreme assumptions. Even
if you did this model and did not make corn the numeraire, it might be
somewhat interesting but it does not destroy an entire body of work.
Especially when there is no empirical evidence to show there case actually
exist. This is like saying the fact Giffen goods exist means that Utility
theory is completely wrong.
John
John J. Weatherby
can you do this if corn is the numeraire? The price of steel will also be
affected by the changing price of corn. Your URL was not very helpful
either. I don't know how you think you can adequately explain a complex
concept in 4 pages. It takes more than righting down a function and placing
graphs. As usual you try to let the math do all your talking. This is your
biggest communication problem.
John
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-6AE0AC....@news.dreamscape.com...
John J. Weatherby
>
writing is about survival strategies for non-mainstream economist. This
guy's course actually takes Marx seriously. This is supposed to be a course
about macro but there is no mention of business cycle theories or even
modern growth models. This is not a mainstream approach.
From his publications it looks as though he was very mainstream until
1978, the time he went to Columbia then started publishing about Marxian
models. I am surprised at the switch. Then again that may be why he long is
at Columbia, since 1982 he only has one publication in mainstream journals.
I find it very strange that someone with such a distinguished record early
on would suddenly have a fascination with Marx and seeming throw away a
very promising career.
John
maximus
> In article <aakun5$bsp$1...@newsflood.osaka.att.ne.jp>, "maximus"
> <mad...@about.com> wrote:
>
> > > "But, as economic theory has learned since the 1930s, the
> > > pattern of activities adopted in the face of long-run
> > > factor-price changes can be complicated and counterintuitive.
> > > Consequently, the long-run demand for factors can be badly
> > > behaved functions of factor prices... The principle of
> > > variation works as an argument for long-run determinancy insofar
> > > as the set of zero-profit activities shift in response to factor
> > > price changes; it is not necessary that newly adopted activities
> > > use cheaper factors more intensively or that production is more
> > > capital intensive when r falls."
> > > -- Michael Mandler, _Dilemmas In Economic Theory: Persisting
> > > Foundational Problems Of Microeconomics_. Oxford, 1999.
> > > p. 34.
>
> > > My assertion was about the (absence of) well-behaved supply and
> > > demand functions in the labor market, particularly a demand
> > > function for labor.
>
> > I can assume that the functions you use are arbitrary, as well as all
> > parameters.
>
Robert
> This is silly. Suppose the theory stated that, given
>
> o Technology as represented by a production function with constant
> returns to scale and diminishing marginal returns to each factor
>
> o Profit-maximizing firms
>
> Firms adopt a no more labor-intensive technique at a higher wage.
>
> If the theory stated this and were logically consistent, I would
> not be able to describe a technology, no matter how arbitrary,
> in which the assumptions are met and the conclusion wasn't.
>
Economists are among some who are silly in their assumptions. But we learn
more from such silliness.
Robert
> Nonsense. The firm needs, by assumption, to adopt both a corn-producing
> process and one of the steel-producing processes in my example. That
> constrains the price of steel to be as shown.
>
But you never give what constrains the choice. When the mechanism is not
clear, assertion of anything may be only a hasty conclusion from jumping too
quick.
> > Probably you can use your time better.
>
> I'm free to choose to give certain people a platform with which to
> amuse our readers, if there are any.
>
> > I am afraid that I will not continue to follow this issue, since I am
too
> > busy with some paper lying around to be finished.
>
> You, of course, are free to remain ignorant of textbook results in
> price theory.
>
I never call my students silly or ignorant, even if they are truly so.
Calling people stupid, silly, ignorant does not make me more intelligent
or knowledgeable. Furthermore, knowledge changes also. If they are ignorant
or silliy, I invite them to take time to look into the issues, and think.
I am ignorant of many theories, no doubt. Yet your argument does not make
much
sense to me.
max
Robert Vienneau
<mad...@about.com> wrote:
> > This is silly. Suppose the theory stated that, given
> >
> > o Technology as represented by a production function with constant
> > returns to scale and diminishing marginal returns to each factor
> >
> > o Profit-maximizing firms
> >
> > Firms adopt a no more labor-intensive technique at a higher wage.
> >
> > If the theory stated this and were logically consistent, I would
> > not be able to describe a technology, no matter how arbitrary,
> > in which the assumptions are met and the conclusion wasn't.
> Economists are among some who are silly in their assumptions. But we
> learn more from such silliness.
Non sequitur.
None of the above is about (un)realism of assumptions. It is about
what and what are not the logical implications of standard assumptions
in mainstream theory.
> > There are no functions I use that I haven't shown, e.g., in PDF
> > files whose URL I have already given.
> > > You setting up the mechanism of price, especially for steel, is
> > > unrealistic.
> > > If firms can set up
> > > their prices as they like, why don't they set up a price that they
> > > can
> > > show
> > > higher profit ?
> > > This profit may be infinite even, in your case.
> > Nonsense. The firm needs, by assumption, to adopt both a corn-producing
> > process and one of the steel-producing processes in my example. That
> > constrains the price of steel to be as shown.
> But you never give what constrains the choice.
I do, even in the paragraph above.
> When the mechanism is not
> clear, assertion of anything may be only a hasty conclusion from jumping
> too quick.
> > > I am afraid that I will not continue to follow this issue, since I am
> > > too
> > > busy with some paper lying around to be finished.
> > You, of course, are free to remain ignorant of textbook results in
> > price theory.
> I never call my students silly or ignorant, even if they are truly so.
> Calling people stupid, silly, ignorant does not make me more intelligent
> or knowledgeable. Furthermore, knowledge changes also. If they are
> ignorant
> or silliy, I invite them to take time to look into the issues, and think.
You will not find me calling any PERSON silly above. You will
find me only characterizing STATEMENTS by somebody who says
he is not interested in looking into textbook results in price
theory. I read many responses to my posts as containing a large
non-rational component.
Nor do you see me calling anybody ignorant, without qualification.
> I am ignorant of many theories, no doubt.
And you are free to remain ignorant of many things, including
textbook results in price theory.
> Yet your argument does not make much sense to me.
I do not dispute that my argument does not make sense to you. That
has nothing to do with whether my argument is sensible, as far as
I can see.
Has anybody acknowledged here that the example in my first post
is correct?
--
John J. Weatherby
However your "long-run" model is only one period. This was part of the
confusion arising in our argument. A dynamic model will completely change
your results.
Second your model does not profit maximizing as you say it is cost
minimizing. You also provide no constraint. Any cost minimization problem
assume that cost is minimized for a given level of output. It is obvious
looking at the model that the given level of output differs according to
which technique is chosen. In a dynamic model the level of output of corn
and steel would be different according to the technique chosen. It is
therefore misleading to show cost minimization assuming that the outputs
under either technique are the same. In this case the static choice for
output does affect the time path for output. You can therefore not seperate
the static allocation from the dynamic allocation. You will get different
answers. If you want to see what happens to factor demands in the long run
you need dynamics.
If you want to see what the short run choice of technique is you still
need to solve the dynamic model. The given level of output will be different
under each technique you need to know that given level of output to
determine which process is the least costly.
BTW Foley's problem set is dynamic it calls for finding growth rates.
You can not discuss growth rates in a static model.
John
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-BED076....@news.dreamscape.com...
John J. Weatherby
> is correct?
>
to Foley and see what he has to say about it. I am sure he will point out
similar issues about the dynamics of the problem. I would send the post and
not the PDF. The PDF looks incomplete, because it is. The post is actually
easier to follow.
John
maximus
While Robert attempts to show a case to his favorite, his construction of
the model
might make him confused later on with many things left out unspecified or
only by
implicit assumptions which also mystify readers.
John's effort to explain to Robert about construction of (dynamic) model is
good enough,
and with details I seldom see in textbooks. In the first post, Robert
appears as if he tries
to raise doubts on economic theory, but then he changed into only a point in
the
production function, which is the "whole" model here, since there is nothing
else.
At least, this construction of model appears to me as "unconventional".
I must be confused, not amused.
max
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-A5A6C5....@news.dreamscape.com...
> > In article <lnnz8.687$Wd5....@newsread1.prod.itd.earthlink.net>,
<http://homepage.newschool.edu/~foleyd/GECO6200/ps1.html>
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
> > Mr. Weatherby's interpretation is highly idiosyncratic, to say
> > the least. I think it convenient to use corn as numeraire in
> > solving the above problem. Since Foley knows what he is talking
> > about, he would agree.
> It is not convenient to use corn as the numeraire it is wrong. You
> completely ignored the demand for corn and its effect on price.
The context here was comments on a problem from Foley's problem set,
not my example.
I will now show you how to begin solving this problem. This will
demonstrate that Mr. Weatherby's comments on the numeraire are
outlandishly mistaken.
Define four techniques in terms of the processes:
CORN-PRODUCING IRON-PRODUCING
TECHNIQUE PROCESS PROCESS
Alpha (0, 1/2, 1) (1/4, 0, 2)
Beta (0, 1/2, 1) (1/4, 1/4, 2)
Gamma (3/8, 1/9,1) (1/4, 0, 2)
Delta (3/8, 1/9,1) (1/4, 1/4, 2)
In the remainder, I consider only the Alpha technique.
Let
p1 = price of a unit of corn
p2 = price of a unit of iron
w = wage
r = rate of profits
Foley's students know to write down the following price equations:
( 1/2 p2 + 1 w )( 1 + r ) = p1 (1)
( 1/4 p1 + 2 w )( 1 + r ) = p2 (2)
No numeraire has been specified as yet.
Given the last clause in Foley's statement of the problem,
the ratio of the wage to the price of corn is of particular
interest:
(1/2 P + 1 W )( 1 + r ) = 1 (3)
( 1/4 + 2 W )( 1 + r ) = P (4)
where
P = ( p2/p1 ) (5)
W = ( w/p1) (6)
Alternatively, one can set the price of corn in equations
(1) and (2) to unity. This, too, will yield equations
(3) and (4).
One can solve Equations (3) and (4) to get:
W = ( 7 - 2r - r^2 )/[ 8 ( r + 1 )( r + 2 ) ] (7)
P = ( r + 9 )/[ 4 ( r + 2 ) ] (8)
Equation 7 is the desired wage-profit rate relation for the
alpha technique.
> Your assumption is that
> the
> level of corn production is the same under both processes this is
> completely
> wrong and I don't care who cite to try to prove differently.
I do not assume that the level of corn production is the same.
> Any competent
> economist will realize this is a short coming in the analysis even if
> they
> still use the model to try to prove a point. When you increase demand for
> corn by a factor of 17 prices will rise and production of corn will rise
> as
> well.
Consider any levels of output of the two processes in the alpha
technique above such that enough corn is produced net to cover
wages. Notice that the price equations (1) and (2) are independent
of the variations in the levels of output in this set.
This is the non-substitution theorem. Clearly Mr. Weatherby is
mistaken.
> Regardless it is pretty obvious from the numbers posted that you had
> to
> spend months finding an example that actually worked.
It's been years since I developed this case. I don't remember how
long it took. I have presented other examples here, some of which
I developed. Mr. Weatherby's claim is a fantasy that he cannot
know.
How long would it take me to figure out how to use a compass and
straight-edge to construct a triangle with angles that sum up to
more than 180 degrees?
> You use these numbers
> only because they are the only numbers you could find to make this work.
My example meets constraints that are non-obvious. It has to be
consistent with an internal solution, so to speak, for the utility
maximization problem in Sraffa3.pdf. It has to contradict the
Blaug quote there; it cannot be a three good model where which
one of two capital goods is used varies with the technique.
> Lets face it here you have to show extremely large differences in
> technique
> to make the theory work. You have to require 1/6 of the labor in the B
> process and 17 times the corn before you even get a slightly higher
> amount
> of profit under alpha when wages rise.
> This is just ridiculous to think that 2 process may be this
> divergent.
Why would one think adjacent techniques on a wage-profit rate frontier
would not have processes that differ dramatically in coefficients
of production? I don't know of any such reason. Continuity along
the frontier need not imply continuity in the chosen coefficients
of production.
> Is it somewhat interesting to show what happens when you have a choice of
> technique? Perhaps.
When one writes down a production function (other than Leontief)
one is postulating a problem of the choice of technique. When one
assumes the existence of land in one's models, one is postulating
a problem of the choice of technique. When one assumes the existence
of fixed capital, one is postulating a choice of technique.
On the other hand, technology evolves through time in my model
Bukharin, but there is no interesting problem of the choice of
technique.
> Samuelson say that these cases were different from
> mainstream theory and it might be interesting to look at different cases.
> Does this extreme case disprove that factor demands are downward sloping
> or
> horizontal? No. It is a special case that has very extreme assumptions.
The above is pure assertion. Mr. Weatherby has not stated what
assumptions on, say, technology he thinks would rule out my
result and related results. He has not shown in any sense that
they only arise in "extreme" cases, nor characterized what he
means by "extreme". He has no theory or model.
> Even
> if you did this model and did not make corn the numeraire, it might be
> somewhat interesting but it does not destroy an entire body of work.
> Especially when there is no empirical evidence to show there case
> actually exist.
Barkley Rosser, for instance, would say there are case studies
that show examples like mine can exist. He's written some. (I
haven't read much of the empirical references I can produce; I
think the point is one of logic.)
> This is like saying the fact Giffen goods exist means that Utility
> theory is completely wrong.
"Demand theorists know there are few Giffen goods. They know why
there are Giffen goods. They can successfully predict that certain
goods in certain economies (potatoes in Ireland, rice in China,
or yams in New Guinea) are likely to be Giffen goods. Capital
theorists, on the other hand, do not know whether capital reversing
is common or rare. Until recently they possessed no theory which
made sense of the phenomenon. The status of that fundamental theory
remains, moreover, questionable. From the perspective of the Austrian
theory or of Clark's theory, capital reversing is nothing but a
disconfirmation. Capital theorists are also unable to predict when
capital reversing will occur. They cannot point to some feature of
an economy and say, 'Ah, we can see that this is one of the
exceptional cases in which we should not expect our simpler capital
theories to work.' There is no justification for the claim that
capital reversing demands only minor qualifications in simplified
capital theories."
-- Daniel Hausmann
Robert Vienneau
> Another note your URL says you are holding the price of steel constant.
I believe that Mr. Weatherby is referring to this:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LaborDemand.pdf>
> How
> can you do this if corn is the numeraire? The price of steel will also be
> affected by the changing price of corn.
I give a version of a standard proof in an appendix there. I explain
what that proof is about. That proof holds the price of steel constant,
while considering the response of the firm at different levels of
wages.
The point of my paper, though, is to argue that the firm can only
be in equilibrim on the curved locus in the figures. On that
curve, the price of steel is non-constant. So I reject the idea
that a good analysis of the amount of labor this firm wants to hire
at different levels of wages should be conducted with the price
of steel held constant.
But it would be untrue to say, "The price of steel will also
be affected by the changing price of corn." Corn, being the numeraire,
does not have a changing price.
So Mr. Weatherby's comment is very muddled.
> Your URL was not very helpful
> either. I don't know how you think you can adequately explain a complex
> concept in 4 pages.
What do I claim is original about that paper? Only the figures for
illustrating this analysis when applied to a very low-dimensional
problem. The analysis itself is textbook, and I give a reference to
a standard textbook. I suppose there might be some originality in
my interpretation of the analysis.
I assume a reader with some ability to read mathematics. I suppose
I might have taken some time to explain why the last column of
Table 3 is obvious when you think about it. (It helps if the
reader has seen a standard notation for coefficients of production
before.) I also assume a reader that is able to think about what
happens when the problem is generalized in various ways, e.g.,
if more production processes are known.
> It takes more than righting down a function and placing
> graphs. As usual you try to let the math do all your talking. This is
> your
> biggest communication problem.
"Writing" is not spelled "righting". Mr. Weatherby is in no position
to blame his lack of understanding on a problem I have with
communication, while always making these sorts of mistakes.
When my response to something technical I am reading is basically,
"Huh", I do not assume the problem must lie with the author.
Robert Vienneau
I would expect Folely would find my original post in this thread
correct, trivial, obvious, and well-known. Thus, I will not bother
him with it. The only point he might find interesting is the
interpretation of the price of steel as an accounting price in
a vertically integrated firm.
Robert Vienneau
> It is funny here that you are arguing that long run decisions are
> difficult.
> However your "long-run" model is only one period. This was part of the
> confusion arising in our argument. A dynamic model will completely change
> your results.
This is not arguing that "long run decisions are difficult",
whatever that is supposed to mean. The reason my one-period
model is arguably long-run relates to its structure and
what variables are endogeneous and exogeneous.
> Second your model does not profit maximizing as you say it is cost
> minimizing.
Profit maximizing and cost minimization are related by duality
arguments in these sort of models. You cannot have one without
the other.
> You also provide no constraint. Any cost minimization problem
> assume that cost is minimized for a given level of output. It is obvious
> looking at the model that the given level of output differs according to
> which technique is chosen.
The proportions of gross levels of the output of corn and steel are
different according to the technique chosen. I showed that.
But levels of gross outputs have no effects on prices in this
model. That's the so-called non-substitution theorem that Mr.
Weatherby doesn't seem to be able to grasp.
> In a dynamic model the level of output of corn
> and steel would be different according to the technique chosen. It is
> therefore misleading to show cost minimization assuming that the outputs
> under either technique are the same. In this case the static choice for
> output does affect the time path for output. You can therefore not
> seperate
> the static allocation from the dynamic allocation. You will get different
> answers. If you want to see what happens to factor demands in the long
> run
> you need dynamics.
> If you want to see what the short run choice of technique is you
> still
> need to solve the dynamic model. The given level of output will be
> different
> under each technique you need to know that given level of output to
> determine which process is the least costly.
> BTW Foley's problem set is dynamic it calls for finding growth rates.
> You can not discuss growth rates in a static model.
Growth rates can be discussed in my example in the same way
they can be discussed in Foley's problem set. Does this make
my model or the problems in Foley's set dynamic? What dynamics
means is a contested subject among economists. Burmeister, who
seems to prefer an analysis based on a sequence of temporary
equilibria, would not call Foley's problem set, for example,
dynamic.
Suppose technology would lead to something like the effect
illustrated by my example in a long-run model. How would this
effect be manifested in something like Burmeister's dynamics
or in Arrow-Debreu intertemporal equilibra? As I understand it,
this is a research question. Economists who have made statements
on this question include Burmeister, Garegnani Hahn, Mandler, and
Schefold. But I don't think the question is settled.
Mr. Weatherby needs to do a lot of work before he will
understand what's being discussed.
Robert Vienneau
of substance here. But I will.
In article <aap726$sh8$1...@newsflood.osaka.att.ne.jp>, "maximus"
<madv...@37.com> wrote:
> While Robert attempts to show a case to his favorite, his construction of
> the model
> might make him confused later on with many things left out unspecified or
> only by
> implicit assumptions which also mystify readers.
Not readers who are familiar with the completely unoriginal point of
my example and the large literature upon which I draw. I specified
everything needed to make my point.
> John's effort to explain to Robert about construction of (dynamic) model
> is
> good enough,
> and with details I seldom see in textbooks. In the first post, Robert
> appears as if he tries
> to raise doubts on economic theory,
You still don't see that I am agreeing with correct economic theory,
e.g., as in that Michael Mandler quote.
> but then he changed into only a point
> in
> the
> production function, which is the "whole" model here, since there is
> nothing
> else.
I'm not sure what you are trying to say. It's probably wrong.
You might notice that the structure of the data in that problem
I quoted from Folely's problem set is the same as in my example.
The numbers, including the number of processes for producing one of
the commodities, differ. That's all.
> At least, this construction of model appears to me as "unconventional".
If you say well-established results appear unconventional to you,
I cannot disagree.
> I must be confused...
You are. For one thing, you don't notice John Weatherby's assertions
are mostly mistaken.
maximus
Since John and you (Robert) have some other related discussions not directly
at your
original post, I would avoid to participate.
Rather, as your origianl post with tables and nothing else, in my view, such
results and
parameters can be viewed as predetermined by some "blackbox" technology of
the
production process, which is exogenous.
Yet, in the setting price for steel, here is an excerpt of your original
post:
****** QUOTE *****
4.1 PRICES WITH LOW WAGES
Accordingly, assume wages are initially $1,338.8 per Person-Year.
By assumption, the firm neither buys nor sells steel on the market.
The firm produces steel solely for its own use. Still, the firm
must enter a price of steel on its books. I assume that the firm
sets this price so that it is making the same rate of profits in
both processes it uses.
******* END QUOTE ******
John has had long discussion on the process of corn price, where he raises
doubt
on the lack of market response.
In contrast, I pay more attention on price for steel. The above paragraph
offers no
other information about how and why firm can set the price only to make a
profit,
but not enough to explain why firm cannot set the price at other values.
That is where the function form must be addressed, no matter how general it
can be.
Lack of elementary information, your argument lacks persuasiveness. Economic
models
may look silly but they must make some sense, otherwise, it can be a toy for
fun until
one can derive from it/them something useful.
max
John J. Weatherby
> correct, trivial, obvious, and well-known. Thus, I will not bother
> him with it.
belief. You have no idea what Foley would say about using this model for
this question. His problem set does not use this model for this question.
>The only point he might find interesting is the
> interpretation of the price of steel as an accounting price in
> a vertically integrated firm.
>
So your model is uninteresting then. You said it not I.
John
John J. Weatherby
> In article <OTSz8.1690$nY5....@newsread1.prod.itd.earthlink.net>,
> "John J. Weatherby" <jjwea...@earthlink.net> wrote:
> This is not arguing that "long run decisions are difficult",
> whatever that is supposed to mean. The reason my one-period
> model is arguably long-run relates to its structure and
> what variables are endogeneous and exogeneous.
>
to make to support your model. This is in fact what you did. Again you need
to learn to communicate and not blindly post quotations to blow smoke around
the real issues.
> > Second your model does not profit maximizing as you say it is cost
> > minimizing.
>
> Profit maximizing and cost minimization are related by duality
> arguments in these sort of models. You cannot have one without
> the other.
>
Yes but the assumption of cost minimization is that it gives you the
same factor demands as profit maximization. The problem you present has a
different profit maximizing output under each technique. Therefore it is
wrong to set up a cost minimizing framework and assume that the given level
of output will be the same for either process. Adding a simple resource
constraint that shows that labor allocated to corn + labor allocated to
steel must be less than some number will show that the profit maximizing
outputs are different.
> The proportions of gross levels of the output of corn and steel are
> different according to the technique chosen. I showed that.
>
However you table shows the cost for the same level of outputs with each
process. In both cases you assume 10,000 units of corn are produced.
> How would this
> effect be manifested in something like Burmeister's dynamics
> or in Arrow-Debreu intertemporal equilibra? As I understand it,
> this is a research question.
You can not research it without first providing the theoritical basis.
> Mr. Weatherby needs to do a lot of work before he will
> understand what's being discussed.
>
On the contrary I beleive you need to do a lot of work to understand how
to correct set up these models and quit just saying this technique is
standard. Nothing is standard for any one question. The question I have had
and still have is if you understand the techniques and how they are used. I
still have question if you understand the application of the techniques.
Your complete inability to explain the technique and why you are using it in
your own words, as opposed to smatter a collection of quotations all over
the net, leads me to seriously doubt if you understand anything. Your
communication skills are lacking.
I don't know sometimes you may have a point but with inability to
explain conclusion and offer anything more than math in your own words
leaves me doubtful that you have a clue as to what you are doing. Instead of
explaining you post a lot of non-arguments that essentially calls your
critics idiots. This is not getting you anywhere. You have to understand
initial discussion of anything in this profesion is somewhat harsh.
Questions are often asked just to see if the author really understands his
material and can explain it. Throwing up your hands and saying you that your
critics do not understand only makes it look like you have no idea what you
are doing and can not explain your methods or your results.
No, this is not done just to those outside of mainstream economics.
Trust me when I presented New Atlantis the last time. I got a host of
questions about why the model was set up that and what drove the results.
Even the "standard" assumption of imperfect competition was commented on.
Yes I did answer them with the reason why this was chosen and did not
automatic assume they knew nothing about the literature. In some cases this
was true, yet even those who specialized in fields far away from mine have
made some valuable comments. No one in this profession is comfortable with
presenting something as standard and leaving it at that. You have to know
why you are using these techniques explain your model and explain your
results. Not copy something out of someone else's work half-way modifying it
and assuming just because Dr. X used this model to answer question Y people
will suddenly just accept that the model explains question Z, at least not
without heavily questioning it and making sure things are done right.
In short you need to learn how to take criticism and use it
constructively rather than throwing your hands up and calling the other
person incompetent, ie. any competent economist knows how to solve this,
instead of actually explaining the work. You remind of someone who took a
long time to finish their doctoral dissertation for the exact same reason.
You can not learn nor prove your models but starting off with the assumption
that you know more than everyone else and commenting on this beleif every
time you encounter criticism.
John
Robert Vienneau
<madv...@37.com> wrote:
> Since John and you (Robert) have some other related discussions not
> directly
> at your
> original post, I would avoid to participate.
You are, of course, free to drop out of any aspect of this thread
at any time.
> Rather, as your origianl post with tables and nothing else, in my view,
> such
> results and
> parameters can be viewed as predetermined by some "blackbox" technology
> of
> the
> production process, which is exogenous.
The first two tables define the technology. Obviously, I chose the
numbers to make the results I wanted come out, at least qualitatively.
Technology is widely treated as exogeneous in economics, including in
my example. That's a problem for economic theory which some have
tried to address, but this problem does not threaten my point.
> Yet, in the setting price for steel, here is an excerpt of your original
> post:
>
> ****** QUOTE *****
> 4.1 PRICES WITH LOW WAGES
>
> Accordingly, assume wages are initially $1,338.8 per Person-Year.
> By assumption, the firm neither buys nor sells steel on the market.
> The firm produces steel solely for its own use. Still, the firm
> must enter a price of steel on its books. I assume that the firm
> sets this price so that it is making the same rate of profits in
> both processes it uses.
> ******* END QUOTE ******
>
> John has had long discussion on the process of corn price, where he
> raises doubt on the lack of market response.
When John complains that I don't take into account how supply and
demand will change the price of the numeraire, doubt about the
correctness of my arithmetic is not what is raised in my mind.
> In contrast, I pay more attention on price for steel. The above paragraph
> offers no
> other information about how and why firm can set the price only to make a
> profit,
> but not enough to explain why firm cannot set the price at other values.
In context it does. I go through specific arithmetic calculations in
that original post showing how the price of steel must adjust to make
the internal rate of return the same in both the corn-producing
process and a steel-producing process.
> That is where the function form must be addressed, no matter how general
> it
> can be.
And I have shown the form of the relevant price equations on this
thread (see my start on a problem from Foley's problem set)
and provided various justifications for them in more detail
in PDF files.
> Lack of elementary information, your argument lacks persuasiveness.
You forgot to say it lack persuasiveness TO YOU.
> Economic models
> may look silly but they must make some sense, otherwise, it can be a toy
> for
> fun until
> one can derive from it/them something useful.
I think showing certain common beliefs lack logical validity
is useful.
Robert Vienneau
> Let me turn on Rob Vienneau mode here.
> "Robert Vienneau" <rv...@see.sig.com> wrote in
> > I would expect Folely would find my original post in this thread
> > correct, trivial, obvious, and well-known. Thus, I will not bother
> > him with it.
> I suppose or I expect is not an argument it is only statement of blind
> belief.
I would hope I would not write something so aesthetically displeasing.
> You have no idea what Foley would say about using this model for
> this question. His problem set does not use this model for this question.
Foley says the problem I drew out of his problem set was drawn from
some textbook. Notice which one. Then notice the references in my
PDF file that you were looking at.
Here's a problem from Foley's problem set:
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
Here's an extension of my example:
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
I've put this extension through a spreadsheet, but haven't sat down
with pen and paper. It appears to be a case with capital-reversing,
but no reswitching.
Foley's problem set is meant to give the student practice in working
with certain analytical tools. Those tools apply to any specific
numbers, for example, his or mine. The point I draw out of those
tools - that a more labor-intensive technique can be preferred at
a higher wage - is well-established in the literature.
Yes, I think I have plenty of reason to think Foley would find my
original post correct, trivial, obvious, and well-known.
> >The only point he might find interesting is the
> > interpretation of the price of steel as an accounting price in
> > a vertically integrated firm.
> So your model is uninteresting then. You said it not I.
You need to work on that wit. If I were to write something along
those lines, I would try to make it more jocular. I might not
suceed.
What I am saying is well-established in the literature. Foley is
familiar with the relevant literature. You don't seem to be, based
on your posts here. And you should familiarize yourself with this
stuff, given your speciality. That's why what I am saying should
be interesting to some, but not to Foley.
Why not see if your library has Kurz and Salvadori's _Theory of
Production_? Luigi Pasinetti's _Lectures on the Theory of Production_
is more introductory, therefore easier to understand, but not as
good at justifying the system of price equations.
John J. Weatherby
> You still don't see that I am agreeing with correct economic theory,
> e.g., as in that Michael Mandler quote.
>
the case in the long run. Yet you are still trying to say this is not a long
run model. Again I ask the question what does the Mandler quotation have
anything to do with this? Not only that but I also have to ask just who is
Mandler and what does he specialize in? I am not familiar with his work.
John
John J. Weatherby
> In article <OMwz8.1666$Wd5.1...@newsread1.prod.itd.earthlink.net>,
> I assume a reader with some ability to read mathematics. I suppose
> I might have taken some time to explain why the last column of
> Table 3 is obvious when you think about it. (It helps if the
> reader has seen a standard notation for coefficients of production
> before.)
Obvious to whom? You? No paper worth reading just leaves math to speak
for itself. Again it tends to make readers think you did not explain your
math or your results becuase you can not. Just pick any journal how many
authors do you see just present a table and not comment on it or even
explain what it means. Granted I could look at econometric tables in say a
labor paper and figure it out but not without questions. Notation and math
is not enough to explain things. You can't expect a reader to take the time
to figure it out. People want to know where the model came why you made
decisions and what you think the results mean not just math. If you can not
explain it which it is apparent that you can not I am not going to waste my
time trying to figure out something that you can not explain. Results
without explanation are meaningless.
> I also assume a reader that is able to think about what
> happens when the problem is generalized in various ways, e.g.,
> if more production processes are known.
>
Again another bad assumption. You need to show this to make the point.
Otherwise it is a blanket assumption and your readers wonder if you know
what happens when the problem is generalized. I have limited time and so do
other readers. It certainly isn't utility maximizing to sit and think of how
a model could be expanded when I am not even sure if the author understands
the model. No publisher would ever print something that left off at this
point. Your URL is incomplete at best.
> "Writing" is not spelled "righting".
Yes and quote is a verb, the correct term for something quoted is
quotation. At least I can blame spell check here.
>Mr. Weatherby is in no position
> to blame his lack of understanding on a problem I have with
> communication, while always making these sorts of mistakes.
>
These post are spit in less than an hour you can not expect them to be
prestine. If you are going to spend the time to publish something on the
internet however, you should take the time to make sure it is prestine. That
means clear, complete, and explained.
John
maximus
> > Rather, as your origianl post with tables and nothing else, in my view,
such
> > results and parameters can be viewed as predetermined by some "blackbox"
technology of the production process, which is exogenous.
Robert
> The first two tables define the technology. Obviously, I chose the
> numbers to make the results I wanted come out, at least qualitatively.
> Technology is widely treated as exogeneous in economics, including in
> my example. That's a problem for economic theory which some have
> tried to address, but this problem does not threaten my point.
>
It is fine with whatever crazy technology you want to define. That is why I
do not
question the table or the numbers you put on the table. But you must at
least give
inof on the most general form of the function you use to calculate.
Otherwise, you
cannot claim, as later you did, that the production function is not
well-behaved.
max
> > Yet, in the setting price for steel, here is an excerpt of your original
> > post:
> >
> > ****** QUOTE *****
> > 4.1 PRICES WITH LOW WAGES
> >
> > Accordingly, assume wages are initially $1,338.8 per Person-Year.
> > By assumption, the firm neither buys nor sells steel on the market.
> > The firm produces steel solely for its own use. Still, the firm
> > must enter a price of steel on its books. I assume that the firm
> > sets this price so that it is making the same rate of profits in
> > both processes it uses.
> > ******* END QUOTE ******
> >
> > John has had long discussion on the process of corn price, where he
> > raises doubt on the lack of market response.
Robert
> When John complains that I don't take into account how supply and
> demand will change the price of the numeraire, doubt about the
> correctness of my arithmetic is not what is raised in my mind.
>
John is correct in questioning the supply-demand interaction.
You are incomplete in not addressing this mechanism. The market may work
in some way as you may figure in your head, but explanation is important.
> > In contrast, I pay more attention on price for steel. The above
paragraph
> > offers no
> > other information about how and why firm can set the price only to make
a
> > profit,
> > but not enough to explain why firm cannot set the price at other values.
>
> In context it does. I go through specific arithmetic calculations in
> that original post showing how the price of steel must adjust to make
> the internal rate of return the same in both the corn-producing
> process and a steel-producing process.
>
> > That is where the function form must be addressed, no matter how general
> > it
> > can be.
Robert
> And I have shown the form of the relevant price equations on this
> thread (see my start on a problem from Foley's problem set)
> and provided various justifications for them in more detail
> in PDF files.
max
> > Lack of elementary information, your argument lacks persuasiveness.
Robert
> You forgot to say it lack persuasiveness TO YOU.
I cannot talk for ANYONE else. Even if you present it in a conference,
nobody will
address you by using the word WE, as a representative to the whole community
of economists. Your perception seems having some misinformation.
> > Economic models
> > may look silly but they must make some sense, otherwise, it can be a toy
> > for
> > fun until
> > one can derive from it/them something useful.
>
> I think showing certain common beliefs lack logical validity
> is useful.
>
There are lots of examples like this when people express their doubt on
beliefs.
But a paper is not a talk.
max
jgo
>> "John Weatherby" wrote:
>> How long did it take to cook up numbers to find this result.
>> This is no theory or refutation of theory. The process are
>> just numbers there is no substance nor a model.
>>> 2.0 DATA ON TECHNOLOGY
>
>> Data? I don't see any data just some cooked up numbers.
>
> In neoclassical economic theory, prices in competitive markets are
> supposed to be determined by the interaction of supply and demand
> curves. The givens in neoclassical theory are technology, tastes,
> and endowments. Another term for the "givens" is the "data".
> If the theory were correct, one would not be able to construct
> ("cooked up numbers" in one incomprehension-revealing formulation)
> a specific numeric example which meets the assumptions of the
> theory but has contradictory conclusions...
It doesn't work, as logical theory or as empirical descriptive.
Yes, some naive classical economists did not recognize the
importance of technological change, or at least did not make
explicit many of their thoughts on the matter. OTOH, Adam
Smith, in the oft-repeated example, did implicitly recognize
the importance of differences in technology.
Many Keynesians also failed to explicitly discuss the effects
of technological change.
Tastes & preferences are what "value" is about, and hence what
economics is about.
Get real. If you want to posit a theory, at least make a token
effort to posit one that fits the facts of a market. And while
you're examining them, recognize the huge role played by force
and fraud, and measures against them.
Robert Vienneau
<madv...@37.com> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-2C1E9F....@news.dreamscape.com...
> > In article <aaro7b$on1$1...@newsflood.osaka.att.ne.jp>, "maximus"
> > <madv...@37.com> wrote:
> > > Rather, as your origianl post with tables and nothing else, in my
> > > view, such
> > > results and parameters can be viewed as predetermined by some
> > > "blackbox"
> > > technology of the production process, which is exogenous.
> Robert
> > The first two tables define the technology. Obviously, I chose the
> > numbers to make the results I wanted come out, at least qualitatively.
> > Technology is widely treated as exogeneous in economics, including in
> > my example. That's a problem for economic theory which some have
> > tried to address, but this problem does not threaten my point.
> It is fine with whatever crazy technology you want to define.
Presumes facts not in evidence, i.e., that the technology is "crazy"
in some way and that this "craziness" drives the interesting results.
> That is why I do not
> question the table or the numbers you put on the table. But you must at
> least give
> inof on the most general form of the function you use to calculate.
Nope. For my purposes all I need is that my example conforms to
common assumptions.
> Otherwise, you
> cannot claim, as later you did, that the production function is not
> well-behaved.
I don't think I did. Where do you misread me as saying the
production functions in my example are not well-behaved? (And
why do you write "the production function" as a singular noun?
Do you not see there are two production functions in my example?)
The production functions in my example are continuous, are differentiable
almost everywhere (that is, everywhere but on a set of measure zero),
exhibit constant returns to scale, and exhibit diminishing marginal
returns.
Anyways, I find your paragraph illogical and confused. Suppose one
wants to show that the assumptions of some model do not imply
certain conclusions. The sort of conclusion I have in mind is
the principle of substitution - for example, that profit-maximizing
firms will adopt a less labor-intensive technique when wages
are higher. It is sufficient to show an example that meets the
assumptions of standard models in which this conclusion is asserted,
but doesn't have the questioned conclusion.
It is no objection to that position to argue that the example has
some additional special-case properties not true of every example
that meets the general case assumptions. The general case has
been proved not to imply the questioned conclusions. That's logic.
One student of logic once phrased it like this on one of my
threads:
"If you are talking about the counterexamples, as a matter of
elementary logic one does not demand generality of them, only
that they fall under the scope of the universal claim made. If
I refute your claim that all sheep are white by observing that
Farmer MacGregor has a black ewe, you cannot come back with
'Well you can hardly demand that all sheep belong to Farmer
MacGregor'."
Your problems with elementary logic, though, seem to be a common
irrational reaction to my sort of examples.
> [ Points about the price of steel Max doesn't feel like saying ]
> [ anything substantial about. ]
> max
> > > Lack of elementary information, your argument lacks persuasiveness.
> Robert
> > You forgot to say it lack persuasiveness TO YOU.
> I cannot talk for ANYONE else. Even if you present it in a conference,
> nobody will
> address you by using the word WE, as a representative to the whole
> community
> of economists. Your perception seems having some misinformation.
Nope. Saying an argument is not persuasive makes a statement about
an objective property of the argument, so to speak. Saying an
argument is not persuasive to me leaves open the possibility the
problem is in my (mis)understanding of the argument, that is, in
my perceptions, not in objective properties of the argument itself.
A few posts back you wrote:
"In the first post, Robert appears as if he tries to raise doubts
on economic theory, but then he changed into only a point in the
production function, which is the 'whole' model here, since there
is nothing else."
Since you cannot correctly echo back the point of my example, I am
afraid I don't give your perception that my argument lacks
persuasiveness much weight. But did I change into a point in the
production function before or after I changed into a pumpkin?
> > > Economic models
> > > may look silly but they must make some sense, otherwise, it can be a
> > > toy
> > > for
> > > fun until
> > > one can derive from it/them something useful.
> > I think showing certain common beliefs lack logical validity
> > is useful.
> There are lots of examples like this when people express their doubt on
> beliefs. But a paper is not a talk.
I have proven the principle of substitution does not apply to long
run models, for example.
Maximus
> In article <aat4uk$sv2$1...@newsflood.osaka.att.ne.jp>, "maximus"
> <madv...@37.com> wrote:
>
> > "Robert Vienneau" <rv...@see.sig.com> wrote in message
> > news:rvien-2C1E9F....@news.dreamscape.com...
> > > In article <aaro7b$on1$1...@newsflood.osaka.att.ne.jp>, "maximus"
> > > <madv...@37.com> wrote:
>
Robert
> It is no objection to that position to argue that the example has
> some additional special-case properties not true of every example
> that meets the general case assumptions. The general case has
> been proved not to imply the questioned conclusions. That's logic.
>
> One student of logic once phrased it like this on one of my
> threads:
>
> "If you are talking about the counterexamples, as a matter of
> elementary logic one does not demand generality of them, only
> that they fall under the scope of the universal claim made. If
> I refute your claim that all sheep are white by observing that
> Farmer MacGregor has a black ewe, you cannot come back with
> 'Well you can hardly demand that all sheep belong to Farmer
> MacGregor'."
>
> Your problems with elementary logic, though, seem to be a common
> irrational reaction to my sort of examples.
>
The logic argument is correct only if you use the same assumptions and same
functions.
You cannot claim your conclusion is logically correct when different
functions and assumptions
are used as compared to those you want to prove they are wrong.
It seems to me that you misuse the logic.
You appear to have same character like James Harris in the newsgroup for
mathematics
where he always think that anyone who refutes his calculation is acting
"irrational".
This sort of view is ridiculous for a trained economist. John has a good
explanation
on the work of economist when presenting to the community for comments. It
is this kind
of blaming others as irrational that renders any discussion into a "fight"
that wastes time
and energy.
max
Maxwelton
> 1.0 INTRODUCTION
>
> This long post presents an example in which higher wages are
> associated with firms choosing to employ more workers per unit output
> produced.
Higher wages are not the motivating factor in choosing to employ more
workers per unit output in this example.
> 4.2 ONE SET OF PRICES WITH HIGH WAGES
>
> Suppose this firm faces a higher wage, namely $2,932 per
> Person-Year. Consider what happens if the firm doesn't
> revalue the price of steel on its books. Table 6 shows this
> case.
>
> TABLE 6: COSTS, WAGE $2,932 PER PERSON-YEAR,
> PRICE OF STEEL $6,013 PER TON
>
> INDUSTRY PROCESS COST PROFITS
>
> Corn 0.2*$6,013 + 0.16889*$10,000
> + 0.82816*$2,932 = $5,320 88%
> Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
> + 0.19321*$2,932 = $2,767
> Steel Beta 0.13329*$6,013 + 0.15590*$10,000
> + 0.033594*$2,932 = $2,459 145%
>
Wages increaseased and profits fell but with all else remaining
constant, the less labour intensive process (Beta) is still the
most profitable.
> 4.3 ANOTHER SET OF PRICES
>
> Perhaps all that is needed is to re-evaluate steel on the
> firm's books.
Here is where you get off track. Regardless of the real value of
steel you are setting it below the point where process alpha
becomes more profitable. You are picking an amount to support your
model. THis sounds like something Enron would do.
> Higher wages have made steel less valuable.
If they are on parity with other steel producers and unit costs
increase there won't be a corresponding drop in unit sale price.
>Table
> 7 shows costs and the rate of profits when steel is
> evaluated at an accounting price of $4,499 per Ton.
>
> TABLE 7: COSTS, WAGE $2,932 PER PERSON-YEAR,
> PRICE OF STEEL $4,499 PER TON
>
> INDUSTRY PROCESS COST PROFITS
>
> Corn 0.2*$4,499 + 0.16889*$10,000
> + 0.82816*$2,932 = $5,017 99%
> Steel Alpha 0.35*$4,499 + 0.0095553*$10,000
> + 0.19321*$2,932 = $2,237
> Steel Beta 0.13329*$4,499 + 0.15590*$10,000
> + 0.033594*$2,932 = $2,257 99%
>
> If the firm were to continue using the Beta process to
> produce steel, this firm would be making the same rate of
> profit in producing corn and in producing its input of
> steel. But the manager of the steel-process would soon
> notice that the cost of operating the Alpha process is
> cheaper.
Yes and they would be exactly the same if we set the cost/price
of steel at $4593.50, that is both alpha and beta would have
equal cost.
>
> 4.4 FINAL EQUILIBRIUM PRICES
>
> So the firm would ultimately switch to using the Alpha
> process to produce steel. The price the firm would enter
> on its books would fall even more. Table 8 shows the accounting
> with a price of steel of $4,414 per ton. The firm has adopted
> the cheapest process for producing steel, and the rate of profits
> is the same in both corn-production and steel-production. The
> accounting for this vertically-integrated firm is internally
> consistent.
>
> TABLE 8: COSTS, WAGE $2,932 PER PERSON-YEAR,
> PRICE OF STEEL $4,414 PER TON
>
> INDUSTRY PROCESS COST PROFITS
>
> Corn 0.2*$4,414 + 0.16889*$10,000
> + 0.82816*$2,932 = $5,000 100%
> Steel Alpha 0.35*$4,414 + 0.0095553*$10,000
> + 0.19321*$2,932 = $2,207 100%
> Steel Beta 0.13329*$4,414 + 0.15590*$10,000
> + 0.033594*$2,932 = $2,246
>
The reason for alpha process becoming more profitable is because of
the lower cost/price of steel and is independent of wages. The reason
is quite simple; the weighted percentage of the steel cost in the alpha
process is much higher than in the beta process .35 vs .13329. However,
the price of steel can't be set by these methods you choose unless you
choose to take a real loss. If you want to use that value for steel
this company would make a lot more profit if they went back to the
the lower wage and the beta process again proving that higher wages
in this instance have nothing to do with higher profitablity.
As I pointed out earlier by raising the wage and leaving all else constant
the Beta process is still more profitable because the labour is weighted
by a lower percentage. .033594 (beta) vs. .19321 (alpha). If you
want to see when the alpha process becomes more profitable then instead
of raising wages by more than 2x try cutting them in half of the original
number. Try these same equations with a wage of $669.40 holding all else
constant and you will see the alpha process become more profitable.
Maxwelton
John Weatherby
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-173A1B....@news.dreamscape.com...
> In article <MqfA8.1494$Ss1....@newsread2.prod.itd.earthlink.net>,
> "John J. Weatherby" <jjwea...@earthlink.net> wrote:
> I would hope I would not write something so aesthetically displeasing.
>
aesthetically pleasing. It leaves a lot for the reader to figure out on
their own which is just bad authoring.
John
John Weatherby
> In article <aat4uk$sv2$1...@newsflood.osaka.att.ne.jp>, "maximus"
> <madv...@37.com> wrote:
> Nope. For my purposes all I need is that my example conforms to
> common assumptions.
>
lot of colloquiums, which are not commonly accepted in any sort of writing
outside of fiction and novels. For someone who strives to be "aesthetically
pleasing" I would think you want to use a correct No rather the slang Nope
which makes you sound highly unintelligent when using this in writing.
> Anyways, I find your paragraph illogical and >confused.
Welcome to our world. Most economist on this group have been saying this
about your work for quite some time Rob. Do you not think by now the problem
may be with your lack of desire for completeness and explanation. Even your
paper you post on your site and is incomplete with no explanation just
conclusions. After all the reading you claim to have done you should know
this is not the way ideas are presented in this field mainstream or
otherwise.
> > [ Points about the price of steel Max doesn't feel like saying ]
> > [ anything substantial about. ]
>
I really do not see why you find how the firm determines transfer
pricing interesting nor do I see why your criterion for transfer pricing has
to hold or even why a firm would use this criterion of equal rate of
profits. Transfer pricing is an interesting issue for the IRS but I am not
sure why it should be included in a model. In fact one probably should
assume perfect competition and set the price of steel to its marginal cost.
This would give an accurate price in terms of theory. In practice transfer
pricing is an issue because marginal cost is not observed.
John
John Weatherby
> In article <aat4uk$sv2$1...@newsflood.osaka.att.ne.jp>, "maximus"
> <madv...@37.com> wrote:
>(And
> why do you write "the production function" as a singular noun?
> Do you not see there are two production functions in my example?)
>
that supply and demand do not affect the amount of labor employed. However
you then go to argue that the demand for labor can slope upward and
therefore as wages rise more labor is employed. This is a contradiction.
Even if you are right labor demand is still determining labor employed.
Wages and Employment are determined by demand in this model, labor supply
is not included.
Second the labor demand functions do not slope upward for either
process!! So again you have not countered the theory that for any given
production function labor demands slope downward. The response to labor
demanded with wage in each example is zero not a postitive number. In this
model there is no substitution of labor for capital in either production
function. So if you look at either technique there is no effect of a
changing wage on labor employed.
What you have possibly shown, although I am unconvinced you did this
right, is that techniques can change under different wages. This is not say
the labor demand function is sloping upward. Factor demands are specificly
derived from a given production function and in your example neither
production function gives an upward sloping demand for labor.
The other problem is that theory will tell you that the marginal
production of labor equals the real wage. The amount of labor demanded
decreases as the real wage rises. By keeping the price of corn constant you
are showing that labor employed can increase as nominal wages increase. This
is not a counter example of theory. You must show what happens to the price
of corn to see what the real wage is. As I have noted if corn is not the
numeraire, and perhaps money is, you will see the price of corn changing
under techniques. So in this example you have no idea what happens to real
wages. Is the increase in wages completely offset by a rise in the price of
corn? Are real wages dropping because prices are rising faster than nominal
wages? Who knows in this model. You are trying to disprove a theory that
says the amount of labor employed is negaticely related to the real wage by
showing that the amount of labor employed may not be negatively related to
the nominal wage. You are comparing apples to oranges and proclaiming
because you found something different with oranges the theory about apples
is wrong.
John
Mason Clark
> For someone who complains about grammar and aesthetics you surely use a
>lot of colloquiums [sic], which are not commonly accepted in any sort of writing
>outside of fiction and novels. For someone who strives to be "aesthetically
>pleasing" I would think you want to use a correct No rather the slang Nope
>which makes you sound highly unintelligent when using this in writing.
I can't resist. An addition to my collection of quotations,
sub-class: "unwitting witticism".
Mason C
P.S. It's good to have an authority on aesthetics in the group
John Weatherby
"Mason Clark" <masonc...@ix.netcom.com> wrote in message
news:8bb8duggsp3cgnrpk...@4ax.com...
> On Sat, 04 May 2002 17:22:45 GMT, "John Weatherby"
<jjwea...@earthlink.net> wrote:
> I can't resist. An addition to my collection of quotations,
> sub-class: "unwitting witticism".
>
John
Robert Vienneau
maxw...@my-deja.com (Maxwelton) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote in message
> news:<rvien-49A723....@news.dreamscape.com>...
> > 1.0 INTRODUCTION
> > This long post presents an example in which higher wages are
> > associated with firms choosing to employ more workers per unit output
> > produced.
> Higher wages are not the motivating factor in choosing to employ more
> workers per unit output in this example.
Higher wages must ultimately result in different relative prices.
Higher wages are ultimately associated with the technique in which
more workers per unit output are employed being more profitable.
> > 4.2 ONE SET OF PRICES WITH HIGH WAGES
> >
> > Suppose this firm faces a higher wage, namely $2,932 per
> > Person-Year. Consider what happens if the firm doesn't
> > revalue the price of steel on its books. Table 6 shows this
> > case.
> >
> > TABLE 6: COSTS, WAGE $2,932 PER PERSON-YEAR,
> > PRICE OF STEEL $6,013 PER TON
> >
> > INDUSTRY PROCESS COST PROFITS
> >
> > Corn 0.2*$6,013 + 0.16889*$10,000
> > + 0.82816*$2,932 = $5,320 88%
> > Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
> > + 0.19321*$2,932 = $2,767
> > Steel Beta 0.13329*$6,013 + 0.15590*$10,000
> > + 0.033594*$2,932 = $2,459 145%
> >
> Wages increaseased and profits fell but with all else remaining
> constant, the less labour intensive process (Beta) is still the
> most profitable.
Thank you for the agreement (except I use the term "labor-intensive"
differently.)
But look. The firm here will not decide to keep on producing corn.
It is not as profitable as producing steel.
What do you think will happen? Will firms exit corn-production and
enter steel-production? (This is a complicated question. I am
not well enough informed about "cross-dual dynamics" - the
technical term - to know if it has been decided whether capital-
reversing has definite impacts on stability analysis here.)
But I do know how to find what the price of steel must be so
that these disequilibrium dynamics do not arise for the higher
wage.
> > 4.3 ANOTHER SET OF PRICES
> >
> > Perhaps all that is needed is to re-evaluate steel on the
> > firm's books.
> Here is where you get off track. Regardless of the real value of
> steel you are setting it below the point where process alpha
> becomes more profitable. You are picking an amount to support your
> model.
Nope. The constraint, that the firm will continue to find it
equally profitable to produce both steel and corn, determines the
price uniquely.
> > Higher wages have made steel less valuable.
> If they are on parity with other steel producers and unit costs
> increase there won't be a corresponding drop in unit sale price.
But then nobody will produce corn. This is a disequilibrium.
What do you think will happen?
> >Table
> > 7 shows costs and the rate of profits when steel is
> > evaluated at an accounting price of $4,499 per Ton.
> >
> > TABLE 7: COSTS, WAGE $2,932 PER PERSON-YEAR,
> > PRICE OF STEEL $4,499 PER TON
> >
> > INDUSTRY PROCESS COST PROFITS
> >
> > Corn 0.2*$4,499 + 0.16889*$10,000
> > + 0.82816*$2,932 = $5,017 99%
> > Steel Alpha 0.35*$4,499 + 0.0095553*$10,000
> > + 0.19321*$2,932 = $2,237
> > Steel Beta 0.13329*$4,499 + 0.15590*$10,000
> > + 0.033594*$2,932 = $2,257 99%
> >
> > If the firm were to continue using the Beta process to
> > produce steel, this firm would be making the same rate of
> > profit in producing corn and in producing its input of
> > steel. But the manager of the steel-process would soon
> > notice that the cost of operating the Alpha process is
> > cheaper.
> Yes and they would be exactly the same if we set the cost/price
> of steel at $4593.50, that is both alpha and beta would have
> equal cost.
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$4,593.5 + 0.16889*$10,000
+ 0.82816*$2,932 = $5,035.77 98.8%
Steel Alpha 0.35*$4,593.5 + 0.0095553*$10,000
+ 0.19321*$2,932 = $2,269.77 102.4%
Steel Beta 0.13329*$4,593.5 + 0.15590*$10,000
+ 0.033594*$2,932 = $2,269.77 102.4%
Notice that here the firm will not find it equally profitable
to produce both corn and steel.
> > 4.4 FINAL EQUILIBRIUM PRICES
> >
> > So the firm would ultimately switch to using the Alpha
> > process to produce steel. The price the firm would enter
> > on its books would fall even more. Table 8 shows the accounting
> > with a price of steel of $4,414 per ton. The firm has adopted
> > the cheapest process for producing steel, and the rate of profits
> > is the same in both corn-production and steel-production. The
> > accounting for this vertically-integrated firm is internally
> > consistent.
> >
> > TABLE 8: COSTS, WAGE $2,932 PER PERSON-YEAR,
> > PRICE OF STEEL $4,414 PER TON
> >
> > INDUSTRY PROCESS COST PROFITS
> >
> > Corn 0.2*$4,414 + 0.16889*$10,000
> > + 0.82816*$2,932 = $5,000 100%
> > Steel Alpha 0.35*$4,414 + 0.0095553*$10,000
> > + 0.19321*$2,932 = $2,207 100%
> > Steel Beta 0.13329*$4,414 + 0.15590*$10,000
> > + 0.033594*$2,932 = $2,246
> The reason for alpha process becoming more profitable is because of
> the lower cost/price of steel and is independent of wages.
As should be clear from above, that is not true. The price of steel
becomes determined in this model once wages are given.
> The reason
> is quite simple; the weighted percentage of the steel cost in the alpha
> process is much higher than in the beta process .35 vs .13329.
If you actually try to create a similar example with my methods,
you will find it's not nearly as clear cut. For example, what
happens depends on the corn-producing processes.
> However,
> the price of steel can't be set by these methods you choose unless you
> choose to take a real loss. If you want to use that value for steel
> this company would make a lot more profit if they went back to the
> the lower wage and the beta process again proving that higher wages
> in this instance have nothing to do with higher profitablity.
The firm, by assumption, doesn't have the ability to independently
set wages. In this sort of model, higher wages are always associated
with a lower rate of profit.
> If you
> want to see when the alpha process becomes more profitable then instead
> of raising wages by more than 2x try cutting them in half of the original
> number. Try these same equations with a wage of $669.40 holding all else
> constant and you will see the alpha process become more profitable.
By my methods (which are textbook), the price of steel must adjust so
that firms want to produce both steel and corn. I get:
w = $9,512.2 $3,928.6 $2,063.5 0
|<--- Beta ---->|<--- Alpha --->|<--- Beta --->|
r = 0% 75% 125% 204.4%
See Figure 1 in
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
(Given the numeraire and the change in whether wages are advanced,
wages are not the same in the figure.)
My point in this thread was what happens around the switch point
at 125%.
Robert Vienneau
<madv...@about.com> wrote:
From the post to which you are pretending to respond:
[>> The production functions in my example are continuous, are ]
[>> differentiable ]
[>> almost everywhere (that is, everywhere but on a set of measure ]
[>> zero), ]
[>> exhibit constant returns to scale, and exhibit diminishing ]
[>> marginal ]
[>> returns. ]
So what assumptions on technology do you want to impose that are not
true in my example?
> It seems to me that you misuse the logic.
It seems to me you have nothing substantial to say. For example,
you refuse to clarify your misstatement about "the" production
function.
> You appear to have same character like James Harris in the newsgroup for
> mathematics
> where he always think that anyone who refutes his calculation is acting
> "irrational".
Nobody here has correctly refuted my example.
> This sort of view is ridiculous for a trained economist.
Here's the thing. I am AGREEING with points well-established in the
literature. Furthermore, many have said that the reaction of some
communities of economists to the results I am showing reflects
perverse norms.
Furthermore, over on sci.math, trained mathematicians can show exactly
where James is wrong. Here all the professional economists do is say,
"Huh".
> John has a good
> explanation
> on the work of economist when presenting to the community for comments.
> It
> is this kind
> of blaming others as irrational that renders any discussion into a
> "fight"
> that wastes time
> and energy.
I would think saying your mistake is common is a nice way of pointing
it out. Would you rather it be the case that nobody but you would
make your sort of mistakes?
Robert Vienneau
The following problem is like one from a problem set Duncan Foley gave
a current class. I have changed the numbers.
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
2.0 THE SOLUTION
Define four techniques in terms of the processes:
TABLE 1: DEFINITION OF TECHNIQUES
CORN-PRODUCING IRON-PRODUCING
TECHNIQUE PROCESS PROCESS
Alpha (0.16889, 0.2, 0.82816) (0.0095553, 0.35, 0.19321)
Beta (0.16889, 0.2, 0.82816) (0.15590, 0.13329, 0.033594)
Gamma (0.16889, 0.25, 0.75) (0.0095553, 0.35, 0.19321)
Delta (0.16889, 0.25, 0.75) (0.15590, 0.13329, 0.033594)
Let corn be numeraire. Let
p = price of a ton iron (in units of bushels corn).
w = wage (in units of bushels corn).
r = rate of profits.
2.1 ALPHA TECHNIQUE
The price equations for the Alpha technique are:
( 0.16889 + 0.2 p + 0.82816 w )( 1 + r ) = 1 (1)
( 0.0095553 + 0.35 p + 0.19321 w )( 1 + r ) = p (2)
The solution in terms of the rate of profits is:
w = ( 0.05720044 r^2 - 0.4044891 r + 0.5383104 )/
[( 1 + r )( 0.576946 - 0.251214 r )] (3)
p = ( 0.1684921 - 0.02471792 r )/( 0.576946 - 0.251214 r ) (4)
2.2 BETA TECHNIQUE
The price equations for the Beta technique are:
( 0.16889 + 0.2 p + 0.82816 w )( 1 + r ) = 1 (5)
( 0.1559 + 0.13329 p + 0.033594 w )( 1 + r ) = p (6)
The solution in terms of the rate of profits is:
w = ( 0.6891513 -0.3195173 r - 0.008668652 r^2 )/
[( 1 + r )( 0.7244934 - 0.1036666 r ) (7)
p = ( 0.1570306 + 0.1234365 r)/( 0.7244934 - 0.1036666 r ) (8)
2.3 GAMMA TECHNIQUE
The price equations for the Gamma technique are:
( 0.16889 + 0.25 p + 0.75 w )( 1 + r ) = 1 (9)
( 0.0095553 + 0.35 p + 0.19321 w )( 1 + r ) = p (10)
The solution in terms of the rate of profits is:
w = ( 0.53783268 - 0.40544465 r + 0.056722675 r^2 )/
[(1 + r)( 0.5358025 - 0.2141975 r )] (11)
p = ( 0.1677452 - 0.02546476 r )/( 0.5358025 - 0.2141975 r ) (12)
2.4 DELTA TECHNIQUE
The price equations for the Delta technique are:
( 0.16889 + 0.25 p + 0.75 w )( 1 + r ) = 1 (13)
( 0.1559 + 0.13329 p + 0.033594 w )( 1 + r ) = p (14)
The solution in terms of the rate of profits is:
w = ( 0.68135635 - 0.3351073 r - 0.016463652 r^2 )/
[(1 + r)( 0.658431 - 0.091569 r ) (15)
p = ( 0.14484531 + 0.11125131 r )/( 0.658431 - 0.091569 r ) (16)
2.5 CHOICE OF TECHNIQUE
It is convenient to restate the four wage-profit rate relations here
together:
w( alpha ) = ( 0.05720044 r^2 - 0.4044891 r + 0.5383104 )/
[( 1 + r )( 0.576946 - 0.251214 r )] (17)
w( beta ) = ( 0.6891513 -0.3195173 r - 0.008668652 r^2 )/
[( 1 + r )( 0.7244934 - 0.1036666 r ) (18)
w( gamma) = ( 0.53783268 - 0.40544465 r + 0.056722675 r^2 )/
[(1 + r)( 0.5358025 - 0.2141975 r )] (19)
w( delta ) = ( 0.68135635 - 0.3351073 r - 0.016463652 r^2 )/
[(1 + r)( 0.658431 - 0.091569 r ) (20)
At any profit rate, the technique that maximizes the wage is
cost-minimizing. By this criterion, which technique is preferred is
shown in the following diagram:
w = 1.035 0.354 0.293 0.20635 0
|<-- Delta --->|<-- Gamma -->|<-- Alpha -->|<-- Beta -->|
r = 0% 85.9% 100.1% 125% 204.4%
Neither the production function for iron nor the production function for
corn is Leontief. Both production functions exhibit constant returns to
scale, exhibit diminishing marginal returns, and are differentiable
almost everywhere.
Neither reswitching nor recurrence of techniques arise along the
wage-profit rate frontier in this example.
The switch point at r = 125%, w = 0.20635 is "perverse" from the
perspective of outdated neoclassical intuition based on the principle
of substitution. Around this point, a higher wage is associated with
the adoption of a more labor-intensive technique. (The fact that there
is at most one such switch in this example is not a general property
of this sort of model.)
In other words, this example illustrates that "the pattern of activities
adopted in the face of long-run factor-price changes can be complicated
and counterintuitive. Consequently, the long-run demand for factors can
be badly behaved functions of factor prices...It is not necessary that
newly adopted activities use cheaper factors more intensively."
Robert Vienneau
"John Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-35287B....@news.dreamscape.com...
> > Nope. For my purposes all I need is that my example conforms to
> > common assumptions.
> For someone who complains about grammar and aesthetics you surely use
> a
> lot of colloquiums, which are not commonly accepted in any sort of
> writing
> outside of fiction and novels. For someone who strives to be
> "aesthetically
> pleasing" I would think you want to use a correct No rather the slang
> Nope
> which makes you sound highly unintelligent when using this in writing.
Whatever, dude.
John J. Weatherby
> In article <e3398e5.02050...@posting.google.com>,
> But look. The firm here will not decide to keep on producing corn.
> It is not as profitable as producing steel.
>
> What do you think will happen? Will firms exit corn-production and
> enter steel-production?
Here again you show you forget or do not understand the assumptions of
your own model.
direct quotation
"By assumption, the firm neither buys nor sells steel on the market.
The firm produces steel solely for its own use. Still, the firm
must enter a price of steel on its books. I assume that the firm
sets this price so that it is making the same rate of profits in
both processes it uses."
How can it be more profitable to sell steel in a one period model? Steel is
not traded therefore firms make no profit on producing steel in the current
period. It will not be available for production until the second period!!!
Steel can only become more profitable if it affects the amount of corn used.
This assumption again is driven from the fact you use the transfer pricing
trick. The price of steel should be its marginal cost.
Again you still have not answered where the model says again about the
amount of labor demanded being negatively related to the real and not
nominal wage.
> Nope. The constraint, that the firm will continue to find it
> equally profitable to produce both steel and corn, determines the
> price uniquely.
>
Again this is an artifical transfer price assumption that no firm would
necessarily use.
> But then nobody will produce corn. This is a disequilibrium.
> What do you think will happen?
>
Why steel is not traded. No production of corn means no profits.
John
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-394E46....@news.dreamscape.com...
> > In article <e3398e5.02050...@posting.google.com>,
> > But look. The firm here will not decide to keep on producing corn.
> > It is not as profitable as producing steel.
> >
> > What do you think will happen? Will firms exit corn-production and
> > enter steel-production?
> Here again you show you forget or do not understand the assumptions
> of your own model. direct quotation
> "By assumption, the firm neither buys nor sells steel on the market.
> The firm produces steel solely for its own use. Still, the firm
> must enter a price of steel on its books. I assume that the firm
> sets this price so that it is making the same rate of profits in
> both processes it uses."
From the post to which Mr. Weatherby is pretending to respond:
maxw...@my-deja.com (Maxwelton) wrote:
[ >> If they are on parity with other steel producers and unit costs ]
[ >> increase there won't be a corresponding drop in unit sale price. ]
John J. Weatherby
> In article <6Ewz8.1662$Wd5.1...@newsread1.prod.itd.earthlink.net>,
> "John J. Weatherby" <jjwea...@earthlink.net> wrote:
>
> > "Robert Vienneau" <rv...@see.sig.com> wrote in message
> > > In article <lnnz8.687$Wd5....@newsread1.prod.itd.earthlink.net>,
> W = ( w/p1) (6)
>
> Alternatively, one can set the price of corn in equations
> (1) and (2) to unity. This, too, will yield equations
> (3) and (4).
>
The problem is that you keep p1 constant. In effect any change here in
the nominal wage is an effect in the real wage. By doing this you make the
effects of the nominal wage the same as the effect of the real wage. The
argument this is not appropiate for the question you are asking. You are
trying to refute the standard theory that the real wage is equal to the
marginal product on labor, which given diminishing returns to labor is
negatively related to the amount of labor. The problem is your example the
two processes will result in two different amount of corn produced. Any
simple demand function will tell you that the price of corn is not the same
under the both process.
The fact that prices are different means that real wage may not be
rising when the process switches if Prices are higher under process alpha
then the real wage for using process alpha is lower than the real wage for
using process beta. Which they will be given any labor constraint the alpha
process will lead to less corn production, meaning higher prices and lower
real wages than the beta process. Without market response you can not
determining what is happening to the real wage. Therefore you are not
contesting standard assumptions rather you are contesting an result that
does not exist that is that the amount of labor demanded decreases as the
nominal wage rises.
No theory I have ever seen predicts that nominal wages are negatively
related to labor demanded. The correct solution of the problem is that labor
demanded decreases as the "real" wage rises. This is a distinct difference
and if you do not know this you seriously need to read a principles book
before commenting.
> Notice that the price equations (1) and (2) are >independent
> of the variations in the levels of output in this set.
>
Which essentially means that demand is completely elastic for every
level of output. This also drives the result in that it lets you equate
changes in the nominal wage to a proportional change in the real wage. This
is a very restrictive assumption. If the demand for corn has an elasticity
of something other than 0 this does not work. In fact in your example the
demand for corn is not of elasticity of 0. A portion of the demand for corn
is determined by the process which is used. If technique beta is used there
will be 17 times as much corn demanded!!! This means the demand curve would
shift upward by a factor of 17, if only corn in the steel process was
demanded. This will result in higher corn prices under the beta process.
However you ignore by choice of the numeraire and holding corn prices
constant. Again this has drastic effects on the real wage.
> "Demand theorists know there are few Giffen goods. They know why
> there are Giffen goods. They can successfully predict that certain
> goods in certain economies (potatoes in Ireland, rice in China,
> or yams in New Guinea) are likely to be Giffen goods.
Yes but they do not title the papers that try to predict this "Quantity,
Prices not affected by Supply, Demand". They realise that demand and supply
are still at work and that the theory for normal goods and correct and
useful unlike what you are trying to argue here.
So what is your argument
A. that Neo-Classical economics does not recognize a category of cases where
the analysis is different
or
B. that Neo-Classical economics is wrong?
If I thought your model was correct I could agree with A but not B. Just as
with utility theory, it does not mean standard assumptions are incorrect nor
non-useful when applied correctly.
>Capital
> theorists, on the other hand, do not know whether capital reversing
> is common or rare.
Which is the problem. Until you can empirically prove that this happens
then standard models have not been proved to be inappropiate. You can not
prove that standard models do predict well until you if these cases exist in
the real world and in what areas. Until then reswitching is an interesting
note like a Giffen good. The fact that no one has ever found one means that
standard models are likely to predict well.
But then again we were not discussing the effect of reswitching
invalidating the assumptions of a production function. The discussion is
does this model show that labor demanded can increase when real wages
increases. I am not convinced.
John
John J. Weatherby
> In article <iOeB8.234$CO3...@newsread1.prod.itd.earthlink.net>, "John
> J. Weatherby" <jjwea...@earthlink.net> wrote:
> From the post to which Mr. Weatherby is pretending to respond:
>
assumptions or that you do not understand them. Your response indicates that
something that can logically happen from your assumptions is happening in
your model.
ONE MORE TIME THE PRICE OF STEEL IS THE COST TO THE FIRM. THIS IS THE
PRICE THAT A FIRM WILL USE TO DETERMINE PRODUCTION. HOW IT ACCOUNTS FOR THE
COST AND HOW IT DECIDES TO TRANSFER PRICE IS BETWEEN THEM AND THE IRS AND
HAS NO EFFECT ON PRODUCTION. (Caps for emphasis)
Let me also reiterate that THE PRICE OF CORN WILL BE DIFFERENT UNDER
EITHER PROCESS UNLESS THE ELASTICITY OF DEMAND IS ZERO. THIS CAN NOT BE
GIVEN YOUR PRODUCTION FUNCTIONS. UNTIL YOU FIND OUT WHAT HAPPENS TO PRICE
YOU DO NOT KNOW WHAT HAPPENS TO REAL WAGES. TO COUNTER THE THEORY THAT THE
MARGINAL PRODUCT OF LABOR EQUALS THE REAL WAGE YOU NEED REAL AND NOT NOMINAL
CHANGES IN THE WAGE. KEEPING THE PRICE OF CORN CONSTANT RIGGS THE MODEL IN
THAT CHANGES IN NOMINAL WAGES ARE EQUAL TO CHANGES IN THE REAL WAGE. Any
market analysis will tell you that your real wages are wrong simply because
you have pegged the price of corn. BTW, Foley was not asking this question
in his problem set so can't claim it is appropiate simply because Foley used
this setup.
John
Robert Vienneau
> Your response indicates
> that
> something that can logically happen from your assumptions is happening in
> your model.
I am not able to understand how the above shows me wrong.
Suppose somebody points to some assumption in my model. Suppose that
person says that if that assumption were relaxed, my conclusions would
not follow. (It is a necessary assumption, not merely sufficient.) I
argue that if this assumption is relaxed, my conclusions still follow.
I am not able to understand why considering the relaxation of the
questioned assumption would be wrong.
> BTW, Foley was not asking this
> question
> in his problem set so can't claim it is appropiate simply because Foley
> used
> this setup.
I am unable to understand what is keeping Mr. Weatherby from solving
the quoted problem in Foley's problem set, either as Foley stated it
or with my modifications in the specific numeric values. Nor am I
able to understand why Mr. Weatherby does not acknowledge correct my
posted solution to the problem with the modified values.
John J. Weatherby
> John J. Weatherby claims I am mistaken about something or other because:
>
firms could produce only steel shows you forgot or do not understand your
own assumptions. Again this silly transfer pricing trick is part of what
gives your result.
Secondly, Wicksell may have pointed out cases of reswitching. Samuelson
may have agreed under certain assumptions it can happen. However this does
not automatically mean that
A. Your conclusions are correct for the question of can quantity of labor
demanded rise when real wages rise.
B. That your conclusion is well established in literature. The only
quotation you have found has said things can get strange in long run
analysis. Your model is one period not long run analysis. I still do see
that your conclusions have been stated anywhere in the literature. The Foley
site you keep refering to ask a completely different question, although the
model is similar.
> Suppose somebody points to some assumption in my model. Suppose that
> person says that if that assumption were relaxed, my conclusions would
> not follow.
Which is exactly what I have done. I have pointed out time and time
again that
A. The price of steel is wrong. It should be cost of steel. The cost of the
steel may be cheaper under process beta meaning you cost functions are
wrong. The transfer pricing trick is part of how the model is rigged to get
the result.
B. The theory of the firm predicts how the amount of labor demanded reacts
to the real wage. By choosing corn as the numeraire you have fixed the
price. This is misleading in that although your nominal wage is rising we do
not what is happening to real wages when the different processes are chosen.
Your only response to this is an allegation that commentors have just
said "huh". This is hardly a counter argument.
>(It is a necessary assumption, not merely sufficient.) I
> argue that if this assumption is relaxed, my conclusions >still follow.
Learn to communicate just what assumption are you refering to relaxing?
> I am unable to understand what is keeping Mr. Weatherby from solving
> the quoted problem in Foley's problem set, either as Foley stated it
> or with my modifications in the specific numeric values.
I have my own models to solve. I am not going to check your algebra. The
problem given by Foley does not ask this question. Part of my argument is
that using this setup may not be appropiate for the question you asked.
Different questions require some modifications for the model presented to be
a pluasible representation for the question asked.
> Nor am I
> able to understand why Mr. Weatherby does not acknowledge correct my
> posted solution to the problem with the modified values.
>
First I am unware that you have redone the problem. In long threads such
as this it is possible to miss messages. I will see if I can find it and if
the modifications answer the fundemental questions raised. Although I doubt
you have changed much.
John
John J. Weatherby
and ignore market demand for corn. This choice is still misleading as to
what is happening to the real wage. Note: the theory does not state that
quantity of labor demanded decreases with an increase in the nominal wage
rather quantity of labor demanded decreases with an increase in the real
wage. This analysis is misleading as to what is happening with the real
wage.
John
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-082533....@news.dreamscape.com...
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-6F5668....@news.dreamscape.com...
<http://homepage.newschool.edu/~foleyd/GECO6200/ps1.html>
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
Define four techniques in terms of the processes:
CORN-PRODUCING IRON-PRODUCING
TECHNIQUE PROCESS PROCESS
Alpha (0, 1/2, 1) (1/4, 0, 2)
Beta (0, 1/2, 1) (1/4, 1/4, 2)
Gamma (3/8, 1/9,1) (1/4, 0, 2)
Delta (3/8, 1/9,1) (1/4, 1/4, 2)
In the remainder, I consider only the Alpha technique.
Let
p1 = price of a unit of corn
p2 = price of a unit of iron
w = wage
r = rate of profits
Foley's students know to write down the following price equations:
( 1/2 p2 + 1 w )( 1 + r ) = p1 (1)
( 1/4 p1 + 2 w )( 1 + r ) = p2 (2)
No numeraire has been specified as yet.
Given the last clause in Foley's statement of the problem,
the ratio of the wage to the price of corn is of particular
interest:
(1/2 P + 1 W )( 1 + r ) = 1 (3)
( 1/4 + 2 W )( 1 + r ) = P (4)
where
P = ( p2/p1 ) (5)
> > W = ( w/p1) (6)
> >
> > Alternatively, one can set the price of corn in equations
> > (1) and (2) to unity. This, too, will yield equations
> > (3) and (4).
> The problem is that you keep p1 constant.
Nope. Notice the first interpretation above. p1 is not constant
under that interpretation. In deriving the wage-profit rate
relation, I consider different levels of the ratio of nominal wage
to the nominal price of corn. This is what Foley asks his students
to do.
One can solve Equations (3) and (4) to get:
W = ( 7 - 2r - r^2 )/[ 8 ( r + 1 )( r + 2 ) ] (7)
P = ( r + 9 )/[ 4 ( r + 2 ) ] (8)
Equation 7 is the desired wage-profit rate relation for the
alpha technique.
> In effect any change here in
> the nominal wage is an effect in the real wage.
So I am considering different levels of the real wage, as is
appropriate for deriving the wage-profit rate relation.
> By doing this you make
> the
> effects of the nominal wage the same as the effect of the real wage. The
> argument this is not appropiate for the question you are asking.
Notice Mr. Weatherby offers no ghost of a hint of a suggestion of
an answer himself to Foley's problem. Of course, the problem asks
one to find a "wage-profit rate relation". That's a technical term.
Somebody not familiar with the literature upon which Foley draws
(it's about growth theory, among other things) might not be aware of
the meaning of that term.
> You are
> trying to refute the standard theory that the real wage is equal to the
> marginal product on labor,
Nope.
> which given diminishing returns to labor is
> negatively related to the amount of labor.
Doesn't follow in long-run models like my example.
> No theory I have ever seen predicts that nominal wages are negatively
> related to labor demanded.
I'll leave out Mr. Weatherby's parochialism. Just above Mr. Weatherby
has correctly said I am considering different levels of the real
wage.
> The correct solution of the problem is that
> labor demanded decreases as the "real" wage rises.
Well, I gave some data for textbook problems. Mr. Weatherby, if he
can, is always free to derive labor demand schedules in those
examples. And, if he wants and needs, he can always append additional
assumptions consistent with the data. I do that in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
(I'm no longer committed to Figure 8 and the surrounding text there.)
> This is a distinct difference
> and if you do not know this you seriously need to read a principles book
> before commenting.
Somebody needs to increase his understanding of the nature of a
numeraire. And it isn't me.
> > "Demand theorists know there are few Giffen goods. They know why
> > there are Giffen goods. They can successfully predict that certain
> > goods in certain economies (potatoes in Ireland, rice in China,
> > or yams in New Guinea) are likely to be Giffen goods.
> Yes but they do not title the papers that try to predict this
> "Quantity,
> Prices not affected by Supply, Demand". They realise that demand and
> supply
> are still at work and that the theory for normal goods and correct and
> useful unlike what you are trying to argue here.
Assume a certain theoretical framework. Economists know that if
substitution effects dominate over income effects, agents will
want to buy more of certain commodities when the price is lower.
They know when income effects might be large.
Titles must be short.
My original post stated:
"This long post presents an example in which higher wages are
associated with firms choosing to employ more workers per unit output
produced...So much for the theory that wages and employment are
determined by the interaction of well-behaved supply and demand curves
on the labor market."
> > Capital
> > theorists, on the other hand, do not know whether capital reversing
> > is common or rare.
> Which is the problem. Until you can empirically prove that this
> happens
> then standard models have not been proved to be inappropiate. You can not
> prove that standard models do predict well until you if these cases exist
> in
> the real world and in what areas.
Nonsense, even after making allowances for Mr. Weatherby's typical
linguistic difficulties. The general case model does not predict, for
example, that in long run models a higher real wage will be associated
with an adoption of a less labor-intensive technique. In other words,
the theory does NOT say that firms will want to decrease employment at
a higher wage.
One can prove this point of logic with specific numeric examples.
If one thinks those examples might violate standard assumptions,
one should be able to state which assumptions are violated.
I suppose one might be able to introduce special case assumptions
to get this prediction out of the resulting special case models.
But economists have been spectacularly unsuccessful at finding
such assumptions. As Hausmann explains,
[>> Until recently they possessed no theory which ]
[>> made sense of the phenomenon. The status of that fundamental ]
[>> theory ]
[>> remains, moreover, questionable. From the perspective of the ]
[>> Austrian ]
[>> theory or of Clark's theory, capital reversing is nothing but ]
[>> a ]
[>> disconfirmation. Capital theorists are also unable to predict ]
[>> when ]
[>> capital reversing will occur. They cannot point to some feature ]
[>> of ]
[>> an economy and say, 'Ah, we can see that this is one of the ]
[>> exceptional cases in which we should not expect our simpler ]
[>> capital ]
[>> theories to work.' There is no justification for the claim that ]
[>> capital reversing demands only minor qualifications in ]
[>> simplified capital theories." ]
[>> -- Daniel Hausmann ]
> Until then reswitching is an
> interesting
> note like a Giffen good. The fact that no one has ever found one means
> that standard models are likely to predict well.
Wrong three times. Reswitching has not been the point of this thread.
And it is not mentioned above by Hausmann.
Barkley Rosser, for instance, would say there are case studies
that show examples with effects like mine and related effects
exist. (Inasmuch as reswitching on the frontier is sufficient for
capital-reversing but is not necessary, it's related.) He's written
some. I haven't read much of the empirical references I can produce;
I think the point is one of logic.
Good economics does NOT predict in long run models that
firms will want to employ less labor at higher wages. I go by,
say, Samuelson's or Mandler's or Burmeister's or Hahn's or ...,
explanations of economic theory.
> But then again we were not discussing the effect of reswitching
> invalidating the assumptions of a production function.
Right, we're not. And I've never asserted that reswitching invalidated
the assumptions of correctly specified production functions in
microeconomics. So why does Mr. Weatherby bring this subject up?
> The discussion is
> does this model show that labor demanded can increase when real wages
> increases.
I carefully left it open whether one would be inclined to say in my
example that labor demand functions slope upward or that supply and
demand does not apply in the labor market.
> I am not convinced.
Well, considering that Mr. Weatherby evidently doesn't know what's being
discussed (e.g., not reswitching), I don't find his position
persuasive.
John J. Weatherby
> Nope. Notice the first interpretation above. p1 is not constant
> under that interpretation. In deriving the wage-profit rate
> relation, I consider different levels of the ratio of nominal wage
> to the nominal price of corn. This is what Foley asks his students
> to do.
>
> Doesn't follow in long-run models like my example.
>
Again which are you arguing you have stated before this is not a long
run model now you are stating it is. Again I asked how can a one period
model be long run?
> Somebody needs to increase his understanding of the nature of a
> numeraire. And it isn't me.
>
I know exactly what a numeraire is. I also know that it used to make
models tractable. I am also aware of the tradeoff pointed by Eugene Sillberg
of tractability versus reality. However I do question if the tractability of
the numeraire in this cases has seriously rigged the model. The question is
if using a numeraire other than money is desirable and appropiate. This is
hard to answer. I do not think you can solve the model as presented if
market demands are considered. It would be easier if it were set up as a two
sector model where steel was produced and traded from downstream firms to
upstream firms. This would imply some sort of utility function to aquire the
demand for corn. The problem in this setting is that demand for corn is
affected by the downstream firm as well. This is what makes the setup
difficult is that the amount of corn demanded depends on factor as well as
consumer demands.
> Titles must be short.
>
And accurate. Your title is completely inaccurate. I have read some of
the non-mainstream economist work for instance the stuff you posted from
Tufts. They are not hostile to mainstream ideas. They do believe it does not
show the whole picture. In some cases I even agree with their points about
principles text. Yes perfect competition is not always presented as the base
line model as it should be. Yes imperfect information is often not dealt
with. Not everyone is exposed to things like Joan Robinson's article what is
perfect competition nor is Alchain's perfect competition historically
contemplated given enough emphasis.
I am very disappointed in the treatment of externalities in that some
principles books do not even mention Coase. However none of these, including
the neo-Marxist, have the hostility toward mainstream theory. Some of the
points about principles are valid. Some are silly such as using the
abbreviation PC confuses Perfect Competition with Politically correct.
However, I do also think that almost any economist who teaches principles
would be considered hetrodox under the definitions given. Even the most
conservative professor I ever had not only mentions many of their examples
but has them also written in to his textbook.
In short I do not understand the complete hostility toward what you
believe is standard economics nor the comtempt you hold for anyone who
trained in anything but an extremely liberal and often Marxist way. I really
beleive your political leanings cloud your judgement. Somehow you think this
is a fight between good and evil and not a discussion of theory. Titles like
Debunking Economics and Wages, Employment Not Determined by Supply, Demand,
are both inaccurate, for instance in your post Wages, Employment are
determined by demand it is just your demand looks a little different, and
hostile to the profession of economics. It seems you are trying to destroy
theory rather than enrich it.
>So much for the theory that wages and employment are
> determined by the interaction of well-behaved supply and demand curves
> on the labor market."
This just proves the point the title is misleading. You are still
determining wages and employment by "supply" and "demand" functions,
although these terms are a bit odd to be used here you use them as if they
were market demand and a supply curve under perfect competition which is not
what this model really suggest. If these functions are really not well
behaved, which I am not convinced they are not, it does not mean that supply
and demand do determine wages and employment only that these functions can
be strange.
>In other words,
> the theory does NOT say that firms will want to >decrease employment at
> a higher wage.
>
Exactly it predicts firms will want to hire less labor at a higher real
wage. Nominal wages are insufficent to predict what will happen. Again you
are saying something may be theoritically possible. Until solid proof exist
that this happens empirically there is nothing to suggest that using
standard analysis is. If fact the empirical evidence overwhelming shows that
the standard methods predict extremely well. Surely you are not saying
abandon all standard methods on empirically work simply because a flaw may
exist in some cases. Are You? Again why are standard methods standard?
Because, they predict well that is why they are used in empirical work. If
this can exist it still will not be noticed much unless you can provided
empirical evidence on its existance and under what cases it can exist. Until
the empirical work is done it is unproven theory which rarely gets attention
for more than 5 years. Sooner or later people want to see the proof before
it is adopted or becomes standard.
John
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-082533....@news.dreamscape.com...
> > John J. Weatherby claims I am mistaken about something or other
> > because:
>>> Your response indicates that
>>> something that can logically happen from your assumptions is
>>> happening in your model.
> > I am not able to understand how the above shows me wrong.
> It shows you are confused your posting on the price of steel and how
> firms could produce only steel shows you forgot or do not understand your
> own assumptions. Again this silly transfer pricing trick is part of what
> gives your result.
Whatever. I would hope somebody reading my original post with
understanding would see that my assumption was that the modelled
firm would want to produce both commodities.
I think Mr. Weatherby's comments on transfer pricing reflect the
fallacy of misplaced concreteness, as well.
> Secondly, Wicksell may have pointed out cases of reswitching.
> Samuelson
> may have agreed under certain assumptions it can happen.
What an amazing claim about Wicksell. Where does he point out
such cases?
And why is Mr. Weatherby harping on reswitching? That is not
on point in this thread.
> The only
> quotation you have found has said things can get strange in long run
> analysis.
Nope.
"The idea that demand and supply for factors of production determine
distribution has become so deeply ingrained in economic thought that
it is almost viewed as an immediate reflection of facts, and not as
the result of an elaborate theory. For the same reason, it is easily
forgotten how comparatively recent that theory is. In the first
systematic analysis of value and distribution by the English classical
economists up to Ricardo, we would look in vain for the conception
that demand and supply for labour and 'capital' achieve 'equilibrium'
as the proportions in which those 'factors' are employed in the
economy change with the wage and rate of profits. Thus, Ricardo saw
no inconsistency between free competition and unemployment of
labour. In his view lower wages could eliminate unemployment only
be decreasing the growth of population or by favouring accumulation...
...Outputs can influence relative prices ... by affecting the relative
scarcity of labour and capital, and thus the wage and rate of
interest, given the supply of the two factors and the state of
technical knowledge. This link between prices and outputs is one and
the same thing as the explanation of distribution by demand and supply
of factors of production: and it becomes untenable once that
explanation is abandoned.
Thus, the separation of the pure theory of value from the study of
the circumstances governing changes in the outputs of commodities,
does not seem to meet any essential difficulty. On the contrary,
it may open the way for a more satisfactory treatment of the
relations between outputs and the technical conditions of production.
Moreover, by freeing the theory of value from the assumption of
consumers' tastes given from outside the economic system, this
separation may favour a better understanding of consumption, and its
dependence on the rest of the system.
With this, the theory of value will lose the all-embracing quality
it assumed with the marginal method. But what will be lost in scope
will certainly be gained in consistency and, we may hope, in
fruitfulness."
-- P. Garegnani, RES, 1970.
"However, as was argued in Section 3 with regard to 'perversely'
shaped, that is, upward sloping, factor-demand functions, this
possibility would question the validity of the entire economic
analysis in terms of demand and supply."
-- H. D. Kurz and N. Salvadori, _Theory of Production: A Long
Period Analysis_, Cambridge University Press, 1995.
"...Specifically,
it must be shown that under ideal conditions, i.e. perfect
competition and absence of disturbing elements like uncertainty
and money, one or more markets do not function properly so that,
even in the long run, no tendency towards full employment exists:
the problem is *not* about possible market failures, but about
principles.
This task has been accomplished by the capital-theory debate, the
main economic implications of which are set out in Garegnani (1970),
Kurz (1985) and Pasinetti (1974, pp. 132-42; 1977, pp. 169-77);
a comprehensive and easily understandable presentation of the crucial
issues is Harcourt (1972).
...As a consequence, no regular (downward-sloping)
associations between profit rates, on the one hand, and capital
and output per worker and the capital-output ratio, on the other
hand, exist. These relationships are, in fact, totally irregular.
Since the 'capital market' does not function in the neoclassical
sense and since factor markets are supposed to be interrelated,
regular *long-period* relationships between 'factor prices' and
'factor quantities' cannot exist in general, i.e. there are no
'factor markets' at all if the long run is considered. This is
the main result of the capital-theory debate...
...The fact that there are no regular relationships between 'factor
prices' and 'factor quantities' is extremely damaging for equilibrium
theory: the market cannot produce a tendency towards some postulated
long-period equilibrium to solve the central economic problems, i.e.
value, distribution and employment....
...These references to the history of the capital-theoretic discussion
show that it is a discussion about fundamentals. The basic question is
whether there are regular relationships between 'factor prices' and
'factor quantities' or not, i.e. normally functioning factor markets.
Examining this question seriously will inevitably shape an economist's
vision in a decisive way. The capital-theoretic debate is a theoretic
watershed dividing two different views of looking at socioeconomic
phenomena, i.e. neoclassical equilibrium theory which emphasizes
behavior and classical-Keynesian political economy which starts from
the functioning of the socioeconomic system, the question being which
approach is more appropriate to tackle fundamental socioeconomic
problems, such as value, distribution and employment. Therefore, as
Geoffrey Harcourt was one of the first to perceive, the Cambridge
controversies are 'not merely about the measurement of capital...but
about the scientific status of neoclassical (equilibrium) theory'
(Dixon 1988, pp. 251-2)...."
-- Heinrich Bortis, _Institutions, Behavior and Economic Theory:
A Contribution to Classical-Keynesian Political Economy_,
Cambridge University Press, 1997.
"Both classical and marginalist economists provided accounts of
the long-period (uniform rate of profit) theory of value and
distribution, but whereas a classical economist could take the
real wage as a datum for the purpose of such analysis (whatever
the implicit 'background' theory of wages might be), the
marginalist economist had to 'close the system' in some other
manner. In effect, since 'resource supplies' were often taken as
given, this meant that 'the supply of capital' had to be taken
as given, IN ONE WAY OR ANOTHER. Just how the given supply of
capital was to be represented was an issue that led to
considerable heterogenity amongst even those marginalist
economists who shared the long-period method of analysis with
the classical economists and with each other. That heterogenity
cannot be entered into here (see Kurz and Salvadori, 1995:
427-43) but it is now widely recognized that each version of
such traditional long-period marginalist theory of value and
distribution encountered insoluble problems (ibid.: 443-48)."
-- Ian Steedman (1998)
"Reswitching debate is relevant for...theories which determine
income distribution on the basis of demand and supply of
all factors including labour and 'capital'."
-- Neri Salvadori, 5 June 2001.
I take Salvadori above to be referring to more than the narrow
issue of reswitching. He is using "reswitching" as a synecdoche.
"But, as economic theory has learned since the 1930s, the
pattern of activities adopted in the face of long-run
factor-price changes can be complicated and counterintuitive.
Consequently, the long-run demand for factors can be badly
behaved functions of factor prices... The principle of
variation works as an argument for long-run determinancy insofar
as the set of zero-profit activities shift in response to factor
price changes; it is not necessary that newly adopted activities
use cheaper factors more intensively or that production is more
capital intensive when r falls."
-- Michael Mandler, 1999.
Mr. Weatherby has never restated that quote well. Perhaps he is
just unaware of the specific points that Mandler says have been
learned since the 1930s.
But what will quotes from the literature reveal to Mr. Weatherby?
He seems incapable of or unwilling to read the literature from
which they are drawn, at least with any understanding.
> Your model is one period not long run analysis.
Nope. Nobody who understands the theory from which the above
quotes are drawn would say so, assuming they accept the short-run/
long-run dichotomy.
> I still do see
> that your conclusions have been stated anywhere in the literature.
Well, why then is Mr. Weatherby arguing with the literature? Perhaps
the problem is he neither reads the literature upon which I draw,
my posts with any care, nor his own posts. Or, perhaps, he just
cannot read well-enough to get anything out of this.
> The
> Foley
> site you keep refering to ask a completely different question, although
> the model is similar.
So what is the answer to Foley's question? How do you find it?
> > Suppose somebody points to some assumption in my model. Suppose that
> > person says that if that assumption were relaxed, my conclusions would
> > not follow.
> Which is exactly what I have done.
But enough about you. This part of this thread was about:
maxw...@my-deja.com (Maxwelton) wrote:
"If they are on parity with other steel producers and unit costs
increase there won't be a corresponding drop in unit sale price."
Of course, anybody that has read my PDF files that I have repeatedly
referred to understands I have a good answer to the above.
> I have pointed out time and time
> again that
> A. The price of steel is wrong. It should be cost of steel. The cost of
> the
> steel may be cheaper under process beta meaning you cost functions are
> wrong. The transfer pricing trick is part of how the model is rigged to
> get the result.
Nope. Mr. Weatherby has not indicated how to calculate the marginal
cost of producing a unit steel in my example.
> B. The theory of the firm predicts how the amount of labor demanded
> reacts
> to the real wage. By choosing corn as the numeraire you have fixed the
> price. This is misleading in that although your nominal wage is rising we
> do
> not what is happening to real wages when the different processes are
> chosen.
The above reveals deep ignorance about what a numeraire is. Besides
Mr. Weatherby, when exposed to some simple algebra, contradicted that:
"you keep p1 constant. In effect any change here in
the nominal wage is an effect in the real wage. By doing this you
make the effects of the nominal wage the same as the effect of
the real wage."
> Your only response to this is an allegation that commentors have just
> said "huh". This is hardly a counter argument.
> >(It is a necessary assumption, not merely sufficient.) I
> > argue that if this assumption is relaxed, my conclusions
> >still follow.
> Learn to communicate just what assumption are you refering to
> relaxing?
The context that Mr. Weatherby fails to understand -
maxw...@my-deja.com (Maxwelton) wrote:
"If they are on parity with other steel producers and unit costs
increase there won't be a corresponding drop in unit sale price."
But, hey, Mr. Weatherby is free to pretend his comprehension problems
are my fault.
> > I am unable to understand what is keeping Mr. Weatherby from solving
> > the quoted problem in Foley's problem set, either as Foley stated it
> > or with my modifications in the specific numeric values.
> I have my own models to solve. I am not going to check your algebra.
I am unable to understand what is keeping Mr. Weatherby from solving
the quoted problem in Foley's problem set.
Of course, Mr. Weatherby is free to refuse to say anything substantial
and correct. He can keep on posting posts that basically amount to
"Huh?"
> The problem given by Foley does not ask this question.
Nothing is stopping Mr. Weatherby from looking up the meaning
of the "wage-profit rate relation" in classic references given
in this thread, determining the solution of Foley's or my problem,
and then noting the implications of that solution in my problem.
After all, I have held his hand every step of the way.
The principle of substitution does not apply, in general, to
long period models. Firms may want to adopt a more labor-intensive
technique at a higher wage.
> Part of my argument is
> that using this setup may not be appropiate for the question you asked.
In other words, "Huh?"
> > Nor am I
> > able to understand why Mr. Weatherby does not acknowledge correct my
> > posted solution to the problem with the modified values.
> First I am unware that you have redone the problem. In long threads
> such
> as this it is possible to miss messages.
Later, Mr. Weatherby wrote:
> Ok I have found your modification, you still use corn as the numeraire
> and ignore market demand for corn. This choice is still misleading as to
> what is happening to the real wage. Note: the theory does not state that
> quantity of labor demanded decreases with an increase in the nominal wage
> rather quantity of labor demanded decreases with an increase in the real
> wage. This analysis is misleading as to what is happening with the real
> wage.
In other words, he writes some combination of ignorance about numeraires
and "Huh?"
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-37BE68....@news.dreamscape.com...
> > Nope. Notice the first interpretation above. p1 is not constant
> > under that interpretation. In deriving the wage-profit rate
> > relation, I consider different levels of the ratio of nominal wage
> > to the nominal price of corn. This is what Foley asks his students
> > to do.
> This is not what you did in the model you orginally posted.
Nope. By making some unit of corn the numeraire, that's what I
did, in effect.
> > Doesn't follow in long-run models like my example.
> Again which are you arguing you have stated before this is not a long
> run model now you are stating it is.
Mr. Weatherby is making crap up. I have never asserted that it is not.
> Again I asked how can a one period model be long run?
I've already explained this in several ways.
There's nothing stopping Mr. Weatherby from trying to read the
literature, e.g., Kurz and Salvadori. Or from trying to work out
what variables are endogeneous and exogeneous in various problems.
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
For one technique, the desired wage-profit rate relation is
w/p1 = ( 7 - 2r - r^2 )/[ 8 ( r + 1 )( r + 2 ) ]
where the variables have been defined in a previous post.
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
The answer to the last question is
w/p1 = 1.035 0.354 0.293 0.20635 0
|<-- Delta --->|<-- Gamma -->|<-- Alpha -->|<-- Beta -->|
r = 0% 85.9% 100.1% 125% 204.4%
where the techniques have been defined in a previous post. Around
a wage of 0.20635 bushels per unit labor, a higher wage is associated
with the adoption of a more labor-intensive technique.
> > Somebody needs to increase his understanding of the nature of a
> > numeraire. And it isn't me.
> I know exactly what a numeraire is. I also know that it used to make
> models tractable.
Hardly correct. Some models are easier to solve with one numeraire
versus another. But in many models, some numeraire must be adopted.
That's not a question of realism versus tractability.
It's been established in the literature that the effect I am
hightlighting is not dependent, qualitatively, on the choice of
a numeraire. Neither is reswitching, which is another effect.
> [Ignorance about numeraires and an example of the fallacy of ]
> [misplaced concreteness - deleted. ]
> It would be easier if it were set up as a
> two
> sector model where steel was produced and traded from downstream firms to
> upstream firms.
Asked and answered repetitively.
> This would imply some sort of utility function to aquire
> the demand for corn.
No, it would not. For instance, one could adopt the assumption that
all of wages are spent on corn and that a fixed percentage of profits
are. Or one could adopt the Kahn-Kaldor-Pasinetti-Robinson theory of
distribution. Or...
But I've already anticipated Mr. Weatherby's ignorance and answered
his question:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
That being the case,
> [ snip ]
> > Titles must be short.
> And accurate. Your title is completely inaccurate.
Here Mr. Weatherby goes off on a non sequitur:
> I have read some of
> the non-mainstream economist work for instance the stuff you posted from
> Tufts. They are not hostile to mainstream ideas. They do believe it does
> not
> show the whole picture. In some cases I even agree with their points
> about
> principles text. Yes perfect competition is not always presented as the
> base
> line model as it should be. Yes imperfect information is often not dealt
> with. Not everyone is exposed to things like Joan Robinson's article what
> is
> perfect competition nor is Alchain's perfect competition historically
> contemplated given enough emphasis.
> I am very disappointed in the treatment of externalities in that some
> principles books do not even mention Coase.
The above is completely irrelevant to this thread.
> However none of these,
> including
> the neo-Marxist, have the hostility toward mainstream theory.
Once again, Mr. Weatherby seems to be making crap up. Of course, given
his linguistic difficulties, it's hard to see what he thinks he's
saying.
> Some of the
> points about principles are valid. Some are silly such as using the
> abbreviation PC confuses Perfect Competition with Politically correct.
> However, I do also think that almost any economist who teaches principles
> would be considered hetrodox under the definitions given. Even the most
> conservative professor I ever had not only mentions many of their
> examples
> but has them also written in to his textbook.
The above is completely irrelevant to this thread.
> In short I do not understand the complete hostility toward what you
> believe is standard economics nor the comtempt you hold for anyone who
> trained in anything but an extremely liberal and often Marxist way.
Once again, Mr. Weatherby seems to be making crap up.
> Titles like
> Debunking Economics
which, I'm fairly sure, Mr. Weatherby hasn't read. So the following
is a matter of making crap up:
> and Wages, Employment Not Determined by Supply,
> Demand,
> are both inaccurate, for instance in your post Wages, Employment are
> determined by demand it is just your demand looks a little different, and
> hostile to the profession of economics.
Mr. Weatherby's is exhibiting his usual linguistic infelicities.
From the post to which Mr. Weatherby is pretending to respond:
I carefully left it open whether one would be inclined to say in my
example that labor demand functions slope upward or that supply and
demand does not apply in the labor market.
> It seems you are trying to destroy theory rather than enrich it.
Mr. Weatherby is making crap up. On this thread, I have repeatedly
stressed I am explaining theory.
> >So much for the theory that wages and employment are
> > determined by the interaction of well-behaved supply and demand curves
> > on the labor market."
> This just proves the point the title is misleading. You are still
> determining wages and employment by "supply" and "demand" functions,
> although these terms are a bit odd to be used here you use them as if
> they
> were market demand and a supply curve under perfect competition which is
> not
> what this model really suggest.
Nope. Nothing is stopping Mr. Weatherby from attempting to draw
supply and demand functions here.
> If these functions are really not well
> behaved, which I am not convinced they are not, it does not mean that
> supply
> and demand do determine wages and employment only that these functions
> can
> be strange.
> >In other words,
> > the theory does NOT say that firms will want to
> >decrease employment at
> > a higher wage.
> Exactly it predicts firms will want to hire less labor at a higher
> real wage.
Nope. It does not.
> Again you
> are saying something may be theoritically possible.
If something is possible in theory, one could always modify the
theory by introducing special-case assumptions to rule out the
relevant effects. But this approach has not been succesful.
That is not an emprical question. So the following is off topic.
> Until solid proof
> exist
> that this happens empirically there is nothing to suggest that using
> standard analysis is. If fact the empirical evidence overwhelming shows
> that
> the standard methods predict extremely well.
I know of no such relevant evidence, and of some contradictory evidence.
I've said the latter repetively in this thread.
> Surely you are not saying
> abandon all standard methods on empirically work simply because a flaw
> may
> exist in some cases.
That is correct. I am not saying such.
> Are You? Again why are standard methods standard?
Well, the textbooks methods I have been explaining on this thread
give a theoretical backing to methods that have been frequently
employed in empirical work. The Von Neumann model, which my
example is an example of a generalization of, is where activity
analysis was invented. Activity analysis found lots of use in applied
work, given the invention of electronic computers and the simplex
algorithm.
> Because, they predict well that is why they are used in empirical work.
The above is questionable. Mason has recently read an essay on the
rhetoric with which economists justify their work in practice.
> If
> this can exist it still will not be noticed much unless you can provided
> empirical evidence on its existance and under what cases it can exist.
As a point of logic, the above is entirely backwards. As a description
of the practices of some communities of economists, sure.
> Until
> the empirical work is done it is unproven theory which rarely gets
> attention
> for more than 5 years. Sooner or later people want to see the proof
> before it is adopted or becomes standard.
Well, I think what Mr. Weatherby describes as "standard theory" is
theory that has been proven incoherent on theoretical grounds long
ago.
John J. Weatherby
determine wages or employment. However in every version of the model you
have shown that labor demand does determine the amount of employment hired.
Any time you have a production function there is a demand for labor. In your
model there are two demands for labor. Which one is used is the question.
You have totally left out labor supply and the wage is exogenously set.
Regardless of what you believe you are doing, you are using labor demand
to determine employment.
> "The idea that demand and supply for factors of production determine
> distribution has become so deeply ingrained in economic thought that
> it is almost viewed as an immediate reflection of facts, and not as
> But what will quotes from the literature reveal to Mr. >Weatherby?
We are not talking about the literature we are talking about if your
model is correct and if your assumptions are pluasible. It does not matter
what the words of a thousand economist say about the issue in review of what
has been done. The question here is your model and paper correct not what is
your motivation for research. Quoting others is fine to show motivation it
does not however automatically make your model right because the question is
interesting to some.
> So what is the answer to Foley's question? How do you find it?
>
Who cares. This has nothing to do with your paper. We are not discussing
Foley's site we are discussing if you model works, are assumptions good, can
it be improved, and what might happen under changes that more closely
resemble the theory you are trying to refute. Again I have my own models to
solve. I will not waste my time setup and solving models that are not in my
field of research.
> Of course, anybody that has read my PDF files that I have repeatedly
> referred to understands I have a good answer to the above.
>
And that answer is wrong given you assumption. You spend a lot of time
figuring out things that your assumptions have already ruled out.
> Nope. Mr. Weatherby has not indicated how to calculate the marginal
> cost of producing a unit steel in my example.
>
The cost of one unit of steel is the cost of production. That is the
cost incurred in units of corn under the technique used. For each technique
of producing steel it is somewhat easy to see the cost. The only problem
area is the initial cost of steel. In fact the correct choice of the
numeraire for this model is probably steel if you are going to use a
numeraire. This allows to you get away from the transfer pricing problem and
also lets the price of corn vary.
>> > Learn to communicate just what assumption are you refering to
> > relaxing?
>
> The context that Mr. Weatherby fails to understand -
>
The context that M. Vienneau refuses to ever refer to much less
explained. Again this is Robs problem in communication, he often uses words
like the context and the theory when it is not obvious what context or what
theory he is refering to. Well at least non-obvious to anyone but Rob. I
really do not even know why I am wasting my time on this hard headed pompus
ass.
> Nothing is stopping Mr. Weatherby from looking up the meaning
> of the "wage-profit rate relation" in classic references given
> in this thread, determining the solution of Foley's or my problem,
> and then noting the implications of that solution in my problem.
> After all, I have held his hand every step of the way.
>
Nothing is stopping Rob from explaining what wage-profit relation rate
means. Nothing is stopping Rob from the noting the implications of solving
Foley's problem in his post. Any good author would do this. I do not go
about posting names for the externalities in my papers without explaining
what they are, although the names given are common in the literature.
> > Part of my argument is
> > that using this setup may not be appropiate for the question you asked.
>
> In other words, "Huh?"
>
No because I have given reasons for it that you can not get through your
hard-head. This is just another pompous ass response. You are nothing but a
troll.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in
> You keep giving these quotations about how demand and supply may not
> determine wages or employment. However in every version of the model you
> have shown that labor demand does determine the amount of employment
> hired.
> Any time you have a production function there is a demand for labor. In
> your
> model there are two demands for labor.
> Which one is used is the question.
That's balderdash.
> You have totally left out labor supply and the wage is exogenously set.
Of course.
> Regardless of what you believe you are doing, you are using labor
> demand
> to determine employment.
What I said in my original post:
"This long post presents an example in which higher wages are
associated with firms choosing to employ more workers per unit output
produced...So much for the theory that wages and employment are
determined by the interaction of well-behaved supply and demand curves
on the labor market."
And a clarification I have repeated:
I carefully left it open whether one would be inclined to say in my
example that labor demand functions slope upward or that supply and
demand does not apply in the labor market.
Mr. Weatherby wrote:
[>>> The only quotation you have found has said things can get ]
[>>> strange in long ]
[>>> run analysis. ]
I responded to this with quotes showing the literature says what
I am saying, more or less. And for the same reasons. To which he
responds:
> We are not talking about the literature... [blah, blah, blah]
Mr. Weatherby makes crap up. He was talking about the literature.
> > So what is the answer to Foley's question? How do you find it?
> Who cares. This has nothing to do with your paper.
Mr. Weatherby makes crap up.
Here is Foley's problem:
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
I have shown that, for one technique, the desired wage-profit rate
relation is:
w/p1 = ( 7 - 2r - r^2 )/[ 8 ( r + 1 )( r + 2 ) ]
where the variables have been defined in previous posts.
Here's my problem, extended:
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
The answer to the last question is
w/p1 = 1.035 0.354 0.293 0.20635 0
|<-- Delta --->|<-- Gamma -->|<-- Alpha -->|<-- Beta -->|
r = 0% 85.9% 100.1% 125% 204.4%
where the techniques have been defined in a previous post. Around
a wage of 0.20635 bushels per unit labor, a higher wage is associated
with the adoption of a more labor-intensive technique.
Obviously, there's a close relationship between Foley's problem
and mine.
> We are not discussing Foley's site
Yes, we are. The techniques that solve Foley's problem solve mine.
> we are discussing if you model works,
As I keep on emphasizing, very little of this model is original
with me. So I don't know about this reference to "you [sic] model".
> are assumptions good, can
> it be improved, and what might happen under changes that more closely
> resemble the theory you are trying to refute. Again I have my own models
> to
> solve. I will not waste my time setup and solving models that are not in
> my
> field of research.
I guess either Mr. Weatherby's field of research does not include
growth theory or he does not realize that that is part of the topic
under discussion.
Mr. Weatherby, of course, is free to remain ignorant of a lot of
work in growth theory.
> > Of course, anybody that has read my PDF files that I have repeatedly
> > referred to understands I have a good answer to the above.
> And that answer is wrong given you assumption.
Proof by assertion and incomprehension.
> You spend a lot of time
> figuring out things that your assumptions have already ruled out.
Mr. Weatherby is being silly. I show alternate ways of deriving
the same price equations. In one derivation, the price of steel is
an accounting price. In another case, it is a price on a market. In
any case, I restrict my attention to stationary prices in which
firms will desire to produce both commodities for sale to final
consumers (corn, in the example) and commodities to replace those
that are used up in production (corn and steel, in the example).
(That's what yields the heavy curved locus in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LaborDemand.pdf>)
As I have repeatedly argued, given the (real) wage, only one
(real) price of steel is compatible with these assumptions.
> > Nope. Mr. Weatherby has not indicated how to calculate the marginal
> > cost of producing a unit steel in my example.
> The cost of one unit of steel is the cost of production. That is the
> cost incurred in units of corn under the technique used. For each
> technique
> of producing steel it is somewhat easy to see the cost. The only
> problem area is the initial cost of steel.
In other words, Mr. Weatherby has yet to indicate how to calculate the
marginal cost of steel in my example.
> In fact the correct choice of the
> numeraire for this model is probably steel if you are going to use a
> numeraire.
The above is mistaken. The results do not depend, qualitatively, on the
choice of numeraire.
I'll help Mr. Weatherby out:
By assumption the firm requires the inputs shown in Table 1
to produce one bushel corn one year later.
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Now, we want to set Marginal Cost (MC) equal to the price of
corn, both costs discounted to the same point of time.
By assumption, the price of a bushel corn is $10,000. Thus,
the price discounted to one year before is $10,000/(1+r), where
r is endogneously determined in this model.
Suppose the wage is $2,932 per person year, and the price of
a ton steel is p2. Then the cost of producing a marginal bushel
of corn is
0.2*p2 + 0.16889*$10,000 + 0.82816*$2,932
So Marginal Cost and price are equated in the production of corn
when:
(0.2*p2 + 0.16889*$10,000 + 0.82816*$2,932)(1+r) = $10,000 (1)
By assumption, the firm has the choice of the two sets of inputs
shown in Table 2 to produce one ton steel one year later.
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
The marginal cost of producing a ton of steel is the cheepest
of
0.35*p2 + 0.0095553*$10,000 + 0.19321*$2,932
and
0.13329*p2 + 0.15590*$10,000 + 0.033594*$2,932
This being a long run model, the (spot) price of a ton steel output
is the same as the input price, p2. The assumption that the firm
will find it equally profitable to produce both steel and corn
means the firm will use the same rate of discount in both steel
and corn production. So the condition that the Marginal Cost and
price are equated in the production of steel implies that one of
the following two relations are met with equality:
(0.35*p2 + 0.0095553*$10,000 + 0.19321*$2,932)( 1 + r ) >= p2 (2)
(0.13329*p2 + 0.15590*$10,000 + 0.033594*$2,932)(1 + r) >= p2 (3)
The price of steel and the profit rate r that solve this system
are shown in Table 8.
TABLE 8: COSTS, WAGE $2,932 PER PERSON-YEAR,
PRICE OF STEEL $4,414 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$4,414 + 0.16889*$10,000
+ 0.82816*$2,932 = $5,000 100%
Steel Alpha 0.35*$4,414 + 0.0095553*$10,000
+ 0.19321*$2,932 = $2,207 100%
Steel Beta 0.13329*$4,414 + 0.15590*$10,000
+ 0.033594*$2,932 = $2,246
Why, given the wage, is there only one solution for this sort of
model? The answer involves advanced mathematics.
> > > Learn to communicate just what assumption are you refering to
> > > relaxing?
> > The context that Mr. Weatherby fails to understand -
[>> maxw...@my-deja.com (Maxwelton) wrote: ]
[>> ]
[>> "If they are on parity with other steel producers and unit costs ]
[>> increase there won't be a corresponding drop in unit sale price."]
[>> ]
[>> But, hey, Mr. Weatherby is free to pretend his comprehension ]
[>> problems are my fault. ]
> The context that M. Vienneau refuses to ever refer to much less
> explained.
Mr. Weatherby makes crap up.
> Again this is Robs problem in communication, he often uses
> words
> like the context and the theory when it is not obvious what context or
> what
> theory he is refering to. Well at least non-obvious to anyone but Rob.
> [ Silliness deleted. ]
The context was when a poster raised a question about what would
happen when the firm had the option of buying steel from another
firm, when firms producing steel and firms producing corn both
exist.
I have repeatedly stressed that there are many economists who
would find the theory upon which I draw for my example trivial,
obvious, and well-established.
> > Nothing is stopping Mr. Weatherby from looking up the meaning
> > of the "wage-profit rate relation" in classic references given
> > in this thread, determining the solution of Foley's or my problem,
> > and then noting the implications of that solution in my problem.
> > After all, I have held his hand every step of the way.
> Nothing is stopping Rob from explaining what wage-profit relation
> rate means.
I have explained it, repetitively.
> Nothing is stopping Rob from the noting the implications of
> solving Foley's problem in his post.
I have, repeatedly. The techniques that solve Foley's problem
can be used to show that the principle of substitution does not
apply, in general, to long run prices.
A cost-minimizing firm in a competitive market might want to
adopt a more labor-intensive technique at a higher wage.
> Any good author would do this. I do not go
> about posting names for the externalities in my papers without explaining
> what they are, although the names given are common in the literature.
I would guess all the "externalities [sic]" are negative in Mr.
Weatherby's papers.
> > > Part of my argument is
> > > that using this setup may not be appropiate for the question you
> > > asked.
> > In other words, "Huh?"
> No because I have given reasons for it that you can not get through
> your hard-head. [ Silliness deleted. ]
Mr. Weatherby has not given any "reasons" that are anything but
mistaken.
John J. Weatherby
"Robert Vienneau" <rv...@see.sig.com> wrote in message
news:rvien-DCF93B....@news.dreamscape.com...
> In article <2ndC8.767$Q76....@newsread2.prod.itd.earthlink.net>,
> > Who cares. This has nothing to do with your paper.
>
> Mr. Weatherby makes crap up.
>
solved a problem that asked a different question. I am asking if your
application of the model to this question is correct. I am debating if your
choice of techniques are the best and correct. Not whether or not a
Neo-Marxist has posted a problem on his website and solved. This would be
like me saying just because Jones solved a problem similar to mine that my
application of his model and extensions from it are necessarily correct. I
would get laughed out of the room if I made this comment in a presentation.
At the very least everyone there would start to get the feeling I had no
idea what I was talking about.
> > We are not discussing Foley's site
>
> Yes, we are. The techniques that solve Foley's problem solve mine.
>
Perhaps but you have made extensions and additional assumptions. Optimal
control methods solve the problems set up in my dissertation does that mean
that any discussion of my work necessarily is a discussion of Dorfman '56? I
think not.
> I guess either Mr. Weatherby's field of research does not include
> growth theory or he does not realize that that is part of the topic
> under discussion.
>
Growth theory is a very wide area. I do not research human capital
models either nor the Solow model does that mean I am not a growth
economist? This is just silly. The arguments you have present may vaguely
apply to the Ramsey-Cass-Koopmans setup and are more direct to the
Solow-Swan which, with the expection of the breif neo-classical (meaning the
Solow model) revival, is not a standard model nor is used very often.
However, these arguments have absolutely zero application to my models or
anything since Romer 1990. No capital exist and consumption goods are not
used in production. This does not even apply to Romer 1990 or anything after
it. Your only answers to this claim about Romer 1990 are highly mistaken and
show that you do not understand the model.
> > In fact the correct choice of the
> > numeraire for this model is probably steel if you are going to use a
> > numeraire.
>
> The above is mistaken. The results do not depend, qualitatively, on the
> choice of numeraire.
>
Maybe mabye not. I am not going to spend the time working through the
model to see. The point is if you use the price of the capital good as the
numeraire you do not have to make up initial prices. You have stated earlier
that the accounting trick you used is the only way to make the model work,
this exposes a potential weak point. It would be a lot more pluasible to set
steel as the numeraire than bringing up this accounting trick.
> I would guess all the "externalities [sic]" are negative in Mr.
> Weatherby's papers.
>
Obviously you know nothing about the growth theory that you say this
post has implications for. Any casual reader will notice that all the
externalities presented in Romer '90 are positive. Jones, Grossman and
Helpman, Aghion and Howitt, etc. show that a both positive and negative
externalities arise from growth models of technological change.
In fact if you knew anything about modern endogenous growth theories you
would realize that in the majority of externalities stated are positive
externalities, meaning the privately optimal allocation falls short of the
socially optimal allocation. Either you just do not know what the term
negative externality means or you know nothing about growth models past
Solow. I can not say which one it is. If it is the former I seriously doubt
that you had any level of education in mainstream eonomics above principles
and if so you seriously need some remedial work.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-DCF93B....@news.dreamscape.com...
> > In article <2ndC8.767$Q76....@newsread2.prod.itd.earthlink.net>,
> > > Who cares. This has nothing to do with your paper.
> > Mr. Weatherby makes crap up.
> I am not making anything up. The point is I do not want to know if
> Foley
> solved a problem that asked a different question.
Here is Foley's problem:
> I am asking if your
> application of the model to this question is correct. I am debating if
> your choice of techniques are the best and correct.
No, Mr. Weatherby is not. He refuses to say anything substantial
and correct about, say, whether the above diagram is correct. And
these questions have been resolved in the literature for a long time.
If he wanted to start on something correct and relevant, he could
always attempt to solve Foley's problem.
> Not whether or not a
> Neo-Marxist has posted a problem on his website and solved.
Not that Neo-Marxism has anything to do with anything coherent
and rational here. Or even that Mr. Weatherby means anything by
the label, other than a dismissal.
> This would be
> like me saying just because Jones solved a problem similar to mine that
> my
> application of his model and extensions from it are necessarily correct.
> I
> would get laughed out of the room if I made this comment in a
> presentation.
> At the very least everyone there would start to get the feeling I had no
> idea what I was talking about.
It's been obvious for some time Mr. Weatherby has no idea what he is
talking about. For example, he refused to address any of the substantial
points in my last post.
> > > We are not discussing Foley's site
> > Yes, we are. The techniques that solve Foley's problem solve mine.
> Perhaps but you have made extensions and additional assumptions.
> [ blah, blah, blah ]
I have changed the numbers, while still maintaining numbers that
satisfy certain viability conditions. I have explicitly asked about
a point of the wage-profit rate relation. And I have pointed
out, as a simple matter of arithmetic, that a vertically-integrated
firm might want to adopt a more labor-intensive technique at a
higher level of wages. All trivial.
> > I guess either Mr. Weatherby's field of research does not include
> > growth theory or he does not realize that that is part of the topic
> > under discussion.
> Growth theory is a very wide area. I do not research human capital
> models either nor the Solow model does that mean I am not a growth
> economist? This is just silly. The arguments you have present may vaguely
> apply to the Ramsey-Cass-Koopmans setup and are more direct to the
> Solow-Swan which, with the expection of the breif neo-classical (meaning
> the
> Solow model) revival, is not a standard model nor is used very often.
That strikes me as a weird statement about the Solow model. It
should be a discarded model.
A one-sector model has not been under discussion in this thread. In
other words, the above is a irrelevancy to my point in this thread.
> [ Further irrelevancies snipped. ]
> > > In fact the correct choice of the
> > > numeraire for this model is probably steel if you are going to use a
> > > numeraire.
> > The above is mistaken. The results do not depend, qualitatively, on the
> > choice of numeraire.
> Maybe mabye not. I am not going to spend the time working through the
> model to see.
That is, Mr. Weatherby is not going to say anything substantial. He's
happy with his ignorance about almost everything under discussion in
this thread.
> The point is if you use the price of the capital good as
> the
> numeraire you do not have to make up initial prices.
Wrong, at least two ways. If the price of steel is the numeraire,
the price of corn becomes an endogeneous variable. Which price is
set to unity is irrelevant, but they both cannot be set simultaneously.
Second, this talk about "initial prices" exhibits a serious
misunderstanding of the long run nature of the model.
> You have stated
> earlier
> that the accounting trick you used is the only way to make the model
> work,
Mr. Weatherby makes crap up.
I have presented (if one includes my PDF files) at least three ways
to justify the system of price equations. So I have said the opposite
of Mr. Weatherby's claim.
> this exposes a potential weak point. It would be a lot more pluasible to
> set
> steel as the numeraire than bringing up this accounting trick.
The above exhibits Mr. Weatherby's usual argument from incomprehension.
Let a( i, j ), i = 0, 1, 2; j = 1, 2; be the inputs per unit output
for each industry for a given technique. The row index ranges over
labor, steel, and corn, respectively. The column index ranges over
the steel and corn industries respectively. Represent these parameters
as a 2-element row vector:
a0 = [ a01 a02 ]
and a 2x2 array
a11 a12
A =
a21 a22
Let p = [ p1 p2 ] be the price of steel and corn, respectively.
Let w be the wage and r the profit rate. If prices are stationary,
one has:
( p A + a0 w )( 1 + r ) = p (*)
No numeraire has been chosen yet. Let's specify one. Suppose the
numeraire consists of e1 units of steel and e2 units of corn.
This choice is specified by a two element column vector, e:
e' = [ e1 e2 ]
where e' is the transpose of e.
Since e is the numeraire, one has:
p e = 1 (**)
Suppose coefficients of production are given. Perhaps Mr. Weatherby
can tell us how many variables does one need to solve for in the
system given by (*) and (**). Then perhaps he can tell us how many
(scalar) equations are in the system. Does this counting suggest
anything?
Here's a well-established algorithm for the choice of technique for,
say, a given wage.
(1) Pick a technique. Find prices and profit rate for the resulting
system (*) and (**)
(2) Pick a process not used in this technique. Using the prices
found from (1), compare the cost of producing one unit of
the commodity produced by this process with the cost of
producing the same commodity by the process that produces
that commodity in the given technique.
(3) If the new process is cheaper, replace the more costly
process in the technique with the chosen technique.
(4) Repeat steps 1, 2, and 3 until all processes have been
examined.
For circulating capital models, the algorithm will find a cheapest
technique no matter what order one examines processes and techniques
in. The algorithm will converge to the same set of prices and
profit rate regardless of the order.
So there is one more way of justifying the diagram Mr. Weatherby
refuses to comment on.
[>>> Any good author would do this. I do not go ]
[>>> about posting names for the externalities in my papers without ]
[>>> explaining ]
[>>> what they are, although the names given are common in the ]
[>>> literature. ]
> > I would guess all the "externalities [sic]" are negative in Mr.
> > Weatherby's papers.
> Obviously you know nothing about the growth theory that you say this
> post has implications for. [ blah, blah, blah ]
Mr. Weatherby failed to notice I was joking, maybe poorly, about his
non-sequitur.
John J. Weatherby
> That strikes me as a weird statement about the Solow model. It
> should be a discarded model.
>
functions not adding anything to grow models was in response to a Jones and
Manuelli in the late 1980's. They added utility maximazation to the solow
model and derived the golden rule of savings as would be done under
Ramsey-Cass-Koopmans. Mankiw, D. Romer, and Wiel modified the Solow model to
include human capital in the late 1980's. The opening statement was that
they take Solow '56 seriously. This should be very telling to the
professional opinion of this model. However, one paper by Dinopolous and
Thompson and one paper by Klenow and Rodriguez-Claire used similar methods
to show that the neo-classical revival had gone too far and that models of
technological change were better models.
> A one-sector model has not been under discussion in this thread. In
> other words, the above is a irrelevancy to my point in this thread.
>
It is relevant to thread becuase you argue your post is at the heart of
the CCP oops CCC. The argument is simple this post applies vaguely to
Solow-Swan and Ramsey-Cass-Koopmans. In this models the capital goods can be
used as consumables as well, as Barro-Sala-i-Martin explain think of it is
like cattle they can be used to make more cattle or sluaghtered for beef.
Under these when a cow is used for beef it is considered different from a
cow that is used for breeding stock.
I can see if you called the goods corn you get a story similar to your
set up. The "weirdness" of this model is that the consumption good is also
used in production, this is something that the Ramsey and Solow models rule
out, they would treat seed corn as a seperate good from corn that is eaten,
or corn used for steel in your example. If you relax this assumption then
the setup could be similar.
The argument is very simple though these sorts of models do apply to
modern growth models. There is no longer this cattle assumption. Capital
goods are differiated, if they even appear in the model. Although capital
goods can be used to make more capital goods the implication is that capital
good Xi is not used to make capital good Xi instead say good Xi+2 is used to
make Xi. Furthermore consumption goods are a completely different good that
made with the variety of capital goods (Romer, Jones) or capital goods of
different qualities (Aghion and Howitt).
These arguments also have zero importance for Grossman and Helpman
(variety or expansion of consumption goods), Peretto (cost reducing R&D and
a variety of consumption goods), or Dinopolous and Thompson (R&D builds a
variety of final goods or final goods of increasing quality). You can not
argue that questions about what is capital apply to models that have no
capital in them. In these models final goods are not used to make final
goods.
> Wrong, at least two ways. If the price of steel is the numeraire,
> the price of corn becomes an endogeneous variable. Which price is
> set to unity is irrelevant, but they both cannot be set simultaneously.
>
I am not arguing that two prices should be set as the numeraire that is
silly. What I am arguing is the real wage should be wages over the price of
the only traded good corn. By choosing a different numeraire than corn it
makes it more obvious how the real wage reacts because you also show a
change in the prices of corn. DO YOU UNDERSTAND?
> Second, this talk about "initial prices" exhibits a serious
> misunderstanding of the long run nature of the model.
>
You keep calling this long run but you have no dynamic solution. Your
calculations show cost minizimation for 1 production unit. The amount of
production will different under each process which means the cost will be
different. Yes if you are producing 10,000 units of corn one technique may
be cheaper given the wage. That does not necessarily mean it will cheaper to
produce 30,000 units of corn using techinque alpha than 20,000 units of corn
using technique beta.
> Here's a well-established algorithm for the choice of technique for,
> say, a given wage.
>
> (1) Pick a technique. Find prices and profit rate for the resulting
> system (*) and (**)
>
Prices and profit rates depend on how much corn is produced you have not
solved for this. This is why you are wrong. You note the production will be
different under each technique and then do not account for that in your
model.
> (2) Pick a process not used in this technique. Using the prices
> found from (1), compare the cost of producing one unit of
> the commodity produced by this process with the cost of
> producing the same commodity by the process that produces
> that commodity in the given technique.
>
Again the cost depends on quantity produced. Because one technique is
cheaper when the quantities are the same does not mean that technique will
be profit maximizing. Imagine if a less costly process lead to producing
1,000 units at a cost 1 of one. Does this mean it will be less costly than
producing 500 units at the cost of 2? Of course not.
> For circulating capital models, the algorithm will find a cheapest
> technique no matter what order one examines processes and techniques
> in. The algorithm will converge to the same set of prices and
> profit rate regardless of the order.
>
The process is also dependant on the dynamic optimizing quantity under
each technique this has not been solved for.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
The point of my example doesn't depend on the consumption good in
the example being simultaneously a capital good or on each capital
good being used in producing more of itself.
The principle of substitution does not apply, in general, to long
run models.
Here's my problem, extended:
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
The answer to the last question is
w/pc = 1.035 0.354 0.293 0.20635 0
|<-- Delta --->|<-- Gamma -->|<-- Alpha -->|<-- Beta -->|
r = 0% 85.9% 100.1% 125% 204.4%
where w is the wage, pc is the price of corn, r is the profit
rate, and the techniques have been defined in a previous post. Around
a wage of 0.20635 bushels per unit labor, a higher wage is associated
with the adoption of a more labor-intensive technique.
> > Wrong, at least two ways. If the price of steel is the numeraire,
> > the price of corn becomes an endogeneous variable. Which price is
> > set to unity is irrelevant, but they both cannot be set simultaneously.
> I am not arguing that two prices should be set as the numeraire that
> is
> silly. What I am arguing is the real wage should be wages over the price
> of
> the only traded good corn.
Which means it is convenient to make corn the numeraire. And I
express wages in that way above. In other words, the following is
completely backward:
> By choosing a different numeraire than corn it
> makes it more obvious how the real wage reacts because you also show a
> change in the prices of corn. DO YOU UNDERSTAND?
I understand the concept of a numeraire is completely beyond
Mr. Weatherby.
> > Second, this talk about "initial prices" exhibits a serious
> > misunderstanding of the long run nature of the model.
> You keep calling this long run but you have no dynamic solution.
Marshal defined the distinction between periods based on what variables
are given:
"Four classes stand out. In each, price is governed by the relations
between demand and supply. As regards MARKET prices, Supply is taken
to mean the stock of the commodity in question which is on hand, or
at all events 'in sight'. As regards NORMAL prices, when the term
Normal is taken to relate to SHORT periods of a few months or a
year, Supply means broadly what can be produced for the price in
question with the existing stock of plant, personal and impersonal,
in the given time. As regards NORMAL prices, when the term Normal
is to refer to LONG periods of several years, Supply means what
can be produced by plant, which itself can be renumeratively
produced and applied within the given time; while lastly, there
are very gradual or SECULAR movements of normal price, caused by
the gradual growth of knowledge, of population and of capital, and
the changing conditions of demand and supply from one generation
to another."
-- Alfred Marshall
As I keep on pointing out, it's a matter of what variables are taken
as exogeneous and endogeneous.
As for Mr. Weatherby's question, there's a large literature on the
matter. The Turnpike Theorem shows how a dynamic solution will
be near something like my example for most of the time. Under these
dynamics, my example has a saddle point (in)stability. Dumenil and
Levy, for example, showed, in a rejoinder to Frank Hahn, that a
model illustrated by my example is a limit of an infinite-time
Arrow-Debreu intertemporal equilibrium. More interesting, I
think, are discussions of cross-dual dynamics where competition
is conceived of in a Classical manner as reflecting no barriers
to entry or exit.
> Your
> calculations show cost minizimation for 1 production unit. The amount of
> production will different under each process which means the cost will be
> different. Yes if you are producing 10,000 units of corn one technique
> may
> be cheaper given the wage. That does not necessarily mean it will cheaper
> to
> produce 30,000 units of corn using techinque alpha than 20,000 units of
> corn
> using technique beta.
Mr. Weatherby is simply mistaken. As I have shown, the equations (*)
below equate marginal cost and price. Since constant-returns-to-scale
are assumed, this equation applies at any level of production. This
is clarified by the so-called Nonsubstitution Theorem.
a0 = [ a01 a02 ]
and a 2x2 array
e' = [ e1 e2 ]
Let x be a column vector showing the net output of the system,
where the first element is the net output of steel, and the
second element is the net output of corn. Let q be a column
vector representing the gross outputs of the system. Net and
gross outputs are related by the following vector equation:
x = q - A q = ( I - A ) q
Given a viable technique, levels of operation of each process
are found in terms of the net output like so:
q = ( I - A )^(-1) x
The labor required to be hired for any level of net outputs is:
L = a0 q = a0 (I - A)^(-1) x
Notice prices do not enter the quantity relations, and quantities
do not enter the price relations. (Of course, one can append
elements of a theory of distribution. For example, one can
assume all wages are consumed, and a given proportion of
profits are saved. Or one can append the Cambridge equation
and take the rate of growth as exogeneously specified. Or...)
> > Here's a well-established algorithm for the choice of technique for,
> > say, a given wage.
> > (1) Pick a technique. Find prices and profit rate for the resulting
> > system (*) and (**)
> Prices and profit rates depend on how much corn is produced
The above is simply wrong.
> > (2) Pick a process not used in this technique. Using the prices
> > found from (1), compare the cost of producing one unit of
> > the commodity produced by this process with the cost of
> > producing the same commodity by the process that produces
> > that commodity in the given technique.
> Again the cost depends on quantity produced.
Nope. Mr. Weatherby's nonsense does not improve with repetition.
(3) If the new process is cheaper, replace the more costly
process in the technique with the chosen technique.
(4) Repeat steps 1, 2, and 3 until all processes have been
examined.
> > For circulating capital models, the algorithm will find a cheapest
> > technique no matter what order one examines processes and techniques
> > in. The algorithm will converge to the same set of prices and
> > profit rate regardless of the order.
> The process is also dependant on the dynamic optimizing quantity
> under each technique this has not been solved for.
Once more, Mr. Weatherby needs to find out about the Nonsubstitution
Theorem.
If he wanted to try to attempt to hint at a ghost of a substantial
point, he could always outline a dynamic model, by his definition
of dynamics - the concept is in dispute among economists - for
my example.
John J. Weatherby
> > Prices and profit rates depend on how much corn is produced
>
> The above is simply wrong.
>
of quantity profits are not. The implication is that higher quantities
produce higher profits. The profit maximization is therefore determined by
the labor and corn constraints. Neither of which you include in the model.
> > Again the cost depends on quantity produced.
>
> Nope. Mr. Weatherby's nonsense does not improve with repetition.
>
This is not nonsense. Cost minimization is equivalent to profit
maximization if you are trying to find factor demands for any given
production function. The problem is that cost minimization assumes that
output is fixed to y0 the profit maximizing output. Under each technique y0
is different. Surely you are not arguing that 10,000 units of steel produced
at $1 is less costly than 4,000 units of steel produced at at $2. Are you?
Again what is profit maximizing depends on the difference in outputs. For
instance if you produce 10 units of corn using process alpha for steel and
you get 100,000 revenue at a cost of 80,000 it is less profit than 20 units
of corn and unsing process beta that gives a cost of 90,000. Can you
comprehend this? This is why the "model" you present is incomplete. I notice
you snipped this argument in your response. Furthermore there is no
assumption steel is used up in the processing of corn so again it is
incomplete in that the model does not account for a stock of capital that is
building over periods. From the very beginning this has been the argument
the model is incomplete.
John
John J. Weatherby
> Marshal defined the distinction between periods based on what variables
> are given:
>
variable in the long run. You have made no provision for a stock of capital,
this is another reason why the model is wrong. You have made no provision
that steel is used up in production but yet you ignore the fact that a
capital stock is building.
John
Robert Vienneau
> You have made no provision
> that steel is used up in production but yet you ignore the fact that a
> capital stock is building.
From my first post on this thread:
---------------------------------------------------------------------
I assume a reader willing to follow tedious arithmetic. Skip down
to the conclusions at the end if you're curious about my point.
2.0 DATA ON TECHNOLOGY
Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, steel, and (seed)
corn. All production processes in this example require a year to
complete. Only one production process is known for producing corn. This
process requires the following inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year:
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Steel is also produced by this firm. Two processes are known for
producing steel:
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
Apparently, inputs of corn and steel can be traded off in producing
steel. The process that uses less corn and more steel, however, also
requires a greater quantity of labor input.
3.0 QUANTITY FLOWS
I want to consider a couple of different levels at which this
firm can operate the corn-producing process and each steel-producing
process. First, suppose the corn-producing process is used to
produce 1.208 Bushels corn and the Alpha process is used to produce
0.3717 Tons steel. The quantity flows shown in Table 3 result.
TABLE 3: THE CORN-PRODUCING TECHNIQUE USING THE
ALPHA STEEL-PRODUCING PROCESS
0.07182 Person-Years 1.0000 Person-Years
0.1301 Tons Steel 0.2416 Tons Steel
0.003552 Bushels Corn 0.2040 Bushels Corn
0.3717 Tons Steel 1.208 Bushels Corn
When the firm operates these processes in parallel, it requires
a total of 0.208 Bushels corn as input. The output of the
corn-producing process can replace this input, leaving a net
output of one Bushel corn. Notice that the total inputs of
steel is 0.1301 + 0.2416 = 0.3717 Tons steel, which is exactly
replaced by the output of the Alpha process. So Table 3 shows
a technique in which 1.072 Person-Years labor is used to produce
a net output of one Bushel corn. The firm, when operating this
technique can produce any desired output of corn by scaling
both processes equally.
---------------------------------------------------------------------
The above shows "that steel is used up in production" (also seed corn).
It shows that some production is dedicated to (re)producing the
capital goods used up in production.
The principle of substitution does not apply, in general, to long
run models.
Clearly, Mr. Weatherby needs to work on articulating some sort of
approximation to an argument that addresses the topic he is
pretending to discuss on this thread.
He could always try to solve a problem Foley gives his students.
Or he can take a break by trying to figure out how to not get
exiled to Siberia with the default parameters in my game.
John J. Weatherby
> run models.
>
applies when using first year grad. techniques of general equilibrium with
production does not mean that is generally true for long run models. Look at
any growth or I/O model of R&D they use different methods and none of these
ever predict firms will not substitute from an equilibrium technique.
Again there are several arguments. The two largest ones are here.
1. Is the setup is appropiate for the question? I think there are other ways
to approach this which have less of a tradeoff between realism and
tractability. The setup ignores market response. This debate is analogous to
Ricardo's argument against Smith using corn as the invariable measure of
value. As I have argued before with using corn as the numeraire it is
misleading to what is happening to the real wage. You can not tell with an
increase of the wage quoted if the wage has risen or the purchasing power of
corn has fallen. Essentially this is Ricardo's argument against Smith.
Ricardo supports something closer to the modern theory of the real wage that
is wages over prices not Smith's theory which was a theory of labor value
where the purchasing power of corn was considered invariant.
2. Is your choice of the equilibrium technique correct? I think not. I think
you misapplied cost minimization. Cost minimization is for a given quantity
of production you still do not know what quantities apply to the cost
minimizing problem. Any standard general equilibrium with production setup
will show that profit maximization is important for finding not only
quantities but the appropiate "technique".
Again it goes back to the argument that just because someone used this
problem to answer a different question does not mean that the setup is
appropiate for asking your question. It is kind of strange that you are
asking whether demand and supply (demand and supply of what you have never
really clearly said, it is obvious labor demands determine employment)
determine wages and employment however, you use a setup that automatically
will result in the demand having no effect and then do not even begin to
contemplate what the supply of labor is. To paraphrase Solow, this is like
baking a plum pie then sticking your thumb and announcing in shock and
surprise that you have found of all things a plum.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in
> > The principle of substitution does not apply, in general, to long
> > run models.
> This is clearly not right. Just because the non-substition theorem
> applies when using first year grad. techniques of general equilibrium
> with
> production does not mean that is generally true for long run models.
> [Irrelevancy deleted.]
That does not attack my claim. Even when the "non-substition" [sic]
theorem does not hold, my claim holds.
"Another route which has been pursued to minimize the importance
of the new results...consists in attributing the irrelevance of
substitution to the 'very special' case of no joint production
and constant coefficients [ = constant returns to scale -RLV ]. But
the inconsistency of this contention is here brought into sharp
relief by the very analysis of the previous pages...
As already pointed out...the joint production and nonconstant
coefficients case is more complicated than, but not basically
different from, the case concerning single products and constant
coefficients. The complication arises from the fact that a
change of the composition of demand may entail a change of the
optimum technique and of the price structure. However, this does
not enable us to say anything about the *direction* in which
the input proportions will change.
...It is precisely the unambiguous direction in which relative
prices and input proportions are related to each other that justifies
talking of 'substitution.' But there is nothing of the sort in a
production context. No general relation exists between the changes
in the price structure and changes in the input proportions. More
specifically, no monotonic inverse relation exists, in general,
between the variation of any price, relative to another price, and
the variation of the proportions among the two inputs to which
these two prices refer. When this is so, to talk of 'substitution'
among these inputs no longer makes any sense."
-- Luigi L. Pasinetti, _Lectures on the Theory of Production_,
Columbia University Press, 1977, pp. 186-188
> Again there are several arguments. The two largest ones are here.
> 1. Is the setup is appropiate for the question? I think there are other
> ways
> to approach this which have less of a tradeoff between realism and
> tractability.
The above is not an argument.
> The setup ignores market response.
As I have made clear repetitively, the above is untrue.
If Mr. Weatherby wants to construct an argument, he is always
free to outline alternative arithmetic.
> 2. Is your choice of the equilibrium technique correct? I think not. I
> think
> you misapplied cost minimization. Cost minimization is for a given
> quantity
> of production you still do not know what quantities apply to the cost
> minimizing problem. Any standard general equilibrium with production
> setup
> will show that profit maximization is important for finding not only
> quantities but the appropiate "technique".
The assumptions of the so-called non-substitution theorem apply
to my example. Therefore, by the theorem, the levels of output
will NOT affect the profit-maximizing technique. Mr. Weatherby
doesn't know what he is talking about.
> Again it goes back to the argument that just because someone used this
> problem to answer a different question does not mean that the setup is
> appropiate for asking your question.
Mr. Weatherby is always free to specify how the following two
problems are not parallel:
Foley's problem:
"1-2. (Adapted from Problem 8.6, Kurz and Salvadori, ch. 3.) In an
economy with two commodities, corn and iron, there are two [processes]
for producing a unit of corn, (0, 1/2, 1) and (3/8, 1/9,1) (where the
first number indicates the corn input, the second the iron input, and
the third the labor input), and two [processes] for producing iron,
(1/4, 0, 2) and (1/4, 1/4, 2). For each of the four possible
combinations of these [processes] that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn."
My problem:
In an economy with two commodities, corn and iron, there are two
processes for producing a unit of corn, (0.16889, 0.2, 0.82816)
and (0.16889, 0.25, 0.75) (where the first number indicates the corn
input, the second the iron input, and the third the labor input),
and two processes for producing iron, (0.0095553, 0.35, 0.19321)
and (0.15590, 0.13329, 0.033594). For each of the four possible
combinations of these processes that will define a simple circulating
capital model where wages are paid at the beginning of the period
calculate the wage-profit rate relation, assuming that the wage
consists only of corn. What technique will be cost-minimizing at
each wage?
The answer to the last question is
w/pc = 1.035 0.354 0.293 0.20635 0
|<-- Delta --->|<-- Gamma -->|<-- Alpha -->|<-- Beta -->|
r = 0% 85.9% 100.1% 125% 204.4%
where w is the wage, pc is the price of corn, r is the profit
rate, and the techniques have been defined in a previous post. Around
a wage of 0.20635 bushels per unit labor, a higher wage is associated
with the adoption of a more labor-intensive technique.
> It is kind of strange that you are
> asking whether demand and supply (demand and supply of what you have
> never
> really clearly said, it is obvious labor demands determine employment)
> determine wages and employment however, you use a setup that
> automatically
> will result in the demand having no effect and then do not even begin to
> contemplate what the supply of labor is. To paraphrase Solow, this is
> like
> baking a plum pie then sticking your thumb and announcing in shock and
> surprise that you have found of all things a plum.
Have I never stated "demand and supply of what"? Well, consider this
from my post on 29 April on this thread:
My assertion was about the (absence of) well-behaved supply and
demand functions in the labor market, particularly a demand
function for labor.
Mr. Weatherby makes crap up. Then there's always this:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
John J. Weatherby
"Robert Vienneau" <rv...@see.sig.com> wrote in message news:rvien-
> The assumptions of the so-called non-substitution theorem apply
> to my example. Therefore, by the theorem, the levels of output
> will NOT affect the profit-maximizing technique. Mr. Weatherby
> doesn't know what he is talking about.
>
think you clearly understand the concept. The problem is that you have
misapplied cost minizimation here. I do not think you went about finding the
equilibrium technique correctly.
> Have I never stated "demand and supply of what"? Well, consider this
> from my post on 29 April on this thread:
>
> My assertion was about the (absence of) well-behaved supply and
> demand functions in the labor market, particularly a demand
> function for labor.
>
Which is clearly not what your model shows. Your model shows that there
are 2 very well behaved labor demand functions. Which one is chosen is the
question.
> Mr. Weatherby makes crap up. Then there's always this:
>
> <http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
>
reposting the same URL does not make it any more correct.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message news:rvien-
> > The assumptions of the so-called non-substitution theorem apply
> > to my example. Therefore, by the theorem, the levels of output
> > will NOT affect the profit-maximizing technique. Mr. Weatherby
> > doesn't know what he is talking about.
> I think you need to look at Varian's discussion on this topic. I do
> not
> think you clearly understand the concept. The problem is that you have
> misapplied cost minizimation here.
I don't like Varian's presentation, anyhow. I prefer Pasinetti's
lectures.
Notice Mr. Weatherby has no comment on my contention (and Pasinetti's)
that my point that the principle of substitution does not apply
in general to long run models, even beyond where the non-substitution
theorem applies.
Notice Mr. Weatherby neither agrees with nor denies my contention
that my example meets the assumptions of the non-substitution
theorem. Notice Mr. Weatherby neither agrees nor disagrees with
Varian's concluding comment (2nd edition) on the non-substitution
theorem - that the "method of production will remain constant"
whatever "the level of output of the different goods".
Varian does directly contradict statements of Mr. Weatherby's
in previous posts. As usual, Mr. Weatherby gets economic theory
completely backward.
> I do not think you went about finding the
> equilibrium technique correctly.
If Mr. Weatherby wanted to actually say anything substantial, he
could always outline how to solve one of the following problems:
Foley's problem:
My problem:
> > Have I never stated "demand and supply of what"? Well, consider this
> > from my post on 29 April on this thread:
> > My assertion was about the (absence of) well-behaved supply and
> > demand functions in the labor market, particularly a demand
> > function for labor.
> Which is clearly not what your model shows. Your model shows that
> there
> are 2 very well behaved labor demand functions. Which one is chosen is
> the question.
Which is clearly mistaken. The amount of labor that firms in my
example want to employ is the sum of the labor they want to employ
in making corn and the labor they want to employ in making steel/iron.
> > Mr. Weatherby makes crap up. Then there's always this:
> >
> > <http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
> reposting the same URL does not make it any more correct.
Is Mr. Weatherby under the illusion that readers of this thread, if
any, are unaware that he has yet to address my example, under
any presentation, in a clear and coherent manner?
One can only wonder if Mr. Weatherby knows he has been rejecting
well-established and accepted results for no particular reason that
can withstand a minute's worth of rational scrutiny.
John J. Weatherby
> Notice Mr. Weatherby has no comment on my contention (and Pasinetti's)
> that my point that the principle of substitution does not apply
> in general to long run models, even beyond where the non-substitution
> theorem applies.
>
All of these will show you how labor and capital can be substituted in the
long run. Especially Romer 1990.
>Notice Mr. Weatherby neither agrees nor disagrees with
> Varian's concluding comment (2nd edition) on the non-substitution
> theorem - that the "method of production will remain constant"
> whatever "the level of output of the different goods".
>
I think you are making crap up. This is not Varians comment in the 3rd.
edition. "Since the equilibruim conditions are independent of demand
conditions (demand for goods not labor), the equilibrium choice of technique
will be independent of demand conditions (again refer to demand for produced
goods). No matter how ***consumer*** demands change the firm will not
substitute away from the equilibrium technique; this is the reason for the
name nonsubstitution theorem. " (Varian, CH. 18, pg. 356)
Again I am not arguing that technique will change becuase consumer
demands are different. The argument is that each production process will
have different levels of profit maximizing production. Why? Each technique
has different demands for labor and corn. An application of a constraint
will show you under a labor and/or corn constraint process alpha will mean a
different level of steel and corn produced than process beta.
What is cost minimizing depends on these levels of production that firm
chooses by choosing techinique. This has nothing to do with consumer demand
rather which process is profit maximizing for the firm. It is simple, a firm
has X labor and Y corn. Using process alpha means A corn is produced at cost
B and C steel is produced at cost D. Using process beta means that E corn is
produced at cost F and G steel is produced at cost H. Your analysis compares
cost of B+D to cost of G+H. Where profit maximization implies the revenue of
A and B minus the cost AB + CD is compared to the revenue of E + the revenue
of G steel minus the cost GH + and EF. This is not the same thing in your
example. In fact your cost should be AB+CD and GH+EF not B+C and F+H.
> Varian does directly contradict statements of Mr. Weatherby's
> in previous posts. As usual, Mr. Weatherby gets economic theory
> completely backward.
>
No it is you have economic theroy completely backward. It is obvious you
do not know the difference between factor and consumer demands or even what
profit maximization and cost minimization imply. It is you that has ignored
in the dual problem cost minimization is solved for a fixed output, the
profit maximizing output. It is you that have ignored in your example the
profit maximizing output depends on technique. That means the cost
minimization problem can not be done on a basis of per unit cost. The
outputs are different are under each techinique meaning altough the per unit
cost under one technique may be cheaper the cost of production using that
technique may be more expensive and may lead to either lower or higher
profits depending on the price of steel under the technique and the revenue
from final sales of corn.
> One can only wonder if Mr. Weatherby knows he has been rejecting
> well-established and accepted results for no particular reason that
> can withstand a minute's worth of rational scrutiny.
>
Well established to whom? You? Just becuase the non-substition theorem
was established in Samuelson 1951 and revisited in Weizsacker in 1971 does
not mean you chose the equilibrium technique correctly. Furthermore you have
not cited one paper other than your own that used a general equilibrium with
production model to show that labor demand may not be well behaved. Finally
this does not make it a realistic model nor do there exist any empirics that
support this claim. The tradeoff between realism and tractability has gone
way too far to the tractability side.
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-D4D1D0....@news.dreamscape.com...
> > Notice Mr. Weatherby has no comment on my contention (and Pasinetti's)
> > that my point that the principle of substitution does not apply
> > in general to long run models, even beyond where the non-substitution
> > theorem applies.
> Yes I do look at Romer 1990 or the Solow or Ramsey-Cass-Koopmans
> model.
> All of these will show you how labor and capital can be substituted in
> the
> long run. Especially Romer 1990.
OK. Mr. Weatherby has a comment that one can only think a joke.
> >Notice Mr. Weatherby neither agrees nor disagrees with
> > Varian's concluding comment (2nd edition) on the non-substitution
> > theorem - that the "method of production will remain constant"
> > whatever "the level of output of the different goods".
> I think you are making crap up. This is not Varians comment in the
> 3rd. edition. "Since the equilibruim conditions are independent of demand
> conditions (demand for goods not labor), the equilibrium choice of
> technique
> will be independent of demand conditions (again refer to demand for
> produced
> goods). No matter how ***consumer*** demands change the firm will not
> substitute away from the equilibrium technique; this is the reason for
> the
> name nonsubstitution theorem. " (Varian, CH. 18, pg. 356)
The second edition also leads me to wonder if Varian has stated
the so-called non-substitution theorem correctly. For example,
Varian states it as applying to a Walrasian equilibrium. How should
the student think about feasiblity constraints in this context?
And isn't utility maximization irrelevant here? Certainly Varian
states it a lot differently than, say,
H. D. Kurz and N. Salvadori, "The Non-Substitution Theorem: Making
Good a Lacuna". Journal of Economics. 59, 1994.
Varian takes labor as the numeraire and doesn't mention the rate of
profit/interest. Coming at the theorem from the traditions that I do,
it is no wonder I prefer other presentations to Varian's.
> Again I am not arguing that technique will change becuase consumer
> demands are different.
No, Mr. Weatherby is not. I don't see any correct and coherent
argument at all from him.
> The argument is that each production process will
> have different levels of profit maximizing production.
That is correct, sort of. If the Alpha technique, say, is profit
maximizing/cost minimizing for a given (real) wage in a model like
my example (generalized to n goods):
(1) The price vector of all produced goods (that is to say, of
all other goods) is uniquely determined
(2) This technique is profit maximizing and cost minimizing for
ANY levels of operation of the processes comprising the
technique.
That is to say, all levels of production for these processes will
result in this technique being profit-maximizing and cost-minimizing
at the given wage.
> Why? Each
> technique
> has different demands for labor and corn. An application of a constraint
> will show you under a labor and/or corn constraint process alpha will
> mean a
> different level of steel and corn produced than process beta.
It is true that, for different techniques, the same net output, say, per
worker will result in different levels of production (gross outputs)
for the various commodities.
> What is cost minimizing depends on these levels of production that
> firm chooses by choosing techinique.
But the above is simply and plainly wrong. As I have explained
previously on this thread, the amount of inputs of the non-labor
inputs are not given parameters in the model, but endogeneously
determined. In fact,
q = (I - A)^(-1) y
where y is a vector of net outputs, q is the vector of inputs of
produced goods, and A is the usual input-output matrix for the
technique.
> This has nothing to do with consumer demand
Part of the net output goes to consumers. Another part is retained
within the production sector for growth.
> rather which process is profit maximizing for the firm.
Nope. The levels of output cannot affect which process is
profit-maximizing under the assumptions of the non-substitution
theorem. In other words, Mr. Weatherby has economic theory, as
usual, completely backwards.
> It is simple, a firm
> has X labor and Y corn.
Already confused. What happened to steel? And why can Mr. Weatherby
invent a notation that's helpful?
> Using process alpha means A corn is produced at
> cost
> B and C steel is produced at cost D. Using process beta means that E corn
> is
> produced at cost F and G steel is produced at cost H. Your analysis
> compares
> cost of B+D to cost of G+H.
Actually it doesn't. I compare the cost of operating each process
to the revenues generated by that process. Only those processes
are operated in which a loss is not made.
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LaborDemand.pdf>
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
> Where profit maximization implies the revenue
> of
> A and B minus the cost AB + CD is compared to the revenue of E + the
> revenue
> of G steel minus the cost GH + and EF.
I think the above is nonsense.
> This is not the same thing in your
> example. In fact your cost should be AB+CD and GH+EF not B+C and F+H.
And the above is irrelevant to my example, too.
> > Varian does directly contradict statements of Mr. Weatherby's
> > in previous posts. As usual, Mr. Weatherby gets economic theory
> > completely backward.
> No it is you have economic theroy completely backward. It is obvious
> you
> do not know the difference between factor and consumer demands or even
> what
> profit maximization and cost minimization imply.
Mr. Weatherby is in a frightful muddle.
> It is you that has ignored
> in the dual problem cost minimization is solved for a fixed output, the
> profit maximizing output.
Nope. In a model like my example, it is solved for any level of
output.
> It is you that have ignored in your example the
> profit maximizing output depends on technique.
There is nothing correct about any interpretation of that statement
that I have ignored. Above I repeat an equation from an earlier
post on this thread that shows how the level of output of each
process depends on the technique.
> That means the cost
> minimization problem can not be done on a basis of per unit cost.
It's hard to say whether the above statement is a non-sequitur. After
all, Mr. Weatherby's preceeding statements were a mixture of error,
nonsense, and misunderstanding.
> > One can only wonder if Mr. Weatherby knows he has been rejecting
> > well-established and accepted results for no particular reason that
> > can withstand a minute's worth of rational scrutiny.
> Well established to whom? You? Just becuase the non-substition
> theorem
> was established in Samuelson 1951 and revisited in Weizsacker in 1971
I believe that Nicholas Georgescu-Roegen was the first to establish
the non-substitution theorem.
> does
> not mean you chose the equilibrium technique correctly.
If Mr. Weatherby wanted to actually say anything substantial, he
could always outline how to solve one of the following problems in
a clear, coherent, and correct fashion.
Foley's problem:
My problem:
Or Mr. Weatherby could always attempt to read Pasinetti's Lectures
or Kurz and Salvadori's textbook.
> Furthermore you have
> not cited one paper other than your own that used a general equilibrium
> with
> production model to show that labor demand may not be well behaved.
Mr. Weatherby makes crap up. My point can be established in a
model of one vertically-integrated sector. It does not need a general
equilibrium framework. Furthermore, what does he imagine these
people are talking about?
"The idea that demand and supply for factors of production determine
distribution has become so deeply ingrained in economic thought that
it is almost viewed as an immediate reflection of facts, and not as
Not to mention other references in my PDF files, particularly a
Steedman paper and a Marglin book.
> Finally
> this does not make it a realistic model nor do there exist any empirics
> that
> support this claim.
Mr. Weatherby is free to ignore certain case studies, for example,
by Barkley Rosser.
> The tradeoff between realism and tractability has gone
> way too far to the tractability side.
The above ignores the point of my example.
One student of logic once phrased it like this on one of my
threads:
"If you are talking about the counterexamples, as a matter of
elementary logic one does not demand generality of them, only
that they fall under the scope of the universal claim made. If
I refute your claim that all sheep are white by observing that
Farmer MacGregor has a black ewe, you cannot come back with
'Well you can hardly demand that all sheep belong to Farmer
MacGregor'."
But, as I have repeatedly claimed, the point of my example
generalizes to much more complicated models. This is well-established
in the literature. Mr. Weatherby, of course, is free to ignore
the literature. In fact, I think Ph. D.'s in economics are
encouraged to be ignorant of the literature not produced by a
narrow selection of schools.
I think showing certain common beliefs lack logical validity is
useful.
John J. Weatherby
> > Again I am not arguing that technique will change becuase consumer
> > demands are different.
>
> No, Mr. Weatherby is not. I don't see any correct and coherent
> argument at all from him.
>
affect price under model. This means that firms face a profit maximization
problem where price is fixed. The profit maximizing quantities depend solely
on the technique of steel of used. This means your cost minimization is
wrong you do not take into account the difference in profit maximizing
output. The argument is simply because per unit cost is lower under a
certain process does not mean profits are higher. There are different levels
of production, given by the profit maximization problem solved for each
technique given the price level of corn.
> That is correct, sort of. If the Alpha technique, say, is profit
> maximizing/cost minimizing for a given (real) wage in a model like
> my example (generalized to n goods):
>
> (1) The price vector of all produced goods (that is to say, of
> all other goods) is uniquely determined
>
> (2) This technique is profit maximizing and cost minimizing for
> ANY levels of operation of the processes comprising the
> technique.
>
Correct if you do cost minimization correctly and account for the
difference in the profit maximizing quantity. Duality says that solving the
unconstrained profit maximizing problem is equilavent to solving the
constrained cost minimizing problem where the output is given. That output
is determined by the profit maximizing solution. In your example each
technique has a different profit maximizing output, therefore simple per
unit cost is not enough to determine which technique will choosen. The
different profit maximizing outputs mean different revenues. What happens if
the more costly technique also brings more revenue (more corn is produced)?
The profits under the more costly technique could be higher or lower.
Without knowing the profit maximizing output you can not say if profits
under the more costly technique are higher or lower.
> It is true that, for different techniques, the same net output, say, per
> worker will result in different levels of production (gross outputs)
> for the various commodities.
>
Exactly which means the revenue under technique is also different. So
per unit cost comparison is invalid. It does not prove that either technique
is cost minimizing for the level of output associated it with it nor that it
is profit maximizing. Per unit cost is the wrong comparison.
> Nope. The levels of output cannot affect which process is
> profit-maximizing under the assumptions of the non-substitution
> theorem.
Then the nonsubstitution theorem does not apply to your setup. Output
affects revenue. Different outputs mean different revenues. If both
processes gave the same profit maximizing output your analysis would
correct. However they do not. In this case it is unclear from your setup
what is happening to revenue. The profit maximizing outputs ultimately are
determined by the amount of labor and the stock of corn at the beginning of
the year. Profit is revenue minus cost. Finding per unit cost for a process
tells you nothing about profit in this example, the revenues are different.
If process beta has a higher revenue than profit maximization would imply
process beta is used with a higher wage if the difference in revenue above
process alpha was greater than the difference in cost above process alpha.
Ultimately this discussion depends on the stock of corn and the amount
of labor. If corn is heavily constrained and labor infinite, then process
alpha will probably be profit maximizing in that it cost less and allows for
more production, more revenue. If labor is heavily constrained and corn
infinite, then process beta for at least some levels of total labor may be
profit maximizing. Although it is more costly, more corn will be produced.
The question is does this mean more profits. It may or not, none the less
you model does not even begin to attempt to answer this. You have no
constraints on either which is not realistic.
> > It is simple, a firm
> > has X labor and Y corn.
>
> Already confused. What happened to steel? And why can Mr. Weatherby
> invent a notation that's helpful?
>
Steel is not constrained you do not start with a stock of it and is a
choice variable. I am simply imposing a constraint of labor and corn. That
Xs (labor used producing steel) + Xc (labor used producing corn) <= X (the
total amount of labor). This also implies a similar constraint on corn.
Anyone familar with modeling should be able to figure this out. You do
understand your model, do you not?
> > Using process alpha means A corn is produced at
> > cost
> > B and C steel is produced at cost D. Using process beta means that E
corn
> > is
> > produced at cost F and G steel is produced at cost H. Your analysis
> > compares
> > cost of B+D to cost of G+H.
>
> Actually it doesn't. I compare the cost of operating each process
> to the revenues generated by that process. Only those processes
> are operated in which a loss is not made.
>
How can you determine if a loss is made or not when you have not
determined the profit maximizing quantities. A loss would imply the price of
corn times the amount of corn produced is less than the cost of corn
production (note: This assumes the price of steel is equal to its per unit
cost. Therefore the price of steel times quantity used is the cost of steel
production and is included in the cost of corn. In short steel is an
intermediate good.) Without determining quantities of corn produced under
each technique you can determine revenue which means you can not determine
losses.
> > It is you that has ignored
> > in the dual problem cost minimization is solved for a fixed output, the
> > profit maximizing output.
>
> Nope. In a model like my example, it is solved for any level of
> output.
>
If you knew what duality was you would realize this is completely wrong.
Cost minimization is solved for a given quantity, the profit maximizing
quantity. This is why you have not solved the model correctly. Again if the
profit maximizing output were the same for each process this would be fine,
but it is not.
> Above I repeat an equation from an earlier
> post on this thread that shows how the level of output of each
> process depends on the technique.
>
Which is exactly the equation you ignored when you pretended to cost
minimize.
> My problem:
>
Repoting the same mistaken technique will never make it right.
> Thus, Ricardo saw
> no inconsistency between free competition and unemployment of
> labour. In his view lower wages could eliminate unemployment only
> be decreasing the growth of population or by favouring accumulation...
>
Completely bogus. I do not have the copy of Ricardo in front of me or I
would quote you the passage. The idea refered to here has nothing to do with
employment. Ricardo formulated an idea close to Malthus' ideas on growth.
The idea that real wages would be below subsistence if populations grew with
an increase in capital or technology. Ricardo's idea of steady state was
similar to Malthus it was a point where real wages were subsistance level
not that unemployment could persist. If you want I will quote the passages.
I have them marked for my introduction to growth theory lecture. This
lecture is about the classical theory of growth and how Solow revived it in
Solow '56 and showed that technological change can mean the steady state
changes.
> ...Outputs can influence relative prices ... by affecting the relative
> scarcity of labour and capital, and thus the wage and rate of
> interest, given the supply of the two factors and the state of
> technical knowledge. This link between prices and outputs is one and
> the same thing as the explanation of distribution by demand and supply
> of factors of production: and it becomes untenable once that
> explanation is abandoned.
>
This has been abandoned becuase modern economist no longer use a labor
theory of value. This is no longer the differentiation between market value
and value. Ricardo and Smith assumed there was a difference. Value was
determined by labor and labor alone. Market value was something different.
This view no longer exist. The quotation you cite assumes that everyone is
still using the labor theory of value and not the modern idea of value
proposed by Debreu.
John
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-DE539E....@news.dreamscape.com...
> > > Again I am not arguing that technique will change becuase
> > > consumer
> > > demands are different.
> > No, Mr. Weatherby is not. I don't see any correct and coherent
> > argument at all from him.
> > It is true that, for different techniques, the same net output, say,
> > per
> > worker will result in different levels of production (gross outputs)
> > for the various commodities.
> Exactly which means the revenue under technique is also different. So
> per unit cost comparison is invalid.
Non sequitur.
> It does not prove that either technique
> is cost minimizing for the level of output associated it with it nor that
> it
> is profit maximizing. Per unit cost is the wrong comparison.
> > Nope. The levels of output cannot affect which process is
> > profit-maximizing under the assumptions of the non-substitution
> > theorem.
> Then the nonsubstitution theorem does not apply to your setup.
If Mr. Weatherby wanted to actually say something substantial
and non-confused, perhaps he could state the assumptions of
the non-substitution theorem. Then he could say whether they
are or are not met in my example.
By the way, I proved, in a note posted yesterday, that the effect
illustrated in my first post on this thread can arise when the
conditions of the so-called non-substitution theorem are not
met. This is not novel.
The second edition of Varian, I think, explains the
non-substitution theorem badly. The student who relies on Varian
will be ill-equipped, for example, to understand the following
passage:
"As was paradoxically to be rediscovered in recent years, in
the form of a 'non-substitution theorem', the system of relative
prices is determined independently of demand conditions and
consumer preferences, once the real wage - or the rate of profits
(interest) - is give, and constant returns to scale are assumed.
We saw how the classical economists could take the real wage
(or, with Sraffa, the rate of profits) as given when approaching
the determination of relative prices. The two things together
mean that in classical theory, under the assumptions of constant
returns to scale (which is generally made in marginal theory), we
shall have: (a) that demand conditions and consumer preferences
are irrelevant for the determination of relative prices (47),
(b) that their irrelevance is due to a different theory of
distribution.
The non-substitution theorem is of course generally knoown. What
has engendered misunderstandings has been a failure to appreciate
the different meaning that that proposition has in two theoretical
settings. In marginal theory, the proposition is a logical
relation of no direct relevance for distribution theory, since
the real wage is NOT given independently of demand conditions and
consumer tastes. In modern theory, therefore, the relevance of
the non-substitution theorem lies merely in making it clear that
consumer preferences can affect prices only to the extent to
which they affect distribution - which, of course, those preferences
do, because they underlie the demand functions for the factors
of production...
The position is entirely different for the classical economists
where the independence of prices and the residual distributive
variable from what are today described as demand conditions and
consumer preferences constitutes a fundamental aspect of the theory.
This is because that independence follows from a theory of
distribution where the real wage (or the rate of profits) can in
fact be taken as known when determining relative prices...
(47) This will perhaps become clearer for people use to envisaging
the determination of prices in partial equilibrium terms of the
demand for and supply of products once it is remembered that the
upward slope of a supply curve, necessary in order to make the
equilibrium price depend on demand conditions, is but an expression
of the dependence of distribution on the output of the commodity
in question (an expression, that is, of the rise in the relative
price of the services required in a higher proportion in the
production of that commodity...).
(48) It is argued at times as if, once constant returns to scale
are granted, the possibility to determine prices independently of
consumer preferences were generally admitted in current economic
theory... This is not correct, as should on the other hand be
evident from the simple fact that consumer preferences are relevant
in any modern general equilibrium system, where constant returns
to scale are assumed..."
-- Pierangelo Garegnani, 1990.
> > > It is simple, a firm
> > > has X labor and Y corn.
> > Already confused. What happened to steel? And why can Mr. Weatherby
> > [not] invent a notation that's helpful?
> Steel is not constrained you do not start with a stock of it and is a
> choice variable. I am simply imposing a constraint of labor and corn.
> That
> Xs (labor used producing steel) + Xc (labor used producing corn) <= X
> (the
> total amount of labor). This also implies a similar constraint on corn.
> Anyone familar with modeling should be able to figure this out. You do
> understand your model, do you not?
The claim that the above "implies a similar constraint on corn", but
not on steel, is simply mistaken. Mr. Weatherby, as usual, has offered
no argument whatsoever for his comments. For example, he has not
pointed to any feature of the model that explains why inputs
of corn and steel are not treated symmetrically in the model.
From my original post:
-----------------------------------------------------------------
2.0 DATA ON TECHNOLOGY
Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, steel, and (seed)
corn. All production processes in this example require a year to
complete. Only one production process is known for producing corn. This
process requires the following inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year:
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Steel is also produced by this firm. Two processes are known for
producing steel:
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
Apparently, inputs of corn and steel can be traded off in producing
steel. The process that uses less corn and more steel, however, also
requires a greater quantity of labor input.
-------------------------------------------------------------------
One can write down two input-output matrices from the above:
A( alpha ) = 0.35 0.2
0.0095553 0.16889
A( beta ) = 0.13329 0.2
0.15590 0.16889
And two vectors of direct labor inputs:
a0( alpha ) = [ 0.19321 0.82816 ]
a0( beta ) = [ 0.033594 0.82816 ]
Following the math I have previously outlined, one calculates the
following two matrices:
[ I - A( alpha ) ]^(-1) = 1.54392 0.371533
0.0177505 1.20748
[ I - A( beta ) ]^(-1) = 1.20599 0.290212
0.226220 1.25765
and two vectors:
a0( alpha ) [ I - A( alpha ) ]^(-1) = [ 0.3130 1.072 ]
a0( beta ) [ I - A( beta ) ]^(-1) = [ 0.2279 1.051 ]
Suppose the net (steady state) output is y1 tons steel and y2 bushels
corn. Under the alpha technique, the required yearly inputs of steel
and corn are:
q1 = ( 1.54392 y1 + 0.371533 y2 ) tons steel
q2 = ( 0.0177505 y1 + 1.20748 y2 ) bushels corn
The required yearly input of labor is:
L = ( 0.3130 y1 + 1.072 y2 ) person-years
Some points to note about this arithmetic: first, the amount of
labor required per bushel corn produced net is 1.072 person-years
for the alpha technique and 1.051 person-years for the beta
technique. These numbers agree with the numbers in my original post
on this thread.
Second, notice that whatever levels of net output one desires,
the gross outputs of steel and corn will not be meaningless
negative levels, according to the above equations. This is
no accident. The Leontief input-output matrices satisfy
the Hawkins-Simon conditions. These properties are related
to a certain theorem of Perron and Frobenius.
Third, steel and corn are treated symmetrically above. But both
steel and corn are treated differently from labor. So when Mr.
Weatherby says constraints are imposed on corn and labor, but not
on steel, he, as usual, doesn't know what he is talking about.
Finally, when figuring out how much labor firms want to employ,
given net outputs and the technique, one does not impose a
constraint that the desired quantity of labor cannot exceed
the available supply. That constraint simply does not arise in
this specific context.
> > > Using process alpha means A corn is produced at
> > > cost
> > > B and C steel is produced at cost D. Using process beta means that E
> > > corn
> > > is
> > > produced at cost F and G steel is produced at cost H. Your analysis
> > > compares
> > > cost of B+D to cost of G+H.
> > Actually it doesn't. I compare the cost of operating each process
> > to the revenues generated by that process. Only those processes
> > are operated in which a loss is not made.
> How can you determine if a loss is made or not when you have not
> determined the profit maximizing quantities.
Mr. Weatherby has not been paying attention. First, he doesn't
acknowledge that he was building people of straw. Second, consider
the following table from my original post:
----------------------------------------------------------------
TABLE 5: COSTS, WAGE $1,338.8 PER PERSON-YEAR,
PRICE OF STEEL $6,013 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$1,338.8 = $4,000 150%
Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
+ 0.19321*$1,338.8 = $2,459
Steel Beta 0.13329*$6,013 + 0.15590*$10,000
+ 0.033594*$1,338.8 = $2,405 150%
----------------------------------------------------------------
Using the same notation as above, let q1 be the gross output
of steel and q2 be the gross output of corn.
The revenues from operating the corn producing process are
$10,000*q2
(By assumption, the price of a bushel corn is $10,000.) The
cost, including interest charges, of operating the corn-producing
process, is:
( 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$1,338.8 )(2.5) q2
= $4,000*2.5*q2 = $10,000*q2
Obviously, the fact that operating this process does not incur
a loss is independent of the level of operation. That is, one
can divide through by q2.
If all the steel were produced by the Alpha steel-producing
process, the revenues from operating this process would be:
$6,013*q1
The cost, including interest charges, is:
$2,459*2.5*q1 = $6,148*q1
Obviously, the cost exceeds the revenues for any level of output.
The cost, including interest charges, of operating the Beta
steel-producing process is:
$2,405*2.5*q1 = $6,013*q1
Once again, one can see that a loss is not made in the Beta
steel-producing process for any level of output.
I can go even further. In which process would an additional dollar
invested yield the greatest return? This question, too, can be
answered without knowing the current scale of the processes.
So, as usual, Mr. Weatherby doesn't know what he is talking
about in the following nonsense:
> A loss would imply the price
> of
> corn times the amount of corn produced is less than the cost of corn
> production (note: This assumes the price of steel is equal to its per
> unit
> cost. Therefore the price of steel times quantity used is the cost of
> steel
> production and is included in the cost of corn. In short steel is an
> intermediate good.) Without determining quantities of corn produced under
> each technique you can determine revenue which means you can not
> determine
> losses.
Foley's problem:
My problem:
[Off-point and incoherent comments about Ricardo - deleted ]
> > "Outputs can influence relative prices ... by affecting the
> > relative
> > scarcity of labour and capital, and thus the wage and rate of
> > interest, given the supply of the two factors and the state of
> > technical knowledge. This link between prices and outputs is one and
> > the same thing as the explanation of distribution by demand and
> > supply
> > of factors of production: and it becomes untenable once that
> > explanation is abandoned."
-- P. Garegnani, RES, 1970.
> This has been abandoned becuase modern economist no longer use a
> labor
> theory of value...
> The quotation you cite assumes that everyone is
> still using the labor theory of value and not the modern idea of value
> proposed by Debreu.
Mr. Weatherby reads as well as he writes. He is commenting on a
quotation that attacks the idea that prices are determined by supply
and demand, that prices are scarcity indices. The author assumes
that some economists have the position attacked. The position
attacked is not the labor theory of value. That is, Mr. Weatherby's
last sentence is, as usual, completely backwards.
What are these economists talking about? (Hint: none of the
following are arguing for or about the labor theory of value.)
"The intractable problems created by the effort to extend into
the unobservable future the terrain over which the forces of
supply and demand hold sway are somehow set aside as questions
that will ultimately yield to a more sophisticated analysis.
Meanwhile, the existence of an alternative framework of thought
based on a revival of classical theory is denied. Certainly
the critics of neoclassical theory committed a great heresy
during the capital theory debate by proving false the analytical
basis for the principle of substitution in so far as it affects
the demand for capital and labour. Those who would defend
neoclassical theory against any attack on its logical structure
fail to see the significance of this result. This is because
they have given up any causal claims for general equilibrium
theory..., thus abandoning the traditional notion of equilibrium
as a centre of gravity relative to which prices and quantities
fluctuate. The revival of interest in classical theory is, in
part, a revival of interest in this old-fashioned idea. It is
also a revival of interest in a broadly based theory that does
not presume to find the essence of all market phenomena in
terms of the single principle of substitution."
-- Harvey Gram, 1990.
--
John J. Weatherby
> the form of a 'non-substitution theorem', the system of relative
> prices is determined independently of demand conditions and
> consumer preferences, once the real wage - or the rate of profits
> (interest) - is give, and constant returns to scale are assumed.
This is not contradictory to Varian. Again I am not arguing that
quantities are changing due to consumer demands. The argument is simple the
technique effects the level of output. Revenues are different under each
process, they produce different amounts of corn under the same price, this
is the case regardless of consumer demand. The argument is exactly stated in
your quotation. You have to know what profits are. You have not solved for
profits. Your cost minimization is wrong because the revenue under each
technique is different, regardless of consumer demands. Even the quotation
you have just posted implies your method is wrong because you have not found
the level of profits for each technique.
> We saw how the classical economists could take the real wage
> (or, with Sraffa, the rate of profits) as given when approaching
> the determination of relative prices.
Again Smith and Ricardo have very important contributions. However, this
is not one of them that has lasted.
>The two things together
> mean that in classical theory, under the assumptions of constant
> returns to scale (which is generally made in marginal theory), we
> shall have: (a) that demand conditions and consumer preferences
> are irrelevant for the determination of relative prices (47),
This is not what Smith, Ricardo or the classical economic argued. You
are muddling the issue by not realizing prices and value were two different
things to classical economist. Consumer demands were very important to
prices, however had no effect on value. Value was determined solely by the
labor used to create the good.
> The non-substitution theorem is of course generally >knoown.
Which means you should have no excuse for not seeing that Varian is
showing the theorem correctly.
> The position is entirely different for the classical economists
> where the independence of prices and the residual distributive
> variable from what are today described as demand conditions and
> consumer preferences constitutes a fundamental >aspect of the theory.
This is a complete misunderstanding of Ricardo and Smith. The classical
economist never posited the real wage as the wage over prices. Prices were
an entirely different process than value. The real wage refered to the value
of goods and how much labor could purchase. Natural price to the classical
economist dealt with a labor standard. That is any good's natural price is
determined by the labor involved. Ricardo extended this to show how capital
can affect natural prices and also showed that the value of labor can drop.
However this has nothing to do with prices in the way modern theory treats
them.
> (47) This will perhaps become clearer for people use to envisaging
> the determination of prices in partial equilibrium terms of the
> demand for and supply of products once it is remembered that the
> upward slope of a supply curve, necessary in order to make the
> equilibrium price depend on demand conditions,
Really? Is this actually implying that under Marshall's idea of decreasing
cost industry consumer demands have no effect on price? Or is the author
aware of what a decreasing cost industry is?
>This is not correct, as should on the other hand be
> evident from the simple fact that consumer preferences are relevant
> in any modern general equilibrium system, where constant returns
> to scale are assumed..."
> -- Pierangelo Garegnani, 1990.
>
I suppose he means relative to prices. hmmm. They what role do consumer
preferences have in determining prices in a constant marginal cost industry
under perfect competition? So much for this statement this is a pretty
standard setup for analyzing many questions. Perhaps Garegnani should skip
the hype. I suppose he has actually picked up some textbooks and maybe read
Smith or Ricardo, then again Marshall warns how easy it is for Ricardo to be
misinterperted and how Marx got Ricardo wrong, so perhaps he should present
the literature correctly.
> The claim that the above "implies a similar constraint on corn", but
> not on steel, is simply mistaken.
Let me explain why there is no constraint on steel. With your porported
mathematical value you should be able to figure this out. Constraints on
labor and corn stocks constrain the amount of final corn produced and the
amount of steel produced. The amount of steel is endogenous and is solved
for in the model. Since your model is a one period model, the amount of
labor is constrained and also the amount of corn used for production
processes is explained. It would be a grave mistake to not include consumer
preferences. Seed corn is essential to production. The stock available at
any given time should be determined by people's preference for eating the
corn. There exist an ignored tradeoff between the subsistance level of corn
+ people's want to consume corn and corn available for production.
> Third, steel and corn are treated symmetrically above. But both
> steel and corn are treated differently from labor. So when Mr.
> Weatherby says constraints are imposed on corn and labor, but not
> on steel, he, as usual, doesn't know what he is talking about.
>
You are referring to the amount of corn produced at the end of the year.
These are not available for production at the beginning of the year.
Therefore the beginning of the year is constrained by the amount of corn you
start with. This depends on the amount of corn produced in the last period
and consumption of corn. The non-substitution theorem simply can not apply
to this model!!! Consumer demand for corn will affect how much corn is
available for production at the beginning of the year, no amount of
production at the end of the year will change this. Consumer demands will
constrain corn. The fact that corn is heavily constrained will mean that
less production is available if the alpha process of steel is used. This
means the beta process although more costly will also bring more revenue,
more production. This means your analysis is wrong. Profits can be higher or
lower if beta is chosen. You will be hard pressed to find numbers where the
alpha technique is ever used if you take into account the constraint on
corn. Under your model consumer demands do affect the choice of technique,
if it is solved correctly.
> Finally, when figuring out how much labor firms want to employ,
> given net outputs and the technique, one does not impose a
> constraint that the desired quantity of labor cannot exceed
> the available supply. That constraint simply does not arise in
> this specific context.
>
Yet it should if you wish to prove that supply conditions have no
effect. You labor the post Demand, Supply have no effect then never mention
labor supply. I do not think it very realistic to assume an infinite supply
of labor. You really do think firms can find as many laborers as they wish
under any wage do you?
> [Off-point and incoherent comments about Ricardo - deleted ]
>
Again once you are refuted the topic changes. It only proves that you do
not understand the classical position on these issues much less the modern
position. The comments were only in response to something you had posted.
Was your quotation off-point?
> The author assumes
> that some economists have the position attacked. The position
> attacked is not the labor theory of value. That is, Mr. Weatherby's
> last sentence is, as usual, completely backwards.
>
You are making crap up. The quatation was refering to Ricardo and Smith
and getting it wrong.
> What are these economists talking about? (Hint: none of the
> following are arguing for or about the labor theory of value.)
>
You are making crap up again. The beginning of the quotation mentioned
how abandoning the labor theory of value left out some richness of the
model. Reread it. Again when you are refuted you attempt to change what was
stated.
<snipped alot of cutting and pasting. Reposting the same tired quotations,
that completely lack analysis (in fact it looks like conclusions without the
models) make them no more convincing.>
John
Robert Vienneau
> "Robert Vienneau" <rv...@see.sig.com> wrote in message news:rvien-
[>> The second edition of Varian, I think, explains the ]
[>> non-substitution theorem badly. The student who relies on Varian ]
[>> will be ill-equipped, for example, to understand the following ]
[>> passage: ]
> > "As was paradoxically to be rediscovered in recent years, in
> > the form of a 'non-substitution theorem', the system of relative
> > prices is determined independently of demand conditions and
> > consumer preferences, once the real wage - or the rate of profits
> > (interest) - is given, and constant returns to scale are assumed.
> This is not contradictory to Varian. Again I am not arguing that
> quantities are changing due to consumer demands. The argument is simple
> the
> technique effects the level of output. Revenues are different under each
> process, they produce different amounts of corn under the same price,
> this
> is the case regardless of consumer demand. The argument is exactly stated
> in
> your quotation. You have to know what profits are. You have not solved
> for
> profits. Your cost minimization is wrong because the revenue under each
> technique is different, regardless of consumer demands. Even the
> quotation
> you have just posted implies your method is wrong because you have not
> found
> the level of profits for each technique.
Wrong, at least three times over.
Saying that the student who relies on Varian will be ill-equipped to
understand that passage and what follows does not say that the passage
contradicts Varian. Varian takes labor as numeraire and doesn't mention
the rate of profits. That has something to do with why I think the
student who relies on Varian will have a hard time with that passage.
Now, the Garegnani passage is talking about the non-substitution
theorem. Mr. Weatherby presents his "argument" as a refutation
of this passage. So he seems to think that the level of outputs
affects what is the cost-minimizing technique under the conditions
of the non-substitution theorem - that is, if we want to pretend
his passage has something to do with the text to which he is
pretending to respond.
So here Mr. Weatherby asserts the non-substitution theorem is
mistaken. He, of course, is wrong. The cost minimizing technique,
under the conditions in which the non-substitution theorem applies,
is determined independently of the levels at which the processes are
operated. Levels of profits/interest payments do NOT need to be known
to determine the cost-minimizing technique.
Furthermore, the quotation talks about the RATE of profits, not
profits.
> > "We saw how the classical economists could take the real wage
> > (or, with Sraffa, the rate of profits) as given when approaching
> > the determination of relative prices."
> Again Smith and Ricardo have very important contributions. However,
> this is not one of them that has lasted.
Arguments from ignorance and unpopularity are not really arguments.
Notice Mr. Weatherby is not actually saying Garegnani is mistaken.
> > "The two things together
> > mean that in classical theory, under the assumptions of constant
> > returns to scale (which is generally made in marginal theory), we
> > shall have: (a) that demand conditions and consumer preferences
> > are irrelevant for the determination of relative prices (47),"
> This is not what Smith, Ricardo or the classical economic argued. You
> are muddling the issue by not realizing prices and value were two
> different
> things to classical economist. Consumer demands were very important to
> prices, however had no effect on value. Value was determined solely by
> the
> labor used to create the good.
I am NOT "muddling the issues". If anybody is, it would be Garegnani.
The distinction between market and natural prices in Smith and
Ricardo is not the same as the distinction between price and labor
values. I don't think Smith thought natural prices were the same as
labor values. Ricardo's relationship to the labor theory of value is
more complicated.
As a matter of fact, Smith and Ricardo generally assumed non-constant
returns, in some sense. Thus, consumer demands had an effect on
value. A higher level of effectual demand in Smith would increase
the extent of the market. The division of labor would be increased
and unit costs would be lower. In Ricardo, changed tastes from,
say, agricultural goods to manufactured goods would change the
(external) margin of cultivation. Consequently, relative labor
values and natural prices would be different. As usual, Mr. Weatherby's
comments are not about texts in this reality.
> > "The non-substitution theorem is of course generally known."
> Which means you should have no excuse for not seeing that Varian is
> showing the theorem correctly.
Mr. Weatherby responds to Garegnani's words as if I wasn't quoting him,
but saying these words directly.
Since Mr. Weatherby has no idea what's being discussed - and we have
gone through this before several years back - he cannot say whether
Varian is correct, misleading, or incorrect. The fact is, the
non-substitution theorem, as presented in much literature, is
applicable to the example in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
Yet, contrary to Varian's presentation, equilibrium there is not a
Walrasian equilibrium. Furthermore, changes in tastes there change
equilibria prices.
Now, Mr. Weatherby has laughably said that the presentation in the
PDF file is mistaken. Yet he cannot and will not point out exactly
where my calculations are in error. Nor will he present a supposed
alternative solution, despite having claimed my assumptions are
too simple and were made for tractability.
> > "The position is entirely different for the classical economists
> > where the independence of prices and the residual distributive
> > variable from what are today described as demand conditions and
> > consumer preferences constitutes a fundamental aspect of the theory."
> [ Confusion I don't feel like dealing with. ]
> > "(47) This will perhaps become clearer for people use to envisaging
> > the determination of prices in partial equilibrium terms of the
> > demand for and supply of products once it is remembered that the
> > upward slope of a supply curve, necessary in order to make the
> > equilibrium price depend on demand conditions,"
> Really? Is this actually implying that under Marshall's idea of
> decreasing
> cost industry consumer demands have no effect on price? Or is the author
> aware of what a decreasing cost industry is?
The last question is a weird question to pose about one of Sraffa's
students. The quote is a footnote to a passage discussing what
happens "under the assumptions of constant returns to scale". So,
per usual, Mr. Weatherby's comments are a complete non sequitur.
>> the
>> upward slope of a supply curve, necessary in order to make the
>> equilibrium price depend on demand conditions,
[>> is but an expression ]
[>> of the dependence of distribution on the output of the commodity ]
[>> in question (an expression, that is, of the rise in the relative ]
[>> price of the services required in a higher proportion in the ]
[>> production of that commodity...). ]
[>> (48) It is argued at times as if, once constant returns to scale ]
[>> are granted, the possibility to determine prices independently of ]
[>> consumer preferences were generally admitted in current economic ]
[>> theory... ]
> > This is not correct, as should on the other hand be
> > evident from the simple fact that consumer preferences are relevant
> > in any modern general equilibrium system, where constant returns
> > to scale are assumed..."
> > -- Pierangelo Garegnani, 1990.
> I suppose he means relative to prices. hmmm. They what role do
> consumer
> preferences have in determining prices in a constant marginal cost
> industry
> under perfect competition?
The answer was, of course in the passages Mr. Weatherby deleted. Changes
in tastes will, in traditional theory, change distribution, e.g., either
real wages or the rate of profits. So, according to statements of
the non-substitution theorem I prefer to Varian's, prices can be
different. The traditional theory presented this as an illustration
of the principle of substitution. But this theory is logically
invalid.
> So much for this statement this is a pretty
> standard setup for analyzing many questions. Perhaps Garegnani should
> skip
> the hype. I suppose he has actually picked up some textbooks and maybe
> read
> Smith or Ricardo, then again Marshall warns how easy it is for Ricardo to
> be
> misinterperted and how Marx got Ricardo wrong, so perhaps he should
> present
> the literature correctly.
Perhaps Mr. Weatherby should figure out who Garegnani is before
spouting off with such ignorance.
There is a large literature arguing that Marshall misrepresented
Ricardo and the development of neoclassical economics as developing
out of classical economics. But I don't think Mr. Weatherby's
misrepresentation or ignorance of this literature on the continuity
of price theory in economics is on-topic for this thread. Nor is
Mr. Weatherby's ignorance of the literature on whether Marx
correctly understood Ricardo. (Samuel Hollander has recently
written a paper on this topic, if I remember correctly.)
> > The claim that the above "implies a similar constraint on corn", but
> > not on steel, is simply mistaken.
> Let me explain why there is no constraint on steel. With your
> porported
> mathematical value you should be able to figure this out.
I have no idea what Mr. Weatherby thinks he is referring to with
my "porported [sic] mathematical value". And I've already figured
out my example.
> Constraints on
> labor and corn stocks constrain the amount of final corn produced and the
> amount of steel produced. The amount of steel is endogenous and is solved
> for in the model. Since your model is a one period model, the amount of
> labor is constrained and also the amount of corn used for production
> processes is explained. It would be a grave mistake to not include
> consumer
> preferences. Seed corn is essential to production. The stock available at
> any given time should be determined by people's preference for eating the
> corn. There exist an ignored tradeoff between the subsistance level of
> corn
> + people's want to consume corn and corn available for production.
Apparently Mr. Weatherby has yet to read the posts to which he is
pretending to respond.
From my original post:
-----------------------------------------------------------------
2.0 DATA ON TECHNOLOGY
Process Alpha Process Beta
-------------------------------------------------------------------
Notice corn, steel, and labor are all inputs into production. It
is not the case that labor and corn are inputs into production,
but steel isn't. There is an asymmetry here. Inputs of corn
and steel are both produced in the previous year. In a sense,
labor is not.
Following the math I have previously outlined, one calculates for
the alpha technique:
[ I - A( alpha ) ]^(-1) = 1.54392 0.371533
0.0177505 1.20748
and the vector:
a0( alpha ) [ I - A( alpha ) ]^(-1) = [ 0.3130 1.072 ]
Suppose the net (steady state) output is y1 tons steel and y2 bushels
corn. Under the alpha technique, the required yearly inputs of steel
and corn are:
q1 = ( 1.54392 y1 + 0.371533 y2 ) tons steel
q2 = ( 0.0177505 y1 + 1.20748 y2 ) bushels corn
The required yearly input of labor is:
L = ( 0.3130 y1 + 1.072 y2 ) person-years
> > Third, steel and corn are treated symmetrically above. But both
> > steel and corn are treated differently from labor. So when Mr.
> > Weatherby says constraints are imposed on corn and labor, but not
> > on steel, he, as usual, doesn't know what he is talking about.
> You are referring to the amount of corn produced at the end of the
> year.
y1 is the amount of steel available at the end of a year in a stationary
state. y2 is the amount of corn available at the end of a year in
a stationary state. Both quantities are net of replacement of used
up inputs, thereby allowing the economy to continue unchanged into
the next year.
> These are not available for production at the beginning of the year.
> Therefore the beginning of the year is constrained by the amount of corn
> you
> start with.
Non sequitur.
> This depends on the amount of corn produced in the last
> period and consumption of corn.
In a stationary state, q1 and q2 are simultaneously (1) the
amounts of steel and corn, respectively, produced at the end of
the year and (2) the amounts of steel and corn produced in the
previous year. Both at the start and at the end of the year
subtracting the quantities y1 and y2 from q1 and q2 leaves
the inputs of steel and corn required to continue production
into the next year.
> The non-substitution theorem simply can not apply
> to this model!!!
Mr. Weatherby is not describing my example, but some model
of his own fantasy. No wonder his conclusion is so mucked up.
> Consumer demand for corn will affect how much corn is
> available for production at the beginning of the year, no amount of
> production at the end of the year will change this. Consumer demands will
> constrain corn. [snip]
No such constraint arises when solving for a stationary state. The
quantities q1 and q2 are solved for endogeneously.
Here's some more of Mr. Weatherby's strangeness:
> > [Off-point and incoherent comments about Ricardo - deleted ]
> Again once you are refuted the topic changes. It only proves that you
> do
> not understand the classical position on these issues much less the
> modern
> position. The comments were only in response to something you had posted.
> Was your quotation off-point?
> > The author assumes
> > that some economists have the position attacked. The position
> > attacked is not the labor theory of value. That is, Mr. Weatherby's
> > last sentence is, as usual, completely backwards.
> You are making crap up. The quatation was refering to Ricardo and
> Smith
> and getting it wrong.
Maybe it is unfair to accuse Mr. Weatherby of making crap up. Perhaps
he is merely a paradigm of post-literacy. Let's go slowly over the
first two paragraphs of my Garegnani quote.
"The idea that demand and supply for factors of production determine
distribution has become so deeply ingrained in economic thought that
it is almost viewed as an immediate reflection of facts, and not as
the result of an elaborate theory. For the same reason, it is easily
forgotten how comparatively recent that theory is. In the first
systematic analysis of value and distribution by the English classical
economists up to Ricardo, we would look in vain for the conception
that demand and supply for labour and 'capital' achieve 'equilibrium'
as the proportions in which those 'factors' are employed in the
economy change with the wage and rate of profits. Thus, Ricardo saw
no inconsistency between free competition and unemployment of
labour. In his view lower wages could eliminate unemployment only
be decreasing the growth of population or by favouring accumulation..."
In the above paragraph, the author contrasts two theories. One theory
is supply and demand. The other is that of "the English classical
economists up to Ricardo". In neither case, does the author mention
the labor theory of value. The author seems well aware of different
time frames in which these theories were dominant. It is simply
untrue to say that this quotation, even here, "assumes that everyone
is still using the labor theory of value..." (Weatherby).
The author went on to criticize supply and demand:
"...Outputs can influence relative prices ... by affecting the relative
scarcity of labour and capital, and thus the wage and rate of
interest, given the supply of the two factors and the state of
technical knowledge. This link between prices and outputs is one and
the same thing as the explanation of distribution by demand and supply
of factors of production: and it becomes untenable once that
explanation is abandoned."
Mr. Weatherby commented on this passage as follows:
>>> This has been abandoned becuase modern economist no longer use a
>>> labor
>>> theory of value. This is no longer the differentiation between
>>> market value
>>> and value. Ricardo and Smith assumed there was a difference. Value
>>> was
>>> determined by labor and labor alone. Market value was something
>>> different.
>>> This view no longer exist. The quotation you cite assumes that
>>> everyone
>>> is
>>> still using the labor theory of value and not the modern idea of
>>> value
>>> proposed by Debreu.
Garegnani is saying that the theory of demand and supply should
be abandoned. He is not commenting in this paragraph at all on Classical
economics, much less the labor theory of value.
Apparently, when Mr. Weatherby says "this has been abandoned" he is
under the illusion that he is refering to what Garegnani's refers
to as "that explanation". But "that explanation", in Garegnani's
passage, is the theory of demand and supply. So the rest of Mr.
Weatherby's comment is a complete non-sequitur based on a complete
fabrication.
In other words,
Mr. Weatherby reads as well as he writes. He is commenting on a
quotation that attacks the idea that prices are determined by supply
and demand, that prices are scarcity indices. The author assumes
that some economists have the position attacked. The position
attacked is not the labor theory of value. That is, Mr. Weatherby
has everything, as usual, completely backwards.
The details of Garegnani's interpretation of classical economics
are not on-topic, unless one wants to argue that (a) the classical
economists had prices caused by the relative scarcity of capital
and labor or (b) that such scarcity prices are NOT closely
tied to theories of demand and supply.
> > What are these economists talking about? (Hint: none of the
> > following are arguing for or about the labor theory of value.)
> You are making crap up again. The beginning of the quotation
> mentioned
> how abandoning the labor theory of value left out some richness of the
> model. Reread it. Again when you are refuted you attempt to change what
> was stated.
Mr. Weatherby is making crap up. Nowhere does any quote I have
posted mention the labor theory of value.
> <snipped alot of cutting and pasting. Reposting the same tired
> quotations,
> that completely lack analysis (in fact it looks like conclusions without
> the
> models) make them no more convincing.>
The analytical basis for these quotes has been presented. Mr. Weatherby
cannot understand it. He probably wouldn't understand any of the texts
from which these quotes come. But nothing's stopping him from trying.
John Weatherby
> In article <YP9G8.1233$jA6....@newsread2.prod.itd.earthlink.net>,
> Saying that the student who relies on Varian will be ill-equipped to
> understand that passage and what follows does not say that the passage
> contradicts Varian. Varian takes labor as numeraire and doesn't mention
> the rate of profits.
maximizing profits is essential to solving the model. In fact each
consumer's share of profits is included in the budget constraint. It is
necessary to maximize profits under Varians approach. This comment shows
that you did not read the chapter or more likely did not understand the
approach. It was based on a paper published after 1960 in a mainstream
journal so it is no surprise you refuse to understand it.
>That has something to do with why I think the
> student who relies on Varian will have a hard time with that passage.
>
Well I suppose if you mean someone who knows how to do the problem right
might disagree. Then yes.
>So he seems to think that the level of outputs
> affects what is the cost-minimizing technique under the conditions
> of the non-substitution theorem - that is, if we want to pretend
> his passage has something to do with the text to which he is
> pretending to respond.
>
No you have it backwards again. The choice of technique affects the
level of output. This effects revenue. It means simply that revenue is
different under each technique. Not taking this into account, ie. only
looking at which technique has a lower per unit cost, is a fatal mistake.
> So here Mr. Weatherby asserts the non-substitution theorem is
> mistaken. He, of course, is wrong.
No actually as was shown later. I do not even believe the
non-substitution theorem applies to your set up.
> Arguments from ignorance and unpopularity are not really arguments.
> Notice Mr. Weatherby is not actually saying Garegnani is mistaken.
>
On the contrary I have argued that Garegnani has either misunderstood or
misrepresented Ricardo and Smith's theory. Marx did the same thing as
Marshall pointed out.
> I am NOT "muddling the issues". If anybody is, it would be Garegnani.
>
Of whow you treat as a guru who is not to be questioned. If you can not
tell the sources you are quoting are muddled then how can anyone believe
that you have not muddled the issues yourself when you cite these authors to
support yourself.
> Mr. Weatherby responds to Garegnani's words as if I wasn't quoting him,
> but saying these words directly.
>
You are the one quoting them. You would not be using them to support
yourself if you did not believe it was correct.
> The fact is, the
> non-substitution theorem, as presented in much literature, is
> applicable to the example in:
>
I do not agree.
> Yet, contrary to Varian's presentation, equilibrium there is not a
> Walrasian equilibrium. Furthermore, changes in tastes there change
> equilibria prices.
>
> Now, Mr. Weatherby has laughably said that the presentation in the
> PDF file is mistaken.
This was not written by me.
>Yet he cannot and will not point out exactly
> where my calculations are in error.
I have pointed it out many times. Your method of cost minimization is
mistaken. Ignoring the fact does not change it.
>Nor will he present a supposed
> alternative solution, despite having claimed my assumptions are
> too simple and were made for tractability.
>
I am already wasting enough time responding to this nonsense. I am not
wasting more time solving your model. I have my own research interest.
> > > "The position is entirely different for the classical economists
> > > where the independence of prices and the residual distributive
> > > variable from what are today described as demand conditions and
> > > consumer preferences constitutes a fundamental aspect of the
theory."
>
> > [ Confusion I don't feel like dealing with. ]
>
This is not my quotation. I do not know where you are pulling this from.
This is not my language. Are you saying your own posting was confused?
>
> Apparently Mr. Weatherby has yet to read the posts to which he is
> pretending to respond.
>
I have. Have you? This does not refute rather reinforce the claim.
" Only one production process is known for producing corn. This
process requires the following inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year:"
Which means consumer demands play a large part of how much corn is
available to make corn and steel in the current period. Surely you are not
saying consumers can eat the corn and plant it or use it in steel production
are you?
>
> TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
>
> 0.82816 Person-years
> 0.2 Tons steel
> 0.16889 Bushels corn
>
> Steel is also produced by this firm. Two processes are known for
> producing steel:
>
> TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
>
> Process Alpha Process Beta
>
> 0.19321 Person-Years 0.033594 Person-Years
> 0.35 Tons Steel 0.13329 Tons Steel
> 0.0095553 Bushels Corn 0.15590 Bushels Corn
>
Now imagine if consumer demands meant only .1 bushels of corn were left for
production. You are not saying this would not be determinate in choice of
technique. Are you? See the non-substitution theorem can not apply. Consumer
preferences matter. The relative amounts of corn available for production
and labor matter in this model. Consumer demands affect the availability of
corn in this model and therefore can affect technique!!!
> Apparently, inputs of corn and steel can be traded off in producing
> steel. The process that uses less corn and more steel, however, also
> requires a greater quantity of labor input.
>
Not under model. Did you read what you posted. The requirements for
making corn are,
> TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
>
> 0.82816 Person-years
> 0.2 Tons steel
> 0.16889 Bushels corn
>
There is only one combination of inputs for making corn which you also
posted in the beginning. This function does not allow for substitution. Do
you understand your model or are you just trying to snowball past critism?
>Both quantities are net of replacement of used
> up inputs, thereby allowing the economy to continue unchanged into
> the next year.
>
You do not have the dynamics to show that this will happen. This is an
assumption which helps to drive your results. In fact rather the economy
grows or shrinks depends on how much corn is eaten. In fact this model
closely resembles Solow without technological change or the classical grow
model. Higher levels of population eat more corn meaning less is available
for production. If population gets too big the economy shrinks. This is just
another form of presenting Malthus. Let me rephrase it should be, the
problem is you have not taken into account consumer demands and what affect
they have on corn to be used for the next year nor have you stated that
population is fixed. Also, if people find new consumption uses for corn,
preference changes, it will have the same effect as a change in population.
> In the above paragraph, the author contrasts two theories. One theory
> is supply and demand. The other is that of "the English classical
> economists up to Ricardo".
And as I argued before his interpertation of Ricardo is wrong. Ricardo
was not talking about unemployment rather something similar to Malthus. I do
believe this is a misinterpertation of Ricardo's work.
> The analytical basis for these quotes has been presented. Mr. Weatherby
> cannot understand it. He probably wouldn't understand any of the texts
> from which these quotes come. But nothing's stopping him from trying.
>
I am sure I could understand the text. I assume published authors
generally write a bit better than you. It is not a misunderstanding. The
only thing misunderstood here is on your part. It is a misunderstanding of
duality.
John
Robert Vienneau
Weatherby" <jjwea...@earthlink.net> wrote:
> Marx...either misunderstood or misrepresented Ricardo and Smith's
> theory...as Marshall pointed out.
Naturally, Mr. Weatherby adopts a position about a half century
out-of-date. Consider:
"Ricardo...regarded cost of production as dependent - not as
Marx asserted him to have done on the mere quantity of labour
used up in production, but - on the quality as well as the
quantity of labour; together with the amount of stored up
capital needed to aid labour, and the length of time during
which such aid was invoked."
-- Alfred Marshall, _Principles_
Both Ricardo and Marx discussed different qualities of labour.
The focus of much discussion on difficulties with Ricardo's value
theory has focused on the role of time. That is my focus in the
remainder of this note.
Marshall is definitely wrong here:
"And yet Robertus and Karl Marx claim Ricardo's authority
for the statement that the natural value of things consists
solely of the labour spent on them..."
-- Alfred Marshall, _Principles_
It was NOT Marx's contention that prices would tend towards labour
values. (See below for a quate from the first volume of Capital.)
Marshall is quite correct is stating that Ricardo considered
relative prices to be influenced by the time necessary for
production, not merely the quantities of labour required for
production:
"Suppose I employ twenty men at an expense of 1000 pounds for a
year in the production of a commodity, and at the end of the year
I employ twenty men again for another year, at a further expense of
1000 pounds in finishing or perfecting the same commodity, and that
I bring it to market at the end of two years, if profits be 10 per
cent., my commodity must sell for 2,310 pounds.; for I have employed
1000 pounds capital for one year, and 2,100 pounds capital for one
year more. Another man employs precisely the same quantity of labour,
but he employs it all in the first year; he employs forty men at an
expense of 2000 pounds, and at the end of the first year he sells it
with 10 per cent. profit, or for 2,200 pounds. Here then are two
commodities having precisely the same quantity of labour bestowed on
them, one of which sells for 2,310 pounds - the other for 2,200
pounds."
-- David Ricardo, _Principles_, Chapter I, Section IV
Marshall is mistaken in stating that Marx asserted Ricardo to have
regarded relative costs to have depended solely on the quantity
of labour used up in production:
"What [Ricardo] does in fact examine is this: supposing that
cost-prices differ from the values of commodities - and the
assumption of a general rate of profit presupposes this
difference - how in turn are these cost-prices (which are now, for
a change, called "relative values") themselves reciprocally modified
by the rise or fall in wages, taking also into account the varying
proportions of the organic component parts of capital? If Ricardo had
gone into this more deeply, he would have found that - owing to the
diversity in the organic composition of capital which first manifests
itself in the immediate production process as the difference between
variable and constant capital and is later enlarged by differences
arising from the circulation process - the mere existence of a general
rate of profit necessitates cost-prices that differ from values. He
would have found that, even if wages are assumed to remain constant,
the difference exists and therefore is quite independent of the rise
or fall in wages."
-- Karl Marx, _Theories of Surplus Value_, Part II, Chapter X,
SectionA.4.a
(Marx is using "cost-price" above to mean what he calls the price of
production in the third volume of _Capital_.)
Marx was aware that other classical economists had considered this
issue:
"Supposing that capitals of different degrees of durability are
employed: if a woolen and a silk manufacturer were each to employ
a capital of 2,000 pounds; and if the former were to employ
1,500 pounds in durable machines, and 500 pounds in wages and
materials; while the latter employed only 500 pounds in durable
machines, and 1,500 pounds in wages and materials...Supposing
that a tenth of these fixed capitals is annually consumed, and
that the rate of profit is ten per cent, then, as the results of
of the woollen manufacturer's capital of 2,000 pounds, must, to
give him this profit, be 2,200 pounds, and as the value of his
fixed capital has been reduced by the progress of production from
1,500 pounds to 1,350 pounds, the goods produced must sell for
850 pounds. And, in like manner, as the fixed capital of the silk
manufacturer is by the process of production reduced one tenth, or
from 500 pounds to 450 pounds, the silks produced must, in order
to yield him the customary rate of profit upon his whole capital
of 2,000 pounds, sell for 1,750 pounds...when capitals equal in
amount, but of different degrees of durability, are employed, the
articles produced, together with the residue of capital, in one
occupation, will be equal in exchangeable value to the things
produced, and the residue of capital, in another occupation."
-- Robert Torrens, _An Essay on the Production of Wealth_
(as quoted by Marx)
As with Ricardo, Torrens is comparing the prices of production of
two commodities. The annual outlay is a capital of 2000 pounds in
both cases. Thus, at profit of 10%, the worth of the output must
be 2,200 pounds, when evaluated at prices of production in both
cases. This output consists of wool or silk, as the case may be,
and the value of fixed capital, after subtracting the loss in
value due to wear and tear. (The treatment of fixed capital as a
kind of joint production was an analytical innovation of Torrens.
It can be separated from the assumption of radioactive depreciation
seen in the above passage.) The original fixed capital is worth
1,500 pounds in the case of wool. The fixed capital left as
output consists of 1,350 pounds, since "a tenth...is annually
consumed". Thus, the wool produced must be worth 850 pounds
(= 2,200 - 1,350).
In the case of silk, the original fixed capital is worth 500
pounds. After wear and tear, 450 pounds of fixed capital remains.
Thus, the silk produced by a capital of 2000 pounds must be
worth 1,750 pounds (= 2,200 - 450).
There is a theory that the value of output consists of the sum
of the value transferred by capital goods and the value added by
labor. The workers are not paid in wages all of this value added.
Suppose the ratio of the value added by labor to the value paid
out in wages were the same in the production of wool and silk.
Then this theory seems to be inconsistent with Torrens' example.
In both cases, the profits consist of 200 pounds. Yet only 500
pounds is annually spent on labor in producing wool, while 1,500
pounds is spent on labor in silk production.
Marx's comments reflect an understanding of this point:
"The merit of this passage does not consist in the fact that Torrens
here merely registers the phenomenon once again without explaining
it, but in the fact that he defines the difference by stating that
equal capitals set in motion unequal quantities of living labour,
though he immediately spoils it by declaring it to be a 'special'
case. If the value is equal to the labour worked up, embodied in a
commodity, then it is clear that - if the commodities are sold at
their value - the surplus-value contained in them can only be
equal to the unpaid, or surplus labour, which they contain. But
this surplus labour - given the same rate of exploitation of the
worker - cannot be equal in the case of capitals which put in
motion different quantities of immediate labour, whether it is the
immediate production process or the period of circulation which is
the cause of this difference. It is therefore to Torren's credit
that he expresses this. What does he conclude from it? That here
within capitalist production the law of value suddenly changes.
That is, that the law of value, which is abstracted from capitalist
production, contradicts capitalist phenomena. And what does he put
in its place? Absolutely nothing but the crude, thoughtless,
verbal expression of the phenomenon which has to be explained..."
-- Karl Marx, _Theories of Surplus Value_, Chapter XX, Section1.b
Notice that Marx thinks variations among industries in the ratio of
the value of capital goods to wages is the general case. No complete
theory of prices that doesn't apply when such variations exist can
claim general validity.
I don't know that the edition of the Theories of Surplus Value
published in Marshall's lifetime (in German) contained these passages.
But the recognition that cost prices are not determined solely by
the quantities of labour required for production is in the first
volume of Capital:
"From the forgoing investigation, the reader will see that this
statement only means that the formation of capital must be possible
even though the price and value of a commodity be the same; for its
formation cannot be attributed to any deviation of the one from the
other. If prices actually differ from values, we must, first of all,
reduce the former to the latter, in other words, treat the difference
as accidental in order that the phenomena may be observed in their
purity, and our observations not interfered with by disturbing
circumstances that have nothing to do with the process in question.
We know, moreover, that this reduction is no mere scientific process.
The continued oscillations in prices, their rising and falling,
compensate each other, and reduce themselves to an average price,
which is their hidden regulator. It forms the guiding star of the
merchant or the manufacturer in every undertaking that requires
time. He knows that when a long period of time is taken, commodities
are sold neither over nor under, but at their average price. If
therefore he thought about the matter at all, he would formulate
the problem of the formation of capital as follows: How can we
account for the origin of capital on the supposition that prices
are regulated by the average price, i.e., ultimately by the value
of the commodities. I say 'ultimately,' because average prices do
not directly coincide with the values of commodities, as Adam
Smith, Ricardo, and others believe."
-- Karl Marx, _Capital_, Volume 1, Chapter V
Here Marx is inconsistent about Ricardo's beliefs, as compared to
the more in-depth examination in Theories of Surplus Value. Of
course, Ricardo knew he did not have these issues fully worked
out; perhaps one can say Ricardo is himself inconsistent. (Marshall
recognizes that Ricardo "did not constantly repeat the interpretation
clauses in...the first chapter of his book".)
I distrust Marshall's claim of continuity in the development of
economic theory from classical to neoclassical economics. I conclude
with noting my view is not novel among contemporary scholars:
"Nowhere in the classics can Marshall's 'measureable motives'
concept be identified, and the real costs concept which Marshall
linked to 'waiting' is certainly not Ricardian. It is in the
treatment of waiting and the role of time that Marshall stretches
the interpretation of Ricardo the most. Ricardo's approach to
the dating of labour taking into account embodied labour and its
distribution over time determined relative values but bears little
resemblance to Marshall's waiting and costs and sacrifices...
...Time also plays a different role in Ricardo's system from that
Marshall assigned to it. For Ricardo, time reflected variations in
production conditions of different commodities. Little wonder that
Marshall criticized Ricardo for his carelessness in the treatment
of time."
-- Ray Petridis, "Marshall, Alfred as an Interpreter of the
Classical Economists". The Elgar Companion to Classical
Economics. 1998.
Robert Vienneau
Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-13C148....@news.dreamscape.com...
> > In article <YP9G8.1233$jA6....@newsread2.prod.itd.earthlink.net>,
> > Saying that the student who relies on Varian will be ill-equipped to
> > understand that passage and what follows does not say that the passage
> > contradicts Varian. Varian takes labor as numeraire and doesn't mention
> > the rate of profits.
> LOL. If you had followed Varians explanation you would find that
> maximizing profits is essential to solving the model.
Which does not say anthing explicit about the wage-rate of profit
relationship, or even about the RATE of profits.
> In fact each
> consumer's share of profits is included in the budget constraint. It is
> necessary to maximize profits under Varians approach. This comment shows
> that you did not read the chapter or more likely did not understand the
> approach. It was based on a paper published after 1960 in a mainstream
> journal so it is no surprise you refuse to understand it.
The above comment, of course, is ignorant. Debreu's book was published
in 1959. It builds on previously published work. Furthermore, I have
cited a lot of papers in mainstream journals published after 1960.
For example, P. Garegnani, RES, 1970. Once again, Mr. Weatherby is
talking about some alternative reality.
> >That has something to do with why I think the
> > student who relies on Varian will have a hard time with that passage.
> Well I suppose if you mean someone who knows how to do the problem
> right might disagree. Then yes.
The context was whether Varian would help the student understand a
passage from Garegnani. So I am not sure what "problem" Mr.
Weatherby is referring to. I certainly think somebody who knows
how to do Foley's problem sets would agree with me. So, per
usual, Mr. Weatherby is upside down.
By the way, Mas-Collel et. al. have a better treatment of the
non-substitution theorem. The student relying on their treatment
might still have a problem with Garegnani's discussion.
> > So he seems to think that the level of outputs
> > affects what is the cost-minimizing technique under the conditions
> > of the non-substitution theorem - that is, if we want to pretend
> > his passage has something to do with the text to which he is
> > pretending to respond.
> No you have it backwards again. The choice of technique affects the
> level of output. This effects revenue. It means simply that revenue is
> different under each technique. Not taking this into account, ie. only
> looking at which technique has a lower per unit cost, is a fatal mistake.
Mr. Weatherby doesn't know what he is talking about frontwards and
backwards. According to Mr. Weatherby - ignorant as usual - the
level of output affects revenue, and revenue must be taken into account
when determining the choice of technique. That is, Mr. Weatherby
is claiming, wrongly, that the level of outputs affects what is the
cost minimizing technique.
The context here was contrasting Varian's treatment of the
non-substitution theorem with a discussion of that theorem by
Garegnani.
> > So here Mr. Weatherby asserts the non-substitution theorem is
> > mistaken. He, of course, is wrong.
> No actually as was shown later. I do not even believe the
> non-substitution theorem applies to your set up.
So in the above, Mr. Weatherby is lying about his own text, or
he phrased his previous comments extremely poorly. Whether he,
in his continued ignorance, thinks the non-substitution theorem
does not apply to my example is irrelevant to this portion of
the discussion. Mr. Weatherby was asserting, without cogent
argument, of course, that the non-substitution theorem was
mistaken.
[>>>> "We saw how the classical economists could take the real wage ]
[>>>> (or, with Sraffa, the rate of profits) as given when approaching ]
[>>>> the determination of relative prices." ]
[>>> Again Smith and Ricardo have very important contributions. ]
[>>> However, this is not one of them that has lasted. ]
> > Arguments from ignorance and unpopularity are not really arguments.
> > Notice Mr. Weatherby is not actually saying Garegnani is mistaken.
> On the contrary I have argued that Garegnani has either misunderstood
> or
> misrepresented Ricardo and Smith's theory. Marx did the same thing as
> Marshall pointed out.
I dealt with some of Mr. Weatherby's ignorance in another post.
Notice that Mr. Weatherby does not present any reason whatsoever to
think that Garegnani is wrong in claiming that the classical economists
thought they could take the real wage as given in their price theory.
In fact, he hasn't even really asserted that Garegnani is wrong
about what the classical economists claimed ON THIS POINT.
> > I am NOT "muddling the issues". If anybody is, it would be Garegnani.
> Of whow you treat as a guru who is not to be questioned.
Mr. Weatherby is making crap up. I have no problem with informed
and intelligent criticisms of Garegnani.
> If you can not
> tell the sources you are quoting are muddled then how can anyone believe
> that you have not muddled the issues yourself when you cite these authors
> to support yourself.
The above is a statement exhibiting complete ignorance about
contemporary literature treating the structure of classical
economics. Perhaps Mr. Weatherby ought to figure out what
communities of economists Garegnani participates in.
Of course, he can continue the Orwellian posture of denying the
existence of whole communities of economists and the literature
that they have produced.
> > The fact is, the
> > non-substitution theorem, as presented in much literature, is
> > applicable to the example in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
> I do not agree.
Mr. Weatherby seems completely ignorant of how to present an
argument. Notice he neither states the conditions of the
non-substitution theorem, nor points out where the example
supposedly does not satisfy any of those conditions.
Somebody interested in or capable of an intelligent conversation
would develop some such point if they wanted to give readers
any reason whatsoever for agreeing with them.
> > Yet, contrary to Varian's presentation, equilibrium there is not a
> > Walrasian equilibrium. Furthermore, changes in tastes there change
> > equilibria prices.
> > Now, Mr. Weatherby has laughably said that the presentation in the
> > PDF file is mistaken.
> This was not written by me.
On 15 May, I said:
"Mr. Weatherby makes crap up. Then there's always this:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>"
He respond on 15 May:
"reposting the same URL does not make it any more correct."
> >Yet he cannot and will not point out exactly
> > where my calculations are in error.
> I have pointed it out many times. Your method of cost minimization is
> mistaken. Ignoring the fact does not change it.
Nope. I've stepped Mr. Weatherby through cost minimization in my
example several times in several different ways. He has deleted all
such explanations and URLs for such explanations with no comment
other than, at best, "Huh?"
He refuses to show how his ignorant comments apply to my example.
> >Nor will he present a supposed
> > alternative solution, despite having claimed my assumptions are
> > too simple and were made for tractability.
> I am already wasting enough time responding to this nonsense. I am
> not
> wasting more time solving your model. I have my own research interest.
Nobody told Mr. Weatherby he had to entertain an international
audience.
If he wanted to say something substantial, he is always free to
outline the solution to the following problems:
Foley's problem:
My problem:
> > > > "The position is entirely different for the classical economists
> > > > where the independence of prices and the residual distributive
> > > > variable from what are today described as demand conditions and
> > > > consumer preferences constitutes a fundamental aspect of the
> > > > theory."
> > > [ Confusion I don't feel like dealing with. ]
> This is not my quotation. I do not know where you are pulling this
> from.
> This is not my language. Are you saying your own posting was confused?
Nope. The passage in brackets is my editorial summary of a passage
of Mr. Weatherby's.
> > Apparently Mr. Weatherby has yet to read the posts to which he is
> > pretending to respond.
> I have. Have you? This does not refute rather reinforce the claim.
Mr. Weatherby's ignorant claim was that inputs of labor
and corn impose constraints, but inputs of steel don't.
> " Only one production process is known for producing corn. This
> process requires the following inputs to be available at the beginning
> of the year for each bushel corn produced and available at the end of
> the year:"
> Which means consumer demands play a large part of how much corn is
> available to make corn and steel in the current period. Surely you are
> not
> saying consumers can eat the corn and plant it or use it in steel
> production are you?
And the above does not address Mr. Weatherby's ignorant claim of
the lack of symmetry between corn and steel.
> >
> > TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
> >
> > 0.82816 Person-years
> > 0.2 Tons steel
> > 0.16889 Bushels corn
> >
> > Steel is also produced by this firm. Two processes are known for
> > producing steel:
> >
> > TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
> >
> > Process Alpha Process Beta
> >
> > 0.19321 Person-Years 0.033594 Person-Years
> > 0.35 Tons Steel 0.13329 Tons Steel
> > 0.0095553 Bushels Corn 0.15590 Bushels Corn
> Now imagine if consumer demands meant only .1 bushels of corn were left
> for
> production. You are not saying this would not be determinate in choice of
> technique. Are you?
The question is innumerate. As I have explained repeatedly in the
posts to which Mr. Weatherby is pretending to reply, the amount of
steel and corn at the start of the production period is found
endogeneously in this sort of model. If that endogeneous quantity
happened to be only 0.1 bushels of corn, yes, that would have no
affect at all on the choice of technique.
> See the non-substitution theorem can not apply.
Nope. Nobody who understands what is being discussed would think
Mr. Weatherby has produced any reason at all for thinking so.
> > Apparently, inputs of corn and steel can be traded off in producing
> > steel. The process that uses less corn and more steel, however, also
> > requires a greater quantity of labor input.
The above is about processes available for making STEEL. So Mr.
Weatherby's response is a complete non sequitur:
> Not under model. Did you read what you posted. The requirements for
> making corn are,
> > TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
> >
> > 0.82816 Person-years
> > 0.2 Tons steel
> > 0.16889 Bushels corn
> There is only one combination of inputs for making corn which you also
> posted in the beginning. This function does not allow for substitution.
> Do
> you understand your model or are you just trying to snowball past
> critism?
False dichotomy.
The question is based on Mr. Weatherby's lack of understanding of
the text he is pretending to read.
Anyway, I have showed how to extend my example to permit a choice
among two processes for producing corn.
[>> Notice corn, steel, and labor are all inputs into production. ]
[>> It is not the case that labor and corn are inputs into ]
[>> production, but steel isn't. There is an asymmetry here. ]
[>> Inputs of corn and steel are both produced in the previous ]
[>> year. In a sense, labor is not. ]
[>> Following the math I have previously outlined, one calculates ]
[>> for the alpha technique: ]
[>> [ I - A( alpha ) ]^(-1) = 1.54392 0.371533 ]
[>> 0.0177505 1.20748 ]
[>> and the vector: ]
[>> a0( alpha ) [ I - A( alpha ) ]^(-1) = [ 0.3130 1.072 ] ]
[>> Suppose the net (steady state) output is y1 tons steel and y2 ]
[>> bushels corn. Under the alpha technique... ]
[>> q1 = ( 1.54392 y1 + 0.371533 y2 ) tons steel ]
[>> q2 = ( 0.0177505 y1 + 1.20748 y2 ) bushels corn ]
[>> The required yearly input of labor is: ]
[>> L = ( 0.3130 y1 + 1.072 y2 ) person-years ]
[>>>> Third, steel and corn are treated symmetrically above. But ]
[>>>> both steel and corn are treated differently from labor. So ]
[>>>> when Mr. Weatherby says constraints are imposed on corn and ]
[>>>> labor, but not on steel, he, as usual, doesn't know what he ]
[>>>> is talking about. ]
[>>> You are referring to the amount of corn produced at the end ]
[>>> of the year. ]
[>> y1 is the amount of steel available at the end of a year in a ]
[>> stationary state. y2 is the amount of corn available at the ]
[>> end of a year in a stationary state. ]
> > Both quantities are net of replacement of used
> > up inputs, thereby allowing the economy to continue unchanged into
> > the next year.
> You do not have the dynamics to show that this will happen.
> [ Various complaints addressed in Sraffa3.pdf, insofar as they ]
> [ are correct - deleted. ]
From my original post:
------------------------------------------------------------------
I want to consider a couple of different levels at which this
firm can operate the corn-producing process and each steel-producing
process. First, suppose the corn-producing process is used to
produce 1.208 Bushels corn and the Alpha process is used to produce
0.3717 Tons steel. The quantity flows shown in Table 3 result.
TABLE 3: THE CORN-PRODUCING TECHNIQUE USING THE
ALPHA STEEL-PRODUCING PROCESS
0.07182 Person-Years 1.0000 Person-Years
0.1301 Tons Steel 0.2416 Tons Steel
0.003552 Bushels Corn 0.2040 Bushels Corn
0.3717 Tons Steel 1.208 Bushels Corn
When the firm operates these processes in parallel, it requires
a total of 0.208 Bushels corn as input. The output of the
corn-producing process can replace this input, leaving a net
output of one Bushel corn. Notice that the total inputs of
steel is 0.1301 + 0.2416 = 0.3717 Tons steel, which is exactly
replaced by the output of the Alpha process. So Table 3 shows
a technique in which 1.072 Person-Years labor is used to produce
a net output of one Bushel corn. The firm, when operating this
technique can produce any desired output of corn by scaling
both processes equally.
-----------------------------------------------------------------------
Suppose the steel and corn-producing processes are operated at the
levels shown. The above shows that production can continue unchanged
into the next year. The net output is 1 bushel corn. Inputs of
0.3717 (= 0.1301 + 0.3416) Tons steel and 0.208 (= 0.004 +
0.204) Bushel corn have been deducted from the gross outputs.
So what explains the gross ignorance of Mr. Weatherby's assertion?
Does he mean anything at all when he says "dynamics"?
> > In the above paragraph, the author contrasts two theories. One theory
> > is supply and demand. The other is that of "the English classical
> > economists up to Ricardo".
> And as I argued before his interpertation of Ricardo is wrong. [snip]
Irrelevant. My point was Mr. Weatherby's claim:
"The quotation you cite assumes that everyone is still using the
labor theory of value and not the modern idea of value proposed
by Debreu."
is crap. The quote I cited made no such assumption. In fact, it did
not even mention the labor theory of value.
> > The analytical basis for these quotes has been presented. Mr. Weatherby
> > cannot understand it. He probably wouldn't understand any of the texts
> > from which these quotes come. But nothing's stopping him from trying.
> I am sure I could understand the text. I assume published authors
> generally write a bit better than you...
Nothing is stopping Mr. Weatherby from trying to understand the
text from which these quotes are taken.
John J. Weatherby
> backwards. According to Mr. Weatherby - ignorant as usual - the
> level of output affects revenue, and revenue must be taken into account
> when determining the choice of technique. That is, Mr. Weatherby
> is claiming, wrongly, that the level of outputs affects what is the
> cost minimizing technique.
>
explains duality. As I have explained many times before the cost
minimization problem is done assume a profit maximizing level of output.
Your method is wrong because it does not take into account what that fixed
quantity is. Again if both techniques meant the same amount of corn was
produced this would be fine. However profit maximization will show that your
method is not the correct dual problem. You can refuse to believe this all
you want, it does not change the fact. The only way you can get around this
is to make a model where the amount of corn production is the same
regardless of technique.
> > > So here Mr. Weatherby asserts the non-substitution theorem is
> > > mistaken. He, of course, is wrong.
>
> > No actually as was shown later. I do not even believe the
> > non-substitution theorem applies to your set up.
>
> So in the above, Mr. Weatherby is lying about his own text, or
> he phrased his previous comments extremely poorly.
Neither it has been clear all along that I am arguing you are
misapplying the theorem.
> Notice that Mr. Weatherby does not present any reason whatsoever to
> think that Garegnani is wrong in claiming that the classical economists
> thought they could take the real wage as given in their price theory.
> In fact, he hasn't even really asserted that Garegnani is wrong
> about what the classical economists claimed ON THIS POINT.
>
The problem is that the assumption of a given real wage is not part of
standard theory. Again you try to apply this to what you call neo-classical
economics which is something that does not exist any longer.
> The above is a statement exhibiting complete ignorance about
> contemporary literature treating the structure of classical
> economics. Perhaps Mr. Weatherby ought to figure out what
> communities of economists Garegnani participates in.
>
I do not care what community you label anyone the questions are is the
work done right (publication does not automatically mean correctness), are
the interpertations correct, are the interpertations applicable, and more
specific are the results applicable to your model?
> Of course, he can continue the Orwellian posture of denying the
> existence of whole communities of economists and the literature
> that they have produced.
>
Oh the old conspiracy theory again.
> > I have pointed it out many times. Your method of cost minimization
is
> > mistaken. Ignoring the fact does not change it.
>
> Nope. I've stepped Mr. Weatherby through cost minimization in my
> example several times in several different ways. He has deleted all
> such explanations and URLs for such explanations with no comment
> other than, at best, "Huh?"
>
If trying to explain to what duality means is huh? then I am at loss to
even begin to ponder how to break your arrogance. Then of course Mr.
Veinneau has had a principles level class that used calculus, how could he
be mistaken on what theory actually says?
> He refuses to show how his ignorant comments apply to my example.
>
Arrogant? I think not. The argument is simple and stated over and over
again. That is you do not understand duality and that your cost minimization
is wrong. The only response to this has been reposting the same misguided
method, or in other words huh?.
> If he wanted to say something substantial, he is always free to
> outline the solution to the following problems:
>
I am not going to solve the problem the way you want it solved. I am not
going to use 2 century old methods to determine the rental rate on capital.
Especially since Romer has present a much better idea of what the price of a
new design should be and the Ramsey-Cass-Koopmans setup explains how
interest rates are set. Using an outdated method to show that modern theory
is mistaken is rather silly.
> Mr. Weatherby's ignorant claim was that inputs of labor
> and corn impose constraints, but inputs of steel don't.
>
No the claim was any constraint on labor will show you that the two
different techniques generate different output of final corn. This means
different revenues. The firm will compare profits on both methods and chose
the profit maximizing technique. If output were the same your method is
valid. However it is not. Just because per unit cost are lower under one
technique does mean that profits are higher. With any labor constraint you
lower cost technique will also mean lower revenue, less corn is produced.
This mean it is not clear from your example which technique is profit
maximizing. Again you cost minimizing method is mistaken because it does not
account for the difference in the fixed output. WHY CAN YOU NOT GET THIS
THROUGH YOUR HEAD? Read Silberg, Varian, or any other graduate micro
textbook. They will show you how duality works.
> > " Only one production process is known for producing corn. This
> > process requires the following inputs to be available at the beginning
> > of the year for each bushel corn produced and available at the end of
> > the year:"
>
> > Which means consumer demands play a large part of how much corn is
> > available to make corn and steel in the current period. Surely you are
> > not
> > saying consumers can eat the corn and plant it or use it in steel
> > production are you?
>
> And the above does not address Mr. Weatherby's ignorant claim of
> the lack of symmetry between corn and steel.
>
This addresses the fact that the nonsubstitution theorem simply can not
apply to a model that has corn as an input to production of corn and steel.
Consumer demands will affect how much corn is available for production. Very
low amounts of corn available for corn, consumer eat a lot or have low
discount rates, can rule out the beta process entirely, which means
techniques never switch and your claim that when wages rise more labor is
employed is mistaken. Simply the nonsubstition theorem can not apply there
are ranges where consumer demand will affect technique simply because there
will not be enough corn available to use the beta technique.
> The question is innumerate. As I have explained repeatedly in the
> posts to which Mr. Weatherby is pretending to reply, the amount of
> steel and corn at the start of the production period is found
> endogeneously in this sort of model.
I realize that. However the model is incomplete in that it does not
include any method of consumer demands. The level of population will affect
the amount of corn needed for subsistence. Consumer preferences will affect
how much corn is used for other products. These demands can several affect
the amount of corn available for production at any one period. How much corn
is allocated to more corn and steel production ultimately depends on the
amount of corn needed for subsistence, the amount of corn demanded above
subsistence, and the discount rate of consumers. Leaving this out is very
misleading. Even if you do consider utility, consider population growth and
levels will show that the nonsubsistion theory does not apply. In a model
like this leaving out population is like leaving capital out of the Solow
model.
John
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message news:rvien-
> > > > So here Mr. Weatherby asserts the non-substitution theorem is
> > > > mistaken. He, of course, is wrong.
> > > No actually as was shown later. I do not even believe the
> > > non-substitution theorem applies to your set up.
> > So in the above, Mr. Weatherby is lying about his own text, or
> > he phrased his previous comments extremely poorly.
> Neither it has been clear all along that I am arguing you are
> misapplying the theorem.
Mr. Weatherby is mistaken. He does not present an argument. For
example, he does not state the assumptions of the theorem and
point out where my example does not meet the assumptions. Instead,
he disputes the conclusions of the theorem, although not very well
there either.
"We saw how the classical economists could take the real wage
(or, with Sraffa, the rate of profits) as given when approaching
the determination of relative prices."
-- P. Garegnani
> > Notice that Mr. Weatherby does not present any reason whatsoever to
> > think that Garegnani is wrong in claiming that the classical economists
> > thought they could take the real wage as given in their price theory.
> > In fact, he hasn't even really asserted that Garegnani is wrong
> > about what the classical economists claimed ON THIS POINT.
> The problem is that the assumption of a given real wage is not part
> of standard theory...
The above reply is a complete non sequitur. The question on the table
is whether Garegnani correctly describes a particular aspect of classical
economics.
I don't see how Mr. Weatherby's agreement with Garegnani, Steedman,
and me, for example, is a problem.
"In marginal theory, the [non-substitution theorem] is a logical
relation of no direct relevance for distribution theory, since
the real wage is NOT given independently of demand conditions and
consumer tastes. In modern theory, therefore, the relevance of
the non-substitution theorem lies merely in making it clear that
consumer preferences can affect prices only to the extent to
which they affect distribution - which, of course, those preferences
do, because they underlie the demand functions for the factors
of production..."
-- P. Garernani
"Both classical and marginalist economists provided accounts of
the long-period (uniform rate of profit) theory of value and
distribution, but whereas a classical economist could take the
real wage as a datum for the purpose of such analysis (whatever
the implicit 'background' theory of wages might be), the
marginalist economist had to 'close the system' in some other
manner."
-- Ian Steedman (1998)
On 21 May, I said:
"The fact is, the non-substitution theorem, as presented in much
literature, is applicable to the example in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
Yet, contrary to Varian's presentation, equilibrium there is not a
Walrasian equilibrium. Furthermore, changes in tastes there change
equilibria prices...
Changes in tastes will, in traditional theory, change distribution,
e.g., either real wages or the rate of profits. So, according to
statements of the non-substitution theorem I prefer to Varian's,
prices can be different."
> > The above is a statement exhibiting complete ignorance about
> > contemporary literature treating the structure of classical
> > economics. Perhaps Mr. Weatherby ought to figure out what
> > communities of economists Garegnani participates in.
> I do not care what community you label anyone the questions are is
> the
> work done right (publication does not automatically mean correctness),
> are
> the interpertations correct, are the interpertations applicable, and more
> specific are the results applicable to your model?
The question on the table was about interpretations of classical
economics. Whether such interpretations are applicable to
present-day mathematical models is a different question.
I think, Samuel Hollander, for instance, would realize Mr. Weatherby's
comments were unargued and ignorant assertions. For example,
"Perhaps Garegnani should skip the hype. I suppose he has actually
picked up some textbooks and maybe read Smith or Ricardo..."
-- John J. Weatherby
> > Of course, he can continue the Orwellian posture of denying the
> > existence of whole communities of economists and the literature
> > that they have produced.
> Oh the old conspiracy theory again.
Just an observation about the ignorance Mr. Weatherby always displays.
> > > I have pointed it out many times. Your method of cost
> > > minimization is
> > > mistaken. Ignoring the fact does not change it.
Mr. Weatherby cannot do arithmetic. I can. That's what this thread
shows.
> > Nope. I've stepped Mr. Weatherby through cost minimization in my
> > example several times in several different ways. He has deleted all
> > such explanations and URLs for such explanations with no comment
> > other than, at best, "Huh?"
> If trying to explain to what duality means is huh? then I am at loss
> to
> even begin to ponder how to break your arrogance. [ Silliness deleted ]
> The argument is simple and stated over and
> over
> again. That is you do not understand duality and that your cost
> minimization
> is wrong. The only response to this has been reposting the same misguided
> method, or in other words huh?.
There we go. Mr. Weatherby refuses to show how his comments apply to
my example, e.g., by doing arithmetic.
Nor has Mr. Weatherby ever commented on, say, Figure A-1 and
the surrounding text in:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
> > If he wanted to say something substantial, he is always free to
> > outline the solution to the following problems:
> I am not going to solve the problem the way you want it solved.
Mr. Weatherby seems to be saying he is willing to solve these problems
in some other way. All the evidence on this thread seems to
say he is making a false statement.
> I am not
> going to use 2 century old methods to determine the rental rate on
> capital.
o The methods I use were (re)invented and justified more recently
o Euclidean geometry, arithmetic, etc. is not invalid just because
it is more than two centuries old.
That dogmatic Marxist Paul Samuelson seems kind of proud to be one
of a small band of contemporaries who have rediscovered the
wage-profit rate relation.
> Especially since Romer [blah, blah, blah ]... Ramsey-Cass-Koopmans
> setup [ blah, blah, blah ]
If Mr. Weatherby wants to say something substantial, he is always
free to outline the solution to the following problems:
Foley's problem:
My problem:
> > Mr. Weatherby's ignorant claim was that inputs of labor
> > and corn impose constraints, but inputs of steel don't.
> No
Mr. Weatherby makes false statements about his own text. He wrote:
"Steel is not constrained you do not start with a stock of it and is
a choice variable. I am simply imposing a constraint of labor and
corn."
"Let me explain why there is no constraint on steel."
Of course, one should always keep in mind Mr. Weatherby's extreme
infelicity with language.
> the claim was any constraint on labor will show you that the two
> different techniques generate different output of final corn. This means
> different revenues. The firm will compare profits on both methods and
> chose
> the profit maximizing technique.
Mr. Weatherby is mistaken. The firm will compare profits to costs
on all processes, not the techniques formed out of the processes.
(I have been using "process" (also known as "activity") and "technique"
consistently throughout.)
> If output were the same your method is
> valid. However it is not. Just because per unit cost are lower under one
> technique does mean that profits are higher. With any labor constraint
> you
> lower cost technique will also mean lower revenue, less corn is produced.
> This mean it is not clear from your example which technique is profit
> maximizing. Again you cost minimizing method is mistaken because it does
> not
> account for the difference in the fixed output. WHY CAN YOU NOT GET THIS
> THROUGH YOUR HEAD?
I understand completely. Mr. Weatherby doesn't know what he is
talking about. And he doesn't know how to formulate a valid
argument.
> Read Silberg, Varian, or any other graduate micro
> textbook. They will show you how duality works.
Not to mention Pasinetti.
Mas-Collel et. al. generalize the idea of a Leontief model to include
the possibility of M(l) elementary activities; l = 1, 2, ..., L - 1;
for a model with L commodities. Although they don't mention this,
their presentation works if M(l) is infinite.
I think they use "technique" to mean what I have been calling a
"process":
"A striking implication of the Leontief structure (constant returns,
no joint products, single primary factor) is that we can associate
with each good a SINGLE OPTIMAL TECHNIQUE (which could be a mixture
of several of the elementary techniques corresponding to that good).
What this means is that optimal techniques (one for each output)
supporting efficient production vectors can be chosen independently
of the particular output vector that is being produced (as long as
the net output of every producible good is positive). Thus, although
substitution is possible in principle, efficient production requires
no substitution of techniques as desired final consumption levels
change. This is the content of the celebrated NON-SUBSTITUTION
THEOREM (due to Samuelson 1951).
Proposition 5.AA.2: (THE NON-SUBSTITUTION THEOREM) Consider a
productive Leontief input-output model with L - 1 producible
goods and M( l ) >= 1 elementary activities for producible
good l = 1, 2, ..., L - 1. Then there exists L - 1 activities
(a(1), a(2), ..., a(L - 1)), with a(l) possibly a nonnegative
linear combination of the M( l ) elementary activities for
producing good l, such that ALL efficient production vectors
with y >> 0 can be generated with these L - 1 activities."
-- Mas-Collel et. al.
Here's how Varian puts it:
"...We will assume that there are n industries producing outputs
y(i), i = 1, ..., n. Each industry produces only one output-
no joint production is allowed. There is only one nonproduced
input to production, usually thought of as labor, denoted
by y(0). The prices of each of the n + 1 goods will be
denoted by w( 0 ), w( 1 ), ..., w( n)...
NONSUBSTITUTION THEOREM. Suppose there is only one non-produced
input to production, this input is indispensable to production,
there is no joint production, and the technology is constant
returns to scale. Let (x, y, w) be a Walrasian equilibrium
with y(i) > 0 for i = 0, 1, ..., n. Then [vector] w is the
unique solution to w(i) = ci(w), i = 1, 2, ..., n
...Since the equilibrium prices are independent of demand conditions,
equilibrium factor demands will be independent of demand conditions.
The level of output of the different goods may change, but the
METHOD of production will remain constant."
-- Varian (2nd edition)
It is interesting how different these two expositions are. Varian
misleadingly restricts the theorem to a Walrasian equilibrium.
He presents the theorem as about the uniqueness of prices, but
doesn't clarify the role of demand on the price of the unproduced
input. Mas-Collel puts the theorem in the setting of activity
analysis. Mas-Collel is clearer (in surrounding text) on the role of
produced inputs.
Neither mentions wage-profit rate relations. Neither mentions that
a higher wage can be associated with the adoption of a more labor-
intensive technique. Thus, talk of (non)substitution here is
misleading.
> [ Weatherby's unwitting rejection of the non-substitution theorem ]
> > As I have explained repeatedly in the
> > posts to which Mr. Weatherby is pretending to reply, the amount of
> > steel and corn at the start of the production period is found
> > endogeneously in this sort of model.
> I realize that. However the model is incomplete in that it does not
> include any method of consumer demands.
That's a feature, not a bug. This openness allows me to take the
wage as given and to consider the example as either a complete
economy or a vertically intergrated industry.
It also allows the model to be closed with various competing theories
of distribution. (If one takes the principle of substitution as
central to neoclassical economics, no closed model will be a
neoclassical theory - even one with intertemporal utility
maximizing.)
> The level of population will
> affect
> the amount of corn needed for subsistence. Consumer preferences will
> affect
> how much corn is used for other products. These demands can several
> affect
> the amount of corn available for production at any one period.
All of this is discussed in Section 2.4 of
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
(I'm no longer sure about Figure 8.)
John J. Weatherby
> The question on the table was about interpretations of classical
> economics. Whether such interpretations are applicable to
> present-day mathematical models is a different question.
>
However if you model is not correct it can not be said to disprove
classical economics.
> Mr. Weatherby cannot do arithmetic. I can. That's what this thread
> shows.
>
No it shows that
A. You do not understand the nonsubstitution theorem.
As Varian shows the nonsubstitution theorem shows that consumer demands
do affect technique. If the nonsubstitution applies. The output of corn is
determined solely by consumer demands. The choice of technique does not
affect this. Your model says something different in your own words you have
stated the amount of corn produced will be different depending on the
technique chosen. This is not the nonsubstition theorem.
B. In addition to your misunderstanding of the non-substitution you miss
understand duality. Again the problem flows from your misunderstanding of
the nonsubstitution theorem. If you had understood this correctly and it
applied to this it would not be an issue. Quantities of corn produced would
be the same regardless of technique chosen meaning your per unit cost
minimization would be correct.
However, you insist that the quantities of corn would be different
depending on which technique is chosen. If this is true your per unit cost
minimization is not equilavent to profit maximization. Cost minimization
assumes a fixed quantity, the profit maximizing quantity. Under your
assumption these profit maximizing quantities are different meaning
different revenues depending on technique used, they result in different
amounts of corn at the same price, steel is not traded and so the price of
steel only affects cost and not revenue. This means using per unit cost is
the wrong measurement.
Personally I believe the problem is in A. That is you have muddled the
nonsubstitution. You were in error to say that the choice of one of the
techniques meant less corn production in the current period. If the
nonsubstitution does apply the previous stated claim is wrong. If the claim
is correct then the criticism in B applies. So which is it? Have you muddled
the nonsubstition theorem or did you make a mistake in saying that choosing
technique alpha would result in a different amount of corn from choosing
technique. If the nonsubstition theorem applies this can not be true,
quantities will be determined solely by consumer demands.
> o The methods I use were (re)invented and justified >more recently
The problem is not the method it is the interpertation of r. This is
still a number you pull out of thin air and have no explanation of how you
came to it. What I was refering to is the term rate of profits is 2
centuries old and applied in this manner by the majority of mainstream
economist. This is a term that is common in neo-marxist literature in some
attempt to bring down something that the majority of economist do not refer
to.
> Mr. Weatherby is mistaken. The firm will compare profits to costs
> on all processes,
Excuse me but my reference to profits is revenue minus cost. I am not
sure how you are defining profits here but under my definition it makes no
since to compare profits to cost. Cost are accounted for in profits.
> "A striking implication of the Leontief structure (constant returns,
> no joint products, single primary factor) is that we can associate
> with each good a SINGLE OPTIMAL TECHNIQUE (which could be a mixture
> of several of the elementary techniques corresponding to that good).
> What this means is that optimal techniques (one for each output)
> supporting efficient production vectors can be chosen independently
> of the particular output vector that is being produced (as long as
> the net output of every producible good is positive).
This is backward to the argument. Again I am not arguing that quantities
effect technique. Your misguided statement was that technique affects
quantities. If you choose process alpha and produce X corn this gives a
different revenue than choosing process beta and producing Y corn. This
means that for the substitution theorm to work, the quantities of corn can
not be dependant on technique. If they are each technique has a different
revenue. Therefore the profit maximizing outputs will affect which technique
is chosen. You can not have this both ways.
>Thus, although
> substitution is possible in principle, efficient production requires
> no substitution of techniques as desired final consumption levels
> change. This is the content of the celebrated NON-SUBSTITUTION
> THEOREM (due to Samuelson 1951).
>
Exactly note that the book says consumption levels. The non-substitution
theorem says the choice of technique will have no effect on output and the
output has no effect on technique. However you insist in stating that your
choice technique affects output. This is why your cost minimization is wrong
and the nonsubstitution theorem does not apply to your example. If
quantities produced are different under each technique, quantities consumed
are also different. This is not the nonsubstitution theorem. If technique
affects output then the difference in output has to be accounted for when
doing cost minimization. This is quite different from saying that the
quantity demanded does not affect technique.
Let me explain think of this way. Take a profit function. Pi = P(C) *
C(L,S,C) - WL - rS - PC. Where Q is quantity, L is labor, and S is steel, C
is corn. Now lets assume two different production functions. Hold P(Q),
consumer demands, and assume that technique 1 gives you a different Q
produced than technique. Just for the sake of argument lets say that P(Q) is
a constant 10,000, like in your model. Now using technique 1 means that you
with the amount of labor and steel left over after steel production your
profit maximizing quantity is 1,000 and takes 100 L, 10 S, and 10 C.
Now assume choicing technique 2 means that profit maximizing quantities are
2,000 and it takes 50 labor, 10 S, and 20 corn. Assume that there is a wage
rate that means technique one is less costly. Will technique 1 be chosen?
Well that depends on if the revenue of 10,000 * 1,000 minus (100*W + r10 +
10,000*10) is more than 10,000 * 2,000 minus (50W + r10, + 10,000*C). It is
obvious that this will not always be case even if technique is less costly.
Now this argument is quite different from assuming that P(C) changes so
that more corn is demanded. In this case, since the price of corn does not
change, it simply means the quantities will rise and the cost are the same.
So will the choice of technique change? No. However this is quite different
from saying given a price or constant consumer demands, differences in
profit maximizing quantities under either technique has no effect on which
technique is chosen. In this case it does effect which technique is chosen
however, if consumer demands change and more quantity is produced under
either technique then this will not change the technique. These are 2
completely different arguments. This is what you do not understand about the
nonsubstitution theorem and why you example of labor increasing when real
wages increase may be wrong.
> Proposition 5.AA.2: (THE NON-SUBSTITUTION THEOREM) Consider a
> productive Leontief input-output model with L - 1 producible
> goods and M( l ) >= 1 elementary activities for producible
> good l = 1, 2, ..., L - 1. Then there exists L - 1 activities
> (a(1), a(2), ..., a(L - 1)), with a(l) possibly a nonnegative
> linear combination of the M( l ) elementary activities for
> producing good l, such that ALL efficient production vectors
> with y >> 0 can be generated with these L - 1 activities."
> -- Mas-Collel et. al.
>
Again I do not disagree with Mas-Collel as stated earlier the
nonsubstitution theorem is not problem. It is your misapplication of the
theorem. The theorem says consumer demands do not affect technique. The
point you miss is consumer demands. This is not saying that firms maximize
profits at a given price, given by consumer demands, that the profit
maximizing quantity will have no effect on the choice of technique. In this
case consumer demands are not determining quantities. In fact consumer
demands can not determine quantities in your model because they do not
exist. Therefore quantities are determined by profit maximization.
> ...Since the equilibrium prices are independent of demand conditions,
> equilibrium factor demands will be independent of demand conditions.
> The level of output of the different goods may change, but the
> METHOD of production will remain constant."
> -- Varian (2nd edition)
>
Again Varian states quantity demanded has no effect on methods not that
given a fixed price from consumer demands that a firm's choice of quantity
of production will not effect the method choosen. Again take the perfect
competition analogy. Lets assume the model is perfectly competitive.
Consumer demands will determine the quantity consumed in the market. Now
each firm takes price as given and can sell his entire profit maximizing
quantity on the market.
This means the choice of technique depends on what is profit maximizing
for the firm. Therefore the firm chooses a level of production for each
technique.
How does the firm choose. Well the firm looks at revenue resulting from
technique 1. He then subtracts cost. This gives profit. He compares that
profit to technique 2. Given that technique 1 and 2 have different profit
maximizing quantities it you can not assume technique 1 is chosen simply
because it cost less.
Now what happens if consumer demands double production. Under the
nonsubstition. The profit maximizing technique found previously does not
change. The firm will produce more with the same technique. The technique
found above is still profit maximizing. There just will be more goods
produced.
Can you see the difference. I have never argued that the second happening, a
change in consumer demands changing quantities affects the choice of
technique. The argument is that under your model cost minimization is not
equilavent to profit maximization and you have done the first wrong.
> It is interesting how different these two expositions are. Varian
> misleadingly restricts the theorem to a Walrasian equilibrium.
Both expositions say the exact same thing. If can not see this you have
bigger problems than I thought.
John
Robert Vienneau
J. Weatherby" <jjwea...@earthlink.net> wrote:
> "Robert Vienneau" <rv...@see.sig.com> wrote in message
> news:rvien-07FBBC....@news.dreamscape.com...
"We saw how the classical economists could take the real wage
(or, with Sraffa, the rate of profits) as given when approaching
the determination of relative prices."
-- P. Garegnani
> > The question on the table was about interpretations of classical
> > economics. Whether such interpretations are applicable to
> > present-day mathematical models is a different question.
> However if you model is not correct it can not be said to disprove
> classical economics.
This comment seems to be about some other thread in some alternative
universe.
What could possibly make Mr. Weatherby think I or Garegnani are
trying to disprove those aspects of classical economics described in
the quote from Garegani?
> > Mr. Weatherby cannot do arithmetic. I can. That's what this thread
> > shows.
> No it shows that
> A. You do not understand the nonsubstitution theorem.
> As Varian shows the nonsubstitution theorem shows that consumer
> demands do affect technique.
Exactly wrong. A technique in my example is specified by coefficients
of production for preferred processes. Consumer demands do not affect
these coefficients. This is what Varian says:
"...Since the equilibrium prices are independent of demand conditions,
equilibrium factor demands will be independent of demand conditions.
The level of output of the different goods may change, but the
METHOD of production will remain constant."
-- Varian (2nd edition)
But I prefer Mas-Collel's wording.
"A striking implication of the Leontief structure (constant returns,
no joint products, single primary factor) is that we can associate
with each good a SINGLE OPTIMAL [PROCESS] (which could be a mixture
of several of the elementary [processes] corresponding to that good).
What this means is that optimal [processes[ (one for each output)
supporting efficient production vectors can be chosen independently
of the particular output vector that is being produced (as long as
the net output of every producible good is positive). Thus, although
substitution is possible in principle, efficient production requires
no substitution of [processes] as desired final consumption levels
change. This is the content of the celebrated NON-SUBSTITUTION
THEOREM (due to Samuelson 1951).
Proposition 5.AA.2: (THE NON-SUBSTITUTION THEOREM) Consider a
productive Leontief input-output model with L - 1 producible
goods and M( l ) >= 1 elementary activities for producible
good l = 1, 2, ..., L - 1. Then there exists L - 1 activities
(a(1), a(2), ..., a(L - 1)), with a(l) possibly a nonnegative
linear combination of the M( l ) elementary activities for
producing good l, such that ALL efficient production vectors
with y >> 0 can be generated with these L - 1 activities."
-- Mas-Collel et. al.
My example is of a model with L = 3 goods. The L - 1 = 2
producible goods are steel and corn. The remaining good is
labor.
Suppose out of the M(1) = 2 activities for producing steel, one
elementary activity a( 1 ) = [ a01, a11, a21 ]' is cost-minimizing
at the specified real wage.
Suppose out of the M( 2 ) activities for producing corn, one elementary
activity a(2) = [ a02, a12, a22 ]' is cost-minimizing
at the specified real wage.
The following table illustrates these activities at a unit
level of production:
INPUTS STEEL INDUSTRY CORN INDUSTRY
Labor a01 Person-Years a02 Person Years
Steel a11 Tons a12 Tons
Corn a21 Bushels a22 Bushels
OUTPUTS 1 Ton Steel 1 Bushel Corn
These optimal processes "(one for each output)" are chosen
"independently of the particular output vector that is being produced."
What is the (net) output vector produced by these processes at the
unit level? The answer is obviously
y' = [ ( 1 - a11 - a12 ) Ton Steel, (1 - a21 - a22) Bushels Corn ]
Now suppose the steel industry produces [ ( 1 - a22 ) y1 + a12 y2 ]/d
Tons Steel, where
d = 1 - a11 - a22 + a11 a22 - a12 a21
Then the inputs and output for the optimal technique in the steel
industry look like so:
INPUTS STEEL INDUSTRY
Labor [ a01( 1 - a22 ) y1 + a01 a12 y2 ]/d Person-Years
Steel [ a11( 1 - a22 ) y1 + a11 a12 y2 ]/d Tons
Corn [ a21( 1 - a22 ) y1 + a12 a21 y2 ]/d Bushels
OUTPUTS [ ( 1 - a22 ) y1 + a12 y2 ]/d Tons Steel
And suppose the corn industry produces [ a21 y1 + ( 1 - a11 ) y2 ]/d
Bushels Corn. The inputs and outputs in the corn industry look like so:
INPUTS CORN INDUSTRY
Labor [ a02 a21 y1 + a02 ( 1 - a11 ) y2 ]/d Person-Years
Steel [ a12 a21 y1 + ( 1 - a11 ) a12 y2 ]/d Tons
Corn [ a21 a22 y1 + ( 1 - a11 ) a22 y2 ]/d Bushels
OUTPUTS [ a21 y1 + ( 1 - a11 ) y2 ]/d Bushels
If you subtract inputs from outputs - assuming you can add, which
Mr. Weatherby cannot - you will find that the (net) output of these
activities, operated at these levels, is y1 Tons Steel and y2 Bushels
Corn. In other words, "ALL efficient production vectors with y >> 0 can
be generated with these L - 1 activities."
> Your model says something different in your own words you
> have
> stated the amount of corn produced will be different depending on the
> technique chosen.
The above is simply untrue. I have never stated that, at a given wage,
the (net) amount of corn produced will be different depending on
the chosen technique.
Now let's turn to what makes a technique cost-minimizing.
> B. In addition to your misunderstanding of the non-substitution you miss
> understand duality. Again the problem flows from your misunderstanding of
> the nonsubstitution theorem. If you had understood this correctly and it
> applied to this it would not be an issue. Quantities of corn produced
> would
> be the same regardless of technique chosen meaning your per unit cost
> minimization would be correct.
> However, you insist that the quantities of corn would be different
> depending on which technique is chosen. If this is true your per unit
> cost
> minimization is not equilavent to profit maximization. Cost minimization
> assumes a fixed quantity, the profit maximizing quantity. Under your
> assumption these profit maximizing quantities are different meaning
> different revenues depending on technique used, they result in different
> amounts of corn at the same price, steel is not traded and so the price
> of
> steel only affects cost and not revenue. This means using per unit cost
> is
> the wrong measurement.
The above is all nonsense. Given a real wage, I look for a price of
steel, a process for producing steel, and a process for producing
corn such that:
o The costs of these processes does not exceed the revenues
obtained.
o A dollar invested in producing steel with the steel-producing
process(es) returns as much profit as a dollar invested in
producing corn with the corn-producing process(es).
o A dollar invested in one of the non-operated processes cannot
return extra profits.
That's what it means for the processes comprising a technique to
be efficient in this context. Which technique is efficient depends
on the wage.
Which technique is efficient does not depend on the level of operation
of the processes. That's what I say, that's what Varian says, and
that's what Mas-Collel says.
I go further and note that the efficient technique at a higher
wage, of two levels of the real wage, may be more labor-intensive
than the efficient technique at a lower wage. Thus, I agree with
Pasinetti that the so-called non-substitution theorem is misleadingly
named. Furthermore, this failure of the principle of substitution
to apply arises even when the assumptions of the so-called
non-substitution theorem are violated.
> Personally I believe the problem is in A.
> [ Nonsense deleted ]
Personally, I believe that Mr. Weatherby does not know what he is
talking about, as has been apparent for some time.
[>>> I am not ]
[>>> going to use 2 century old methods to determine the rental rate ]
[>>> on capital. ]
> > o The methods I use were (re)invented and justified >more recently
> The problem is not the method it is the interpertation of r.
Mr. Weatherby, once again, makes untrue statements about his own text.
It's like this. Suppose the inputs for producing, say, steel with
some steel-producing activity at some level are $1. And suppose the
revenues from selling the produced steel at this level are, say,
$1.50. I say the rate of profits is 50%.
> This is
> still a number you pull out of thin air and have no explanation of how
> you
> came to it.
Mr. Weatherby is, of course, free to write as much nonsense as he
likes.
From my first post on this thread:
-----------------------------------------------------------------
The price of corn is assumed constant at $10,000 per Bushel...
TABLE 5: COSTS, WAGE $1,338.8 PER PERSON-YEAR,
PRICE OF STEEL $6,013 PER TON
INDUSTRY PROCESS COST PROFITS
Corn 0.2*$6,013 + 0.16889*$10,000
+ 0.82816*$1,338.8 = $4,000 150%
Steel Alpha 0.35*$6,013 + 0.0095553*$10,000
+ 0.19321*$1,338.8 = $2,459
Steel Beta 0.13329*$6,013 + 0.15590*$10,000
+ 0.033594*$1,338.8 = $2,405 150%
------------------------------------------------------------------
Notice the rate of profits is calculated from numbers that have
been previously specified. And I have given several explanations
of how the price of steel is found, given the real wage. I did
it once again above with my explanation of what makes a technique
efficient.
If Mr. Weatherby wanted to say something substantial, he could
always attempt to explain the solution of these problems:
Foley's problem:
My problem:
Mr. Weatherby then went on with his usual illiteracy:
> What I was refering to is the term rate of profits is 2
> centuries old and applied in this manner by the majority of mainstream
> economist.
And his usual Orwellian red-baiting:
> This is a term that is common in neo-marxist literature in some
> attempt to bring down something that the majority of economist do not
> refer to.
BFD.
Mr. Weatherby has never and will never explain what he means by
"neo-marxist".
Let's see who uses terms like "rate of profit" or "rate of profits":
"(4) The rate of profit on capital has a horizontal trend,
apart from occasional violent changes associated with sharp
variations in effective demand."
-- Robert M. Solow, Growth Theory: An Exposition. 1970, p. 3.
"Measure as in Fig. 1 the rate of profit P/K on the horizontal
axis..."
-- James E. Meade, "The Outcome of the Pasinetti-Process:
A Note". Economic Journal. V. 76, March 1966.
Now it is true I think economists interested in price theory in
long run models should learn that the principle of substitution
does not apply there, in general.
If Mr. Weatherby thinks he should reject logic on grounds of
political correctness, he, of course, is free to do so. Of
course, serious scholars should thereby consider him a figure
of fun.
> [ More ignorance - deleted. ]
John J. Weatherby
> equilibrium factor demands will be independent of demand conditions.
> The level of output of the different goods may change, but the
> METHOD of production will remain constant."
> -- Varian (2nd edition)
>
profit maximizing decision is made. Not to ignore the fact that two
different techniques have 2 different processes. I think this is clearer in
Mas-Collel and Varian's third edition, that is assuming you have not left
something important out of this quotation.
> But I prefer Mas-Collel's wording.
>
> "A striking implication of the Leontief structure (constant returns,
> no joint products, single primary factor) is that we can associate
> with each good a SINGLE OPTIMAL [PROCESS] (which could be a mixture
> of several of the elementary [processes] >corresponding to that good).
There is no debate over a single process. The debate is how the single
optimal process is found. I argue you have done this wrong. In my argument
there still will be a single optimal process chosen regardless of consumer
demand. The problem is that you have used the proper method to find it.
> Thus, although
> substitution is possible in principle, efficient production requires
> no substitution of [processes] as desired final consumption levels
> change. This is the content of the celebrated NON-SUBSTITUTION
> THEOREM (due to Samuelson 1951).
>
Again note the pharse "requires no substitution as desired final
consumption levels change." I am not arguing that this is incorrect, only
that you were mistaken in your attempt to find the correct process. This has
nothing to do with consumption levels rather how you chose the profit
maximizing solution. You did not do cost minimization correctly. It is
dependent on the profit maximizing quantity which in your model depends on
the technique as you have stated.
>
> Suppose out of the M( 2 ) activities for producing corn, one elementary
> activity a(2) = [ a02, a12, a22 ]' is cost-minimizing
> at the specified real wage.
>
That is fine if you do cost minimization correctly. However you argue
the choice of activity affects the amount of production you have to take
this into account.
> INPUTS STEEL INDUSTRY CORN INDUSTRY
>
> Labor a01 Person-Years a02 Person Years
> Steel a11 Tons a12 Tons
> Corn a21 Bushels a22 Bushels
>
> OUTPUTS 1 Ton Steel 1 Bushel Corn
>
> These optimal processes "(one for each output)" are chosen
> "independently of the particular output vector that is being produced."
>
Not in your model if these two process lead to different amounts of
profit maximizing corn. Look at the example in Varian and Mas-Collel. The
quantity is independent of the process it is chosen solely by consumer
demands. You have argued that quantities in the current period will depend
on the technique chosen. This is a completely different story.
> The above is simply untrue. I have never stated that, at a given wage,
> the (net) amount of corn produced will be different depending on
> the chosen technique.
>
Yes you have I will have to find the exact quotation when I get back to
my other computer. This is the comment that has caused all the confusion.
Originally I had argued that with a labor constraint that given the nature
of the processes that quantity of corn could vary. In other words more labor
intensive techniques in steel would lead to less corn production or less
steel production. Your response was the quantities of corn will vary by
technique. I will find this and show this to you. If you were incorrect this
is fine and your method was ok. If you were correct in the statement then
the method is highly mistaken.
> The above is all nonsense. Given a real wage, I look for a price of
> steel, a process for producing steel, and a process for producing
> corn such that:
>
> o The costs of these processes does not exceed the revenues
> obtained.
>
Of which the revenues are off if the choice of technique in steel leads
to different amounts of corn production in the current period. This will
happen if labor is constrained. You can not use a process that will require
more labor for making steel and not expect to have less corn production or
less steel production, unless there is a high level of unemployment.
> Which technique is efficient does not depend on the level of operation
> of the processes. That's what I say, that's what Varian says, and
> that's what Mas-Collel says.
>
Only if the same quantities are produced regardless of the process. The
nonsubstitution theorem works both ways. Quantities do not influence
technique and technique does not influence quantities. Quantity is chosen
solely by consumer demands, therefore if the nonsubstitution theorem applies
technique can not affect quantity. The claim, which you denied making, that
the two techniques will produce different levels of corn production in the
same period means the nonsubstitution theorem does not apply.
> I go further and note that the efficient technique at a higher
> wage, of two levels of the real wage, may be more labor-intensive
> than the efficient technique at a lower wage. Thus, I agree with
> Pasinetti that the so-called non-substitution theorem is misleadingly
> named.
It is not misleading it refers to the effect of consumer demands only.
In a general equilibrium model the real wage is endogenous.
> Personally, I believe that Mr. Weatherby does not know what he is
> talking about, as has been apparent for some time.
>
On the contrary it is poorly written comments that you later deny or
simply retract without admitting the fact that have started this discussion.
Even if you do deny the claim, the claim is still valid. If all resources
are employed the two techniques will mean that the level of corn production
is different depending on the technique. With all labor employed you have to
decrease the quantity of steel or the quantity of corn produced if you
switch to a more labor intensive process. Therefore quantities will be
determined by technique and not solely consumer demands. This means although
consumer demands will not affect the technique, when profit maximizing or
cost minimizing you must take into the difference of production.
Again this does not state that the choice of technique is dependent on
consumer demands or quantity produced. The claim is exactly opposite that is
the quantity produced depends on the technique employed if all resources are
being used. This means your per unit cost evaluation is wrong.
> Notice the rate of profits is calculated from numbers that have
> been previously specified.
Really you call this explaining your method. I hardly think so.
> Mr. Weatherby has never and will never explain what he means by
> "neo-marxist".
>
Those are attempting to restructure Marxist's methods. There are many of
these who you cite. Just look at their webpages.
> Now it is true I think economists interested in price theory in
> long run models should learn that the principle of substitution
> does not apply there, in general.
>
I still have not seen any empirical evidence to support the
nonsubstitution. It is derived solely from a general equilibrium model that
is not used very much. There are much better long run models.
> If Mr. Weatherby thinks he should reject logic on grounds of
> political correctness, he, of course, is free to do so. Of
> course, serious scholars should thereby consider him a figure
> of fun.
>
I have not rejected anything on the basis of political correctness. Only
observed that many of the current researchers that you post in support of
your claims are Neo-Marxist. There is a strong pararel between Neo-Marxism
and your post. If think using the term is an insult that is your problem. I
do use the term with any since of political correctness or to say the
argument was wrong simply because it parallels a Neo-Marxist argument.
Furthermore, if you would show some logic rather muddled text and claims
that are made in one post and retracted in another I could refute it.
Instead you have answer the correct application of theory with huh?. It is
your own blind belief that economist are ignorant that will not let you see
the logic. Instead you continue to support your model by attacking a claim
that is the exact opposite of the claim I have made for the past 20 posts.
I also notice how you snipped a great deal showing how the choice of
technique affecting quantity was quite a different argument than quantities
affect technique.
John