Reminder: Wages, Employment Not Determined By Supply, Demand
Robert Vienneau
which means stubborn persistence in an error that has been
exposed."
-- Joan Robinson
1.0 INTRODUCTION
If you take a class on economics, your teacher might tell you that
wages and employment are determined by the demand and supply of
labor, abstracting from price and wage stickiness, rigidities,
information asymmetries, etc. Your teacher might tell you that the
demand function for labor is necessarily a declining function of
wages, given profit-maximizing firms and standard assumptions about
technology. And the teacher might say, incorrectly, that this theory
applies in both the short and long run. The teacher teaching this
incorrect theory might tell you that the labor-demand function is
more elastic in the long run and that those elements abstracted from
in the theory are often less important in the long-run.
Here is a simple set of questions, with postulated answers, that you
can ask that will expose this theory as the incoherent nonsense that
it is:
Q: When one draws a demand function for labor, D(w), are the workers
hired assumed to be employed in only one (non-vertically) integrated
industry, or is it possible that some hired workers might be
producing commodities different from others?
A: The latter. The demand for labor is the demand by firms across
industries.
Q: Can some of these commodities be consumption goods?
A: Sure.
Q: Can some of these commodities also be capital goods, that is,
produced goods used in the production of other goods?
A: Yes.
Q: Under the assumptions of perfect competition, would the firm
be profit-maximizing at each point on the labor demand curve?
A: Yes. That is how the function is derived.
Q: If the data under which the curve is derived remains unchanged
(e.g., technology) and the wage and prices for a given point
on the long run labor demand curve actually prevailed, would
there be forces within firms moving firms away from that point.
A: No.
Q: And does the labor demand function show that firms will not
want to hire more labor at a lower wage, all else constant.
A: Yes.
An economist giving those answers cannot explain the possibility
of the numerical example presented in this post. This example shows
a case in which higher wages are associated with firms choosing to
employ more workers per unit output produced. I have an Excel
spreadsheet that permits you to experiment with the numerical values
behind this model:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/ChoiceOfTechnique
.xls>
So, as good economists have long recognized, the theory I am attacking
is incorrect, as a matter of mathematics and logic.
For some reason, very few economists posting here will acknowledge
this simple truth. I once again give economists a chance to agree
with arithmetic.
2.0 DATA ON TECHNOLOGY
Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, iron, and (seed)
corn. All production processes in this example require a year to
complete. Two production processes are known for producing corn. These
processes require 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 TON CORN PRODUCED
Process A Process B
1 Person-Year 1 Person-Year
2 Tons Iron 1/2 Tons Iron
2/5 Bushels Corn 3/5 Bushels Corn
Apparently, inputs of iron and corn can be traded off in producing
corn outputs.
Iron is also produced by this firm. Two processes are known for
producing iron:
TABLE 2: INPUTS REQUIRED PER TON IRON PRODUCED
Process C Process D
1 Person-Year 275/464 Person-Years
1/10 Tons Iron 113/232 Tons Iron
1/40 Bushels Corn 0 Bushels Corn
Inputs of corn and iron can be traded off in producing iron. The
process that uses less iron and more corn, however, also requires
a greater quantity of labor input.
2.1 PRODUCTION FUNCTIONS
The data above allow for the specification of two well-behaved
production functions, one for corn and the other for iron. For
illustration, I outline how to construct the production function
for corn.
Let L be the person-years of labor, Q1 be tons iron, and Q2 be
bushels corn available for inputs for corn-production during the
production period (a year). Let X1 be the bushels corn produced
with Process A, and X2 be the bushels corn produced with Process B.
The production function for corn is the solution of an optimization
problem in which as much corn as possible is produced from the
given inputs. Accordingly, the production function for corn is
found as the solution to the Linear Program in Display 1:
Max X = X1 + X2
X1 + X2 <= L
2*X1 + (1/2)*X2 <= Q1 (1)
(2/5)*X1 + (3/5)*X2 <= Q2
X1 >= 0, X2 >= 0
Let f(L, Q1, Q2) be the solution of this LP, that is, the production
function for corn. (This production function is not Leontief.) The
production functions constructed in this manner exhibit properties
typically assumed in neoclassical economics. In particular, they
exhibit Constant Returns to Scale, and the marginal product, for
each input, is a non-increasing step function. The production
functions are differentiable almost everywhere.
The point of this example, that sometimes a vertically integrated
firm will want to hire more labor per unit output at higher wages,
is compatible with the existence of many more processes for producing
each commodity. As more processes are used to construct the production
functions, the closer they come to smooth, continuously-differentiable
production functions. The point of this example seems to be compatible
with smooth production functions. It also does not depend on the
circular nature of production in the example, in which corn is used
to produce more corn.
2.2 TECHNIQUES
A technique consists of a process for producing iron and a process
for producing corn. Thus, there are four techniques in this example.
They are defined in Table 3.
TABLE 3: TECHNIQUES AND PROCESSES
Technique Processes
Alpha A, C
Beta A, D
Gamma B, C
Delta B, D
3.0 QUANTITY FLOWS
I want to consider a couple of different levels at which this
firm can operate the processes comprising the techniques. First,
suppose Process A is used to produce 1 41/49 Bushels corn, and
Process C is used to produce 4 4/49 Tons iron. The quantity flows
shown in Table 4 result.
TABLE 4: THE ALPHA TECHNIQUE PRODUCING CORN NET
INPUTS Process C Process A
Labor 4 4/49 Person-Years 1 41/49 Person-Years
Iron 20/49 Tons Iron 3 33/49 Tons Iron
Corn 5/49 Bushels Corn 36/49 Bushels Corn
OUTPUTS 4 4/49 Tons Iron 1 41/49 Bushels Corn
LABOR-INTENSITY: 5 45/49 Person-Years Per Bushel
When the firm operates these processes in parallel, it requires
a total of 41/49 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
iron are 20/49 + 3 33/49 = 4 4/49 Tons iron, which is exactly
replaced by the output of Process C. So Table 4 shows a technique
in which 5 45/49 Person-Years labor are 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.
Table 5 shows the application of the same sort of arithmetic to
the Beta technique. The labor-intensity of the Beta technique is
listed.
TABLE 5: THE BETA TECHNIQUE PRODUCING CORN NET
INPUTS Process D Process A
Labor 3 304/357 Person-Years 1 2/3 Person-Years
Iron 3 59/357 Tons Iron 3 1/3 Tons Iron
Corn 0 Bushels Corn 2/3 Bushel Corn
OUTPUTS 6 178/357 Tons Iron 1 2/3 Bushel Corn
LABOR-INTENSITY: 5 185/357 Person-Years Per Bushel
Neither the Gamma nor the Delta technique are profit-maximizing
for the prices considered below.
+------------------------------------------+
| THE FIRM |
| |
| Inventory <--------------------------+ |
| | | |
Labor | | Steel+Corn+Labor -> Steel -->+ |
Market | \|/ /|\ /|\ |
------->+-------------+ | | Corn
(wage | \|/ | | Market
given) | Steel+Corn+Labor -> Corn --->+------->
| | (price
+------------------------------------------+ given)
FIGURE 1: A VERTICALLY INTEGRATED FIRM
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 iron,
corn, and labor are charged at the start of the year. Corn is
the numeraire; its price is unity throughout. Two different
levels of wages are considered.
4.1 PRICES WITH LOW WAGE
Accordingly, assume wages are initially 3/2780 Bushels per
Person-Year. By assumption, the firm neither buys nor sells iron on
the market. The firm produces iron solely for its own use. Still,
the firm must enter a price of iron on its books. I assume an
initial price of 55/1112 Bushels per Ton.
Table 6 shows accounting with these prices. The column labeled
"cost" shows the cost of the inputs needed to produce one unit
output, a bushel corn or a ton iron, depending on the process.
Accounting profits for a unit output are the difference between
the price of a unit output and this cost. The rate of (accounting)
profits, shown in the last column, is the ratio of accounting
profits to the cost. The rate of profits is independent of
the scale at which each process is operated.
TABLE 6: COSTS, WAGE 3/2780 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 55/1112 BUSHELS PER TON
INDUSTRY PROCESS COST PROFITS
Corn A 2*(55/1112) + (2/5)*1
+ 1*(3/2780) = 1/2 100%
Corn B (1/2)*(55/1112) + (3/5)*1
+ 1*(3/2780) = 6959/11120 60%
Iron C (1/10)*(55/1112) + (1/40)*1
+ 1*(3/2780) = 69/2224 59%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(3/2780) = 55/2224 100%
These prices are compatible with the use of the Beta technique
to produce a net output of corn. The Beta technique specifies that
Process A be used to produce corn and process D be used to produce
iron. Notice that Process B is more expensive than Process A, and
that process C is more expensive than Process D. These prices do
not provide signals to the firm that processes outside the Beta
technique should be adopted. The vertically-integrated firm is
making a rate of profit of 100% in producing corn with the Beta
technique. The same rate of profits are earned in producing corn
and in reproducing the used-up iron by an iron-producing process.
4.2 ONE SET OF PRICES WITH HIGHER WAGE
Suppose this firm faces a wage more than 20 times higher, namely
109/4040 Bushels per Person-Year. Consider what happens if the firm
doesn't revalue the price of iron on its books. Table 7 shows this
case. Since labor enters into each process, the rate of profits
has declined for all processes. The ratio of labor to the costs of
the other inputs is not invariant across processes. Thus, the
rate of profits has declined more in some processes than in
others. Notice especially, than the rate of profits is no longer
the same in the processes, A and D, that comprise the Beta
technique.
TABLE 7: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 55/1112 BUSHELS PER TON
INDUSTRY PROCESS COST PROFITS
Corn A 2*(55/1112) + (2/5)*1
+ 1*(109/4040) = 0.5259 90.1%
Corn B (1/2)*(55/1112) + (3/5)*1
+ 1*(109/4040) = 0.6517 53.4%
Iron C (1/10)*(55/1112) + (1/40)*1
+ 1*(109/4040) = 0.05693 -13.1%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(109/4040) = 0.04008 23.4%
This accounting data does not reveal the firm's rate of return
in operating the Beta technique. The firm cannot be simultaneously
making both 23% and 90% in operating that technique. Furthermore,
this data provides a signal to the firm to withdraw from iron
production and make only corn. So this data says that something
must change.
4.3 ANOTHER SET OF PRICES
Perhaps all that is needed is to re-evaluate iron on the
firm's books. Higher wages have made iron more valuable. Table
8 shows costs and the rate of profits when iron is
evaluated at an accounting price of 0.106 Bushels per Ton.
TABLE 8: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 0.10569123726 BUSHELS PER TON
INDUSTRY PROCESS COST PROFITS
Corn A 2*(0.106) + (2/5)*1
+ 1*(109/4040) = 0.6384 56.65%
Corn B (1/2)*(0.106) + (3/5)*1
+ 1*(109/4040) = 0.6798 47.10%
Iron C (1/10)*(0.106) + (1/40)*1
+ 1*(109/4040) = 0.06255 68.97%
Iron D (113/232)*(0.106) + 0
+ (275/464)*(109/4040) = 0.06747 56.65%
This revaluation of iron reveals that the firm makes a rate
of profits of 57% in operating the Beta technique. The firm makes
the same rate of profits in producing corn and in producing its
input of iron. But the manager of the iron-producing process would
soon notice that the cost of operating process C is cheaper.
4.4 FINAL EQUILIBRIUM PRICES
So the firm would ultimately switch to using process C
to produce iron. The price of iron the firm would enter on its
books would fall somewhat. Table 9 shows the accounting with a
price of iron of 10/101 Bushels per Ton. The firm has adopted
the cheapest process for producing iron, and the rate of profits
is the same in both corn-production and iron-production. The
accounting for this vertically-integrated firm is internally
consistent.
TABLE 9: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 10/101 BUSHELS PER TON
INDUSTRY PROCESS COST PROFITS
Corn A 2*(10/101) + (2/5)*1
+ 1*(109/4040) = 5/8 60%
Corn B (1/2)*(10/101) + (3/5)*1
+ 1*(109/4040) = 2553/4040 58%
Iron C (1/10)*(10/101) + (1/40)*1
+ 1*(109/4040) = 25/404 60%
Iron D (113/232)*(10/101) + 0
+ (275/464)*(109/4040) = 24,075/374,912
54%
5.0 CONCLUSIONS
Table 10 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 10: PROFIT-MAXIMIZING FIRM ADOPTS MORE LABOR-INTENSIVE
TECHNIQUE AT HIGHER WAGE
LABOR-INTENSITY OF
WAGE CORN-PRODUCING TECHNIQUE
3/2780 Bushels Per Person-Year 5 185/357 Person-Years Per Bushel
109/4040 Bushels Per Person-Year 5 45/49 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.
APPENDIX A: A FORMAL MODEL
Let
Xa = Bushels corn produced (gross) by process A
Xb = Bushels corn produced by process B
Xc = Tons iron produced by process C
Xd = Tons iron produced by process D
p = the accounting price of iron (corn is numeraire)
w = wage
r = rate of (accounting) profits
Q1 = Tons iron in firm's inventory at start of period
Q2 = Bushels corn in firm's inventory at start of period
The profit-maximizing firm solves the following program:
Given p, w, Q1, and Q2
Choose Xa, Xb, Xc, and Xd
To Maximize (1 - w - 2 p - (2/5)) Xa
+ (1 - w - (1/2) p - (3/5)) Xb
+ (p - w - (1/10) p - (1/40)) Xc
+ (p - (275/464) w - (113/232) p) Xd
Such that
(w + 2 p + (2/5)) Xa
+ (w + (1/2) p + (3/5)) Xb
+ (w + (1/10) p + (1/40)) Xc
+ ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
Xa, Xb, Xc, Xd >= 0
The dual Linear Program is:
Given p, w, Q1, and Q2
Choose r
To Minimize (Q1 p + Q2) r
Such That
(w + 2 p + (2/5)) r >= 1 - w - 2 p - (2/5)
(w + (1/2) p + (3/5)) r >= 1 - w - (1/2) p - (3/5)
(w + (1/10) p + (1/40)) r >= p - w - (1/10) p - (1/40)
((275/464) w + (113/232) p) r >= p - (275/464) w - (113/232) p
r >= 0
Or:
Given p, w, Q1, and Q2
Choose r
To Minimize (Q1 p + Q2) r
Such That
(w + 2 p + (2/5))(1 + r) >= 1
(w + (1/2) p + (3/5))(1 + r) >= 1
(w + (1/10) p + (1/40))(1 + r) >= p
((275/464) w + (113/232) p)(1 + r) >= p
r >= 0
If a constraint in the dual is met with inequality in the solution, the
corresponding process in the primal will be operated at a level of zero.
For firms to continue production unaltered from period to period, both
corn and iron must be produced each period. For corn to be produced,
either the first or the second constraint in the dual must be met with
equality. Likewise, for iron to be produced, the third or the fourth
constraint in the dual must be met with equality. Hence, for the
analyzed firms to be in equilibrium, the vertically-integrated industry
must be on the so-called factor-price frontier for that industry.
Nothing guarantees that the firms will be able to sell their output
at any given location on the factor-price frontier. Whether prices that
allow firms to be in equilibrium are realized is a question that is
not addressed by this formal model.
--
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
Robert Vienneau
Perhaps no economist who has read it feels able to adequately
defend textbook teaching.
Or perhaps all economists who have read it see that I, echoing the
literature, have shown that tradional intro and intermediate
teaching in economics is crap. But none have felt courageous
enough to say so.
I can understand both attitudes.
jonah thomas
> Notice I have received no response to this thread.
> Perhaps no economist who has read it feels able to adequately
> defend textbook teaching.
> Or perhaps all economists who have read it see that I, echoing the
> literature, have shown that tradional intro and intermediate
> teaching in economics is crap. But none have felt courageous
> enough to say so.
> I can understand both attitudes.
Compare this to physics. Intro and intermediate physics teaching
isn't crap. But it's special cases at best. An intermediate-level
physics student is in no shape to understand at all what's going on
with the work of the leading researchers. He might think he has a
better idea what's going on than a complete layman, and in a
qualitative sense he might. But likely he'll have a bunch of
misunderstandings that leave him even worse off -- he thinks he
understands much more than he actually does.
Beginning physics students get some fundamental useful ideas. Like,
there's the idea that some things are conserved, and if you measure
and they're disappearing then you should look for where they went or
what they turned into.
Maybe beginning econ students get some similar useful ideas. There's
the idea that things tend toward some sort of equilibrium, and that
tendency can be predicted, that even if you can't measure quite where
you are or how fast it's changing you can at least estimate to better
than random guess which direction you're heading.
It would be good for the world if we found better ways to teach
physics and economics. But that isn't particularly what economists or
physicists get rewarded for.
Robert Vienneau
<j2th...@cavtel.net> wrote:
[ snip ]
Notice I received no substantial on-topic response on this thread.
Perhaps no economist who has read this thread feels able to adequately
defend textbook teaching.
Or perhaps all economists who have read it see that I, echoing the
literature, have shown that tradional intro and intermediate
teaching in economics is crap. But none have felt courageous
enough to say so.
I can understand both attitudes.
--
jonah thomas
> jonah thomas <j2th...@cavtel.net> wrote:
> [ snip ]
> Notice I received no substantial on-topic response on this thread.
;)
Thomas Blankenhorn
> Notice I have received no response to this thread.
>
> Perhaps no economist who has read it feels able to adequately
> defend textbook teaching.
>
> Or perhaps all economists who have read it see that I, echoing the
> literature, have shown that tradional intro and intermediate
> teaching in economics is crap. But none have felt courageous
> enough to say so.
Or perhaps the premise of your accusation against mainstream economics
is false, and you never bothered to give it a reality check. To the
best of my knowledge, the best-selling college textbook in economics
is Samuelson/Nordhaus, as it has been for 50 years. They explicitly
discuss backward bending supply curves in the labor market.
(Samuelson, Nordhaus: _Economics_, 16th edition, Chapter 12:
"Determination of factor prices by supply and demand" -- note the two
graphs on page 219, both of which show backward-bending labor supply
curves.)
On the Web, one of the most prominent resources is David Friedman's
textbook _Price Theory_. It, too, mentions the backward-bending supply
curve for labor in several chapters. In particular, it is quite
prominently discussed in Chapter 5, in a section titled "Income
effects in production and the backward-bending supply curve for
labor". How could you miss it?
> I can understand both attitudes.
Quite frankly, I don't understand the attitude that caused you to
voice such utterly incorrect accusations. With just 20 minutes of
research, you could have avoided making a fool of yourself in front of
the whole Usenet population. Why didn't you?
Puzzled
-- Thomas
Robert Vienneau
Thomas.Bl...@gmx.net (Thomas Blankenhorn) wrote:
> Or perhaps the premise of your accusation against mainstream economics
> is false, and you never bothered to give it a reality check. To the
> best of my knowledge, the best-selling college textbook in economics
> is Samuelson/Nordhaus, as it has been for 50 years. They explicitly
> discuss backward bending supply curves in the labor market.
I had nothing to say about backward-bending labor supply curves. I
am quite aware of them. For example, J. R. Hicks discusses them
in Value and Capital, an important work in forming post-war
mainstream Anglo-American economics.
Here was my argument, again:
1.0 INTRODUCTION
A: Sure.
A: Yes.
A: No.
A: Yes.
2.0 DATA ON TECHNOLOGY
Process A Process B
Process C Process D
2.1 PRODUCTION FUNCTIONS
2.2 TECHNIQUES
Technique Processes
3.0 QUANTITY FLOWS
4.0 PRICES
INDUSTRY PROCESS COST PROFITS
INDUSTRY PROCESS COST PROFITS
INDUSTRY PROCESS COST PROFITS
4.4 FINAL EQUILIBRIUM PRICES
INDUSTRY PROCESS COST PROFITS
5.0 CONCLUSIONS
Or:
--
Thomas Blankenhorn
Fool, because I misunderstood you to be saying that the supply curve
for labor necessarily slopes upward, when you were really saying that
the demand curve for labor necessarily slopes downward. So I
definitely owe you an apology for my snide remarks.
Nevertheless, mainstream economist's do have a solution to the
challenge you posed in the following lines:
> An economist giving those answers cannot explain the possibility
> of the numerical example presented in this post. This example
> shows a case in which higher wages are associated with firms
> choosing to employ more workers per unit output produced.
The solution is that while the demand curve for labor is "well
behaved", the supply curve is not. Labor supply curves can slope
backward, and when they do, rising wages can increase employment. If
you have read a fair number of introductory level college textbooks,
you must have come across these backward bending supply curve. You
neglected to mention them in your analysis, and this lead you to
condemn mainstream economists for a failure that wasn't theirs.
And that's why I think I only made a semi-fool out of myself. Feel
free to return the snideness of my remarks anyway ;-)
-- Thomas
Thomas Blankenhorn
I am not an economist, let alone a mainstream economist, but let me
play one in this thread anyway. Having discovered my earlier
misunderstanding, I read your initial post again, this time with more
attention. I now suspect that the weird outcome produced by your
simulation depends on (at least) one of two oddities you've assumed
into your model. I would challenge you to reproduce your outcome with
these oddities removed. My prediction is you can't do it.
Oddity #1: There's no supply curve for labor in your model.
If I understand you correctly, you assume that labor comes at a fixed
wage, and that the company can recruit any quantity it wants at that
wage. In the real world, workers can respond to prices by adjusting
their supply of labor. I would predict that you can't reproduce the
weirdness of your simulation with an upward-sloping labor supply
curve, as measured in wheat and steel. You might be able to reproduce
it if you allow the curve to bend backward though -- as predicted by
mainstream economics.
Oddity #2: Your economy can't run multiple processes simultaneously
In your setup, there's only one firm. It has the choice of running one
out of four processes, but it doesn't have the choice of running a
combination of processes. In any real (free) economy, you have a
competition between processes, all of which are employed by some
company at any given time. To account for this, let me suggest the
following experiment:
Instead of having one firm, run a simulation with 100 firms. For
initialization, randomly assign one of your four processes to each
company. Then iterate. In each iteration step, make a random firm
switch to the process that maximizes its profit, leaving the other 99
companies unchanged. Mainstream economics predicts that things
converge towards a distribution of processes at which all factor
prices reflect their marginal productivity. Do they?
Curious
-- Thomas
Christopher Auld
>I am not an economist, let alone a mainstream economist, but let me
>play one in this thread anyway. Having discovered my earlier
>misunderstanding, I read your initial post again, this time with more
>attention. I now suspect that the weird outcome produced by your
>simulation depends on (at least) one of two oddities you've assumed
>into your model.
Mr. Vienneau is sci.econ's most notorious kook. He didn't
get an answer to this post not becuase no one can address
it but rather because it's the zillionth time he's spammed
it, he never understands or addresses counterarguments, and
he's unbearably obnoxious. This particular bit o' spam is
riddled with mathematical and conceptual errors; factor
demand curves cannot slope up.
--
Chris Auld
Department of Economics
University of Calgary
au...@ucalgary.ca
Jeremy Boden
Vienneau <rv...@see.sig.com> writes
...
> Accordingly, assume wages are initially 3/2780 Bushels per
>Person-Year. By assumption, the firm neither buys nor sells iron on
>the market. The firm produces iron solely for its own use. Still,
>the firm must enter a price of iron on its books. I assume an
>initial price of 55/1112 Bushels per Ton.
Surely this is some kind of joke?
--
Jeremy Boden
David Lloyd-Jones
>
> Mr. Vienneau is sci.econ's most notorious kook.
Takes one to know one, Chris.
At least Robert has never been caught doctoring message quotes to make
them say the opposite of their original meaning.
-dlj.
ro...@telus.net
Yes.
-- Roy L
David Lloyd-Jones
Look who's talking.
-dlj.
susupply
"Jeremy Boden" <jer...@jboden.demon.co.uk> wrote in message
news:4RIkO1BZ...@jboden.demon.co.uk...
One that everyone but Robert is in on.
David Lloyd-Jones
> "Jeremy Boden" <jer...@jboden.demon.co.uk> wrote in message
> news:4RIkO1BZ...@jboden.demon.co.uk...
>>
>>> Accordingly, assume wages are initially 3/2780 Bushels per
>>>Person-Year. By assumption, the firm neither buys nor sells iron on
>>>the market. The firm produces iron solely for its own use. Still,
>>>the firm must enter a price of iron on its books. I assume an
>>>initial price of 55/1112 Bushels per Ton.
>>....
>>Surely this is some kind of joke?
>
> One that everyone but Robert is in on.
Patrick & Jeremy,
I think you're roughly half or 60% right. Robert's slightly manic model
building is more than a little odd.
On the other hand it's a very peculiar kind of joke. Robert has spent
roughly the past eight years educating himself in a very orthodox way in
very orthodox economics, and he's done a throroughly competent job of it.
There was a time, a couple of years ago, when a pompous and ordinary soi
disant "professor" like Chris Auld could make fun of Robert if they
wanted to. That's no longer the case. Robert has passed the pack and
Chris ends up with mud on his face every time he tries it these days.
One aspect of the humor is that Robert is playing a very ordinary
economics game: he is building artificial models to prove artificial
points. He has shown, with rather too straight a face, imho, that with
sufficiently contrived assumptions you can disprove any of the rules
that apply to the conomics of the real world, where such assumptions
don't operate.
This always has been a part of economics education -- though not usually
with the degree of grim determination and relentless intelligence that
Robert brings to the task.
Thus I'm not sure that Robert is aware of it, but what he succeeds in
doing every time he builds one of these creations is satirising
conventional model-building economics. That's the peculiar joke he has
achieved, it seems to me.
-dlj.
Thomas Blankenhorn
> Thus I'm not sure that Robert is aware of it, but what he succeeds in
> doing every time he builds one of these creations is satirising
> conventional model-building economics. That's the peculiar joke he has
> achieved, it seems to me.
Aha -- thanks for letting me in on that one, David!
It sure seemed to me as if Robert was honestly attempting to
understand labor economics -- and lashing out at mainstream economists
a bit too while he was at it. Now that I've read your post, it seems
kind of obvious that when someone builds a model without a labor
supply curve, and then finds out employment isn't determined by supply
and demand for labor, that must be some kind of in-joke.
Again, thanks!
-- Thomas
Robert Vienneau
> I am not an economist, let alone a mainstream economist, but let me
> play one in this thread anyway.
I have no degree in economics either.
> Having discovered my earlier
> misunderstanding, I read your initial post again, this time with more
> attention.
In your post before this - the semi-fool one - you did not
restate my argument correctly either.
> I now suspect that the weird outcome produced by your
> simulation depends on (at least) one of two oddities you've assumed
> into your model. I would challenge you to reproduce your outcome with
> these oddities removed. My prediction is you can't do it.
You are mistaken. See, for example:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
I am no longer committed to calling any curve in any graph in that paper
"demand".
> Oddity #1: There's no supply curve for labor in your model.
>
> If I understand you correctly, you assume that labor comes at a fixed
> wage, and that the company can recruit any quantity it wants at that
> wage...
This is "perfect competition", as defined by mainstream economists
and used in their introductory textbook stories.
> Oddity #2: Your economy can't run multiple processes simultaneously
>
> In your setup, there's only one firm. It has the choice of running one
> out of four processes, but it doesn't have the choice of running a
> combination of processes.
The above is incorrect. The example illustrates prices at which
a firm will choose to run one corn-producing process and one one
iron-producing process. That's two processes.
There are points (called "switch points" in the literature) at
which the firm will be indifferent between two of the, say,
corn-producing processes. Switch points arise in the example.
> Instead of having one firm, run a simulation with 100 firms. For
> initialization, randomly assign one of your four processes to each
> company. Then iterate. In each iteration step, make a random firm
> switch to the process that maximizes its profit, leaving the other 99
> companies unchanged.
There's issues of stability here. But, generally, my example
illustrates equilibria of the firm under perfect competition. My
example does not depend on there being only one firm. It does not
even depend on the firms being vertically integrated.
> Mainstream economics predicts that things
> converge towards a distribution of processes at which all factor
> prices reflect their marginal productivity. Do they?
In the discrete technology illustrated in my example, the value
of marginal products are generally defined to be a closed interval
bounded by quantities calculated from the right-hand and left-hand
derivatives of the production functions and from prices.
It is incorrect to say "factor prices reflect their marginal
productivity" as if marginal productivity is defined prior to
prices. But, in my example, the prices of labor (wage), corn inputs,
and iron inputs, are in the intervals defined above, when the
firm has chosen the cost-minimizing processes.
By the way, "capital" is not a factor, and the equilibrium interest
(profit) rate is generally not equal to the marginal product of
capital, even in the interval sense referred to above. This
inequality results from "price Wicksell effects", to use the jargon.
Robert Vienneau
<jer...@jboden.demon.co.uk> wrote:
Do you find humorous the intellectual bankrupty of mainstream economic
teaching in North America?
Robert Vienneau
Thomas.Bl...@gmx.net (Thomas Blankenhorn) wrote:
> it seems
> kind of obvious that when someone builds a model without a labor
> supply curve, and then finds out employment isn't determined by supply
> and demand for labor, that must be some kind of in-joke.
You misunderstand. One does not need a supply curve in examining the
derivation of the demand curve. The two curves are independent.
Notice no mainstream economist has yet shown the intellectual
honesty to admit my original post in this thread is correct. Nor
has any economist pointed out any errors in it.
Robert Vienneau
(Christopher Auld) wrote:
> [Silliness deleted] He didn't
> get an answer to this post not becuase no one can address
> it but rather because it's the zillionth time he's spammed
> it,
Poor Chris Auld defines "spam" to mean "a substantial argument he
cannot answer". I have never previously posted the post with which
I began this thread.
> [Silliness deleted] This particular bit o' spam is
> riddled with mathematical and conceptual errors;
Poor Chris Auld cannot name one.
> factor demand curves cannot slope up.
Although some literature does refer to the effect I am describing
as an upward-sloping factor demand curve, my post explicitly
does not say that factor demand curves can slope up.
"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..."
-- Michael Mandler, 1999.
jonah thomas
> Jeremy Boden <jer...@jboden.demon.co.uk> wrote:
>>Surely this is some kind of joke?
> Do you find humorous the intellectual bankrupty of mainstream economic
> teaching in North America?
Yes, certainly. Don't you?
Jeremy Boden
>In article <4RIkO1BZ...@jboden.demon.co.uk>, Jeremy Boden
><jer...@jboden.demon.co.uk> wrote:
>
>> In message <rvien-B03284....@news.dreamscape.com>, Robert
>> Vienneau <rv...@see.sig.com> writes
>
>> ...
>> > Accordingly, assume wages are initially 3/2780 Bushels per
>> >Person-Year. By assumption, the firm neither buys nor sells iron on
>> >the market. The firm produces iron solely for its own use. Still,
>> >the firm must enter a price of iron on its books. I assume an
>> >initial price of 55/1112 Bushels per Ton.
>> ....
>
>> Surely this is some kind of joke?
>
>Do you find humorous the intellectual bankrupty of mainstream economic
>teaching in North America?
>
measure value.
Is it just the USA or the USA and Canada which are intellectual
bankrupt?
--
Jeremy Boden
jonah thomas
> Notice no mainstream economist has yet shown the intellectual
> honesty to admit my original post in this thread is correct. Nor
> has any economist pointed out any errors in it.
I thought some of them said that your model doesn't fit the real
world; that it has some fundamental flaws, notably the assumption of
equilibrium.
As you pointed out, intro economy books often make very similar
assumptions. No mainstream economist has defended the intro economics
teaching. They have also failed to heap scorn on intro economics
teaching, though.
jonah thomas
> Robert Vienneau <rv...@see.sig.com> writes
>> Do you find humorous the intellectual bankrupty of mainstream economic
>> teaching in North America?
> I found it amusing that you use an archaic unit of volume with which to
> measure value.
That is certainly defensible. Rather than considering money directly,
he picks a key commodity and prices things in terms of that commodity.
Nothing at all wrong with doing that. And he modified his model from
a traditional one, that used those measures.
Thomas Blankenhorn
> You misunderstand. One does not need a supply curve in examining the
> derivation of the demand curve. The two curves are independent.
So far I agree. But remember that the title of your thread is "Wages,
employment not determined by supply, demand." To convince me that this
claim is true, you would have to present some economical situation,
tell me what the supply and demand for labor is, tell me what [neo-]
classical economics would predict, and demonstrate a result that
differs from that. Your model tells me what the demand for labor is --
it pops out of the processes your economy uses, if I understand
correctly. Your model does not tell me what the supply of labor is.
What doesn't convince me about your argument is that if your model
ignores supply, the conclusion that wages aren't determined by supply
and demand is meaningless even if it's true within your model. Of
course you are under no obligation to convince me, but I suspect
economists' objections would be fairly similar to mine.
> Notice no mainstream economist has yet shown the intellectual
> honesty to admit my original post in this thread is correct. Nor
> has any economist pointed out any errors in it.
Nevertheless, at least one claim in your original post is *not*
correct, and you haven't addressed its incorrectness yet. You claimed
that economists have no way of explaining how a rise in wages can
correlate with a rise in employment. Your claim is false because
economists do have a way of explaining such a correlation. It's called
a backward bending supply curve, and you are familiar with them, if
you say so yourself.
-- Thomas
Christopher Auld
>(Christopher Auld) wrote:
>> [Silliness deleted] He didn't
>> get an answer to this post not becuase no one can address
>> it but rather because it's the zillionth time he's spammed
>> it,
>Poor Chris Auld defines "spam" to mean "a substantial argument he
>cannot answer". I have never previously posted the post with which
>I began this thread.
LOL!!! What, did RV make another "new" essay by changing the numbers
from 113/743rds of a bushel of corn to 113/217ths?
>> [Silliness deleted] This particular bit o' spam is
>> riddled with mathematical and conceptual errors;
>Poor Chris Auld cannot name one.
Where to start? Just for kicks, let's go through this yet again. Start
with a firm which hires one input, labor, denoted L, and faces competive
markets. Its profits are f(L) - wL, where f() is the production function
and w the wage rate. Maximizing over L yields a schedule L(w), the labor
demand schedule. It cannot slope up and slopes down if f() is at least
eventually decreasing. In a previous version of this same spam
(charmingly titled "Mainstream economists teach bosh"), Vienneau wrongly
blathers
>The labor-demand
>function is supposed to be downward-sloping because higher
>wages induce profit-maximizing firms to substitute relatively
>cheaper factors of production for labor.
This is of course wrong: *one* reason factor demand curves slope down
is substitution. Even when substitution is not possible because, for
example, there're no other factors to substitute, factor demand curves do
not slope up and generally slope down.
Vienneau consider a different question. Suppose a firm faces a constant
wage rate but exists over time, hiring labor in each each period. It
would certainly be troubling if his claim that total labor hired over some
interval can be an increasing function of the wage rate --- since
"periods" exist in logical time, the result from the static model would
hold much less force. But we needn't be troubled because Vienneau's math
is, as usual, wrong (maybe he screwed up the "deteminate" of a matrix!).
Suppose a firm doesn't discount, exists T periods, hires labor in each
period, and has a production technology which isn't necessarily seperable
in time (because, for example, it produces a non-traded capital good).
This is a general statement of the problem RV purports to consider with
his weirdness about 119/237ths of a bushel of corn. If the firm faces the
same wage over time (as RV assumes) its profits are
f(L) - w \sum_i L_i
where L is now a T-vector of labor inputs, f() is the production function.
Let L_i(w) denote the T response schedules describing the solution to this
problem. The greatest profits the firm can make as a function of w are by
definition f(L(w)) - w\sum_i L_i(w), the "profit function." Differentiate
twice with respect to w, invoke the envelope theorem and use the convexity
of the profit function to find:
\partial \sum_i L_i(w)
---------------------- \le 0.
\partial w
That is, total labor hired is a non-increasing function of the wage in
the model in which RV describes. This is hardly surpising, as all it
really says is that an increase in marginal costs induces the firm to
produce less (technically, not more) output.
Where does RV go wrong? Many, many places. RV's assumption of constant
returns implies the problem is poorly posed because total labor demanded
is either zero, undefined, or (at a unique wage) undetermined. Posing the
problem this way then varying the wage rate and asking what happens "if
the firm does not change its output" is dishonest and mathematically
mistaken. Notice that if even one does hold output constant RV's result
is impossible, as the solution to minimizing w(sum_i L_i) subject to
f(L)=K does not depend on w. That is, holding output constant the firm
would change nothing at all in response to changes in the wage rate. Most
notably, there is no need to make assumptions about the "accounting price"
of an intermediate good. RV pulls numbers out of thin air to make his
example work --
> Still, the firm must enter a price of iron on its books. I assume an
> initial price of 55/1112 Bushels per Ton.
pathetically, weirdly, and profoundly wrong as either economics or
mathematics.
>> factor demand curves cannot slope up.
>Although some literature does refer to the effect I am describing
>as an upward-sloping factor demand curve, my post explicitly
>does not say that factor demand curves can slope up.
LOL! What a weasel. Apparently one is not supposed to conclude from, for
example,
>Q: And does the labor demand function show that firms will not
> want to hire more labor at a lower wage, all else constant.
>A: Yes.
> An economist giving those answers cannot explain the possibility
>of the numerical example presented in this post
that the "numerical example presented in this post" shows an example of a
labor demand curve that slopes up. This rivals the hilarious time Robert
spammed his essay with the subject header "Upward-sloping labor demand
curves," then announced he never claimed to be demonstrating the
existence of upward-sloping labor demand curves.
Of course, while it's entertaing to point out the numerous errors Vienneau
makes in his dour economic creationism, it's also beside the point. There
are lots of models in which "wages, employment are not determined by
supply and demand" even in the evil mainstream literature, and even taught
by evil professors to poor impressionable freshmen. I guess it's not as
satisfying to a kook to say something like "hey, what about monopsony
power?" as it is it spam and spam and spam about the vast conspiracy to
suppress the kook's noble truths.
Robert Vienneau
> Nevertheless, at least one claim in your original post is *not*
> correct, and you haven't addressed its incorrectness yet. You claimed
> that economists have no way of explaining how a rise in wages can
> correlate with a rise in employment.
That's not what I claimed. I claim an economist with the
understanding of labor demand exhibited in my imaginary
dialog "cannot explain the possibility of the numerical
example".
In my first sentence, I exhibited an awareness of some
other ways ("price and wage stickiness, rigidities,
information asymmetries, etc.") of explaining how a rise
in wages can correlate with a rise in employment.
Poor Chris Auld has provided empirical evidence for my
claim. You might reply it is unfair of me to generalize
from one economist going on and on, and on, and still
on, and on, in blissful ignorance.
Robert Vienneau
<j2th...@cavtel.net> wrote:
> Robert Vienneau wrote:
>
> > Notice no mainstream economist has yet shown the intellectual
> > honesty to admit my original post in this thread is correct. Nor
> > has any economist pointed out any errors in it.
> I thought some of them said that your model doesn't fit the real
> world; that it has some fundamental flaws, notably the assumption of
> equilibrium.
No, nobody has said that here.
By the way, just because somebody follows up one of my posts does
not imply they are making a substantial, relevant, and on-topic
point.
What would be an on-topic response? One possibility would be
to contrast the assumptions of the textbook story of supply and
demand with my example. For example, one might name some
special-case assumption, if there were one, that the textbooks
make and that rules out the data of my example. Or one might
draw, if it were possible, a downward-sloping textbook labor
demand function for the data of my example.
> As you pointed out, intro economy books often make very similar
> assumptions. No mainstream economist has defended the intro economics
> teaching...
Yes, I noticed.
"The view which is adopted here however is that there is
insufficient robust theoretical ground to support the
notion, underlying virtually all economic discussions of
employment, that real wages and employment are related in a
systematically inverse way. In other words,the view is
adopted here that no clear economic reasoning can be provided
by which to suppose that in general a fall in real wages would
lead to an increase in labour employment.
Some, particularly economists, might find this rather
confronting, since the real wage-employment nexus has been a
part of economic folklore for so long, that, to use the words
of one economist, this notion is no longer seen as a theory of
employment, but as an 'immediate reflection of the facts'."
-- Graham White, "The Poverty of Conventional Economic
Thinking and the Search for Alternative Economic and
Social Policies". November 2001.
<http://www.econ.usyd.edu.au/drawingboard/journal/0111/white.pdf>
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >(Christopher Auld) wrote:
>
> >> He didn't
> >> get an answer to this post not becuase no one can address
> >> it but rather because it's the zillionth time he's spammed
> >> it,
> >Poor Chris Auld defines "spam" to mean "a substantial argument he
> >cannot answer". I have never previously posted the post with which
> >I began this thread.
> LOL!!! What, did RV make another "new" essay by changing the numbers
> from 113/743rds of a bushel of corn to 113/217ths?
It is pointed out to poor Chris Auld that his statement is incorrect.
Does he graciously retract it? Of course not.
> Vienneau consider a different question. Suppose a firm faces a constant
> wage rate but exists over time, hiring labor in each each period.
Time supposedly enters the textbook presentation. The quantity axis in
a supply and demand graph is the flow of labor inputs per unit time.
If the conditions taken as exogeneous in drawing the demand curve
(e.g., technology) persist, the demand curve should persist.
Firms are supposed to be in equilibrium at each point on the labor
demand schedule. Suppose the managers of a firm:
o Choose the cost-minimizing processes for producing a certain
commodity.
o Require inputs of certain produced commodities in their
production processes.
o Observe that they are drawing down inventories.
o Do not produce some of these produced inputs themselves (because
it is not as profitable as producing the commodities that
they do produce)
o Observe that no other firm, responding to the current configuration
of prices, will produce those inputs.
Is such a firm in equilibrium? I would say not. It is obvious that
there are endogeneous forces within the firms that will change
their quantity decisions. The textbook labor demand schedule
cannot be drawn, as poor Chris Auld wants to draw it, in such a
case. My example illustrates.
The above was part of the point of the Q and A dialog in my
original post. Naturally, poor Chris Auld had nothing substantial
to say about that dialog:
> >Although some literature does refer to the effect I am describing
> >as an upward-sloping factor demand curve, my post explicitly
> >does not say that factor demand curves can slope up.
> Apparently one is not supposed to conclude from, for example,
> >Q6: And does the labor demand function show that firms will not
> > want to hire more labor at a lower wage, all else constant.
>
> >A: Yes.
>
> > An economist giving those answers cannot explain the possibility
> >of the numerical example presented in this post
> that the "numerical example presented in this post" shows an example of a
> labor demand curve that slopes up.
It is pointed out to poor Chris Auld that my text explicitly does not
say that factor demand curves can slope up. Does he graciously
retract his incorrect suggestion otherwise? Of course not.
As for a formal treatment of my example, consider the appendix in
my original post. I think of Linear Programming and of duality
theory as fairly sophisticated mathematics. No wonder poor Chris
Auld did not address it, preferring to distract the reader with
mathematics he does not and cannot apply to my example.
As far as I can tell, poor Chris Auld's attempt to list my
supposed mistakes boils down to this:
o I can add fractions.
o I make the textbook assumption of Constant Returns to
Scale.
o An incorrect assertion that he has proven that my
numerical example must be wrong, even if he cannot
say where, because my example shows the profit-maximizing
firm chooosing different mixes of inputs at different
levels of the wage, given its (net) output.
o An incorrect assertion that I choose the price of iron
from the air.
By the way, this sort of stuff is just stupid:
> ... wrongly blathers ... his weirdness ... dishonest ...
> ... pathetically, weirdly, and profoundly wrong as either economics
> or mathematics... What a weasel ... the hilarious time ...
> numerous errors ... dour economic creationism ...
A string of adjectives and abuse is not an argument. Poor Chris Auld
has yet to find a mistake in my mathematics, despite all his
whining.
And contrast the first sentence of my first post on this thread:
If you take a class on economics, your teacher might tell you that
wages and employment are determined by the demand and supply of
labor, abstracting from price and wage stickiness, rigidities,
information asymmetries, etc.
with poor Chris Auld's distortions and personalities:
> There
> are lots of models in which "wages, employment are not determined by
> supply and demand" even in the evil mainstream literature, and even taught
> by evil professors to poor impressionable freshmen. I guess it's not as
> satisfying to a kook to say something like "hey, what about monopsony
> power?" as it is it spam and spam and spam about the vast conspiracy to
> suppress the kook's noble truths.
Obviously, nothing poor Chris Auld says should be believed.
"The idea of an inverse relation between wages and employment is
central to the marginalist or neoclassical wage theory. In that
context it depends on the possibility of substitution between
production factors (direct substitution) and consumer goods
(indirect substitution) following changes in distribution. It is
argued that when, for example, the labor supply increases, the
fall in wages due to competition among workers will make it
advantageous for employers to use more labour-intensive production
techniques, and this, other things being equal, will bring an
increase in employment (and vice versa if wages rise).
In addition, it is argued that (in the same situation) a drop in
wages will reduce the prices of those goods whose production
requires relatively more labour. On the basis of the marginalist
theory of consumer behavior this will lead to an increase in demand
for such goods compared to those whose production is less labour-
intensive. This will result in increased employment in the economy
as a whole.
[Footnote 16:] Both of these substitution mechanisms are subject
to serious difficulties and criticisms, which I shall not go into
here; suffice it to mention that both direct and indirect
mechanisms fail because, as was shown by Sraffa and then during
the 1960s in the debate on capital theory, relative prices do not
necessarily change in the direction predicted by marginalist
theory following variations in distribution: if wages fall the
prices of more labour-intensive products may actually go up
rather than down, and the more labour-intensive techniques may
become *less* advantageous. The marginalist theory of demand
also meets serious problems in demonstrating that changes in
relative prices really do lead to substitution in consumption
favoring goods whose relative price has fallen; on the latter
point see Kirman, 1989."
-- Antonella Stirati, _The Theory of Wages in Classical
Economics_, Edward Elgar, 1994.
jonah thomas
>>>Notice no mainstream economist has yet shown the intellectual
>>>honesty to admit my original post in this thread is correct. Nor
>>>has any economist pointed out any errors in it.
>>I thought some of them said that your model doesn't fit the real
>>world; that it has some fundamental flaws, notably the assumption of
>>equilibrium.
> No, nobody has said that here.
OK, sorry. I thought I remembered a claim that this type of model is
inadequate, whether you do it or whether the oldfashioned economists
who used this sort of model did it, and inadequate even though it
still gets used for teaching purposes.
> By the way, just because somebody follows up one of my posts does
> not imply they are making a substantial, relevant, and on-topic
> point.
> What would be an on-topic response? One possibility would be
> to contrast the assumptions of the textbook story of supply and
> demand with my example. For example, one might name some
> special-case assumption, if there were one, that the textbooks
> make and that rules out the data of my example. Or one might
> draw, if it were possible, a downward-sloping textbook labor
> demand function for the data of my example.
You are choosing what sort of response is acceptable to you. But we
have a sort of market of posts here. Since we don't get money for
posting, for most of us the reward is fun. (Maybe there are a few
people here who hope to demonstrate their competence enough to improve
their chances of getting jobs. Or possibly they might get ideas they
could turn into publishable papers etc. But I think for most of us
the currency is enjoyment.) If you aren't getting the responses you
want, perhaps those responses wouldn't be enough fun for the people
who would make them.
One way people have fun is to prove you wrong. Perhaps you should
give them some chances to do that. But if it's too easy to prove you
wrong then it stops being fun.
If you find some established economists you can defer to, they might
find it rewarding to praise you for your insight and tell you you're
right. They get to be the authority who tells you that you're right,
that can be even better than being the competitor who proves you're wrong.
If nobody answers you, look at what's in it for them. There's a
chance that you're providing novel ideas that are just too
challenging. What fun is it to follow very complex thinking when the
reward at the end if the thinking is right, is that you can share some
arcane ideas that hardly anybody else understands. Much more pleasant
to do that when you're the one who gets to have the ideas in the first
place, rather than following somebody else.
>>As you pointed out, intro economy books often make very similar
>>assumptions. No mainstream economist has defended the intro economics
>>teaching....
> Yes, I noticed.
Say they defend the intro teaching. What does that get them even if
it's defensible?
Say they agree that it's rotten. What does that get them?
Look at who benefits. For a lot of people the benefit of recognising
pure truth that somebody else presents is a lot less than that of
having fun.
Christopher Auld
[ irrelevancies ]
> o An incorrect assertion that he has proven that my
> numerical example must be wrong, even if he cannot
> say where, because my example shows the profit-maximizing
> firm chooosing different mixes of inputs at different
> levels of the wage, given its (net) output.
I noted in my initial post to this thread that Vienneau never responds to
criticism of his spam partially because he doesn't understand it. The
post he's responding to clearly points out several mathematical/conceptual
errors and demonstrates quite simply the result the spam purports to show
must be wrong. True to form, Vienneau's response is to snip that out of
his response, insist it wasn't there in Orwellian fashion, and favor us
with the irrelevant crap in this post. Explaining economics to Robert
Vienneau has all the same impact, and for all the same reasons, as
explaining evolutionary biology to a "creation scientist."
I guess we'll see this same spam another few more dozen times.
[ snip -- more irrelevancies ]
Christopher Auld
>What would be an on-topic response? One possibility would be
>to contrast the assumptions of the textbook story of supply and
>demand with my example. For example, one might name some
>special-case assumption, if there were one, that the textbooks
>make and that rules out the data of my example. Or one might
>draw, if it were possible, a downward-sloping textbook labor
>demand function for the data of my example.
Too funny. Robert Vienneau is aware of the fact -- because it's been
pointed out to him a zillion times -- that there is a simple axiomatic
argument showing that factor demand curves cannot slope up. The labor
demand curve (even if we abuse the term to mean "total labor demanded over
many periods as a function of an unvarying wage over time") in his example
of course does slope down, although because of his goofy assumptions it's
not a very interesting function: It's a horizontal line at a unique wage
where the firm is indifferent over labor demanded, zero at every higher
wage, and undefined at every lower wage.
Now, RV says in his spam that someone who thinks labor demand schedules do
not slope up "cannot explain the numerical example" in the spam, then he
told me that despite that attack on a strawman economist he doesn't in
fact claim to be showing an upward-sloping labor demand schedule, then a
few minutes later he implies (above) he's shown it's impossible to draw a
downward-sloping labor demand schedule for the firm in his spam. So,
which is it, Bobby? Do you or do you not claim to be showing an example
of an upward-sloping labor demand schedule? If not, then what exactly are
all of us evil mainstream economists supposed to be guilty of, and why do
you keep using the phrase "labor demand"? If so, how do you explain why I
was able to show in a very straightforward fashion that even in much more
general circumstances, and even if we abuse the definition of "factor
demand schedule" to allow intemporal aggregation, that labor demand cannot
be an in increasing function of wages?
> "The view which is adopted here however is that there is
> insufficient robust theoretical ground to support the
> notion, underlying virtually all economic discussions of
> employment, that real wages and employment are related in a
> systematically inverse way. In other words,the view is
No one but Robert Vienneau -- who doesn't understand the radical
literature he paraphrases -- claims a profit-maximizing firm in
competitive markets would respond to an increase in a factor price by
increasing demand for that factor. Ironically, the dramatically different
claim that real wages and employment are not necessarily "related in a
systematically inverse way" isn't even controversial -- even Econ 101
students using the simplest of models of the labor market can explain
situtations in which real wages and employment will move in the same
direction. One of the myriad conceptual errors in Vienneau's
jihad-by-spam against the economics profession is the apparent inability
to understand the difference between these two claims.
Christopher Auld
It occurs to there's an extremely simple way of seeing
Vienneau's result is wrong:
>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.
The only input this firm buys is labor, so obviously its costs depend only
on how much labor it hires. Then asserting the firm will hire more labor
to produce the same output in response to a price change is equivalent to
stating the firm will incur more costs than it needs to in order to
produce that output. Therefore, the firm does not minimize costs and
therefore does not maximize profits. (This is of course implied by "the
solution to the cost minimization problem does not depend on the wage,"
[in this context], as someone already said.)
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> > o An incorrect assertion that he has proven that my
> > numerical example must be wrong, even if he cannot
> > say where, because my example shows the profit-maximizing
> > firm chooosing different mixes of inputs at different
> > levels of the wage, given its (net) output.
> I noted in my initial post to this thread that Vienneau never responds to
> criticism of his spam [blah, blah, blah]. The
> post he's responding to clearly points out several mathematical/conceptual
> errors
No, it does not point out any mathematical or conceptual errors in my
original post on this thread. What it points out, in addition to the
above, is that:
o I can add fractions.
o I make the textbook assumption of Constant Returns to
Scale.
o An incorrect assertion that I choose the price of iron
from the air.
> and demonstrates quite simply the result the spam purports to show
> must be wrong.
I think poor Chris Auld really doesn't understand that a supposed
demonstration that my conclusion is in error doesn't address my
argument, in some sense. That is, it does not locate any supposed
error in my argument.
In my original post, I postulated four processes were known, two
for producing corn and two for producing iron. Here are two of
those four processes:
CRS PRODUCTION PROCESSES
INPUTS Process A Process D
Labor 1 Person-Year 275/464 Person-Years
Iron 2 Tons 113/232 Tons
Corn 2/5 Bushels 0 Bushels
OUTPUT 1 Bushel Corn 1 Ton Iron
I also described various configurations of wages, the rate of
(accounting) profits, and the price of iron. (I assumed a
bushel corn was the numeraire.) One such configuration
was a wage, w, of 3/2780 Bushels per Person-Year, a price of
iron, p, of 55/1112 Bushels per Ton, and a rate of profits, r,
of 100%. I pointed out the following cost accounting for
these prices and these processes:
INDUSTRY PROCESS COST PROFITS
Corn A 2*(55/1112) + (2/5)*1
+ 1*(3/2780) = 1/2 100%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(3/2780) = 55/2224 100%
One can write down the following system of equations:
(2 p + (2/5) + 1 w)(1 + r) = 1
((113/232) p + 0 + (275/464) w)(1 + r) = p
Notice that the coefficients come from the postulated
production processes. Note this is a system in three variables
of two equations. If the wage is given, it is a system in two
variables of two equations. By a theorem of Perron and Frobenius,
a unique, economically meaningful, solution corresponds to each
value of w in an interval from zero to some maximum.
So the price of iron is not taken from the air. Once a wage
is given, the price of iron is determined.
So the following is, at least mistaken, if not completely
ignorant:
>RV pulls numbers out of thin air to make his example work --
>> Still, the firm must enter a price of iron on its books. I assume an
>> initial price of 55/1112 Bushels per Ton.
>pathetically, weirdly, and profoundly wrong as either economics or
>mathematics.
Notice that poor Chris Auld does not offer an argument in the
string "pathetically, weirdly, and profoundly wrong".
Now notice that the exposition, above or in my original post,
is not in terms of dated labor quantities. It is true that
one can consider the iron and corn inputs as produced by the
labor of the previous year and the iron and corn inputs for
that year. And so on. So one could go through some math to
find dated labor quantities. (In the general case of
joint production, one CANNOT reduce inputs to dated
labor quantities, as I understand it.)
Notice that in the above system of equations, the value of
iron and corn inputs are multiplied by a term of (1 + r).
Thus, in determining which technique is cost minimizing,
the quantities of dated labor would be multiplied by powers
of (1 + r). That is, if one wanted to present this analysis
in terms of dated labor quantities - which I did not do -
the dated labor quantities would be time-discounted. (If
they were not, the analysis would be wrong.)
Some points about this reduction to dated labors:
o I don't see how poor Chris Auld could expect newcomers to
follow along. So he should not think other participants
on this thread should accept that he has analyzed my
example.
o I doubt poor Chris Auld even understands this process
himself. What does he think the value of T is for my
example?
o My argument had something to do with the price of iron
and what it means for a firm to be in equilibrium. He
avoids addressing that argument, for iron and corn
inputs do not even appear in his formulation.
Anyways, I have shown that the following is, as usual, mistaken:
> Suppose a firm DOESN'T DISCOUNT, [emphasis added]
> exists T periods, hires labor in each
> period, and has a production technology which isn't necessarily seperable
> in time (because, for example, it produces a non-traded capital good).
> This is a general statement of the problem RV purports to consider
> [stupidity deleted]
But there is a valid point hidden in poor Chris Auld's balderdash.
The textbook story cannot be criticized by my point in this
thread under the special case assumption that there are no capital
goods. Now what mainstream textbook states this? Which incorrectly
state the opposite, that they are considering an analysis with
capital?
By the way, notice that poor Chris Auld, true to form, snips my
appendix out of my original post, insists it wasn't there in Orwellian
fashion, and favors us with the irrelevant crap in his posts. But,
then, why would anybody take poor Chris Auld seriously on price
theory?
"...marginalist economists provided [an] account of the long-period
(uniform rate of profit) theory of value and distribution, ... the
marginalist economist had to 'close the system' in some ...
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 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)
Robert Vienneau
(Christopher Auld) wrote:
> > "The view which is adopted here however is that there is
> > insufficient robust theoretical ground to support the
> > notion, underlying virtually all economic discussions of
> > employment, that real wages and employment are related in a
> > systematically inverse way. In other words,the view is
adopted here that no clear economic reasoning can be provided
by which to suppose that in general a fall in real wages would
lead to an increase in labour employment.
Some, particularly economists, might find this rather
confronting, since the real wage-employment nexus has been a
part of economic folklore for so long, that, to use the words
of one economist, this notion is no longer seen as a theory of
employment, but as an 'immediate reflection of the facts'."
-- Graham White, "The Poverty of Conventional Economic
Thinking and the Search for Alternative Economic and
Social Policies". November 2001.
<http://www.econ.usyd.edu.au/drawingboard/journal/0111/white.pdf>
> Robert Vienneau doesn't understand the ... literature he paraphrases
(I have deleted a word of no cognitive value.)
> the
> claim that real wages and employment are not necessarily "related in a
> systematically inverse way" isn't even controversial -- even Econ 101
> students using the simplest of models of the labor market can explain
> situtations in which real wages and employment will move in the same
> direction.
It was pointed out to Chris Auld that I exhibited an understanding of
a point he says I don't understand. I exhibited this understanding
in the first sentence of the post with which I began this thread.
If you take a class on economics, your teacher might tell you that
wages and employment are determined by the demand and supply of
labor, abstracting from price and wage stickiness, rigidities,
information asymmetries, etc.
So does Chris Auld graciously retract his nonsense? Of course not.
He deliberately repeats his untruths. What is his excuse for his
behavior?
"if this criticism were taken as being no less applicable to the real
world than the theoretical, then it follows, as already noted, that
orthodox economics is unable to make any reliable statements concerning
the relationship of production to the various input markets. That is,
the neoclassical vision of a market-coordinated production system,
along with derivative growth and distribution theories, are all
invalidated. As a consequence, the nature of the entire traditional
circular flow conception is called into question...
...It is one thing to say that this conception of indirect economic
management does not satisfactorily achieve its goals because of the
existence of such real-world problems as bottlenecks, power, premature
inflation, inflationary expectations, random shocks, ratchet and
spillover effects, and the like. In such situations, an economically
coherent and consistent market-based system of production and
distribution is still assumed to exist, though it is overlaid with
political, institutional, and psychological factors that affect
economic adjustments and performance...
It is quite another thing to argue that key markets in the system,
particularly those in the resource or input sector, do not possess the
fundamental economic characteristics necessary to the orderly
systematic functioning that is postulated by mainstream theory..."
-- Richard X. Chase, "Production Theory," in _A Guide to
Post-Keynesian Economics_, (edited by Alfred S. Eichner), M. E.
Sharpe, 1978, p. 79-80
"...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...
...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...
...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....
...The basic question is whether there are regular relationships
between 'factor prices' and 'factor quantities' or not, i.e. normally
functioning factor markets...."
-- Heinrich Bortis, _Institutions, Behavior and Economic Theory:
A Contribution to Classical-Keynesian Political Economy_,
Cambridge University Press, 1997.
Christopher Auld
>(Christopher Auld) wrote:
>> I noted in my initial post to this thread that Vienneau never responds to
>> criticism of his spam [blah, blah, blah]. The
>> post he's responding to clearly points out several mathematical/conceptual
>> errors
>No, it does not point out any mathematical or conceptual errors in my
>original post on this thread.
Dorothy, there is no man behind the curtain.
Look, let's make this really, really, easy. Your firm hires labor and
produces corn. It does so using a process involving an intermediate good,
iron, which it neither buys nor sells, so its costs depend only on the
amount of labor it hires and its revenues are simply equal to output given
your choice of numeraire. Adding the (inappropriate) assumption of
steady-state solutions you use, the firm is supposed to cost-minimizing at
some position like
t 1 2 3 ...
Q 4 4 4 ...
L 5 5 5 ...
then the wage increases and holding output constant it is supposed to
hire more labor, something like
t 1 2 3 ...
Q 4 4 4 ...
L 7 7 7 ...
Everyone, even those not mathematically inclined, should be able to see
that this is impossible. The manner in which the firm transforms a given
amount of labor into output is a technological problem -- it doesn't
depend on how much the firm paid for that labor. So why can't the firm in
the second panel make four units of output each period using the initial
allocation (slowly, for Bobby: ie, the initial production plan, including
the allocation of iron), which obviously reduces costs without changing
output?
I've already pointed out a number of errors in Vienneau's exposition.
There are of course many more. But regardless of which errors are
leading him to his erroneous conclusion, it's obvious the conclusion is
erroneous. Another error seems to be
Notice everything I've said goes through unaltered under geometric
discounting, except that the objective function for the general statement
of the problem becomes more difficult to work with.
>Notice that in the above system of equations, the value of
>iron and corn inputs are multiplied by a term of (1 + r).
Without wading though the hilariously tedious and opaque "long essay"
again I can't be sure, but this implies Vienenau is actually letting the
discount rate vary endogenously with the wage rate, which could be yet
another error explaining his goofy result.
> o I doubt poor Chris Auld even understands this process
> himself. What does he think the value of T is for my
> example?
It doesn't matter if you let T go off to infinity, Bobby, but it does mean
one would have to use explicitly dynamic methods to demonstrate your
conclusion is wrong. One day you really might want to look up "dynamic
programming" and similar methods, commonly taught to undergraduates. Then
you might stop writing hilarious nonsense using incorrect solution methods
then blathering about "endogenous forces within the firm" and such.
> o My argument had something to do with the price of iron
> and what it means for a firm to be in equilibrium. He
> avoids addressing that argument, for iron and corn
> inputs do not even appear in his formulation.
And again, slowly: This firm buys labor and produces corn. The fact that
it does so using a non-traded capital good simply means the production
function is not seperable in time, but we can still write a function
which maps a given vector of labor inputs into a given corn output. Why
don't you try reading what I explained to you before again.
Bobby favors us with another quote:
> "...marginalist economists provided [an] account of the long-period
> (uniform rate of profit) theory of value and distribution, ... the
> marginalist economist had to 'close the system' in some ...
Notice Bobby has YET AGAIN mixed up remarks about how an ECONOMY might
respond to, say, a shock to wages and how a GIVEN FIRM might respond to a
change in the wage rate.
Christopher Auld
>> claim that real wages and employment are not necessarily "related in a
>> systematically inverse way" isn't even controversial -- even Econ 101
>> students using the simplest of models of the labor market can explain
>> situtations in which real wages and employment will move in the same
>> direction.
>It was pointed out to Chris Auld that I exhibited an understanding of
>a point he says I don't understand. I exhibited this understanding
>in the first sentence of the post with which I began this thread.
>
> If you take a class on economics, your teacher might tell you that
> wages and employment are determined by the demand and supply of
> labor, abstracting from price and wage stickiness, rigidities,
> information asymmetries, etc.
>
>So does Chris Auld graciously retract his nonsense? Of course not.
>He deliberately repeats his untruths. What is his excuse for his
>behavior?
Suppose we are in Economics 101 and the demand curve shifts out. In what
direction to both quantity and price move? Do we need to "abstract from
price and wage stickiness, etc" to get this result?
[ snip: More Jay Hansonesque regurgitations of quotes indicating yet again
Bobby doesn't get the difference between considering equilibria in
economies and individual agents' optimal response schedules ]
Keith Ramsay
|The only input this firm buys is labor, so obviously its costs depend only
|on how much labor it hires. Then asserting the firm will hire more labor
|to produce the same output in response to a price change is equivalent to
|stating the firm will incur more costs than it needs to in order to
|produce that output. Therefore, the firm does not minimize costs and
|therefore does not maximize profits. (This is of course implied by "the
|solution to the cost minimization problem does not depend on the wage,"
|[in this context], as someone already said.)
But the firm also borrows corn for the year. In the scenario described
by Robert Vienneau, rising wages cause the ratio between the price of
iron and the price of corn to rise, making it cheaper for an iron
manufacturer to switch from a process that uses more iron to one which
uses more corn as well as more labor per unit of iron output.
Is this sort of thing possible (even supposing for the sake of
argument that he hasn't described his scenario well)?
Previously:
Christopher Auld:
|This particular bit o' spam is
|riddled with mathematical and conceptual errors; factor
|demand curves cannot slope up.
I always thought "spam" meant something broadcast much more widely.
This may seem picky, but as a sci.math regular, I'd say that it seems
pretty common for people to describe as "mathematical errors" things
which aren't mathematical errors. There is little mathematics in what
he wrote; what math there is, is almost entirely arithmetic. I have
been too lazy to check Robert Vienneau's arithmetic, but I haven't
seen you identify any _mathematical_ errors yet. It may be a moot
point, but for the benefit of sci.math readers, could you perhaps
clarify?
Elsewhere:
|Of course, while it's entertaing to point out the numerous errors Vienneau
|makes in his dour economic creationism, it's also beside the point. There
|are lots of models in which "wages, employment are not determined by
|supply and demand" even in the evil mainstream literature, and even taught
|by evil professors to poor impressionable freshmen. I guess it's not as
|satisfying to a kook to say something like "hey, what about monopsony
|power?" as it is it spam and spam and spam about the vast conspiracy to
|suppress the kook's noble truths.
From this remark,
Robert Vienneau:
|So, as good economists have long recognized, the theory I am attacking
|is incorrect, as a matter of mathematics and logic.
I was under the impression he was happily acknowledging that what he
claims to be showing is well-known in economics.
Keith Ramsay
Christopher Auld
>au...@acs.ucalgary.ca (Christopher Auld) wrote in message news:<bbelpj$d...@acs4.acs.ucalgary.ca>...
>|The only input this firm buys is labor, so obviously its costs depend only
>|on how much labor it hires. Then asserting the firm will hire more labor
>|to produce the same output in response to a price change is equivalent to
>|stating the firm will incur more costs than it needs to in order to
>|produce that output.
>But the firm also borrows corn for the year. In the scenario described
>by Robert Vienneau, rising wages cause the ratio between the price of
>iron and the price of corn to rise, making it cheaper for an iron
>manufacturer to switch from a process that uses more iron to one which
>uses more corn as well as more labor per unit of iron output.
Recall there is no "price of iron" because iron is not traded. Along an
optimal path one could calculate what's called a "shadow price" for iron
by economists, which may or may not be the same number as Vienneau's
"accounting price." Neither is needed to solve for the optimal input
quantities. Note again that this firm's outlays are proportional to
labor hired per period: Vienneau's claim that labor hired per period
*changes* (we don't even need "increases") with increases in the wage
rate holding output constant is clearly incorrect. That is, the solution
to the program {min_L wf(L) s.t. g(L)=0} does not depend on w (regardless
of whether L is a scalar or a vector).
I believe what's going on here is that Vienneau has paraphrased (without
due credit) an archaic model of a vertically integrated *industry* and
mistakenly applied it to a *firm*. In the body he says he's "assuming"
various things about the "accounting price" of iron, but in the appendix
he solves for that price by moving along the "factor price frontier." He
says:
Likewise, for iron to be produced, the third or the fourth
constraint in the dual must be met with equality. Hence, for the
analyzed firms to be in equilibrium, the vertically-integrated industry
must be on the so-called factor-price frontier for that industry.
The factor price frontier gives zero profit combinations of input prices.
But a firm's profits are a decreasing function of input prices: An
increase in wages will not be accompanied by a change in the "accounting
price" of iron or any other parameter that leaves profits at zero, it will
instead decrease profits (notice the "accounting price" of iron *falls*
when the wage rate rises). Vienneau's solution instead involves an
endogenous change in other parameters such that profits are held at zero --
even abusing the term "labor demand curve" to allow aggregation over time,
the object he's talking about is not a labor demand curve, and the
properties of the object he's talking about are not surprising. Notice
too the use of "industry" and "firm*S*" when what we are supposed to be
considering is the optimal response of *a* firm to a change in input
prices.
>|This particular bit o' spam is
>|riddled with mathematical and conceptual errors; factor
>|demand curves cannot slope up.
>I always thought "spam" meant something broadcast much more widely.
Vienneau has a small cache his "long essays" which he regularly posts all
over the place. Google suggests minor variants of this particular piece
have been posted about 70 times to a variety of groups. I think such
behavior is accurately described as "spamming."
>This may seem picky, but as a sci.math regular, I'd say that it seems
>pretty common for people to describe as "mathematical errors" things
>which aren't mathematical errors.
Whether one wishes to call the errors in this piece "mathematical" or
"conceptual" is a matter of semantics. Vienneau claims to be showing
properties of a mathematical relationship which do not in fact hold, but
this is a result of misunderstood concepts rather than an arithmetic error
in the solution (not that's I've checked his ludicrous arithmetic --- for
all I know it's wrong too).
>From this remark,
>
>Robert Vienneau:
>|So, as good economists have long recognized, the theory I am attacking
>|is incorrect, as a matter of mathematics and logic.
>
>I was under the impression he was happily acknowledging that what he
>claims to be showing is well-known in economics.
You misunderstand Vienneau's intent. Recall the preamble to the
arithmetic features an economist who is supposed to be "unable to explain"
the analysis Vienneau is about to present. The "good economists" in the
quote above are the tiny band of aging political idealogues Vienneau loves
to paraphrase; the vast majority of economists are the, er, non-good
economists not in that camp. Unfortunately Vienneau rarely gets even the
radical critiques (of economics as it stood in the late 19th century) he
paraphrases right, as this thread amply demonstrates.
Keith Ramsay
| Keith Ramsay <kra...@aol.com> wrote:
| >au...@acs.ucalgary.ca (Christopher Auld) wrote in message news:<bbelpj$d...@acs4.acs.ucalgary.ca>...
|
| >|The only input this firm buys is labor, so obviously its costs depend only
| >|on how much labor it hires. Then asserting the firm will hire more labor
| >|to produce the same output in response to a price change is equivalent to
| >|stating the firm will incur more costs than it needs to in order to
| >|produce that output.
|
| >But the firm also borrows corn for the year. In the scenario described
| >by Robert Vienneau, rising wages cause the ratio between the price of
| >iron and the price of corn to rise, making it cheaper for an iron
| >manufacturer to switch from a process that uses more iron to one which
| >uses more corn as well as more labor per unit of iron output.
|
| Recall there is no "price of iron" because iron is not traded.
I should have been clearer about what I was trying to say. First,
based on his assumptions I still don't see how your simple argument
against his thingy takes into account the firm's borrowing corn at the
start of the year. Second, my question about the possibility of
certain features of the scenario holding wasn't meant to ask whether
it's consistent to make all the assumptions Robert Vienneau states or
otherwise makes, hence not based on the details (like the seemingly
useless claim that it's an "integrated" firm not trading in iron). I
think there may be a worthwhile point here which is being obscured by
certain things he seems to be saying badly.
| Along an
| optimal path one could calculate what's called a "shadow price" for iron
| by economists, which may or may not be the same number as Vienneau's
| "accounting price." Neither is needed to solve for the optimal input
| quantities. Note again that this firm's outlays are proportional to
| labor hired per period: Vienneau's claim that labor hired per period
| *changes* (we don't even need "increases") with increases in the wage
| rate holding output constant is clearly incorrect. That is, the solution
| to the program {min_L wf(L) s.t. g(L)=0} does not depend on w (regardless
| of whether L is a scalar or a vector).
I don't see why (using his assumptions) their outlays are proportional
to labor hired, when they are also tying up varying quantities of corn
for the year depending upon the process being used.
| I believe what's going on here is that Vienneau has paraphrased (without
| due credit) an archaic model of a vertically integrated *industry* and
| mistakenly applied it to a *firm*.
That seems plausible, although there are few enough details that I'd
be surprised if one could really be sure it was cribbed.
| In the body he says he's "assuming"
| various things about the "accounting price" of iron, but in the appendix
| he solves for that price by moving along the "factor price frontier."
In the calculations outside of the appendix, it appeared to me that he
was solving by finding the price that made the rate of profit of the
two processes equal, and my impression is that such an assumption
could be inferred from various more basic assumptions (idealizing, of
course).
| He says:
|
| Likewise, for iron to be produced, the third or the fourth
| constraint in the dual must be met with equality. Hence, for the
| analyzed firms to be in equilibrium, the vertically-integrated industry
| must be on the so-called factor-price frontier for that industry.
|
| The factor price frontier gives zero profit combinations of input prices.
| But a firm's profits are a decreasing function of input prices: An
| increase in wages will not be accompanied by a change in the "accounting
| price" of iron or any other parameter that leaves profits at zero, it will
| instead decrease profits (notice the "accounting price" of iron *falls*
| when the wage rate rises). Vienneau's solution instead involves an
| endogenous change in other parameters such that profits are held at zero --
| even abusing the term "labor demand curve" to allow aggregation over time,
| the object he's talking about is not a labor demand curve, and the
| properties of the object he's talking about are not surprising.
Perhaps not if a person is thinking carefully, no, but as I explain
below I see a lot of not-so-careful thinking, and I think some people
would be surprised to find anything even roughly like it true.
| Notice
| too the use of "industry" and "firm*S*" when what we are supposed to be
| considering is the optimal response of *a* firm to a change in input
| prices.
|
| >|This particular bit o' spam is
| >|riddled with mathematical and conceptual errors; factor
| >|demand curves cannot slope up.
|
| >I always thought "spam" meant something broadcast much more widely.
|
| Vienneau has a small cache his "long essays" which he regularly posts all
| over the place. Google suggests minor variants of this particular piece
| have been posted about 70 times to a variety of groups. I think such
| behavior is accurately described as "spamming."
Point taken.
| >This may seem picky, but as a sci.math regular, I'd say that it seems
| >pretty common for people to describe as "mathematical errors" things
| >which aren't mathematical errors.
|
| Whether one wishes to call the errors in this piece "mathematical" or
| "conceptual" is a matter of semantics.
The meaning of terms is always a matter of semantics. What I'm saying
is that in my opinion (as a formerly professional mathematician) this
semantics stretches the term further than it seems like it should, and
my impression is that a lot of mathematicians would feel the same
way. We especially dislike seeing the flip side of this, which is that
someone calls an argument "mathematical" when it only has elements of
mathematics in it, as if that necessarily made things better.
| Vienneau claims to be showing
| properties of a mathematical relationship which do not in fact hold, but
| this is a result of misunderstood concepts rather than an arithmetic error
| in the solution (not that's I've checked his ludicrous arithmetic --- for
| all I know it's wrong too).
It doesn't seem as if you two are dealing with a mutually understood
set of axioms but disagree about what the consequences are. If you
did, I would agree would involve one of you making a "mathematical
error" in a way. (And to be fair, his reference to "arithmetically"
incorrect opinions of economists seems to be stretching the term in at
least as bad a way. I really doubt that the problem is incorrect
mathematics. But his reference is to an arbitrary econ 101 instructor,
so I don't know who it's supposed to be.)
| >From this remark,
| >
| >Robert Vienneau:
| >|So, as good economists have long recognized, the theory I am attacking
| >|is incorrect, as a matter of mathematics and logic.
| >
| >I was under the impression he was happily acknowledging that what he
| >claims to be showing is well-known in economics.
|
| You misunderstand Vienneau's intent. Recall the preamble to the
| arithmetic features an economist who is supposed to be "unable to explain"
| the analysis Vienneau is about to present. The "good economists" in the
| quote above are the tiny band of aging political idealogues Vienneau loves
| to paraphrase; the vast majority of economists are the, er, non-good
| economists not in that camp. Unfortunately Vienneau rarely gets even the
| radical critiques (of economics as it stood in the late 19th century) he
| paraphrases right, as this thread amply demonstrates.
It seems as though you are arguing against him as if the thesis in
question was that the typical economist has gone wrong in a certain
way. That's fine, since he makes it sound like that's what he means
(and if he doesn't mean so, he should step in and say so right away).
Take a bit of time to look at it from my point of view, though. I
don't care too much about whether some random guy on the internet is
right or not. They are very often wrong, after all. We have plenty of
real serious crackpots in the rest of sci.* outside of sci.econ, and
if the worst you have to deal with is someone who's confused about the
meaning of "demand curve" and the like, you're lucky. I also am not
too seriously worried about the health of the economics profession
itself.
I'm more concerned with the kind of stuff that gets passed around in
the general public that is somehow loosely based on economics. It may
be that no "real" economists say the kind of thing he has in his
little "dialogue", but it seems to be just the kind of bowdlerized
economics that people will trot out when explaining to me why they
think various government policies are a bad idea, and I would like to
be able to explain to them why they're being simplistic.
It is of course normal for most "everyday" arguments not to have much
rigor to them. To someone trained in rigorous proof it should be
reasonably obvious. For me the disturbing parts are the claims of
people who seem VERY convinced that the argument for their particular
claim is entirely conclusive, as if from a fallacious sense of
rigor. I'm thinking especially of libertarians (I've probably read
more than my share of libertarian propaganda) arguing the advantages
of libertarian governmental policy, but also of more mainstream
arguments on similar lines (e.g., that our state's "right to work" law
can only help workers and could not possibly hurt them because it
"gives them more options", or e.g. that raising the minimum wage is
bad because it will "obviously" cause more unemployment). It's not
mainly economists' fault if people go around saying that a tax on an
industry will "only get passed on to the consumer", but I think it's
unfortunate that so many people feel comfortable with saying this kind
of thing with so little support.
I like to get ammunition against this sort of glibness. I'd like for
them to feel obligated to tell me the kinds of additional considerations
that really would justify their conclusions (or not).
There are a couple of cute examples from other fields. In physics,
there is a simple example of a system consisting of a weight suspended
from a ceiling by a combination of ropes and springs that has two
stable equilibria. In one equilibrium, the tension in both springs is
the full weight of the weight. In the other, each supports half of the
weight, and because they are shorter, the weight is held higher. The
counterintuitive feature of the particular simple arrangement is that
it's possible to switch the system from the first equilibrium to the
second one by untying a rope whose tension is also the full weight of
the weight, connecting the two springs together.
It would be possible to provide a rigorous, correct demonstration that
starting from an equilibrium state like this one (filling in some
specifics on just what I mean by a system of "cords and springs"),
untying the rope will _initially_ result in the distance between the
two former endpoints of the cord increasing, and the weight
falling. The end of the spring in the equilibrium is under a
combination of forces that adds to zero, and removing one of the
forces causes motion in the expected direction, away from other end of
the rope. But there is a distinct effect that sets in quickly that
causes the counterintuitive effect of the weight rising. It is not of
course that we should expect that cutting supporting ropes should
*usually* cause the objects they support to rise, but one can at least
point out to people that it's not just a foregone conclusion.
Another example is a dinky model of a traffic system in which adding
an additional road causes longer delays in travel. Opening the new
route causes individually time-optimizing drivers to concentrate more
heavily on certain otherwise good roads, which causes them to slow
down. I've read that something like this actually happened in New York
city, although perhaps more due to turning traffic causing too much
interference in the flow along adjoining streets.
What I'm really hoping is that I'll be able to get an analogous
example from economics, or if not, some good explanation of why it
really doesn't happen. If I thought Robert Vienneau's thingies were
perfect okay as they stood obviously I wouldn't be asking; on the
other hand if they didn't have a certain family resemblance to what
I'd like to see, I wouldn't be asking right now.
Keith Ramsay
Robert Vienneau
kra...@aol.com (Keith Ramsay) wrote:
> au...@acs.ucalgary.ca (Christopher Auld) wrote in message
> news:<bbo8m5$1c...@acs4.acs.ucalgary.ca>...
> | Keith Ramsay <kra...@aol.com> wrote:
> | >au...@acs.ucalgary.ca (Christopher Auld) wrote in message
> | >news:<bbelpj$d...@acs4.acs.ucalgary.ca>...
> |
> | >|The only input this firm buys is labor, so obviously its costs depend
> | >|only
> | >|on how much labor it hires. Then asserting the firm will hire more
> | >|labor
> | >|to produce the same output in response to a price change is
> | >|equivalent to
> | >|stating the firm will incur more costs than it needs to in order to
> | >|produce that output.
> | >But the firm also borrows corn for the year. In the scenario described
> | >by Robert Vienneau, rising wages cause the ratio between the price of
> | >iron and the price of corn to rise, making it cheaper for an iron
> | >manufacturer to switch from a process that uses more iron to one which
> | >uses more corn as well as more labor per unit of iron output.
> | Recall there is no "price of iron" because iron is not traded.
Note that Chris Auld simply refused to answer your question, which
was:
Is this sort of thing possible (even supposing for the sake of
argument that he hasn't described his scenario well)?
The correct answer is "Yes".
> I should have been clearer about what I was trying to say. First,
> based on his assumptions I still don't see how your simple argument
> against his thingy takes into account the firm's borrowing corn at the
> start of the year. Second, my question about the possibility of
> certain features of the scenario holding wasn't meant to ask whether
> it's consistent to make all the assumptions Robert Vienneau states or
> otherwise makes, hence not based on the details (like the seemingly
> useless claim that it's an "integrated" firm not trading in iron).
The claim allows me to consider the decision processes of a single
firm.
> I
> think there may be a worthwhile point here which is being obscured by
> certain things he seems to be saying badly.
> | That is, the
> | solution
> | to the program {min_L wf(L) s.t. g(L)=0} does not depend on w
> | (regardless
> | of whether L is a scalar or a vector).
> I don't see why (using his assumptions) their outlays are proportional
> to labor hired, when they are also tying up varying quantities of corn
> for the year depending upon the process being used.
> | I believe what's going on here is that Vienneau has paraphrased
> | (without
> | due credit) an archaic model of a vertically integrated *industry* and
> | mistakenly applied it to a *firm*.
> That seems plausible, although there are few enough details that I'd
> be surprised if one could really be sure it was cribbed.
I don't know why you give any such comment as Chris Auld's above any
plausibility.
Chris Auld is being stupid in his comment, "without due credit",
just as he is being stupid in his comment, "not that's I've checked
his ludicrous arithmetic --- for all I know it's wrong too". His
comments are not the kind an adult would make.
And "archaic" is a word directed to no cognitive values. After all,
saying a model is "archaic" doesn't say it is wrong.
> | In the body he says he's "assuming"
> | various things about the "accounting price" of iron, but in the
> | appendix
> | he solves for that price by moving along the "factor price frontier."
> In the calculations outside of the appendix, it appeared to me that he
> was solving by finding the price that made the rate of profit of the
> two processes equal,
Correct.
> and my impression is that such an assumption
> could be inferred from various more basic assumptions (idealizing, of
> course).
> | notice the "accounting price" of iron *falls*
> | when the wage rate rises.
Can I call *this* a mathematical error?
> | Vienneau's solution instead involves an
> | endogenous change in other parameters such that profits are held at
> | zero --
> | even abusing the term "labor demand curve" to allow aggregation over
> | time,
I never aggregated over time.
> | the object he's talking about is not a labor demand curve,
I never claimed to be deriving a labor demand curve. But the
literature is not univocal.
"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..."
-- Michael Mandler, 1999.
> | and the
> | properties of the object he's talking about are not surprising.
They are so surprising that Chris Auld says below:
Vienneau claims to be showing properties of a mathematical
relationship which do not in fact hold
> Perhaps not if a person is thinking carefully, no, but as I explain
> below I see a lot of not-so-careful thinking, and I think some people
> would be surprised to find anything even roughly like it true.
Yes, including some economists.
> | >|This particular bit o' spam is
> | >|riddled with mathematical and conceptual errors; factor
> | >|demand curves cannot slope up.
> | >I always thought "spam" meant something broadcast much more widely.
> | Vienneau has a small cache his "long essays" which he regularly posts
> | all
> | over the place. Google suggests minor variants of this particular
> | piece
> | have been posted about 70 times to a variety of groups.
And yet Chris Auld does not yet have a clear answer. He does not
even address the argument.
> | I think such
> | behavior is accurately described as "spamming."
> Point taken.
I don't consider, for example, the following two posts as "minor
variants of this particular piece":
<http://www.google.com/groups?as_umsgid=2uh5pt%24klq%40samba.oit.unc.edu>
<http://www.google.com/groups?as_umsgid=rvien-2712981530020001%40ua3-p38.
dreamscape.com>
When responses to my posts provide no rational argument against them,
I will repeat those ideas.
> | >This may seem picky, but as a sci.math regular, I'd say that it seems
> | >pretty common for people to describe as "mathematical errors" things
> | >which aren't mathematical errors.
> | Whether one wishes to call the errors in this piece "mathematical" or
> | "conceptual" is a matter of semantics.
> The meaning of terms is always a matter of semantics. What I'm saying
> is that in my opinion (as a formerly professional mathematician) this
> semantics stretches the term further than it seems like it should, and
> my impression is that a lot of mathematicians would feel the same
> way. We especially dislike seeing the flip side of this, which is that
> someone calls an argument "mathematical" when it only has elements of
> mathematics in it, as if that necessarily made things better.
> | Vienneau claims to be showing
> | properties of a mathematical relationship which do not in fact hold,
> | but
> | this is a result of misunderstood concepts rather than an arithmetic
> | error
> | in the solution (not that's I've checked his ludicrous arithmetic ---
> | for
> | all I know it's wrong too).
> It doesn't seem as if you two are dealing with a mutually understood
> set of axioms but disagree about what the consequences are. If you
> did, I would agree would involve one of you making a "mathematical
> error" in a way.
Notice that Chris Auld has not disagreed with the formulation of
the firm's problem as the primal LP in the appendix in my post. Nor
has he disagreed with my statement:
For firms to continue production unaltered from period to period,
both corn and iron must be produced each period.
Nor has he disagreed with:
For corn to be produced, either the first or the second constraint
in the dual must be met with equality.
Nor has he disagreed with:
Likewise, for iron to be produced, the third or the fourth
constraint in the dual must be met with equality.
So I think he has made no point whatsoever. (My presentation presumes
a knowledge of duality theory in Linear Programming; it is a
mathematical argument.)
> (And to be fair, his reference to "arithmetically"
> incorrect opinions of economists seems to be stretching the term in at
> least as bad a way. I really doubt that the problem is incorrect
> mathematics.
My post draws upon a decades-long dispute in economics in which all
sides agreed that certain neoclassical economists made mathematical
errors. Inasmuch as some economists have yet to accept certain
agreed-upon results of these debates and, in fact, make claims
incompatible with those results, they are making mathematical
errors.
> | >From this remark,
> | >Robert Vienneau:
> | >|So, as good economists have long recognized, the theory I am
> | >|attacking
> | >|is incorrect, as a matter of mathematics and logic.
> | >I was under the impression he was happily acknowledging that what he
> | >claims to be showing is well-known in economics.
> | You misunderstand Vienneau's intent. Recall the preamble to the
> | arithmetic features an economist who is supposed to be "unable to
> | explain"
> | the analysis Vienneau is about to present. The "good economists" in
> | the
> | quote above are the tiny band of aging political idealogues
"aging political idealogues" is a phrase directed to no cognitive
values.
> | Vienneau loves
> | to paraphrase; the vast majority of economists are the, er, non-good
> | economists not in that camp. Unfortunately Vienneau rarely gets even
> | the
> | radical critiques (of economics as it stood in the late 19th century)
> | he
> | paraphrases right, as this thread amply demonstrates.
This thread demonstrates no such thing.
> It seems as though you are arguing against him as if the thesis in
> question was that the typical economist has gone wrong in a certain
> way. That's fine, since he makes it sound like that's what he means
> (and if he doesn't mean so, he should step in and say so right away).
Am I not simply echoing some claims in the literature?
"The issue was settled in favour of Cambridge University when
Samuelson wrote (1976) that wherever 'informed economic theory
is taught', the 'paradoxes' are accepted, and their consequences
for the concept of capital known. It is another matter that, on
the basis of this criterion, many seats of learning in North
America, as perhaps also elsewhere, do not teach informed
economic theory."
-- Syed Ahmad (1998)
"After Sraffa's book in 1960 the next decades saw major battles
in the journals, battles which resulted in conclusions widely
held today: to wit, the technical errors are conceded, but their
significance is contested. This has a practical meaning: open
any major journal at random today, and there will be marginal
products... - with no hint that any technical error is
involved. The critique is simply ignored. It can't be answered,
but it is held to be unimportant."
-- Edward Nell (1998)
"But something even more interesting and intriguing has
happened. After only a few years, even the admissions initially
made no longer found any mention... The typical economics student
entering university from the 1980s onwards has heard nothing of
the re-switching difficulties involved in the neoclassical theory
of capital and income distribution."
-- Luigi L. Pasinetti (200?).
"The critique of Robinson and Sraffa is more than forty years old.
Yet for psychological and political reasons, rather than for logical
and mathematical ones, the capital critique has not penetrated
mainstream economics. It likely never will. Today only a handful of
economists seem aware of it... Ostensible liberals are not exempt;
their arguments for higher public infrastructure investment (based
on its alleged marginal productivity) are precisely of this type,
as are arguments for increased investment in education based on
the higher marginal productivity of human skill."
-- James Galbraith (2001).
"Of course, the average economist would never tell you that
economic theory has suffered such a devasting blow. This is
because the average YOUNG economist doesn't even know that
this intellectual bout took place - the concepts in this
debate don't make it onto the curriculum for either
undergraduate or postgraduate students. Older economists
cannot avoid some knowledge of the war, but they erroneously
believe that their camp won, or they dismiss the issue
completely.
Today economic theory continues to use exactly the same
concepts which Sraffa's critique showed to be completely
invalid...
There is no better sign of the intellectual bankruptcy of
economics than this."
-- Steve Keen (2001)
"The arguments necessary to surmount these confusions started
becoming available in English only with Garegnani (1976), which
was quickly followed by a number of other papers and books
among which Petri (1978, 1991, 1998, 1999), Garegnani (1978-9,
1989, 1990, 2000), Eatwell (1979, 1982), Milgate (1979, 1982),
Eatwell and Milgate (1983), Schefold (1985, 1997), Kurz (1987).
This wave of contributions finally started clarifying the
difference between long-period and neo-Walrasian versions of the
marginalist/neoclassical approach, as well as the different roles
of the conception of capital as a single factor, roles some of
which were argued to be present even in the neo-Walrasian
versions... The neoclassical reaction was striking: no reply at
all. Some of the neoclassical assessments of the Cambridge
controversies (e.g. Blaug, 1974; Stiglitz, 1974; Bliss, 1975b)
antedate the writings of this second critical wave, but other ones
do not (e.g. Dougherty, 1980; Burmeister, 1980, 1991; Hahn, 1982)
and yet contain no reference to any of the post-1975 critical
writings just mentioned. One possible interpretation ...
is that no reply came forth because a satisfactory reply was not
easy to find. Be that as it may, the fact is that up to now
(end 2002) none of the post-1975 critical writings just remembered
is mentioned in any of the writings of Hahn or Solow or F. M. Fisher
or Burmeister even when they return on the themes of the Cambridge
controversy. No wonder that considerable misunderstandings persist,
which is what prompted me to write the present essay."
-- Fabio Petri, Somewhere off:
<http://www.econ-pol.unisi.it/docenti/petri.html>
I don't see where the political leanings of any of the above is
relevant to correctness of what they say.
> It is of course normal for most "everyday" arguments not to have much
> rigor to them. To someone trained in rigorous proof it should be
> reasonably obvious. For me the disturbing parts are the claims of
> people who seem VERY convinced that the argument for their particular
> claim is entirely conclusive, as if from a fallacious sense of
> rigor. I'm thinking especially of libertarians (I've probably read
> more than my share of libertarian propaganda) arguing the advantages
> of libertarian governmental policy, but also of more mainstream
> arguments on similar lines (e.g., that our state's "right to work" law
> can only help workers and could not possibly hurt them because it
> "gives them more options", or e.g. that raising the minimum wage is
> bad because it will "obviously" cause more unemployment).
That's what the following source is about, for example:
"The view which is adopted here however is that there is
insufficient robust theoretical ground to support the
notion, underlying virtually all economic discussions of
employment, that real wages and employment are related in a
systematically inverse way. In other words,the view is
adopted here that no clear economic reasoning can be provided
by which to suppose that in general a fall in real wages would
lead to an increase in labour employment.
Some, particularly economists, might find this rather
confronting, since the real wage-employment nexus has been a
part of economic folklore for so long, that, to use the words
of one economist, this notion is no longer seen as a theory of
employment, but as an 'immediate reflection of the facts'."
-- Graham White, "The Poverty of Conventional Economic
Thinking and the Search for Alternative Economic and
Social Policies". November 2001.
<http://www.econ.usyd.edu.au/drawingboard/journal/0111/white.pdf>
--
Christopher Auld
>au...@acs.ucalgary.ca (Christopher Auld) wrote:
>| rate holding output constant is clearly incorrect. That is, the solution
>| to the program {min_L wf(L) s.t. g(L)=0} does not depend on w (regardless
>| of whether L is a scalar or a vector).
>I don't see why (using his assumptions) their outlays are proportional
>to labor hired, when they are also tying up varying quantities of corn
>for the year depending upon the process being used.
Not selling output ("corn") today isn't an outlay, although there is of
course an opportunity cost involved. Briefly laying out the two-period
version of Vienneau's problem might clarify: A firm sells corn Q in
periods 1 and 2, produced using iron, corn, and labor L. It does not buy
or sell iron and buys labor at rate w. If it discounts at rate b and the
price of corn is normalized to unity, it's revenues are (Q_1 + bQ_2) and
its costs are (wL_1 + bwL_2). Notice this is true whether or not corn is
both an input and an output or just an output.
>In the calculations outside of the appendix, it appeared to me that he
>was solving by finding the price that made the rate of profit of the
>two processes equal, and my impression is that such an assumption
>could be inferred from various more basic assumptions (idealizing, of
>course).
Which assumptions would those be? Recall he claims to be considering the
response of a firm to a change in wages all else equal. There is no
reason why a change in relative prices should leave the rate of profit of
the two processes equal, indeed, an epsilon change in wages will cause his
firm to send output off to infinity or shut down, if the initial wage was
such that the firm used both processes. Notice Vienneau's solution
changes parameters other than the wage rate (he is not holding all else
equal).
>The meaning of terms is always a matter of semantics. What I'm saying
>is that in my opinion (as a formerly professional mathematician) this
>semantics stretches the term further than it seems like it should, and
>my impression is that a lot of mathematicians would feel the same
>way.
It is fine with me if Vienneau's errors are attributed to mistaken
economics rather than mistaken mathematics.
>It seems as though you are arguing against him as if the thesis in
>question was that the typical economist has gone wrong in a certain
>way. That's fine, since he makes it sound like that's what he means
>(and if he doesn't mean so, he should step in and say so right away).
Again, Vienneau is obsessed with broadcasting that economists have "gone
wrong" in profound ways -- that is the "thesis in question." For example,
one of the previous times this "long essay" was spammed it featured the
autobiographical note
| I do not teach economics. That is, I do not stand up before
| a roomful of students and use my authority to try to get them
| to believe nonsense and lies.
Vienneau's goal isn't to discuss economics, except inasmuch one could say
that creationists wish to "discuss" evolutionary biology.
>right or not. They are very often wrong, after all. We have plenty of
>real serious crackpots in the rest of sci.* outside of sci.econ, and
>if the worst you have to deal with is someone who's confused about the
>meaning of "demand curve" and the like, you're lucky. I also am not
>too seriously worried about the health of the economics profession
>itself.
Neither am I, but I am irritated that reasonable people cannot have a
discussion on sci.econ because of Robert Vienneau.
>Another example is a dinky model of a traffic system in which adding
>an additional road causes longer delays in travel. Opening the new
>route causes individually time-optimizing drivers to concentrate more
>heavily on certain otherwise good roads, which causes them to slow
>down.
>What I'm really hoping is that I'll be able to get an analogous
>example from economics, or if not, some good explanation of why it
>really doesn't happen.
Economics is chock full of examples such as you describe: economists just
love mechanisms which yield counterintuitive results, particularly if the
result overturns the anticipated outcome of some policy. The example you
give of traffic systems could be claimed to be economics --- goal-driven
behavioral response to a change in incentives yields an outcome which
wasn't anticipated or desired. Sometimes such results are said to be
examples of the "Law of Unintended Consequences."
An example I like to use is vehicle safety legislation. If we force auto
makers to make safer cars -- with airbags and collapsible steering columns
and side impact braces and such -- we will save lives, right? Not
necessarily. If people respond to being in safer cars by driving faster
with cell phones in their ears, we may actually increase traffic
fatalities by making cars safer. And those drivers in safer cars may be
running over more pedestrians and bicyclists, so the result of the
legislation may be deemed to be particularly unwanted. There is some
evidence this is what actually happened in the U.S. in the mid-seventies.
Another (analytically closely related) example can be found in economic
epidemiology. Suppose a partially effective preventative vaccine for AIDS
were made available. It would seem obvious that if lots of people get
vaccinated, AIDS incidence would fall. But that is only necessarily true
if people don't change their behavior in response to being vaccinated. If
they respond to being vaccinated by having more risky sex, it's possible
that the net effect is to spur the epidemic.
A possibly surprising result related to Vienneau's crap is the response of
a monopsonist to an increase in minimum wages. If a firm cannot hire all
the labor it wants at a given wage but rather must pay higher wages to
attract more workers, then it may respond to an increase in a minimum wage
by hiring more workers. This is an Economics 101 result.
Unfortunately off the top of my head I can't think of a book compiling a
bunch of such examples in economics.
Christopher Auld
> 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..."
Pay attention. Notice ZERO PROFIT. Now consider the response of A FIRM
to an increase in factor prices. Will an increase in factor prices leave
a firm's profits unaltered?
Are you EVER going to get the difference between A FIRM's equilibrium and
a MARKET's equilibrium?
>> It seems as though you are arguing against him as if the thesis in
>> question was that the typical economist has gone wrong in a certain
>> way. That's fine, since he makes it sound like that's what he means
>> (and if he doesn't mean so, he should step in and say so right away).
>
>Am I not simply echoing some claims in the literature?
No, you're not. Not only do you obsess over a minor technical issue in a
narrow area of microeconomics, you don't even understand the technical
issue.
Robert Vienneau
(Christopher Auld) wrote:
> Keith Ramsay <kra...@aol.com> wrote:
> >au...@acs.ucalgary.ca (Christopher Auld) wrote:
> >What I'm really hoping is that I'll be able to get an analogous
> >example from economics, or if not, some good explanation of why it
> >really doesn't happen.
[>> If I thought Robert Vienneau's thingies were ]
[>> perfect okay as they stood obviously I wouldn't be asking; on the ]
[>> other hand if they didn't have a certain family resemblance to what ]
[>> I'd like to see, I wouldn't be asking right now. ]
> Economics is chock full of examples such as you describe: economists just
> love mechanisms which yield counterintuitive results, particularly if the
> result overturns the anticipated outcome of some policy.
> [blah, blah, blah]
Notice Keith Ramsay asked whether my example, maybe explained somehow
different, could be used to attack certain naive views on "right to
work" laws, minimum wages, etc. Notice that Chris Auld changes the
subject. He does not say yea or nay.
Instead he goes off about other ways those naive views can be attacked.
In other words, he agreed with my first sentence in my first post on
this thread, with Richard X. Chase, and with Heinrich Bortis, for
example. But the point of every mention I have made of these other
ways was that this is not the point of this thread.
On the other hand, the paper at this URL:
<http://www.econ.usyd.edu.au/drawingboard/journal/0111/white.pdf>
says that Keith Ramsay is right in thinking my example can be used
to attack those naive views.
Robert Vienneau
> There is no
> reason why a change in relative prices should leave the rate of profit of
> the two processes equal, indeed, an epsilon change in wages will cause
> his
> firm to send output off to infinity or shut down, if the initial wage was
> such that the firm used both processes.
Recall that Chris Auld thinks that both the price of iron, p, and
the discount rate, 1/(1 + r), should be taken as exogeneous. So,
for arbitrary values of p and r, he is not entitled to draw even
a horizontal labor demand curve. (The firm is supposed to be in
equilibrium at each point along a labor demand curve.) That is,
his position, if he were consistent, should be that wages and
employment are not determined by the demand and supply of labor
in my simple example (except in exceptional cases).
> Briefly laying out the two-period
> version of Vienneau's problem might clarify: A firm sells corn Q in
> periods 1 and 2, produced using iron, corn, and labor L. It does not buy
> or sell iron and buys labor at rate w. If it discounts at rate b and the
> price of corn is normalized to unity, it's revenues are (Q_1 + bQ_2) and
> its costs are (wL_1 + bwL_2). Notice this is true whether or not corn is
> both an input and an output or just an output.
1.0 INTRODUCTION
Chris Auld refuses to consider the structure of my example.
So let's consider an example with dated labor inputs. The only
input to the firm, in this new example, is labor. Some of that
labor, at a given time, is dedicated to producing consumer goods
immediately, some is dedicated to producing consumer goods for
the next year, etc.
Consider two islands, Alpha and Beta. A competitive capitalist
economy exists on both islands. The inhabitants of these islands
consume a single consumption good, corn. They both have access
to the same technology.
This technology consists of two techniques for producing corn.
Alpha has adopted the alpha technique, and Beta has adopted the
beta technique. (They've each adopted the technique they have
because it is cheapest on their respective island.) Assume each
island is in a stationary state.
2.0 DESCRIPTION OF TECHNOLOGY
Both techniques exhibit constant returns to scale. Both techniques
produce corn at the end of a yearly harvest. Dated labor quantities
are the only input required to produce this corn. The beta technique
requires inputs of labor in the year in which corn is harvested
and the previous year. The alpha technique requires inputs of labor
for three years before the harvest. Table 1 shows the specific
quantities required. (By the way, as I understand it, an example
with the properties highlighted here can be constructed with smooth
production functions.)
TABLE 1: INPUTS OF LABOR NEEDED PER QUARTER CORN PRODUCED
YEAR
BEFORE
OUTPUT ALPHA TECHNIQUE BETA TECHNIQUE
0 142 person-years 10 person-years
1 10 person-years 240 person-years
2 100 person-years
31,500 workers are employed on both islands. Some of these workers
are directly producing corn, while others are producing goods that will
be used in producing corn in future year(s). Table 2 shows the
allocation of labor on Alpha. Notice that the annual output of corn is
125 quarters corn with this allocation.
TABLE 2: LABOR INPUTS ON ALPHA
1998 1999 2000 2001 2002 2003 2004
...17,750
1,250 17,750
12,500 1,250 17,750
12,500 1,250 17,750
12,500 1,250 17,750
12,500 1,250 17,750
12,500 1,250 17,750
12,500 1,250...
12,500
Table 3 shows the allocation of labor on Beta. Here the output is
126 quarters corn.
TABLE 3: LABOR INPUTS ON BETA
1998 1999 2000 2001 2002 2003 2004
...1,260
30,240 1,260
30,240 1,260
30,240 1,260
30,240 1,260
30,240 1,260
30,240 1,260
30,240...
TABLE 4: LABOR INTENSITY
Alpha: 31500/125 = 252 Person Years Per Bushel
Beta: 31500/126 = 250 Person Years Per Bushel
3.0 COSTS
Since I have assumed these islands are in a stationary state, the
price of corn, the wage, and the rate of profits will be stationary.
The price of corn, assumed unity, will just cover costs (including
profits - sometimes known as interest). Thus, Equation 1 will obtain
on Alpha:
142 w + 10 w (1 + r) + 100 w (1 + r)^2 = 1 (1)
where w is the wage in quarters corn per person year and r is the
rate of profits. Equation 1 implicitly defines a relation between the
wage and the rate of profits. Equation 2 provides an explicit
statement of that relation:
w( alpha ) = 1/( 252 + 210 r + 100 r^2 ) (2)
An island in a stationary state using the alpha technique will have
a lower wage the higher the rate of profits. This statement generalizes.
By the same logic behind Equation 1, Equation 3 holds on Beta:
10 w + 240 w (1 + r) = 1 (3)
Equation 4 provides the wage-rate of profits curve for Beta:
w( beta ) = 1/( 250 + 240 r ) (4)
Just any configuration of wages consistent with Equation 1 or 2
cannot prevail on Alpha. Only those configurations can exist in a
stationary state in which the beta technique is not cheaper than the
alpha technique. Likewise, a configuration of wages and the rate of
profits consistent with Equation 3 or 4 will only prevail on Beta
when the alpha technique is not cheaper. Some algebra is needed to
draw out the implications of these remarks. The alpha and beta
techniques will be equally cheap when Equation 5 holds:
142 w + 10 w (1 + r) + 100 w (1 + r)^2 = 10 w + 240 w ( 1 + r ) (5)
Those who bother to solve this will find that these switch points
in which both techniques are equally cheap arise at rates of profit
of r = 10% and 20%. Since the beta technique has a sum of direct
and indirect labor inputs less than that required for the alpha
technique, beta will be cheaper at a rate of profits of 0% in
which no time discounting is performed. If you think about the
quadratic nature of Equation 5, you might see that Figure 1 shows
which technique is cheaper at all possible wages and rates of
profits.
Beta cheaper Alpha cheaper Beta cheaper
r 0% 10% 20%
+-----------------+-----------------+------------>
w 1/250 1/274 1/298
FIGURE 1: CHOICE OF TECHNIQUE
Notice that the wage declines to the right in the figure. And
that around a wage of (1/298), a lower wage is associated
with the adoption of a LESS labor-intensive technique.
Notice that the above analysis has only been of equilibria of
firms. Nothing has been said about consumer choice, labor supply,
savings, effective demand, the policy of the monetary authorities,
or whatever other elements are needed to determine equilibria of
the economy, depending on which of several theories of
distribution one may adopt.
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> quotes, again:
"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..."
-- Michael Mandler, 1999.
> Pay attention. Notice ZERO PROFIT. Now consider the response of A FIRM
> to an increase in factor prices. Will an increase in factor prices leave
> a firm's profits unaltered?
Notice LONG-RUN. For a firm in a competitive market, ECONOMIC profits
will be zero in the long run. This is how Mandler defines long-run
factor demand for unproduced inputs.
And in my example, a lower rate of (accounting) profits is associated
with a higher level of wages.
Notice poor Chris Auld's refusal to explain what Michael Mandler
could possibly be talking about with his phrase "the long-run demand
for factors can be badly behaved functions of factor prices".
As for textbook nonsense:
"the long-run demand curve for labor is more elastic than the
short-run demand curve."
-- D. Bellante and M. Jackson, Labor Economics: Choice in
Labor Markets. McGraw-Hill, 1979.
"The demand for labor is more elastic in the long-run than in
the short run."
-- R. G. Ehrenberg and R. S. Smith, Modern Labor Economics:
Theory and Public Policy. Scott, Foresman and Co., 1982.
(Both quoted in Ian Steedman, "On Input 'Demand Curves'".
Cambridge Journal of Economics, 1985.)
> Are you EVER going to get the difference between A FIRM's equilibrium and
> a MARKET's equilibrium?
In the last paragraph of my first post on this thread, I made the
point that I was not discussing market equilibria. Anybody who
doubts that point can verify it by looking at my essay
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf>
which does discuss market equilibria. Notice how my example in this
thread is missing half of the model in that essay, so to speak. (I am
no longer committed to calling any curves in that essay "demand"
functions.)
> >> It seems as though you are arguing against him as if the thesis in
> >> question was that the typical economist has gone wrong in a certain
> >> way. That's fine, since he makes it sound like that's what he means
> >> (and if he doesn't mean so, he should step in and say so right away).
> >Am I not simply echoing some claims in the literature?
> No, you're not. Not only do you obsess over a minor technical issue in a
> narrow area of microeconomics, you don't even understand the technical
> issue.
Dear reader, poor Chris Auld thinks you are an idiot. He thinks you
cannot tell that the question was, in this context, whether I was
echoing some literature with the thesis that typical economists have
gone wrong in a certain way. And he thinks that you cannot see that
the correct answer to this question is yes. And those claims
I am echoing are based on something like my example, whether my
understanding of that example is correct or not.
susupply
Keith Ramsay <kra...@aol.com> wrote:
> >It seems as though you are arguing against him as if the thesis in
> >question was that the typical economist has gone wrong in a certain
> >way. That's fine, since he makes it sound like that's what he means
> >(and if he doesn't mean so, he should step in and say so right away).
Vienneau has a long (and paranoid) history on sci.econ, for instance this
from him recently:
<< so many economists have provided empirical evidence here that
most mainstream economists do not understand price theory. I might
as well provide a (non-complete) list: Chris Auld, Don Dale,
Edward Flaherty, David Friedman, Paul Gomme, James McCown,
Robert A. Simon, Markku Stenborg, John J. Weatherby, and Mark
Witte. To describe certain posts from these economists as merely
ignorant is to be kind.>>
Christopher Auld
[ same misunderstood quote, snipped ]
>> Pay attention. Notice ZERO PROFIT. Now consider the response of A FIRM
>> to an increase in factor prices. Will an increase in factor prices leave
>> a firm's profits unaltered?
>Notice LONG-RUN. For a firm in a competitive market, ECONOMIC profits
>will be zero in the long run.
Sigh. That's because other prices varies with the wage rate to keep
profits at zero. That doesn't mean A FIRM would change those prices
itself such that its profits remain at zero if wages decreased, for
example. A FIRM'S profits are a non-increasing function of factor
prices. This is ridiculously simple stuff.
>And in my example, a lower rate of (accounting) profits is associated
>with a higher level of wages.
Yes. Vienneau considers two firms, one facing a high wage and low
interest rate (call this A), the other facing a low wage and high interest
rate (call this B). Both have zero profits. Now notice the difference
between these two claims:
Firm A does not necessarily have lower labor intensity than
firm B.
and
A firm would respond to an increase in the wage rate, all else equal,
by hiring more labor.
The first statement is correct; the second statement is just plain wrong.
Naturally, Vienneau's obnoxious blather about the failings of the
economics profession is based on his misunderstanding that the second
claim is true.
[ snip: more brutal misunderstandings of intermediate microeconomics,
notably that the meaning of "long run" in the textbooks Vienneau derides
differs from the meaning of "long run" in the Sraffian literature ]
Christopher Auld
>Recall that Chris Auld thinks that both the price of iron, p, and
>the discount rate, 1/(1 + r), should be taken as exogeneous. So,
Recall rather that I've repeatedly said that the "price of iron" is not a
parameter of this model. If one wanted, for some reason, to calculate
the shadow price of iron, it would be a function of the parameters of the
model. That is, endogenous.
Jonah Thomas
> Robert Vienneau <rv...@see.sig.com> wrote:
>>Recall that Chris Auld thinks that both the price of iron, p, and
>>the discount rate, 1/(1 + r), should be taken as exogeneous. So,
> Recall rather that I've repeatedly said that the "price of iron" is not a
> parameter of this model. If one wanted, for some reason, to calculate
> the shadow price of iron, it would be a function of the parameters of the
> model. That is, endogenous.
It sounds like you two are continually misunderstanding each other.
The way we used to handle that back when I was first learning to do math
proofs, was when somebody disagreed with somebody else, *first* they had
to repeat what the other guy was saying in their own words. And when
the other guy said that yes, that's what he meant, *then* they got to
say what they disagreed with.
Somehow when we did it that way we understood what the issues were.
When we just kept telling each other who was wrong we never got it settled.
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >Recall that Chris Auld thinks that both the price of iron, p, and
> >the discount rate, 1/(1 + r), should be taken as exogeneous. So,
> Recall rather that I've repeatedly said that the "price of iron" is not a
> parameter of this model. If one wanted, for some reason, to calculate
> the shadow price of iron, it would be a function of the parameters of the
> model. That is, endogenous.
"Rob, a 'labor demand curve' is, by definition, derived when only one
price changes. It does not matter if, in the model, changes in that
price will alter other prices: if we allow those other prices to
alter,
THE RESULTING OBJECT IS NO LONGER A LABOR DEMAND CURVE.
Damnit, what is so hard to understand about this? I've spent years
trying to get this point across."
-- Poor Chris Auld, sci.econ, 6 February 2000
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> [ same misunderstood quote, snipped ]
Notice poor Chris Auld's refusal to explain what Michael Mandler
could possibly be talking about with his phrase "the long-run demand
for factors can be badly behaved functions of factor prices".
> Vienneau considers two firms, one facing a high wage and low
> interest rate (call this A), the other facing a low wage and high
> interest
> rate (call this B).
No. I consider a firm facing a (non-exclusive) choice between:
(1) Producing corn with the 1st corn-producing process
(2) Producing corn with the 2nd corn-producing process
(3) Producing iron with the 1st iron-producing process
(4) Producing iron with the 2nd iron-producing process
(5) Carrying the firm's resources over unchanged to the
start of the next period
(For (5), consider the primal LP in my appendix in the post with
which I began this thread. That LP is unchanged by the insertion
of a slack variable, which converts the inequality to an equality.)
The firm faces a given wage, w.
It does not matter whether we model the firm as facing a given
price of iron, p, or setting that price with an internally
consistent accounting system. The firm is in equilibrium only
along a certain locus (w, p).
In either case, the rate of profits, r, emerges endogeneously
from the analysis. As illustrated in my first post in this
thread, which poor Chris Auld has yet to address.
At any rate, a higher wage can be associated with the adoption
of more labor-intensive technique. The two examples I have
presented on this thread illustrate.
These examples are not consistent with neoclassical theory
as still presented in the textbooks.
The phrase "brutal misunderstandings", instead of merely
"misunderstandings" is another example of poor Chris Auld being
stupid:
> [ snip: more brutal misunderstandings of intermediate microeconomics,
> notably that the meaning of "long run" in the textbooks Vienneau derides
> differs from the meaning of "long run" in the Sraffian literature ]
Notice poor Chris Auld's refusal to outline any difference at all in
these supposed different meanings. Notice he did not look up the
Steedman paper from which I obtained these quotes.
--
Christopher Auld
>In article <bc2fv5$14...@acs4.acs.ucalgary.ca>, au...@acs.ucalgary.ca
>(Christopher Auld) wrote:
>
>> Robert Vienneau <rv...@see.sig.com> wrote:
>
>> >Recall that Chris Auld thinks that both the price of iron, p, and
>> >the discount rate, 1/(1 + r), should be taken as exogeneous. So,
>
>> Recall rather that I've repeatedly said that the "price of iron" is not a
^^^
^^^
>> parameter of this model. If one wanted, for some reason, to calculate
>> the shadow price of iron, it would be a function of the parameters of the
>> model. That is, endogenous.
>
> "Rob, a 'labor demand curve' is, by definition, derived when only one
> price changes.
Vienneau apparently thinks that what I say above is in conflict
with the quote immediately above. Too funny.
Hey Bobby, if the wage rate changes, does the wage rate squared
also change? Since both these variables changed, does that mean
the resulting object isn't a labor demand curve?
Christopher Auld
>> Vienneau considers two firms, one facing a high wage and low
>> interest rate (call this A), the other facing a low wage and high
>> interest
>> rate (call this B).
>
>No. [...]
>In either case, the rate of profits, r, emerges endogeneously
>from the analysis.
A FIRM's dicount rate is endogenous to the wage rate? LOL.
Let's try this another way. Write down the firm's objective function,
which depends on the choice variables: the allocation of labor and capital
to both processes in every period (ie, another error in the "long essay"
is the static choice problem for a firm in a dynamic setting). Since
you're supposed to be using textbook assumptions for a competitive firm,
impose the conditions that the firm takes the wage, discount rate, and
output price as parametric. Vary the wage, which is supposed to obtain in
every period. Obtain optimal response functions. Show the optimal
response to a ceteris paribus increase in the wage rate is to increase
labor demanded.
Since this is impossible, conclude that the "arithmetic" in your "long
essay" is wrong. You aren't holding all else equal.
>> [ snip: more brutal misunderstandings of intermediate microeconomics,
>> notably that the meaning of "long run" in the textbooks Vienneau derides
>> differs from the meaning of "long run" in the Sraffian literature ]
>
>Notice poor Chris Auld's refusal to outline any difference at all in
>these supposed different meanings.
I shouldn't have to explain how these meanings differ to someone who has
spent much of the last fifteen years incessantly and obnoxiously spamming
the net with his kooky ideas about, amongst other things, why economics
textbooks are wrong. Why don't you try to figure it out for yourself?
Robert Vienneau
o Poor Chris Auld suggests the square of the wage is a price - of
what, he does not say.
o He expresses surprise at the notion that the best return a
firm can obtain depends on the choices open to the firm.
o He describes a model in which there are four processes as one
in which there are two.
o He asks me to write down an objective function in my exposition
of a model, even though I have already explicitly written
down (dual) objective functions. (When each basic solution
in the primal is optimal is shown in the "Region Analysis"
worksheet in the spreadsheet I linked to in my post starting
this thread.)
o A standing challenge of my example is to draw a labor demand
curve in my example that matches up with the curve in the
intro textbook story. He changes the subject to "dynamics".
o He displays his ignorance of some of the literature on
dynamics, even though I've already given references in
previous posts.
o He is requested to state what he thinks the distinction
between "long run" and "long run" to be. He responds with
absolute stupidity.
In my first post on this thread, I presented a formal analysis of
the equilibrium of a firm in my example. This analysis allows one
to see how "the set of zero-" (economic) "profit activities shift
in response to factor price changes" such as the wage. The example
illustrates that "the pattern of activities adopted in the face of
long-run factor-price changes can be complicated and
counterintuitive." In fact, "it is not necessary that newly adopted
activities use cheaper factors more intensively." Sometimes the
firm in long-run equilibrium will want to employ more workers at
a higher wage.
Notice poor Chris Auld's refusal to explain what Michael Mandler
could possibly be talking about with his phrase "the long-run demand
for factors can be badly behaved functions of factor prices".
I wonder if Keith Ramsay will comment publicly any more on this
thread.
"...marginalist economists provided accounts of the long-period
(uniform rate of profit) theory of value and distribution, ...the
marginalist economist had to 'close the system' in some ...
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 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)
--
Keith Ramsay
| Unfortunately off the top of my head I can't think of a book compiling a
| bunch of such examples in economics.
I hope people will excuse my delayed response here, but I finally had
a chance to look at a "Curiosum" as discussed by Real Economists. Even
better, it's an admitted example of an error due to an admitted
mathematical mistake, one that I would agree was indeed a mathematical
mistake and not a mistake in applying mathematics or whatnot.
I didn't get around to reading the whole original argument (which
failed) but the key mistake is described as being that Levinari takes
a nonzero vector v>=0 such that Av>=Bv for two matricies (and someone
pointed out that one can always assume the entries of A and B are
strictly positive), and then infers that since certain quantities
produced by taking an inner product of another vector >=0 with v are
zero, the other vector is =0. But this is supposed to have overlooked
the possibility of zero coordinates for v. Allegedly some efforts were
made to patch up the result in "generic" circumstances (where perhaps
it was hoped that v could be chosen not to have any zero
coordinates?), but the theorm fails in an open set of matrices A and B.
The November 1966 issue of Quart. J. Econ. (the oldest issue that the
University of Colorado hasn't yet whisked off into cold storage) is
devoted to "paradoxes of capital theory". After reading some of the
articles I can only say I feel a little sorry for Mr. Levinari of
1966, because several articles explain in detail why he is
wrong. There's also a short joint paper of Samuelson and Levinari
titled something like "The Samuelson-Levinari theorem is false".
Apparently Samuelson had conjectured that in a simple model something
like the kind we had been discussing here, when one set of techniques
A is preferred to a second set B at one interest rate r1, but B is
preferred to A at a second rate r2>r1, one does not have "reswitching"
back to A at a third rate r3>r2>r1. But one can. One of the examples
was called the "Ruth Cohen Curiosum", so I suppose she's given credit
for it.
The result seems to be interesting not so much for the possibility of
the very *same* technology "reappearing", but for the fact that it
means one doesn't have any necessary ordering on the technologies that
become preferable as the real interest rate moves in a given direction.
They might be more "capital intensive" or less, more "labor intensive"
or less, and so on. Samuelson says in a separate paper that this makes
things more difficult for the working economist, but (from memory,
words to the effect that) nobody promised economics would be easy.
I have two questions. Samuelson refers to something called the "golden
rule", which from the context appeared to refer to an idealized
situation which would occur at a real interest rate of zero. Perhaps
someone could explain.
The second question is, assuming the kind of thing assumed in the
model, what can one say about the effect on the "size" of the economy
as a whole as one moves through one of the "switching points" in
question. I thought for a little bit about how things might go as one
switched between techniques, but it wasn't clear to me that it doesn't
depend upon which of various effects runs more quickly, such as
responses of prices to supplies of goods and responses of investors to
changes in profitability of techniques. I think this was also one of
the main sources of my confusion during this thread. It seems like
some kind of assumption needs to be made.
For example, one of the papers in this journal issue simply assumes
that one has an economy with a fixed population of workers, who are
always employed. If that were so, then a decrease in the ratio
between the amount of some capital good used and the amount of labor
used would presumably just mean that the capital good would just be
used up until it reached a lower level. Perhaps these toy economies
have idealized away the reasons why in the real world we get
unemployment, and one cannot really make a satisfactory assumption
about what happens in such a model. I suspect, though, that one could
analyze the situation more thoroughly, though.
Keith Ramsay
Steven E. Landsburg
Keith Ramsay <kra...@aol.com> wrote:
>
>I have two questions. Samuelson refers to something called the "golden
>rule", which from the context appeared to refer to an idealized
>situation which would occur at a real interest rate of zero. Perhaps
>someone could explain.
From a textbook on macroeconomics (which I wrote):
\Bhead{The Golden Rule}
The Bible tells us to do unto others as we would have them do
unto us. That Golden Rule, applied to future generations,
can be used to analyze the desirability of different rates of
economic growth.
How do we know when an investment project is socially
desirable? The answer depends on what we mean by socially
desirable. One reasonable criterion---and a plausible
interpretation of the biblical Golden Rule---is that a
project is desirable when its benefits (as measured by
people's willingness to pay for them) exceed its costs,
without regard to who pays the costs and who receives the
benefits.
Within a single time period, it is relatively easy to
interpret this criterion. If a certain project costs me \$1
and confers benefits on you worth \$2, then it is a good
project. If it costs me \$1 and confers benefits on you
worth 50\cents, it is a bad one.
(To relate this criterion to the Golden Rule, notice that you
would certainly be willing to incur \$1 in costs to gain
benefits of \$2 for yourself, and that you would certainly be
{\it un\/}willing to incur \$1 in costs to gain benefits of
50\cents for yourself. The suggestion here is that you
should evaluate benefits to others exactly the way you
evaluate benefits to yourself.)
However, when we think about investments, such calculations
become trickier, because we are usually thinking about at
least two separate time periods. Costs (building factories,
educating workers, accumulating inventory) can occur in the
present while benefits (increased output) occur in the
future. Now the question arises: When we compare this
year's costs with next year's benefits, how should we measure
next year's benefits: by their {\it face\/} values or by
their {\it present\/} values?
Suppose, for example, that by spending \$1 today you can
produce \$1.05 worth of output next year, and that the market
interest rate is 10\% per year. Is this project a good one
because \$1.05 (the face value of the benefits) exceeds \$1?
Or is it a bad one because the present value of that \$1.05
is {\it less\/} than \$1?
From the individual investor's point of view, the answer is
easy: Only present values matter. In the example, an
investor can earn more by lending his \$1 at interest than by
investing it, so the project will be rejected.
But from a broader social viewpoint, it is less clear which
criterion is the right one. If we imagine that next year's
population consists of the same individuals who are alive
today, then it is surely still correct to use present values.
After all, each individual makes choices with an eye to the
future, and chooses an optimal mix of consumption and
investment. Those individuals---quite rationally---make
present value calculations, and any alternative would lead to
inferior decisions (that is, decisions which would leave
people less happy).
But suppose we imagine next year's population to be quite
different from this year's, because children are born and
their grandparents die. Those who will not be born until
next year do not get to participate in the advantages of
consuming earlier rather than later---indeed, today's
consumption is of no benefit to them whatsoever. That makes
a present value calculation much harder to justify. If
people can invest \$1 today to create \$1.05 worth of
benefits for their descendants, and if we treat all
generations as equally worthy, then the \$1.05 benefit
exceeds the \$1 cost and the project is desirable.
In other words:
\law{If all generations are treated equally, then the
``golden rule'' tells us to undertake a project if its future
benefits exceed its current costs, where those future
benefits are assessed at their {\it face\/} values.}
On the other hand:
\law{Individual investors will undertake a project if its
future benefits exceed its current costs, where those future
benefits are assessed at their {\it present\/} values.}
That is, individual investors do {\it not\/} follow the
Golden Rule. Instead, they reject some projects than the
Golden Rule would recommend.
\danger{On the other hand, if individual investors value
their descendant's happiness as much as their own, then they
might choose to follow the golden rule.}
\danger{The golden rule is an ethical principle, not an
economic one; nothing in economic theory can tell us whether
it is the ``right'' guide to policy. Many economists reject
the notion that people living today have as strong an
obligation to future generations as the golden rule requires.
Here is one argument {\it against\/} asking the present
generation to make sacrifices according to the golden rule:
Because of the forward march of technology, future
generations will almost surely be much wealthier than we are.
Should the relatively poor (that is, us) eat less so that the
relatively rich (our descendants) can eat more?}
\Chead{Applying the Golden Rule}
If you believe the Golden Rule is the right social criterion
for evaluating investment, you will want to encourage
investors to undertake more projects than they are naturally
inclined to. This is the motivation behind many government
programs that give favorable tax treatment to investors, and
it has been used to justify government-sponsored research and
development.
Steven E. Landsburg
www.landsburg.com/about2.html
--
Robert Vienneau
kra...@aol.com (Keith Ramsay) wrote:
> Samuelson refers to something called the "golden
> rule", which from the context appeared to refer to an idealized
> situation which would occur at a real interest rate of zero. Perhaps
> someone could explain.
1.0 INTRODUCTION
"At i = 0, we are in the Schumpeter-Ramsey Golden Rule state of
Bliss with maximum N[et] N[ational] P[roduct]."
-- Paul Samuelson
Steven Landsburg's response is not on topic.
The Golden Rule of Growth states that along a steady state growth
path, consumption per head is maximized when the interest rate, r,
is equal to the rate of growth g.
A proof in a very restricted setting follows. This proof would not
be interesting if the theorem did not generalize to a multicommodity
economy. In such an economy, no measure exists of the quantity of
capital that is prior to and independent of prices.
2.0 TECHNOLOGY
Consider a very simple economy in which a single commodity is
produced from inputs of itself and labor:
Q = F1( K, L) (1)
where Q is (gross) output, K is capital (measured in the same units as
output), L is labor input, and F1 is the production function. Assume
the capital goods are totally used up in a production cycle:
Y = Q - K = F(K, L) = F1(K, L) - K (2)
where Y is net output. Assume an increased amount of each input
increases net output:
dF/dL = dF1/dL > 0 (3)
dF/dK > 0 or dF1/dK > 1 (4)
Assume diminishing marginal returns for each factor:
d^2 F/(dL)^2 = d^2 F1/(dL)^2 < 0 (5)
d^2 F/(dK)^2 = d^2 F1/(dK)^2 < 0 (6)
Assume Constant Returns to Scale:
F( c K, c L ) = c F( K, L) (7)
The assumption of CRS allows one to write the production function
in per-capita form:
y = f(k) (8)
where
y = Y/L, k = K/L (9)
and the assumptions imply
df/dk > 0 (10)
d^2 f/(dk)^2 < 0 (11)
The above exposition is probably over-detailed.
3.0 ECONOMIC PROFIT-MAXIMIZATION
Consider a representative firm maximizing economic profit:
Choose K, L
To maximize F1(K, L) - (1 + r) K - w L (12)
The mathematical program in Display 12 is equivalent to the
following mathematical program:
Choose K, L
To maximize F(K, L) - r K - w L (13)
The resulting first-order conditions are:
r = dF/dK = df/dk (14)
w = dF/dL = f(k) - k f'(k) (15)
4.0 THE OPTIMAL STEADY STATE GROWTH PATH
In a simple economy with no government and no foreign trade,
all income is either consumed or saved:
Y = C + S (16)
where C is consumption and S is savings. In per capita terms:
y = c + s (17)
Equation 18 defines a constant (steady-state) rate of growth:
g = (1/Y) dY/dt = (1/L) dL/dt = (1/K) dK/dt (18)
If all savings are invested:
S = dK/dt (19)
Thus,
S/L = (K/L) (1/K) dK/dt (20)
Or:
s = k g (21)
Equation 22 follows from Equations 17, 8, and 21
c = f(k) - k g (22)
I get (where I have taken the rate of growth as given):
dc/dr = df/dk dk/dr - g dk/dr = dk/dr (r - g) (23)
d^2 c/ (dr)^2 = (r - g) d^2 k/(dr)^2 + dk/dr (24)
A steady state growth path maximizes consumption per worker if:
dc/dr = 0 (25)
d^2 c/(dr)^2 < 0 (26)
In this sort of simple model,
dk/dr < 0 (27)
That is, a higher interest rate is associated with a steady state
growth path with a lower value of capital per worker. Thus, the
conditions in Displays 25 and 26 are satisfied if and only if
r = g (28)
which was to be shown.
Samuelson, in his "Summing Up" article, considers a steady state
with a rate of growth of zero, that is, a stationary state. Display
27 says that if the interest rate is too high, there is not enough
capital for the golden rule to be satisfied. Symmetrically, if the
interest rate is too low, there is too much capital. As you now
know, these implications do not follow from the assumptions of
mainstream economists. Also, the mathematical programs in Section 3
are incorrect in multicommodity models.
Steven E. Landsburg
Keith Ramsay wrote:
> > Samuelson refers to something called the "golden
> > rule", which from the context appeared to refer to an idealized
> > situation which would occur at a real interest rate of zero. Perhaps
> > someone could explain.
>
To which I replied with a long quote from my textbook on macroeconomics,
and to which Robert Vienneau responded:
>
> Steven Landsburg's response is not on topic.
Yes it is, actually. Vienneau goes on:
>
> The Golden Rule of Growth states that along a steady state growth
> path, consumption per head is maximized when the interest rate, r,
> is equal to the rate of growth g.
I said in essence that the "golden rule" is to weight the interests
of all generations equally.
*In a model where consumption approaches a steady state*, the golden
rule dictates that we should maximize steady state consumption per head.
That's because the interests of the infinitely many generations who
will live at (or, more accurately, very near) the steady state outweigh
the interests of the finitely many generations who will pay for
the cost of getting there.
In *some* models where consumption approaches a steady state,
consumption per head is maximized when the interest rate r is equal
to the growth rate g.
So to summarize:
1) The golden rule says to do whatever maximizes benefits minus
costs, summed up over all generations.
2) In some subset of economic models, the golden rule dictates
maximization of steady state per capita consumption. In
some other subset, the golden rule cannot dictate the
maximization of steady state per capita consumption, because
there is no steady state. Speaking very broadly, "old"
growth models tend to predict a steady state whereas more
"modern" growth models tend not to.
3) In some subset of the subset from 2), the golden rule dictates
an interest rate equal to the growth rate.
So I gave the general principle, whereas Vienneau gave the application
of that principle to a particular (and in my opinion not very
interesting) class of models.
David Lloyd-Jones
> From a textbook on macroeconomics (which I wrote):
> \Bhead{The Golden Rule}
> The Bible tells us to do unto others as we would have them do
> unto us.
Steven,
It does? Chapter and verse please.
The Categorical Imperative is usually credited to Hegel, surely (or
is it Kant? I can never keep them straight) -- and is a leap of a
country mile away from Biblical teaching, which generally runs to
things like the parable of the talents or Jesus' wise virgins.
-dlj.
jonah thomas
> Steven E. Landsburg wrote:
>> From a textbook on macroeconomics (which I wrote):
>> \Bhead{The Golden Rule}
>> The Bible tells us to do unto others as we would have them do
>> unto us.
> It does? Chapter and verse please.
Matthew 7:12.
Buddha said it the other way around, Don't do to others what you don't
want them to do to you.
David Lloyd-Jones
OK, You're right. On the other hand, don't you think Matthew is the
"nicest" of the the evangelists, and pretty untypical of the
Christian Bible as a whole?
-dlj.
jonah thomas
> On the other hand, don't you think Matthew is the
> "nicest" of the the evangelists, and pretty untypical of the Christian
> Bible as a whole?
There's a tremendous diversity in the christian new testament, as
there is in their selections for their old testament.
This is useful for a religion to survive with the same name for a long
time. People use what they need and ignore the rest.
I have no idea why they included Revelation, though. It reads like a
bad acid trip. Those guys were a small splinter sect that was losing
badly, the thing could almost have been one of the last communiques
coming out of biafra.
Paul was an evil bastard but he knew how to organise fanatics.
Robert Vienneau
> I hope people will excuse my delayed response here, but I finally had
> a chance to look at a "Curiosum" as discussed by Real Economists...
One might notice that poor Chris Auld's statement about which economists
I classify as good and not good was, as I've come to expect, incorrect.
> The November 1966 issue of Quart. J. Econ. (the oldest issue that the
> University of Colorado hasn't yet whisked off into cold storage) is
> devoted to "paradoxes of capital theory".
The appendix in the post with which I started this thread is a
justification, in some sense, of the analysis in those papers.
I wonder if any economist will have the intellectual honesty
and courage to publicly acknowledge here the correctness of the
example in my post originating this thread.
> Apparently Samuelson had conjectured that in a simple model something
> like the kind we had been discussing here, when one set of techniques
> A is preferred to a second set B at one interest rate r1, but B is
> preferred to A at a second rate r2>r1, one does not have "reswitching"
> back to A at a third rate r3>r2>r1. But one can. One of the examples
> was called the "Ruth Cohen Curiosum", so I suppose she's given credit
> for it.
As I understand it, Ruth Cohen discovered capital-reversing - the
phenomenon you say is more interesting - but not reswitching. Joan
Robinson often called her reference to the Ruth Cohen case a
"private joke." As far as I know, she never expanded on the
history here. Joan Robinson didn't put too much emphasis on
capital-reversing.
Piero Sraffa, I guess, discovered reswitching. Its possibility, and
that of capital-reversing, seems much more important in his
presentation. Perhaps the first published discussion of reswitching
is by D. G. Champernowne.
> The result seems to be interesting not so much for the possibility of
> the very *same* technology "reappearing", but for the fact that it
> means one doesn't have any necessary ordering on the technologies that
> become preferable as the real interest rate moves in a given direction.
> They might be more "capital intensive" or less, more "labor intensive"
> or less, and so on. Samuelson says in a separate paper that this makes
> things more difficult for the working economist, but (from memory,
> words to the effect that) nobody promised economics would be easy.
"...Such an unconventional behavior of the capital-output ratio
is seen to be definitely possible. It can perhaps be understood
in terms of so-called Wicksell and other effects. But no
explanation is needed for that which is definitely possible: it
demonstrates itself. Moreover, this phenomenon can be called
'perverse' only in the sense that the conventional parables did
not prepare us for it...
...If all this causes headaches for those nostalgic for the old
time parables of neoclassical writing, we must remind ourselves
that scholars are not born to live an easy existence. We must
respect and appraise, the facts of life."
-- Paul A. Samuelson, 1966.
Generally, I agree on which is more important. I do use reswitching
to point out that one cannot necessarily map from quantity flows in
production to a unique (range of) distribution. But physical marginal
products would be known in this case. Hence, I conclude, marginal
productivity cannot be a theory of distribution.
> I have two questions...
> The second question is, assuming the kind of thing assumed in the
> model, what can one say about the effect on the "size" of the economy
> as a whole as one moves through one of the "switching points" in
> question. I thought for a little bit about how things might go as one
> switched between techniques, but it wasn't clear to me that it doesn't
> depend upon which of various effects runs more quickly, such as
> responses of prices to supplies of goods and responses of investors to
> changes in profitability of techniques. I think this was also one of
> the main sources of my confusion during this thread. It seems like
> some kind of assumption needs to be made.
>
> For example, one of the papers in this journal issue simply assumes
> that one has an economy with a fixed population of workers, who are
> always employed. If that were so, then a decrease in the ratio
> between the amount of some capital good used and the amount of labor
> used would presumably just mean that the capital good would just be
> used up until it reached a lower level. Perhaps these toy economies
> have idealized away the reasons why in the real world we get
> unemployment, and one cannot really make a satisfactory assumption
> about what happens in such a model. I suspect, though, that one could
> analyze the situation more thoroughly, though.
A perceptive question. (Steven Landsburg once commented on one of
my examples (on 27 and 28 October 1997), displaying a naive
understanding of such transverse paths. He did acknowledge the
correctness of that example.)
The economy, or a vertically-integrated industry, will not move
immediately from one point on the so-called factor-price frontier
to another. That is why I, like others, try, probably not
successfully, to avoid "dynamic" language. I try to say a higher level
of wages is associated with profit-maximizing firms having adopted a
technique with a greater ratio of labor to output. I try to avoid
saying that firms adopt techniques with a greater labor-output ratio
as wages rise.
Samuelson once justified the latter sort of language. He says that
when a mathematical economist says that Y falls as X rises, he is
merely describing the slope of a mathematical function. In this
case, every point on the function would describe firms in a long
run position. It is not to the point that firms in a real economy
will not move smoothly along such a function. That is not the
claim being made by that sort of language.
The analysis of tranverses is difficult. Generally, economists
do not analyze effective demand failures very well, as I understand
it. You might notice that issues of disppointed and diverse
expectations come into play, as well.
I do know of some analyses of the impact of reswitching and capital-
reversing on transverse paths. The analyses I know tend to put aside
business-cycle concerns. There's something called the turnpike
theorem that is important in thinking about transverses. Still,
a consensus seems to exist that reswitching and so on has
implications for such paths:
"On the manner in which such a [full neoclassical] equilibrium
is supposed to come about, neoclassical theory is highly
unsatisfactory. Sraffa's work shows that certain simplified
routes are very risky and not free from logical difficulties."
-- Frank Hahn, 1982.
G. Dumenil and D. Levy had one answer to Hahn. Luigi Pasinetti
has commented on Hahn's "polemical and dogmatic paper".
"Now, zones of instability of the system can always occur, in models
with heterogeneous capital goods, even in the case of perfectly
convex and well-behaved production functions... (Hahn 1966) ...
Conclusion: re-switching had nothing new to tell us. As if the
difficulties, when they are already known could, by this very fact,
acquire a justification for being ignored, no matter whether they crop
up in a different context, where they are reiterated and extended!
Surprisingly enough, however, this is precisely what has happened...
And here we finally come to the non sequitur of the conclusion:
the 'Neo-Ricardians' could safely be ignored."
-- Luigi L. Pasinetti, "Critique of the Neoclassical Theory of
Growth and Distribution", 2000?
<http://www.unicatt.it/docenti/pasinetti/paper1.asp>
Barkley Rosser related reswitching to a "cusp catastrophe" in a
Journal of Economic Theory paper in, I think, 1984. Last time
I looked, I did not fully understand Rosser's analysis of
structural (in)stability. Nevertheless, Appendix B in my
essay Sraffa3.pdf at my web site points out the existence of
bifurcations of equilibria in the model examined there, pointing
out the possibility of complex dynamics.
Good current writers to read on Cambridge capital controversy
implications for dynamics are P. Garegnani, Michael Mandler,
Fabio Petri, and Bertram Schefold. Mandler, Petri, and Schefold
have papers available on their websites.
I still think that I don't need to solve dynamic riddles. One
long-run framework in which reswitching arises is a standard
mainstream approach. Reswitching can be (and has been) used
successfully for an internal critique of neoclassical theory.
Robert Vienneau
> Keith Ramsay wrote:
>
> > > Samuelson refers to something called the "golden
> > > rule", which from the context appeared to refer to an idealized
> > > situation which would occur at a real interest rate of zero. Perhaps
> > > someone could explain.
> To which I replied with a long quote from my textbook on macroeconomics,
> and to which Robert Vienneau responded:
> > Steven Landsburg's response is not on topic.
> Yes it is, actually. Vienneau goes on:
> > The Golden Rule of Growth states that along a steady state growth
> > path, consumption per head is maximized when the interest rate, r,
> > is equal to the rate of growth g.
> I said in essence that the "golden rule" is to weight the interests
> of all generations equally...
> 3) In some subset of the subset from 2), the golden rule dictates
> an interest rate equal to the growth rate.
> So I gave the general principle, whereas Vienneau gave the application
> of that principle to a particular (and in my opinion not very
> interesting) class of models.
Nobody asked about what Steven Landsburg finds interesting. The question
on the table was what Paul Samuelson meant by the golden rule in his
1966 paper. Do try to keep up.
"At i = 0, we are in the Schumpeter-Ramsey Golden Rule state of
Bliss with maximum N[et] N[ational] P[roduct]."
-- Paul Samuelson
In the paper which Keith Ramsay and I are discussing, Samuelson
considers steady states in which the rate of growth is zero
(otherwise known as stationary states). Any answer to Keith
Ramsay's question, I should think, should explain why Samuelson
identifies an interest rate of zero with the golden rule. My
answer brought out the connection between the rate of interest
with the steady-state rate of growth. Steven Landsburg's original
answer did not.
"The golden rule of accumulation...states that the steady-growth
state that gives the maximum path of consumption - the path
layered on top of all other steady-growth consumption tracks -
is the one along which national consumption equals the national
wages bill and thus national saving equals 'profits' (gross of
interest in the present use of the term). Equivalently, the
consumption-maximizing steady growth path is the steady state
along which the competitive rate of interest, which is the
social rate of return to investment and to saving, is equal to
the natural rate of growth."
-- Edmund S. Phelps, "Golden Rule". New Palgrave, 1987.
Christopher Auld
>The result seems to be interesting not so much for the possibility of
>the very *same* technology "reappearing", but for the fact that it
>means one doesn't have any necessary ordering on the technologies that
>become preferable as the real interest rate moves in a given direction.
These results are specific to certain (archaic) classes of (general equilibrium) models
with restrictive notions of "equilibrium" and technologies. Notice in particular that
Vienneau's idea that one can simply take results which apply to economies as vectors of
prices vary and apply them wholesale to *a* firm's responses to changes in *a* parameter
is completely wrong. The important result -- the one you noted Samuelson and coauthor
initially had wrong -- is not about "reswitching" per se but rather the argument over
whether heterogenous capital goods can be treated as if they are one capital good.
Turns out they generally can't -- yet another aggregation problem.
>The second question is, assuming the kind of think assumed in the
>model, what can one say about the effect on the "size" of the economy
>as a whole as one moves through one of the "switching points" in
>question.
You have as much opportunity to answer this question yourself as any economist reading
this. This class of model was always a niche literature, and that literature as been
all but dead for more than thirty years. Try jstor.
Robert Vienneau
(Christopher Auld) wrote:
> Keith Ramsay <kra...@aol.com> wrote:
>
> >The result seems to be interesting not so much for the possibility of
> >the very *same* technology "reappearing", but for the fact that it
> >means one doesn't have any necessary ordering on the technologies that
> >become preferable as the real interest rate moves in a given direction.
> These results are specific to certain (archaic) classes of
"Archaic", of course, is a word directed to no cognitive value.
> (general equilibrium) models
"It is sufficient to compare positions on the wage-rent-interest-
rate frontier to show that input use and 'price' need not be
inversely related; one does not need to 'close the system' in
any way. Our point, then, is not identical to the general
equilibrium one that changes in the data have complicated
consequences for the endogeneous variables."
-- Ian Steedman, "On Input 'Demand Curves'". Cambridge Journal
of Economics. 1985.
> with restrictive notions of "equilibrium" and technologies.
Poor Chris Auld is simply wrong. And he disagrees with what
Samuelson has been saying for years. This has all been pointed
out to him before. What is his excuse for his behavior?
"These complexities have naught to do with *finiteness* of the number
of alternative activities, and naught to do with the phenomenon in
which, to produce a good like steel you need directly or indirectly
to use steel itself as an input. In other words, what is wrong and
special in the simplest neoclassical or Austrian parables can be
completely divorced from the basic critique of marginalism that Sraffa
was ultimately aiming at when he began in the 1920s to compose his
classic: Sraffa (1960)...
...these Robinson-Sraffa-Pasinetti-Garegnani contributions deepen
our understanding of how a time-phased competitive microsystem works."
-- Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and
Modern Economic Theory_ (edited by G. R. Feiwel), New York
University Press, 1989.
Why does poor Chris Auld continue to repeat balderdash, in ignorance
of results long-established in the literature? Probably, among other
reasons, because his teachers shared his ignorance.
"Would you care to explain what the 'factor-price frontier' is?
Perhaps I am a little thick, but I haven't a clue what your story
means in economic terms."
-- Chris Auld, sci.econ, 15 June 1994.
"...Of course, most [neoclassical economists] do not [pay the
slightest attention to reswitching]. I've never seen it covered in
any micro text, and, anecdotally, it was certainly never mentioned
in any class I ever took."
-- Chris Auld, sci.econ, 28 June 1994.
> The important result -- the one you noted Samuelson
> and coauthor
> initially had wrong
> -- is not about "reswitching" per se
Actually, the way I remember it is the result that Samuelson and
Levhari had wrong was a statement that reswitching could not
happen under certain conditions. So even here, poor Chris Auld
is mistaken.
> but rather the
> argument over
> whether heterogenous capital goods can be treated as if they are one
> capital good.
> Turns out they generally can't -- yet another aggregation problem.
Once again, poor Chris Auld is simply wrong. Here he contradicts
Samuelson. Samuelson looks at Net National Product, the ratio of
output to labor, in examples where NNP consists of a single good
and labor is homogeneous. So there is no aggregation problem in
such examples.
"Yet there finally came a third very curious phase, which should
appear rather strange, given its weak theoretical and empirical
underpinning, but which was greeted with relief by the theorists of
mainstream economics. The essence of this third phase can be
summed up with the following proposition: the criticisms of the
traditional theory of capital raised by the phenomenon of re-switching
(and consequent reverse capital-deepening) are valid, but only with
reference to the neoclassical model conceived in aggregate terms.
They do not apply to the neoclassical case of the general economic
equilibrium model, conceived in disaggregated terms and based on the
behaviour of individuals maximising inter-temporal functions of
profits and of utility.
This proposition actually has no objective foundation:
phenomena of non-convexity, re-switchings of techniques and
badly-behaved production functions, to take an expression that
has been widely used ('behaving badly' meaning simply that they
behave in a way as not to obey the assumptions of neoclassical
economics), are not as has been amply demonstrated a consequence
or a characteristic of any particular process of 'aggregation'.
They may occur at any time and in any context, aggregated or
disaggregated. Various authors have continued to demonstrate this
point (e.g. Kurz 1987, Schefold 1997, Garegnani 1998, and others).
But so things go. The contrary conviction had taken root and has
continued to spread. Above all, the proposition cited above has been
trundled out again and again, with no proof, but simply referring
back to other sources, which in turn are either insufficient or
inconsistent."
-- Luigi L. Pasinetti, "Critique of the Neoclassical Theory of
Growth and Distribution", 2000?
<http://www.unicatt.it/docenti/pasinetti/paper1.asp>
> >The second question is, assuming the kind of think assumed in the
> >model, what can one say about the effect on the "size" of the economy
> >as a whole as one moves through one of the "switching points" in
> >question.
> You have as much opportunity to answer this question yourself as any
> economist reading
> this. This class of model was always a niche literature, and that
> literature as been
> all but dead for more than thirty years. Try jstor.
"Niche" and "all but dead" are phrases directed to no cognitive
value.
Consider:
"...The immigration scenario now is a movement... [in which]
in order to preserve full employment by moving from a technique
with a high capital-labour ratio to one with a low capital-
labour ratio..., the real wage has to be raised in reaction to
the immigration of labour...
...We may therefore say that the intertemporal equilibrium
shows a transition from one steady state to another ... such
that a rising real wage rate is ... associated with a rise
in the demand for labour through a 'perverse' substitution
effect...
It has been shown that transitions involving reswitching and
employment opportunity reversals can be represented within
intertemporal equilibrium models... A rising supply of labor
is absorbed by raising the real wage rate... The conclusion
seems inevitable: intertemporal equilibrium does not provide
a stronghold which could be better defended against the
critiques from capital theory than the older notions of
long-period neoclassical equilibrium. They stand or fall
together."
-- Bertram Schefold, "Paradoxes of Capital and
Counterintuitive Changes of Distribution in an
Intertemporal Equilibrium Model". _Critical Essays
on Piero Sraffa's Legacy in Economics_. (edited by
H. D. Kurz), Cambridge University Press, 2000.
The above, for example, directly contradicts:
"Suppose the number of carpenters suddenly increases, due to the
immigration of thousands of new carpenters from Mexico. Both before
and after the change, carpenters receive their marginal revenue
product. Both before and after, they receive a wage equal to the
marginal value of the last hour of leisure they give up...
Increases in the other factors of production will tend to increase
the marginal product of labor, and hence its wage; decreases will
have the opposite effect. Changes in technology can also alter the
marginal product of labor or other inputs. If someone invents a
computer program that does a better job than a human of teaching
children basic skills, perhaps by converting reading, writing and
arithmetic lessons into exciting video games, a substantial amount
of human labor will have been replaced by capital. The demand for
labor has decreased, the demand for capital has increased, so when
equilibrium is reestablished wages will be a little lower than
before the change and the return on capital, the interest rate, a
little higher...
...But the wage after the migration is lower than the wage before.
Since the supply of carpenters is higher than before, the equilibrium
wage is lower.
The answer, put simply, is that an increase in the supply of an input
I own drives down its price (and marginal revenue product) and so
decreases my income..."
-- David Friedman, _Price Theory: An Intermediate Text_, Chapter 14.
<http://www.daviddfriedman.com/Academic/Price_Theory/PThy_ToC.html>
What kind of mistake is David Friedman making here?
Christopher Auld
>"Archaic", of course, is a word directed to no cognitive value.
Vienneau likes to repeat this over and over. These models *are* archaic:
They have little to do with modern economic thought; they are
uninteresting; they were not particularly interesting even thirty years
ago. Precluding Vienneau's reply that no one asked what I think is
interesting: NO ONE thinks the thousandth spam of a tedious "long essay"
about 23/113ths of a bushel of corn is interesting. I don't recall
anyone asking Mr. Vienneau to single-handedly destroy sci.econ by
incessantly spamming "long essays" on his kooky interests for year after
year.
>Why does poor Chris Auld continue to repeat balderdash, in ignorance
>of results long-established in the literature? Probably, among other
>reasons, because his teachers shared his ignorance.
> -- Chris Auld, sci.econ, 15 June 1994.
Wow, 1994, LOL. Yes, Robert, these models are ARCHAIC. I was of course
not taught the properties of uninteresting out of date models ten years
ago, and I of course would not teach the properties of uninteresting out
of date models in a micro theory course in 2003. It is amusing to note
again Vienneau's contempt for education, another of the many traits he
shares with his intellectual fellow travellers at the Institute for
Creation Science.
[ snip: more misunderstandings, Hansonesque quotes ]
In passing, I note that Bobby is apparently never going to explain how the
solution to the program { min_L wf(L) s.t. g(L)=0 } depends on w. He
keeps reeling off his highly selected, often dishonestly edited, and
generally irrelevant quotes, but even these quotes do not support the
laughable claims he keeps sharing with the net several times a week for
year after year.
David Lloyd-Jones
>... NO ONE thinks the thousandth spam of a tedious "long essay"
> about 23/113ths of a bushel of corn is interesting.
Chris,
Are you "NO ONE" or are you lying?
It's pretty obvious to the rest of us that this 23/113ths of a
bushel of corn has you fascinated. If not indeed hyponotised.
-dlj.
Robert Vienneau
> Notice in
> particular that
> Vienneau's idea that one can simply take results which apply to economies
> as vectors of
> prices vary and apply them wholesale to *a* firm's responses to changes
> in *a* parameter
> is completely wrong.
Notice poor Chris Auld has yet to find an error in the post with
which I began this thread. I here repeat core claims in that example.
Did I mention that, in passing, poor Chris Auld likes to pretend
the argument in this post has never been made?
Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, iron, and (seed)
corn. All production processes in this example require a year to
complete. Two production processes are known for producing corn. These
processes require 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 TON CORN PRODUCED
Process A Process B
1 Person-Year 1 Person-Year
2 Tons Iron 1/2 Tons Iron
2/5 Bushels Corn 3/5 Bushels Corn
Apparently, inputs of iron and corn can be traded off in producing
corn outputs.
Iron is also produced by this firm. Two processes are known for
producing iron:
TABLE 2: INPUTS REQUIRED PER TON IRON PRODUCED
Process C Process D
1 Person-Year 275/464 Person-Years
1/10 Tons Iron 113/232 Tons Iron
1/40 Bushels Corn 0 Bushels Corn
Inputs of corn and iron can be traded off in producing iron. The
process that uses less iron and more corn, however, also requires
a greater quantity of labor input.
Let
Xa = Bushels corn produced (gross) by process A
Xb = Bushels corn produced by process B
Xc = Tons iron produced by process C
Xd = Tons iron produced by process D
p = the price of iron (corn is numeraire)
w = wage
r = rate of (accounting) profits
Q1 = Tons iron in firm's inventory at start of period
Q2 = Bushels corn in firm's inventory at start of period
The profit-maximizing firm solves the following program:
Given p, w, Q1, and Q2
Choose Xa, Xb, Xc, and Xd
To Maximize (1 - w - 2 p - (2/5)) Xa
+ (1 - w - (1/2) p - (3/5)) Xb
+ (p - w - (1/10) p - (1/40)) Xc
+ (p - (275/464) w - (113/232) p) Xd
Such that
(w + 2 p + (2/5)) Xa
+ (w + (1/2) p + (3/5)) Xb
+ (w + (1/10) p + (1/40)) Xc
+ ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
Xa, Xb, Xc, Xd >= 0
The dual Linear Program is:
Given p, w, Q1, and Q2
Choose r
To Minimize (Q1 p + Q2) r
Such That
(w + 2 p + (2/5))(1 + r) >= 1
(w + (1/2) p + (3/5))(1 + r) >= 1
(w + (1/10) p + (1/40))(1 + r) >= p
((275/464) w + (113/232) p)(1 + r) >= p
r >= 0
If a constraint in the dual is met with inequality in the solution, the
corresponding process in the primal will be operated at a level of zero.
For a corn-producing firm to continue production unaltered from
period to period, both corn and iron must be produced each period. For
corn to be produced, either the first or the second constraint in the
dual must be met with equality. Likewise, for iron to be produced, the
third or the fourth constraint in the dual must be met with equality.
Hence, for the analyzed firm to be in equilibrium, the
vertically-integrated industry must be on the so-called factor-price
frontier for that industry.
Nothing guarantees that the firm will be able to sell its output
at any given location on the factor-price frontier. Whether prices that
allow a firm to be in equilibrium are realized is a question that is
not addressed by this formal model.
Christopher Auld
> Notice poor Chris Auld has yet to find an error in the post with
>which I began this thread. I here repeat core claims in that example.
>Did I mention that, in passing, poor Chris Auld likes to pretend
>the argument in this post has never been made?
Welcome to the world of Robert Vienneau.
Vienneau's "argument" is wrong for the numerous reasons I've pointed out in
this thread (it is quite a talent I have pointing out problems with an
argument while simultaneously pretending it hasn't been made). Vienneau
has deleted or misrepresented most of these reasons -- he doesn't appear
to understand the points made.
In a nutshell, Vienneau has borrowed some creaky old results that describe
what happens to an economy which has multiple equilibria as the price
vectors characterizing those equilibria change and simply applied those
results wholesale to *a* firm. He has not shown that a ceteris paribus
increase in the wage his firm faces will increase its use of labor, he
has shown there exist (w, r, p) triples with the property that labor
demanded to produce a given output is higher for (w, r, p) than (w', r',
p') where w < w' and profits are zero at both triples. That is, HE ISN'T
HOLDING ALL ELSE EQUAL when he varies the wage rate.
Notice Vienneau has once again deleted the simple disproof of his claimed
result. What is that, the sixth time?
Notice his claimed result is with respect to changes in multiple prices,
ie, the price of labor in every time period. Keeping in mind that result
doesn't obtain, observe the point of the exercise is to reveal to the
world the errors in textbook microeconomics. In textbook microeconomics
labor at time t and s, t\ne s, are *different* factors. So Vienneau's
task is is show that holding all other prices constant, an increases in
the wage rate in *a* period causes the firm to hire more labor in that
period. Doing so would provide a counterexample to the trivial axiomatic
proof that that is impossible for a cost-minimizing firm, and would make
Robert Vienneau very famous. The floor's yours Vienneau: where exactly
is the overt mathematical error in this proof?
Alex Huemer
Chris, how about applying Occam's Razor to this problem? Have you
considered the repetitive content of his responses? The baffling
obtuseness?
I think Robert is really Eliza, and this is all an elaborate Turing Test. I
think we failed.
David Lloyd-Jones
>
> I think Robert is really Eliza, and this is all an elaborate Turing Test. I
> think we failed.
>
Alex,
That was rather my thought the other day when Chris said that
Robert's stuff was uninteresting.
Like, hunh?
-dlj.
Christopher Auld
>I think Robert is really Eliza, and this is all an elaborate Turing Test. I
>think we failed.
Damn! I guess the programmer of "Robert Vienneau v1.1" is quite clever.
Robert Vienneau
(Christopher Auld) wrote:
> These models...
> have little to do with modern economic thought...
I think I'll stick with what serious economists have to say.
"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, cover blurb for Kurz and Salvadori (1995)
"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.
> ...I was of course
> not taught the properties of ... out of date models ten years
> ago, and I of course would not teach the properties of ... out
> of date models in a micro theory course in 2003...
By observation, the above is untrue.
A problem set that poor Chris Auld cannot do:
<http://homepage.newschool.edu/~foleyd/GECO6200/ps1.html>
Robert Vienneau
(Christopher Auld) wrote:
> [Additional stupidity - deleted.]
> In a nutshell, Vienneau has borrowed some creaky old results that
> describe
> what happens to an economy which has multiple equilibria as the price
> vectors characterizing those equilibria change and simply applied those
> results wholesale to *a* firm.
The above, of course, is mostly directed to no cognitive values. My
essay Sraffa3.pdf at my website describes equilibria of an economy.
The model I have been presenting in this thread does not describe
equilibria of an economy. It has been pointed out to poor Chris Auld
before that he is simply wrong here.
Poor Chris Auld simply refuses to address my argument.
> He has not shown that a ceteris paribus
> increase in the wage his firm faces will increase its use of labor, he
> has shown there exist (w, r, p) triples with the property that labor
> demanded to produce a given output is higher for (w, r, p) than (w', r',
> p') where w < w' and profits are zero at both triples. That is, HE ISN'T
> HOLDING ALL ELSE EQUAL when he varies the wage rate.
Notice poor Chris Auld has yet to figure out what can be exogeneous
and what must be endogeneous in the analysis of the equilibrium
of the firm I presented (even after Keith Ramsay pointed out some
aspects of the math). Notice that poor Chris Auld's formulation
fails to observe the different roles of p and r, say, in the argument
that I presented.
Poor Chris Auld has simply refused to address my argument.
> Notice his claimed result is with respect to changes in multiple prices,
> ie, the price of labor in every time period.
In my formulation of the problem, the firm purchases labor, corn, and
iron inputs in a single period. Poor Chris Auld is not addressing my
argument, as I've said.
Consider the intro textbook presentation of the supply and demand
story for the labor market. This is the story that poor Chris Auld
is supposed to be defending. And labor is not indexed by time in
the intro textbook story. Poor Chris Auld tells untruths.
Of course, I've already pointed out that, according to the
literature, examples like mine do have implications for the
Arrow-Debreu model of intertemporal equilibrium and for Hicks'
model of sequences of temporary equilibria. Poor Chris Auld
refuses to address this contemporary literature.
> [Further strawperson deleted]
Keep in mind that my analysis is of a firm in long run equilibrium.
I show how that equilibrium will differ for different levels of the
wage.
If there was an error below, one would be able to point out a
statement that is untrue. Poor Chris Auld never has.
David Lloyd-Jones
> (Christopher Auld) wrote:
>
>>In a nutshell, Vienneau has borrowed some creaky old results that
>>describe
>>what happens to an economy which has multiple equilibria as the price
>>vectors characterizing those equilibria change and simply applied those
>>results wholesale to *a* firm.
>
>
> The above, of course, is mostly directed to no cognitive values.
Robert,
I think you're being too fast off the blocks. As I read what Chris
said above, he's saying you're right, and he can't find a damn thing
wrong with it no matter how hard he tried.
Graceful apology is not one of Chris's major skills, but at least
you should recognise his attempts when he makes them.
-dlj.
Robert Vienneau
<da...@rogers.com> wrote:
> Robert Vienneau wrote:
> > (Christopher Auld) wrote:
> >>In a nutshell, Vienneau has borrowed some creaky old results that
> >>describe
> >>what happens to an economy which has multiple equilibria as the price
> >>vectors characterizing those equilibria change and simply applied those
> >>results wholesale to *a* firm.
> > The above, of course, is mostly directed to no cognitive values.
> I think you're being too fast off the blocks. As I read what Chris
> said above, he's saying you're right, and he can't find a damn thing
> wrong with it no matter how hard he tried.
>
> Graceful apology is not one of Chris's major skills, but at least
> you should recognise his attempts when he makes them.
David,
A fair point. Of course, you are being unduly strong in your last
statement. Grace in any aspect of his posts is not one of Chris's
major skills.
Christopher Auld
>(Christopher Auld) wrote:
>> p') where w < w' and profits are zero at both triples. That is, HE ISN'T
>> HOLDING ALL ELSE EQUAL when he varies the wage rate.
>
> Notice poor Chris Auld has yet to figure out what can be exogeneous
>and what must be endogeneous in the analysis of the equilibrium
For anyone who cares, the above summarizes Vienneau's major error. He
isn't holding all else equal, as I explained, to no avail.
But perhaps I am wrong, along with every other economist on the planet
(recalling Vienneau is not, as he claims, merely repeating results in the
literature -- this whopper is one of his own invention, not unlike the
theory that the universe is a plutonium atom). Perhaps the simple
axiomatic proof that factor demand curves cannot slope up is wrong. It is
odd Vienneau simply (again) deleted my request that he show the error in
that proof, as such a demonstration would make him very famous. The world
waits with bated breath, Mr. Vienneau. Dazzle us.
Of course, the above is a little unfair because it's only in his last
very confused post that he's claimed to be showing the result of a change
in wages in one period. What his arithmetic actually concerns is steady
states of dynamical systems. Cost minimization in the framework he
considers takes the form {min_L wf(L) s.t. g(L)=0}. I have the nutty idea
that the solution to that problem does not depend on w, which disproves
Vienneau's claims, but perhaps Vienneau would care to further startle the
academy by proving otherwise. Or perhaps he'll just delete this
observation yet again.
Christopher Auld
>(Christopher Auld) wrote:
>> These models...
>> have little to do with modern economic thought...
>
>I think I'll stick with what serious economists have to say.
Recall I just noted Vienneau's highly selective and dishonest quoting?
Nice examples, Bobby! To repeat: these models have little do do with
modern economic thought, and one need merely open a random journal or any
common theory text to find, well, nothing related to these models, proving
the point.
>A problem set that poor Chris Auld cannot do:
>
> <http://homepage.newschool.edu/~foleyd/GECO6200/ps1.html>
LOL. Amongst the thousands upon thousands of micro theory courses that of
course don't teach this sort of archaic model, Bobby finds a single
example of some Marxist still obstinately teaching this stuff. Of course,
one should not be too hard on Foley, because Foley explicitly notes that
the course "lectures will be organized from a history of thought
perspective" and the first bit of the course -- from which problem set 1
would presumably be drawn -- is explicitly about historical "precursors of
general equilibrium theory."
In short, Bobby is very enthused because he's found an example of someone
teaching archaic models as part of a lecture on history of economic
thought, which he offers as proof that these models are not archaic.
"Robert Vienneau v1.1" clearly needs lots more work.
David Lloyd-Jones
> Recall I just noted Vienneau's highly selective and dishonest quoting?
Chris,
Pot. Kettle. Black.
I still have not seen your recantation and apology for the way you
selectively edited my position on Lott/Bellesiles being political,
in the Vorosholovian attempt to make me say the opposite of what I
had actually said.
It is on file, and it will haunt you throughout your career until
you clear it up. At the moment you are a cheap crook who has been
caught dead to rights and has not yet faced up to the reality of his
guilt.
-dlj.
JT
>
> The above, of course, is mostly directed to no cognitive values. My
> essay Sraffa3.pdf at my website describes equilibria of an economy.
> The model I have been presenting in this thread does not describe
> equilibria of an economy. It has been pointed out to poor Chris Auld
> before that he is simply wrong here.
It's not really an equilibrium model of a firm either. There is no
reason that a firm needs to be integrated. Nothing procludes a firm
from producing only corn or only iron, and buying inputs rather than
manufacturing them. A firm equilibrium involves taking input and
output prices as given to maximize some kind of objective function
(profits). Vector of prices exists such that a firm would choose only
to produce one good. This is consistent with a firm
equilibrium...there is no requirement that the various actors of the
economy will actually behave in a way that supports a firm
equilibrium. Clearly in the example above, if prices were such that
no firm would produce iron, then it would be difficult to produce corn
as well. Integration is essentially a way of building an equilibrium
between the two markets (corn and iron), so that the production plans
match up in a self-perpetuating way. However, this is now an
equilibrium condition between *markets* (iron supply meets future
demand by corn and iron producers, etc.). The zero (or equal) profit
conditions are also not firm equilibrium conditions, but are justified
on the basis of market equilibria concepts (entry/competition).
>
> Consider the intro textbook presentation of the supply and demand
> story for the labor market. This is the story that poor Chris Auld
> is supposed to be defending. And labor is not indexed by time in
> the intro textbook story. Poor Chris Auld tells untruths.
It's not clear what your story has to do with the textbook
presentation. Your firm is producing *two* outputs, which makes your
usage of the term labor intensity non-standard. In a given period,
some labour is allocated towards production of iron, some towards
production of corn. Doesn't matter that that iron is for future corn
production...it's still an output of this period. The textbook
treatment would involve two diagrams: one for the labor demand of each
endeavor.
>
> Keep in mind that my analysis is of a firm in long run equilibrium.
> I show how that equilibrium will differ for different levels of the
> wage.
Again, your terminology is non-standard, and maybe nonsense. What is
a long run equilibrium at a firm level? You've buried a couple of
factor markets with the vertically integrated firm...what you are
referring to as a firm equilibrium includes a steady-state equilibrium
in two factor markets.
Beyond that, I don't think there are any errors in you programming
problem. I'm just not convinced that your essay has any real point to
make...
Christopher Auld
>(Christopher Auld) wrote:
>> He has not shown that a ceteris paribus
>> increase in the wage his firm faces will increase its use of labor, he
>> has shown there exist (w, r, p) triples with the property that labor
>> demanded to produce a given output is higher for (w, r, p) than (w', r',
>> p') where w < w' and profits are zero at both triples. That is, HE ISN'T
>> HOLDING ALL ELSE EQUAL when he varies the wage rate.
> Notice poor Chris Auld has yet to figure out what can be exogeneous
>and what must be endogeneous in the analysis of the equilibrium
>of the firm I presented
Pointing out to creationists that eyes, indeed, can evolve evokes similar
responses.
Vienneau's arithmetic applies to zero-profit price vectors. He is here
supposed to be varying *a* price faced by *a* firm. It is true that one
"must" vary other prices as the wage varies *if* one wants to find prices
such that profits are zero and the firm wishes to neither shut down nor
send output off to infinity, but that *if* is invalid. The firm's
discount rate is supposed to be given and the "price of iron" is not even
a parameter of this problem.
One does wonder why Bobby has YET AGAIN deleted my request he point out
exactly where the overt mathematical error in the simple axiomatic proof
that factor demands do not slope up lies.
Of course -- his recent confusion over whether he's considering stready
states of dynamic systems as many prices change (wages in each period) or
one-shot problems notwithstanding -- Bobby also refuses to acknowledge
that the solution to the cost-minimization problem he's supposed to be
solving does not depend on the wage rate. I'll ask him a seventh time to
explain.
> Consider the intro textbook presentation of the supply and demand
>story for the labor market. This is the story that poor Chris Auld
>is supposed to be defending. And labor is not indexed by time in
>the intro textbook story. Poor Chris Auld tells untruths.
LOL. Vienneau v1.1 is supposed to be "collapsing the entire intellectual
world" of economists with his "long essays." Now we find that it really
only wants to attack parables taught to 18 year olds in freshman
economics; parables clarified in such a way that the attack doesn't apply
to theory taught to 19 year olds a year later.
Not to imply, of course, that Bobby's example even overturns the simple
101 story. Consider a firm with a nicely behaved (we are in 101, after
all) technology f(L,K) with objective pf(L,K)-wL-rK. Simple question
Bobby: if L(w,r,p) denotes the firm's labor demand schedule, what is the
sign of (\delta L)(\delta w)?
> Of course, I've already pointed out that, according to the
>literature, examples like mine do have implications for the
>Arrow-Debreu model of intertemporal equilibrium and for Hicks'
>model of sequences of temporary equilibria. Poor Chris Auld
>refuses to address this contemporary literature.
You mean Arrow-Debreau (1953) and Hicks (1939)!? I see Vienneau v.1.1 has
not been programmed to know the current year.
Let's play the quotes game. Michael Mandler, who Vienneau has been
incessantly quoting, notes
The Sraffa-neoclassical debate terminated long ago as a
two-sided argument, and the Sraffian championing of models
with constant relative prices is so distant from comtemporary
neoclassical concerns that I doubt the debate is on the
verge of revival.
(Amusingly given the way Vienneau has been quoting him, Mandler goes on to
note he "does not wish to endorse repeal of the law of supply and
demand.") Mandler should be chided for even using the term "neoclassical"
in this context; his sentence would be more accurate if "neoclassical"
were simply stricken and the phrasing made it clear it certainly isn't
merely "constant relative prices" that push this debate into obscurity.
Usually Vienneau dismisses anyone telling him something like this on the
grounds that mainstream economists are evil, stupid, etc, etc. What to
make of Michael Mandler's comment?
>Hence, for the analyzed firm to be in equilibrium, the
>vertically-integrated industry must be on the so-called factor-price
>frontier for that industry.
Simple question: what are (economic, as if that needs to be said) profits
at every point on the factor price frontier? Now, if we vary a factor
price holding all else equal, what *ought* to happen to a firm's economic
profits? What does this tell you about where your principal conceptual
error lies?
Robert Vienneau
> It's not really an equilibrium model of a firm either. There is no
> reason that a firm needs to be integrated.
It does not matter in my model whether firms are integrated or
not along the (w, p) locus I describe.
> Nothing procludes a firm
> from producing only corn or only iron, and buying inputs rather than
> manufacturing them. A firm equilibrium involves taking input and
> output prices as given to maximize some kind of objective function
> (profits).
E.g.,
Given p, w, Q1, and Q2
Choose Xa, Xb, Xc, and Xd
To Maximize (1 - w - 2 p - (2/5)) Xa
+ (1 - w - (1/2) p - (3/5)) Xb
+ (p - w - (1/10) p - (1/40)) Xc
+ (p - (275/464) w - (113/232) p) Xd
Such that
(w + 2 p + (2/5)) Xa
+ (w + (1/2) p + (3/5)) Xb
+ (w + (1/10) p + (1/40)) Xc
+ ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
Xa, Xb, Xc, Xd >= 0
> Vector of prices exists such that a firm would choose only
> to produce one good.
Yes.
> This is consistent with a firm
> equilibrium.
Perhaps, no.
For a corn-producing firm to continue production unaltered from
period to period, both corn and iron must be produced each period.
> there is no requirement that the various actors of the
> economy will actually behave in a way that supports a firm
> equilibrium.
And, in the model I present in my appendix, there is no
requirement that consumers will actually behave in a way that
supports the equilibrium of the firms (the representative
firm?).
Contrast Sraffa3.pdf on my website, which does analyze
equilibria of the economy.
I have been analyzing in this thread the production-side
aspects of equilibrium alone. If you don't want to call that
"equilibria of the firm", what would you call it?
> Clearly in the example above, if prices were such that
> no firm would produce iron, then it would be difficult to produce corn
> as well. Integration is essentially a way of building an equilibrium
> between the two markets (corn and iron), so that the production plans
> match up in a self-perpetuating way.
Notice that, since corn is a consumption good and consumers are
not modeled, I am not describing the corn market as being in
equilibrium.
Anyway, JT has examined how the model works and is addressing it.
> However, this is now an
> equilibrium condition between *markets* (iron supply meets future
> demand by corn and iron producers, etc.). The zero (or equal) profit
> conditions are also not firm equilibrium conditions, but are justified
> on the basis of market equilibria concepts (entry/competition).
That's all semantics. But why does the firm operate on the
minimum of the U-shaped long run cost curve in long run
equilibrium? It's certainly the case that textbooks present
graphs at the level of the firm here.
> It's not clear what your story has to do with the textbook
> presentation. Your firm is producing *two* outputs, which makes your
> usage of the term labor intensity non-standard.
I don't think the conclusion follows. And it's not too relevant to
my point about how the intuition of supply and demand on the
labor market, as presented in intro texts, is wrong. My point is
not one of semantics, but what can logically be concluded.
My point involves the ratio (L/Y) for a vertically-integrated
industry, or for the economy as a whole.
> In a given period,
> some labour is allocated towards production of iron, some towards
> production of corn. Doesn't matter that that iron is for future corn
> production...it's still an output of this period. The textbook
> treatment would involve two diagrams: one for the labor demand of each
> endeavor.
So JT disagrees with my initial post. Recall this bit of a dialog:
Q: When one draws a demand function for labor, D(w), are the workers
hired assumed to be employed in only one (non-vertically) integrated
industry, or is it possible that some hired workers might be
producing commodities different from others?
A: The latter. The demand for labor is the demand by firms across
industries.
I did not think of that as controversial.
By the way, examples exist with the structure of my example
in which the more labor per gross output in, say, the (non-vertically
integrated) corn sector is associated with a higher wage (in
both sectors).
> Beyond that, I don't think there are any errors in you programming
> problem. I'm just not convinced that your essay has any real point to
> make...
Not to the non-ignorant who have accepted what Samuelson accepted
long ago. But ignorance is what many mainstream economists teach.
Notice Keith Ramsay's query about whether my example, perhaps with
a better exposition can be used to critique certain naive views about
minimum wages and "right to work" laws. Or Schefold's point about
an immigration scenario. As I documented, at least in the latter
case, with a quote from David Friedman, intro texts are used to
treat mistaken naive views.
Robert Vienneau
(Christopher Auld) wrote:
> [Strawpersons - deleted.]
> Vienneau ... is supposed to be "collapsing the entire intellectual
> world" of economists with his "long essays."
I have used the phrase "long essays" frequently. I doubt I
have ever used the phrase "collapsing the entire intellectual
world". Poor Chris Auld is lying.
> [Strawperson - deleted.]
> [Exposition of an erroneous (...rK...) textbook model - deleted.]
> > Of course, I've already pointed out that, according to the
> >literature, examples like mine do have implications for the
> >Arrow-Debreu model of intertemporal equilibrium and for Hicks'
> >model of sequences of temporary equilibria. Poor Chris Auld
> >refuses to address this contemporary literature.
> You mean Arrow-Debreau (1953) and Hicks (1939)!? I see Vienneau...
> has not been programmed to know the current year.
Notice that poor Chris Auld is lying. The contemporary
literature points out implications of examples like mine for
certain models of "dynamics". It is not literature first
presenting the models that would be under discussion, if
poor Chris Auld were to address that literature.
How can I know poor Chris Auld is deliberately lying? Well,
look where he immediately turns:
> Let's play the quotes game.
For the dishonest Chris Auld, this is a matter of ripping quotes out
of context.
> Michael Mandler, who Vienneau has been
> incessantly quoting, notes
> "The Sraffa-neoclassical debate terminated long ago as a
> two-sided argument, and the Sraffian championing of models
> with constant relative prices is so distant from comtemporary
> neoclassical concerns that I doubt the debate is on the
> verge of revival.
Notice poor Chris Auld's refusal to even notice the substantial
issues that Mandler discusses. Anyway, the very next sentence is:
Leaving politics aside, the pitched battles of the past were
fuelled by the joint recognition that Sraffian capital theory
had identified genuine defects in prominent elements of the
neoclassical synthesis of the 1960's. Today the neoclassical
side sees no serious capital-theoretic difficulties outstanding."
-- Michael Mandler, "Classical and neoclassical indeterminacy
in one-shot vs. ongoing equilibria"
Notice Mandler's implicit suggestion that the Sraffian side sees
serious outstanding capital-theoretic difficulties. Which I'll get
to below.
But here's the thing. Poor Chris Auld, and many other economists, still
do not know what the acknowledged defects are. Let me quote somebody
who is not ignorant:
"Even people who have made no study of economic theory
are familiar with the idea that when something is more
plentiful its price will be lower, and introductory
courses on economic theory reinforce this common
presumption with various examples. However, there is no
support from the theory of general equilibrium for the
proposition that an input to production will be cheaper
in an economy where more of it is available. All that
the theory declares is that the price of the use of an
input which is more plentiful cannot be higher if all
other inputs, all other outputs and all other input
prices are in constant proportions to each other."
-- Christopher Bliss, _Capital Theory and the
Distribution of Income_, North Holland, 1975.
In short, prices are not scarcity indices. A greater supply
of labor need not lower wages. Poor Chris Auld's initial reaction
in this thread was to respond to my point with beside-the-point
qualifications about market power. He could equally well have
responded with beside-the-point comments on asymetric information.
Since Mandler knows what he is talking about, I don't think he would
dispute that my example can be used to show that, in a vertically-
integrated industry, a higher ratio of labor-hours to a unit of
net output can be associated with a higher wage. (I've deliberately
put aside disputes about the wording "equilibrium of the firm" in
that statement.) Notice poor Chris Auld has never acknowledged
this simple fact.
Mandler being a serious person, discusses matters of substance.
Here's where he finds some issues:
"In the recent collection edited by Heinz Kurz, Critical Essays
on Piero Sraffa's Legacy in Economics (2000), Bertram Schefold
and Pierangelo Garegnani argue in separate essays that the Sraffian
critique of neoclassical capital theory applies just as much to
general equilibrium as to aggregative models. This work attempts
to bridge the long-standing gulf between the Sraffian and general
equilibrium camps, and deserves serious comment."
That is, Mandler supports what I've said above about what
claims are made in contemporary literature.
The General Equilibrium models do not have constant relative prices
through time. So Mandler has qualified the quote that poor Chris
Auld has wrenched out of context. In other words, Mandler recognizes
that prominent Sraffians are addressing models more current than
the ones that should have been destroyed as a result of debates
during the 1960s. Mandler argues that Schefold and Garegnani have
not made their case.
What I have done is provided references to both sides in an ongoing
dispute about how capital-theoretic differences emerge in models
of intertemporal (very short run) equilibrium. The reader should
note that this is a change of subject from my point about the
textbook errors in the use of long-run labor demand curves.
How did we get on this changed subject? The dishonest Chris
Auld has been continually insisting on changing the subject.
Consider my model in Sraffa3.pdf. I find long period equilibria
in which consumers are modeled by overlapping generations of a
representative agent. I'd like to see the solution of the
following problem. Take a sequence of overlapping agents where
before some time t1, all agents have one value of the parameter
in their utility function, and after time t1 all have agents
have another value. These two values should be around the "perverse"
switch point in my example. Let the initial endowments be those
of the long run equilibria consistent with the former value of
the parameter in the utility function.
What would the intertemporal equilibrium price path be? I
guess one could construct a path in which a rising wage is
associated with a rise in the ratio of labor-hours to net
output. In other words, a shift to less forward-looking
preferences on the part of consumers would result in a
rise of wages (which is associated with a lower interest
rate in long run models). This would be a manifestation
of capital-reversing in a model of a sequence of temporary
equilibrium.
And what would the stability properties of such a path be?
> [Further strawpersons and stupidities - deleted.]
Christopher Auld
>> Vector of prices exists such that a firm would choose only
>> to produce one good.
>
>Yes.
>
>> This is consistent with a firm
>> equilibrium.
>
>Perhaps, no.
"Perhaps, no." ? What do you think it means to say a
firm is "in equilibrium" given prices, Bobby?
>For a corn-producing firm to continue production unaltered from
>period to period, both corn and iron must be produced each period.
Pay attention: Most price vectors will not induce the firm to
"continue production unaltered from period to period." If
the initial wage was such that the firm was in steady state
and you alter the wage holding all else equal, the firm will
not find it profit maximizing to "continue production unaltered
from period to period." You have adjusted other prices along
with the wage rate *such that* the firm will "continue production
unaltered." That is, you haven't held all else equal.
>> However, this is now an
>> equilibrium condition between *markets* (iron supply meets future
>> demand by corn and iron producers, etc.). The zero (or equal) profit
>> conditions are also not firm equilibrium conditions, but are justified
>> on the basis of market equilibria concepts (entry/competition).
>That's all semantics.
LOL.
Christopher Auld
>I have used the phrase "long essays" frequently. I doubt I
>have ever used the phrase "collapsing the entire intellectual
>world". Poor Chris Auld is lying.
Oh, sorry, I had the phrasing slightly wrong, naturally
Vienneau's was slightly more hilariously arrogant and
obnoxious:
| No wonder so many economists have abandoned sci.econ. It cannot be
| comforting to see your complete intellectual bankruptcy proven.
(Vienneau is proud of driving economists off sci.econ with his
incessant spamming. Being a nutter, he misinterprets frustration
with his idiocy as evidence he's shown the "complete intellectual
bankruptcy" of mainstream economics.)
>> [Strawperson - deleted.]
One of the many entertaining aspects of going through the looking
glass is noting what Vienneau deletes. Here's the "strawperson":
One does wonder why Bobby has YET AGAIN deleted my request he point out
exactly where the overt mathematical error in the simple axiomatic proof
that factor demands do not slope up lies.
Of course -- his recent confusion over whether he's considering stready
states of dynamic systems as many prices change (wages in each period) or
one-shot problems notwithstanding -- Bobby also refuses to acknowledge
that the solution to the cost-minimization problem he's supposed to be
solving does not depend on the wage rate. I'll ask him a seventh time to
explain.
Why, why does Bobby refuse to address these points?
>> [Exposition of an erroneous (...rK...) textbook model - deleted.]
I asked Robert Vienneau to state, as a matter of mathematics, whether
the textbook labor demand curve slopes down. Recall the whole point
of this inanity is to show that the textbooks are "logically and
mathematically" wrong. Why did Robert Vienneau delete the question?
>Notice Mandler's implicit suggestion that the Sraffian side sees
>serious outstanding capital-theoretic difficulties. Which I'll get
>to below.
I don't even know what to make of this: My quoting is not dishonest,
and the rest of Mandler's essay isn't in conflict, as far as I
can see, with anything I've said. Perhaps what Mandler means by
"distant from contemporary neoclassical concerns" is simply
beyond Vienneau's comprehension, as Vienneau doesn't appear to
be aware that there is anything in economic thought beyond narrow
issues in capital theory.
>Since Mandler knows what he is talking about, I don't think he would
>dispute that my example can be used to show that, in a vertically-
>integrated industry, a higher ratio of labor-hours to a unit of
>net output can be associated with a higher wage.
Mandler or any other competent economist on the planet would dispute your
idea that a ceteris paribus change in the wage rate would cause a
competitive firm to hire more labor, with or without conditioning on
output. You have misunderstood the "literature you draw on."
>> [Further strawpersons and stupidities - deleted.]
Here's the "further strawpersons and stupidities":
Simple question: what are (economic, as if that needs to be said) profits
at every point on the factor price frontier? Now, if we vary a factor
price holding all else equal, what *ought* to happen to a firm's economic
profits? What does this tell you about where your principal conceptual
error lies?
Why does Vienneau refuse to address the question?
JT
> In article <9f2ad7a3.03062...@posting.google.com>,
> ji...@hotmail.com (JT) wrote:
>
> > It's not really an equilibrium model of a firm either. There is no
> > reason that a firm needs to be integrated.
>
> It does not matter in my model whether firms are integrated or
> not along the (w, p) locus I describe.
Test question: Is vertical integration a necessary condition for
profit maximization? Hint: does the firm in your exercise continue to
produce its own iron if it can purchase iron from an outside source
for a price of .00000001 a ton? This should suggest to you that
vertical integration is only neccessary as some kind of market
mechanism and is not behaviour that follows for standard assumptions
about cost minimization.
> > Nothing procludes a firm
> > from producing only corn or only iron, and buying inputs rather than
> > manufacturing them. A firm equilibrium involves taking input and
> > output prices as given to maximize some kind of objective function
> > (profits).
>
> E.g.,
>
> Given p, w, Q1, and Q2
> Choose Xa, Xb, Xc, and Xd
> To Maximize (1 - w - 2 p - (2/5)) Xa
> + (1 - w - (1/2) p - (3/5)) Xb
> + (p - w - (1/10) p - (1/40)) Xc
> + (p - (275/464) w - (113/232) p) Xd
> Such that
> (w + 2 p + (2/5)) Xa
> + (w + (1/2) p + (3/5)) Xb
> + (w + (1/10) p + (1/40)) Xc
> + ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
> Xa, Xb, Xc, Xd >= 0
>
> > Vector of prices exists such that a firm would choose only
> > to produce one good.
>
> Yes.
And so why force the firm to produce both in your solution? Nothing
in your model precludes splitting up the activity across two types of
firms (corn-producing firms and iron-producing firms) that buy inputs
from each other. Your "firm" solution simply replicates the market
equilibrium that would exist between these two firms in a steady-state
equilibrium. How would you describe the factor intensities of these
individual firms? You results are driven by bundling up sets of these
separate firms, and calculating labour demand of the total activity.
The "paradox" arises because of how the share of different types of
firms changes with with the wage. A combination of the two markets
does result in higher net production of corn when the wage rate rises.
But neither of the individual firms (in the non-integrated solution)
behaves paradoxically to the wage change (and subsequent changes in
iron prices that occur as a result of defining a new market
equilibrium).
>
> > This is consistent with a firm
> > equilibrium.
>
> Perhaps, no.
>
> For a corn-producing firm to continue production unaltered from
> period to period, both corn and iron must be produced each period.
Again, that's an economy solution. You can't preclude the possibility
of iron production outside the firm and state that you are solving the
problem of the firm. I'm not going to give you vertical integration
as an innocuous assumption until you are able to justify it on the
basis of profit maximization, rather than as simply a means of
brushing off the working of factor markets (and separate market
equilibria). The economics literature usually justifies such
arrangements on the basis of such things as eliminating double
marginalization (monopolist selling to monopolist) or minimizing
transaction costs. None of these features are present in your model.
As I've said before, you are simply internalizing a set of factor
markets with vertical integration.
> > there is no requirement that the various actors of the
> > economy will actually behave in a way that supports a firm
> > equilibrium.
>
> And, in the model I present in my appendix, there is no
> requirement that consumers will actually behave in a way that
> supports the equilibrium of the firms (the representative
> firm?).
Who said anything about consumers?
> Contrast Sraffa3.pdf on my website, which does analyze
> equilibria of the economy.
>
> I have been analyzing in this thread the production-side
> aspects of equilibrium alone. If you don't want to call that
> "equilibria of the firm", what would you call it?
Equilibrium in production markets, precisely because of the outcome
the integrated firm is replicating.
> > Clearly in the example above, if prices were such that
> > no firm would produce iron, then it would be difficult to produce corn
> > as well. Integration is essentially a way of building an equilibrium
> > between the two markets (corn and iron), so that the production plans
> > match up in a self-perpetuating way.
>
> Notice that, since corn is a consumption good and consumers are
> not modeled, I am not describing the corn market as being in
> equilibrium.
>
> Anyway, JT has examined how the model works and is addressing it.
>
> > However, this is now an
> > equilibrium condition between *markets* (iron supply meets future
> > demand by corn and iron producers, etc.). The zero (or equal) profit
> > conditions are also not firm equilibrium conditions, but are justified
> > on the basis of market equilibria concepts (entry/competition).
>
> That's all semantics. But why does the firm operate on the
> minimum of the U-shaped long run cost curve in long run
> equilibrium? It's certainly the case that textbooks present
> graphs at the level of the firm here.
A U-shaped cost curve is justified on the basis of changing returns to
scale (and fixed input prices). The production technology in your
model exhibits constant returns to scale. Other firms adopt the same
technology, driving down output prices until further entry would push
the price below average cost. Note the role of competition in a
*market*.
> > It's not clear what your story has to do with the textbook
> > presentation. Your firm is producing *two* outputs, which makes your
> > usage of the term labor intensity non-standard.
>
> I don't think the conclusion follows. And it's not too relevant to
> my point about how the intuition of supply and demand on the
> labor market, as presented in intro texts, is wrong. My point is
> not one of semantics, but what can logically be concluded.
>
> My point involves the ratio (L/Y) for a vertically-integrated
> industry, or for the economy as a whole.
I think your point is closer to the line that partial equilibrium
analysis (what is emphasized in first year class), leads to intuitions
that may be incorrect, because feedback mechanisms between markets
(through prices changes) may lead to "counter-intuitive" results.
This is my interpretation of what your are saying...correct me if I'm
wrong.
> > In a given period,
> > some labour is allocated towards production of iron, some towards
> > production of corn. Doesn't matter that that iron is for future corn
> > production...it's still an output of this period. The textbook
> > treatment would involve two diagrams: one for the labor demand of each
> > endeavor.
>
> So JT disagrees with my initial post. Recall this bit of a dialog:
>
> Q: When one draws a demand function for labor, D(w), are the workers
> hired assumed to be employed in only one (non-vertically) integrated
> industry, or is it possible that some hired workers might be
> producing commodities different from others?
>
> A: The latter. The demand for labor is the demand by firms across
> industries.
>
> I did not think of that as controversial.
Demand for labour can be talked about in a variety of ways. Firm
demand curves would in any case hold the shadow price of iron fixed
(on the assumption that the firm can always purchase the output on a
market...the competitive firm is a price taker). You seem to be
talking about labour demand of an individual firm. Aggregation around
an industry or the economy as a whole is possible, given certain
aggregation properties. The crossing of the labour supply/demand in
any of these cases is not sufficient to determine market clearing
across the economy. In this sense, you are correct...the standard
diagram used to discuss minimum wages may result in a naive (and maybe
false) view of the effect of the policy. A general equilibrium
treatment would involve working through all the markets, and shifting
aggregate labour demand in response to changes of various goods. The
final labour demand curve would likely not be the same as the original
at the new equilibrium. Again though, this suggests that you are
arguing that partial equilibrium analysis can lead to incorrect
predictions. Nothing new there, though its not generally spelled out
in first year classes.
Cheers,
-JT
Robert Vienneau
ji...@hotmail.com (JT) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote in message
> news:<rvien-1185D1....@news.dreamscape.com>...
> > In article <9f2ad7a3.03062...@posting.google.com>,
> > ji...@hotmail.com (JT) wrote:
> > > It's not really an equilibrium model of a firm either. There is no
> > > reason that a firm needs to be integrated.
> > It does not matter in my model whether firms are integrated or
> > not along the (w, p) locus I describe.
> Test question: Is vertical integration a necessary condition for
> profit maximization?
No.
> Hint: does the firm in your exercise continue to
> produce its own iron if it can purchase iron from an outside source
> for a price of .00000001 a ton?
For the two values of w I considered in my first post, that value
of p would not be on the (w, p) locus I describe.
> This should suggest to you that
> vertical integration is only neccessary as some kind of market
> mechanism
That's cryptic. Once again, it does not matter in my appendix
model whether firms are vertically-integrated or not. That is,
vertical integration of firms is not necessary.
> > > Nothing procludes a firm
> > > from producing only corn or only iron, and buying inputs rather than
> > > manufacturing them. A firm equilibrium involves taking input and
> > > output prices as given to maximize some kind of objective function
> > > (profits).
> > E.g.,
> >
> > Given p, w, Q1, and Q2
> > Choose Xa, Xb, Xc, and Xd
> > To Maximize (1 - w - 2 p - (2/5)) Xa
> > + (1 - w - (1/2) p - (3/5)) Xb
> > + (p - w - (1/10) p - (1/40)) Xc
> > + (p - (275/464) w - (113/232) p) Xd
> > Such that
> > (w + 2 p + (2/5)) Xa
> > + (w + (1/2) p + (3/5)) Xb
> > + (w + (1/10) p + (1/40)) Xc
> > + ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
> > Xa, Xb, Xc, Xd >= 0
> > > Vector of prices exists such that a firm would choose only
> > > to produce one good.
> > Yes.
> And so why force the firm to produce both in your solution?
Suppose either
(1) No cost-minimizing firm would produce corn for some given
(w, p)
or
(2) No cost-minimizing firm would produce iron.
Then there would be disequilibrating forces within the production/
firm side of the markets under consideration.
> Nothing
> in your model precludes splitting up the activity across two types of
> firms (corn-producing firms and iron-producing firms) that buy inputs
> from each other.
That's what I'm agreeing with.
> Your "firm" solution simply replicates the market
> equilibrium that would exist between these two firms in a steady-state
> equilibrium. How would you describe the factor intensities of these
> individual firms? You results are driven by bundling up sets of these
> separate firms, and calculating labour demand of the total activity.
As I said in my previous post, examples can be constructed with
"paradoxical" behavior arising in just the (non-vertically integrated)
corn or iron sectors.
> The "paradox" arises because of how the share of different types of
> firms changes with with the wage. A combination of the two markets
> does result in higher net production of corn when the wage rate rises.
> But neither of the individual firms (in the non-integrated solution)
> behaves paradoxically to the wage change (and subsequent changes in
> iron prices that occur as a result of defining a new market
> equilibrium).
At the lower wage of 3/2780 Bushels Per Person-Year, the Beta technique
is cost-minimizing. At a wage of 109/4040 Bushels Per Person-Year, the
Alpha technique is cost minimizing. This means that Process D is used
to produce iron at the lower wage, while Process C is used to produce
iron at the higher of these two wages. That is, to say a higher
ratio of direct labor inputs to iron output is associated with the
higher of the two wages under consideration.
Again, a higher labor-intensity in (non-vertically integrated)
iron production is cost-minimizing for the long period position
resulting from the higher of the two levels of wages under
consideration.
So JimT seems to be wrong about my example.
> > > This is consistent with a firm
> > > equilibrium.
> > Perhaps, no.
> > For a corn-producing firm to continue production unaltered from
> > period to period, both corn and iron must be produced each period.
> Again, that's an economy solution.
I am not describing an equilibrium of an economy. I am not
even describing an equilibrium of a vertically-integrated industry
for producing corn (whether the firms in that industry are
vertically-integrated or not).
> You can't preclude the possibility
> of iron production outside the firm and state that you are solving the
> problem of the firm.
All the firms in my model face identical prices and technologies.
It does not matter whether they decide to integrate vertically
or not. Only along the (w, p) locus I construct could there not
be disequilibriating forces within the firms.
> I'm not going to give you vertical integration
> as an innocuous assumption until you are able to justify it on the
> basis of profit maximization, rather than as simply a means of
> brushing off the working of factor markets (and separate market
> equilibria). The economics literature usually justifies such
> arrangements on the basis of such things as eliminating double
> marginalization (monopolist selling to monopolist) or minimizing
> transaction costs. None of these features are present in your model.
Agreed. None of these features are present.
> As I've said before, you are simply internalizing a set of factor
> markets with vertical integration.
But you don't seem to understand I am not describing equilibia
in any market whatsoever.
> > > there is no requirement that the various actors of the
> > > economy will actually behave in a way that supports a firm
> > > equilibrium.
> > And, in the model I present in my appendix, there is no
> > requirement that consumers will actually behave in a way that
> > supports the equilibrium of the firms (the representative
> > firm?).
> Who said anything about consumers?
I did. The point is I am not describing, in this thread, an
equilibrium of the economy, an equilibrium of the corn market,
or even, necessarily, an equilibrium of the iron market.
For the latter point, suppose iron was also a consumer good.
Then we could describe both a vertically-integrated iron
industry and a vertically-integrated corn industry. Only when
both industries were on the (w, p) locus I derive would
dis-equibriating forces not be arising in the production
side of the markets.
But there is no requirement that consumers will actually behave
in a way that supports the equilibrium of the firms.
> > Contrast Sraffa3.pdf on my website, which does analyze
> > equilibria of the economy.
> >
> > I have been analyzing in this thread the production-side
> > aspects of equilibrium alone. If you don't want to call that
> > "equilibria of the firm", what would you call it?
> Equilibrium in production markets, precisely because of the outcome
> the integrated firm is replicating.
But the markets for corn and iron need not be in equilibrium at every
point on the (w, p) locus I describe.
> > > It's not clear what your story has to do with the textbook
> > > presentation. Your firm is producing *two* outputs, which makes your
> > > usage of the term labor intensity non-standard.
Net output consists of one commodity.
> > I don't think the conclusion follows. And it's not too relevant to
> > my point about how the intuition of supply and demand on the
> > labor market, as presented in intro texts, is wrong. My point is
> > not one of semantics, but what can logically be concluded.
> > My point involves the ratio (L/Y) for a vertically-integrated
> > industry, or for the economy as a whole.
> I think your point is closer to the line that partial equilibrium
> analysis (what is emphasized in first year class),
When is the first-year class story applicable? What special-case
assumptions rule out the technology of my story about firms in
competitive markets? If none, how can the first-year story be
told in my example? Where is your downward-sloping labor demand
curve that will result in equilibria for each point on that
curve? (If the data (e.g., technology) behind that supply-and-
demand equilibrium persisted, the equilibrium would persist
in the first-year story.)
> leads to intuitions
> that may be incorrect, because feedback mechanisms between markets
> (through prices changes) may lead to "counter-intuitive" results.
> This is my interpretation of what your are saying...correct me if I'm
> wrong.
My point involves the ratio (L/Y) for a vertically-integrated industry,
or for the economy as a whole.
Let's see what the literatire says.
"Hicks has written that
There is, however, the further possibility that some of the
inputs which may be substituted for A-labour in the X-industry
are themselves products of A-labour in some other industry. In
that case their prices are also likely to have risen...
Consequently, though the possibility of substitution will
ordinarily will still be present, it will be somewhat
damped down (1968, p. 327).
...These remarks imply the need to go beyond the usual partial
equilibrium analysis of the demand for inputs, WHETHER IN ITS
SHORT-RUN OR ITS LONG-RUN FORM. It was just this need to go
beyond partial equilibrium analysis that our examples were
intended to illustrate. It does not follow, of course, that
one must have recourse to a 'full neoclassical general
equilibrium' - indeed our point has already been made in terms
of long-period positions alone. It is sufficient to compare
positions on the wage-rent-interest-rate frontier to show that
input use and 'price' need not be inversely related; one does
not need to 'close the system' in any way. Our point, then, is
not identical to the general equilibrium one that changes in
the data have complicated consequences for the endogeneous
variables"
-- Ian Steedman, On Input 'Demand Curves'". Cambridge Journal
of Economics, 198?.
> Demand for labour can be talked about in a variety of ways. Firm
> demand curves would in any case hold the shadow price of iron fixed
> (on the assumption that the firm can always purchase the output on a
> market...the competitive firm is a price taker).
The assumptions that
(1) the price of iron is fixed and
(2) that a firm can always purchase iron on a market for any level
of wages
are inconsistent.
By the way, notice that JimT contradicts poor Chris Auld's position
(this week) on the price of iron. They won't publicly discuss their
differences.
> You seem to be
> talking about labour demand of an individual firm.
A vertically-integrated representative firm.
> Aggregation around
> an industry or the economy as a whole is possible, given certain
> aggregation properties. The crossing of the labour supply/demand in
> any of these cases is not sufficient to determine market clearing
> across the economy. In this sense, you are correct...the standard
> diagram used to discuss minimum wages may result in a naive (and maybe
> false) view of the effect of the policy.
So why do you attempt to get your first year students to echo
naive (and maybe) false views back?
> A general equilibrium
> treatment would involve working through all the markets, and shifting
> aggregate labour demand in response to changes of various goods.
But the example with which I began this thread is not of general
equilibrium.
Robert Vienneau
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> [ Stupidity - deleted.]
> >> [Strawperson - deleted.]
> One of the many entertaining aspects of going through the looking
> glass is noting what Vienneau deletes. Here's the "strawperson":
> [ Strawperson - deleted.]
But let me leave part of this strawperson in:
> Of course -- his recent confusion over whether he's considering stready
> states of dynamic systems as many prices change (wages in each period)
> or
> one-shot problems notwithstanding
Now JimT had written:
"In a given period, some labour is allocated towards production of
iron, some towards production of corn. Doesn't matter that that
iron is for future corn production...it's still an output of this
period."
-- JimT
Why doesn't poor Chris Auld ask JimT about his "confusion"?
I had written:
Of course, I've already pointed out that, according to the
literature, examples like mine do have implications for the
Arrow-Debreu model of intertemporal equilibrium and for Hicks'
model of sequences of temporary equilibria. Poor Chris Auld
refuses to address this contemporary literature.
In response, poor Chris Auld quoted an essay by Michael Mandler
which contains the following:
"In the recent collection edited by Heinz Kurz, Critical Essays
on Piero Sraffa's Legacy in Economics (2000), Bertram Schefold
and Pierangelo Garegnani argue in separate essays that the Sraffian
critique of neoclassical capital theory applies just as much to
general equilibrium as to aggregative models. This work attempts
to bridge the long-standing gulf between the Sraffian and general
equilibrium camps, and deserves serious comment."
-- Michael Mandler, "Classical and neoclassical indeterminacy
in one-shot vs. ongoing equilibria"
> I don't even know what to make of this: My quoting is not dishonest...
> >Since Mandler knows what he is talking about, I don't think he would
> >dispute that my example can be used to show that, in a vertically-
> >integrated industry, a higher ratio of labor-hours to a unit of
> >net output can be associated with a higher wage.
> [ Non-sequitur - deleted. ]
> [snip]
JT
> In article <9f2ad7a3.0306...@posting.google.com>,
> ji...@hotmail.com (JT) wrote:
> > The "paradox" arises because of how the share of different types of
> > firms changes with with the wage. A combination of the two markets
> > does result in higher net production of corn when the wage rate rises.
> > But neither of the individual firms (in the non-integrated solution)
> > behaves paradoxically to the wage change (and subsequent changes in
> > iron prices that occur as a result of defining a new market
> > equilibrium).
>
> At the lower wage of 3/2780 Bushels Per Person-Year, the Beta technique
> is cost-minimizing. At a wage of 109/4040 Bushels Per Person-Year, the
> Alpha technique is cost minimizing. This means that Process D is used
> to produce iron at the lower wage, while Process C is used to produce
> iron at the higher of these two wages. That is, to say a higher
> ratio of direct labor inputs to iron output is associated with the
> higher of the two wages under consideration.
>
> Again, a higher labor-intensity in (non-vertically integrated)
> iron production is cost-minimizing for the long period position
> resulting from the higher of the two levels of wages under
> consideration.
>
> So JimT seems to be wrong about my example.
>
I'm only going to respond to this point for the time being. I concede
I am probably wrong in my previous claim about the factor intensities.
However, it's been many months since I read through the essay.
Here's the *real* question for you, Robert. If *only* the wage rate
increases (i.e holding the price of iron and corn constant), will a
cost-minimizing firm switch to the more labour intensive method of
producing either corn or iron? Whether or not either type of firm
will actually produce either output is irrelevant.
You seem to be confused about the notion of a firm equilibrium.
Markets consist of more than interactions between firms and consumers.
When a corn producer sells corn to a firm to produce iron, that is a
market interaction.
Whether you recognize it or not, you have introduced factor models
into your model. Since you have introduced a zero profit condition
without any justification (this is a market condition) you are able to
determine the price of the commodities without demand side
considerations.
Zero profits are *not* part of a firm equilibrium. They are justified
on the basis of market considerations such as competition and entry.
There is no reason from the perspective of the firm that price could
not exceed or fall below cost...of course these cases would involve
the firm wanting to produce an infinite amount of output or shutdown.
Being at the minimum of the cost curve is not a long-run firm
equilibrium. It's a long-run market equilibrium. The story is used
to justify the existence of a horizontal long-run supply curve (i.e
price=average cost=marginal cost), which is essentially what you are
doing.
JT
I glanced back at your original post. I realize that you don't
actually use a zero profit condition. Your notion of a rate of
profits is, not surprisingly, also non-standard. A "rate" of profits
generally refers to a return on one's investment (capital). I suppose
we could talk about the return to labour of an entreneurial laborer.
In any case, equating profit rates across the two activities and using
this condition to determine a price of iron amounts to a variant of
the zero profit condition I described...it's justification is based on
entry into a particular market i.e. a market rather than a firm
condition.
If the set of prices is such that one activity has a lower rate of
return, that activity is not undertaken in the firm equilibrium.
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote in message
> news:<rvien-00923F....@news.dreamscape.com>...
>
> > In article <9f2ad7a3.0306...@posting.google.com>,
> > ji...@hotmail.com (JT) wrote:
>
> > > The "paradox" arises because of how the share of different types of
> > > firms changes with with the wage. A combination of the two markets
> > > does result in higher net production of corn when the wage rate
> > > rises.
> > > But neither of the individual firms (in the non-integrated solution)
> > > behaves paradoxically to the wage change (and subsequent changes in
> > > iron prices that occur as a result of defining a new market
> > > equilibrium).
> > ...Again, a higher labor-intensity in (non-vertically integrated)
> > iron production is cost-minimizing for the long period position
> > resulting from the higher of the two levels of wages under
> > consideration.
> >
> > So JimT seems to be wrong about my example.
> I'm only going to respond to this point for the time being. I concede
> I am probably wrong in my previous claim about the factor intensities.
> However, it's been many months since I read through the essay.
> Here's the *real* question for you, Robert.
JimT misspells "completely different" as "real".
> If *only* the wage rate
> increases (i.e holding the price of iron and corn constant), will a
> cost-minimizing firm switch to the more labour intensive method of
> producing either corn or iron?
As I understand it, no. That's clear, I suppose, if you think
about the worksheet "Region Analysis" in the spreadsheet I
linked to in the post with which I started this thread:
<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/ChoiceOfTechnique
.xls>
> Whether or not either type of firm
> will actually produce either output is irrelevant.
It is irrelevant to the specific question JimT asked. It is not
irrelevant to whether or not disequilibriating forces exist
within the set of firms (or within the representative vertically-
integrated firm) wanting to purchase labor.
Maybe JimT ought to work out if the introductory textbook story
of a downward-sloping labor demand curve can be drawn when:
o Some of the firms hiring labor are using it to produce
capital goods and some are using it to produce consumption
goods with previously-produced capital goods
o There do not exist disequilibriating forces within those
firms at each point on the labor demand curve.
If one does not consider a different level of the price of
iron with each different level of the wage, the second condition
is not satisfied. If one does change the price of iron with
the wage, as I indicate, the total amount of labor that firms
want to hire can be higher at a higher level of wages.
Later, JimT writes:
> I glanced back at your original post. I realize that you don't
> actually use a zero profit condition. Your notion of a rate of
> profits is, not surprisingly, also non-standard.
I don't know what "also" is doing there.
> A "rate" of profits generally refers to a return on one's
> investment (capital).
Which it does in my case too.
"...the system can 'end up' in a variety of states in which
the real wage of labor and the interest rate (or, what is the
same thing with our stipulation of no uncertainty, the
percentage rate of profit) are determined."
-- Paul A. Samuelson, "Parable and Realism in Capital Theory:
The Surrogate Production Function". (1962).
In my first post on this thread, I speak of the "rate of
(accounting) profits". Same usage.
> In any case, equating profit rates across the two activities and using
> this condition to determine a price of iron amounts to a variant of
> the zero profit condition I described...it's justification is based on
> entry into a particular market i.e. a market rather than a firm
> condition.
It's justification for the accounting story arises from the
determination of the return on investment.
For some reason, JimT has failed to acknowledge that no
markets (corn, iron, labor) need be in equilibrium in my
analysis. After all, I did not model consumers.
> If the set of prices is such that one activity has a lower rate of
> return, that activity is not undertaken in the firm equilibrium.
Which is what I say.
JT
<rv...@see.sig.com> wrote:
>
>> I'm only going to respond to this point for the time being. I
concede
>> I am probably wrong in my previous claim about the factor
intensities.
>> However, it's been many months since I read through the essay.
>> Here's the *real* question for you, Robert.
>
>JimT misspells "completely different" as "real".
That's the only question that's relevant if we're talking about labour
demand. See below for clarification.
>
>> If *only* the wage rate
>> increases (i.e holding the price of iron and corn constant), will a
>> cost-minimizing firm switch to the more labour intensive method of
>> producing either corn or iron?
>
>As I understand it, no. That's clear, I suppose, if you think
>about the worksheet "Region Analysis" in the spreadsheet I
>linked to in the post with which I started this thread:
>
><http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/ChoiceOfTechnique
>.xls>
>
>> Whether or not either type of firm
>> will actually produce either output is irrelevant.
>
>It is irrelevant to the specific question JimT asked. It is not
>irrelevant to whether or not disequilibriating forces exist
>within the set of firms (or within the representative vertically-
>integrated firm) wanting to purchase labor.
>
>Maybe JimT ought to work out if the introductory textbook story
>of a downward-sloping labor demand curve can be drawn when:
>
> o Some of the firms hiring labor are using it to produce
> capital goods and some are using it to produce consumption
> goods with previously-produced capital goods
>
> o There do not exist disequilibriating forces within those
> firms at each point on the labor demand curve.
Your locus of (w,p) are not firm equilibrium conditions. This is part
of economy equilibrium which insures agents have to reason to relocate
factors between sectors. They are conditions that insure that profits
are zero in each industry. To see that this is all you are doing,
replace your notion of a wage plus profits, w(1+r), with simply a wage
rate w*...then all revenues are paid out. For the w*,p pairs that you
stipulate, profits are zero in both industries...hence no incentives
to switch sectors, etc. by firms in either industry. This is similar
to the economy equilibrium in the small open economy version of the
Herscher-Ohlin model...the only different being in that model
commodity prices are exogeneous, while you are taking factor prices as
exogeneous. The solution is block recursive, hence you can determine
a set of prices without referencing supply and demand conditions. It
is nevertheless a feature of the equilibrium of the economy.
There is no equilibrium condition in the firm...as a price taker the
firm goes to an external factor market. It doesn't do an ad hoc
change to accounting prices to equilibrate profit rates, but rather
enters a market price on iron and sticks to the production process
with the highest profit rate.
In any case, you've failed to show that firms hire more labour as the
wage increases. For CRS production technology in competitive markets,
you can only determine factor *intensities*, not factor demands, at
the firm level. Without further structure, you haven't established
that overall employment has increased with the wage increase, even
within the firm, because the firm's level of output, and hence input,
is indeterminate. This of course ignores the fact that notions of
firm demand have nothing to do with the set of (w,p) that you are
considering.
>
>If one does not consider a different level of the price of
>iron with each different level of the wage, the second condition
>is not satisfied. If one does change the price of iron with
>the wage, as I indicate, the total amount of labor that firms
>want to hire can be higher at a higher level of wages.
But those conditions that you refer to have nothing to do with the
firm problem. If they aren't satified with equality for a given set
of prices, then one activity is not undertaken. I wonder how many
times I need to repeat myself.
>> I glanced back at your original post. I realize that you don't
>> actually use a zero profit condition. Your notion of a rate of
>> profits is, not surprisingly, also non-standard.
>
>I don't know what "also" is doing there.
>
>> A "rate" of profits generally refers to a return on one's
>> investment (capital).
>
>Which it does in my case too.
>
> "...the system can 'end up' in a variety of states in which
> the real wage of labor and the interest rate (or, what is the
> same thing with our stipulation of no uncertainty, the
> percentage rate of profit) are determined."
> -- Paul A. Samuelson, "Parable and Realism in Capital Theory:
> The Surrogate Production Function". (1962).
>
>In my first post on this thread, I speak of the "rate of
>(accounting) profits". Same usage.
Sure, but as I said before, this is really no different than the
zero-profit condition. The zero profit conditions consist of two
equations in three unknowns (price of commodities, wage)...because
you've set the corn to one (numeraire), the wage and price are
completely determined by the system. Since you want to take the wage
as exogenous, you are forced to use a fudge factor (the rate of
profits) to insure that the system isn't overdetermined.
So the rate of profits ends up being endogenous.
>
>> In any case, equating profit rates across the two activities and
using
>> this condition to determine a price of iron amounts to a variant of
>> the zero profit condition I described...it's justification is based
on
>> entry into a particular market i.e. a market rather than a firm
>> condition.
>
>It's justification for the accounting story arises from the
>determination of the return on investment.
There is no accounting story to be told. If a price taking firm can
buy inputs, why invent a nonsense price to generate nonsense profit
rates? (Enron is another issue.) And don't repeat the line about the
firm not being able to buy one input because no one is producing
it...you're simply betraying a lack of understanding of firm theory
vs. a step in the block recursive solution to an economy with perfect
competition and entry in several sectors.
>For some reason, JimT has failed to acknowledge that no
>markets (corn, iron, labor) need be in equilibrium in my
>analysis. After all, I did not model consumers.
Again, the block recursive nature of the problem doesn't require
reference to the demand side for determination of the prices. But
zero profits in itself is a condition of the equilibrium of an
*economy*. The firm solution assumes that for any set of prices the
firm can buy and sell as much input and output as it wishes. The
integrated firm is a special case where both activities are equally
profitably...i.e. zero profits in both sectors, *which* is a condition
of the economy (or at least the competitive sectors of the economy).
>> If the set of prices is such that one activity has a lower rate of
>> return, that activity is not undertaken in the firm equilibrium.
>
>Which is what I say.
Yes, but there is no reason for the firm to adjust the accounting
price of iron. There is nothing to proclude an external market for
iron. You're forcing unnecessary and unjustified structure into the
firm problem.
JT
various equilbrium concepts from an introductory level economics
textbook. I say loose because I don't have any textbooks at hand.
Competitive firm - takes the prices of *all* inputs and outputs as
given. Maximizes profits using these prices.
Short-run vs. long-run for firm. In the short-run some inputs may be
fixed. Supply curve consists of the portion of the MC curve that lies
on or above average variable cost curve. In the long-run, the firm
may alter all inputs. The firm may also exit the industry. Exit (and
entry by new firms) implies that the firm's supply curve lies above
the average total cost curve.
Your model: The textbook example assumes decreasing returns to scale
after some level of output. Your techology exhibits CRS. As a
result, a firm will wish to provide an infinite amount of output if
P>ATC, an indeterminate amount if P=ATC, and no amount (exit) if
P<ATC.
Competitive equilibrium in an industry. All firms are identical (not
necessary, though the same technology is available to all firms in the
long-run) and are price-takers. In the short run, the number of firms
is fixed, though individual firms may shut down production if the
price is below the cost of variable inputs. Industry supply is the
horizontal aggregation of the supply curves of all firms. In the
long-run, firms will enter as long as the rate of return is the same
as elsewhere in the economy. Entry/exit occur until "economic
profits" are zero. Since firms are assumed to be homogeneous, this
occurs when each firm is operating at the minimum of its operating at
the minimum point of the ATC curve. Since this point can be
determined with only reference to the input costs, demand
considerations are not necessary to determine the equilibrium price of
output in a market. Of course, since a firm will always find it
profitable to sell one more unit, provided that p>marginal cost=(ATC),
the industry supply and demand curves meet at this point. However,
supply and demand are not used directly to solve for p. P can be
expressed as a function of the input prices.
Your model: Shouldn't be relevant, since supposedly there is no
industry. However, since you're using the zero profit condition this
clearly isn't the case. So...for a non-integrated industry producing
only one output using the available technologies, the price is
determined finding the zero profit conditions for whatever
technologies are being used. Note that price determination happens at
the industry level.
In addition, you have imposed an additional condition, which is that
multiple industries are in long-run competitive equilibrium. So your
price combinations are the result of:
1) Competitive firms maximizing profits.
2) Intra-industry competition driving profits to zero. (long-run
competitive equilibrium in an industry)
3) Requiring factor prices to be a triplet such that profits are zero
in both industries.
If you are going to attack the first-year treatment, you better
understand where it comes from. Your programming problem doesn't have
the implications that you want it to. It's not the outcome for a
competitive firm, but rather a comparison of the position of
competitive firms after two *industries* have reached new, compatiable
long-run equilibria in response to a change in the wage. It also has
no implications about either firm-specific or overall employment
responses to a change in the wages. And no bearing on factor demand
functions either.
Christopher Auld
In his (non)response to my last post, I restored text Vienneau
had deleted and posed several questions again:
One does wonder why Bobby has YET AGAIN deleted my request he point out
exactly where the overt mathematical error in the simple axiomatic proof
that factor demands do not slope up lies.
Of course -- his recent confusion over whether he's considering stready
states of dynamic systems as many prices change (wages in each period) or
one-shot problems notwithstanding -- Bobby also refuses to acknowledge
that the solution to the cost-minimization problem he's supposed to be
solving does not depend on the wage rate. I'll ask him a seventh time to
explain.
Why, why does Bobby refuse to address these points?
I asked Robert Vienneau to state, as a matter of mathematics, whether
the textbook labor demand curve slopes down. Recall the whole point
of this inanity is to show that the textbooks are "logically and
mathematically" wrong. Why did Robert Vienneau delete the question?
Simple question: what are (economic, as if that needs to be said) profits
at every point on the factor price frontier? Now, if we vary a factor
price holding all else equal, what *ought* to happen to a firm's economic
profits? What does this tell you about where your principal conceptual
error lies?
Why does Vienneau refuse to address the question?
Vienneau deleted these points YET AGAIN, substituting some feeble,
irrelevant quotes he doesn't understand. Gosh, why?
> "...the system can 'end up' in a variety of states in which
> the real wage of labor and the interest rate (or, what is the
> same thing with our stipulation of no uncertainty, the
> percentage rate of profit) are determined."
> -- Paul A. Samuelson, "Parable and Realism in Capital Theory:
> The Surrogate Production Function". (1962).
>In my first post on this thread, I speak of the "rate of
>(accounting) profits". Same usage.
His response to JimT above merely reiterates the same conceptual errors,
yet again. Samuelson is talking about a *market* equilibrium where firms
discount at the same rate as the market. The "interest rate" and the
"rate of profit" are then equal in equilibrium in this sort of model.
Vienneau is supposed to be considering *a firm's* response to a change in
*a price*. The firm's discount rate does not vary with its own rate of
profits as the wage rate is varied, ie, the interest rate and the firm's
rate of profits will not generally be equal. Yet again, Vienneau is wrong
for many reasons, the major one simply being that he isn't holding all
else equal.
He goes on the display complete ignorance of dynamic optimization, which
should harldy surprise anyone. Vienneau's firm makes decisions over
purchases of labor and sales of corn each period, and allocation of corn,
labor, and iron to the production of iron and corn each period. Collect
the choice variables at time t into a vector x_t and denote the set of
these vectors x; collect the state variables into a vector k_t. Letting
the horizon be T and l_t be labor purchases, Vienneau's problem can be
written,
\max_{{x_t}_{t=0}^T} \sum_t b^t (f(x_t, k_t) - w_t l_t}
subject to the initial stocks of corn and iron and the law of motion
for k(t). Note that:
1. This problem is a special case of the form for which I showed
earlier which has the property that an increase in the wage
rate in every period induces the firm to hire less labor.
2. Compactly writing this problem as max f(x) - w'l, we see the
textbook proof that labor demand curves slope down directly
applies to this problem. HOLDING ALL ELSE EQUAL, this firm
will never respond to an increase in w_t by increasing l_t.
3. The "price of iron" does not appear in this problem. Incidentally,
JimT's comment that the shadow price of iron ought to be fixed is
correct so far as Vienneau's arithmetic is concerned but incorrect
as far as Vienneau's explanation of his arithmetic is concerned.
Much of the problem with Vienneau's tedious, incoherent "long essays"
is they are both poorly exposited and improperly explained --
Vienneau is badly paraphrasing a literature he doesn't actually
understand.
4. The discount rate b is exogenous.
5. The solution to this problem x(\theta), where \theta is the
collection of parameters, has the property that at every point
the firm is "in equilibrium," ie, maximizing profits. One set
of objects in the solution is the set of labor demand schedules,
which slope down as per textbook _proofs_. Vienneau's blather
about "disequilibrating forces within the firm" is complete
rubbish, an artifact of his attempt to solve a dynamic problem
using a static method. Notice that, as in very simple 101
models, the MARKET will generally not be in equilibrium for a
gievn \theta, but the FIRM by definition is in equilibrium at
every point x(\theta).
6. It is not necessarily the case that the solution to this problem
involves the same values of the choice variables in each period.
If it does not and one nonetheless imposes this condition on the
solution, the solution is not profit maximizing. Vienneau doesn't
appear to even understand what "equilibrium of the firm" means
in intro textbooks (he's already amply demonstrated he has no
idea what "long run" means, laughably enough).
Robert Vienneau
JimT hasn't phrased his point well. He should say these are part of
the equilibrium conditions for the sectors within a vertically-integrated
industry. (The integration need not be more than notional.)
I need not care for my point if that's so. In other words, I can
easily accept that way of talking. The appendix in my first post on
this thread should have made this clear.
> which insures agents have to reason to relocate
> factors between sectors. They are conditions that insure that profits
> are zero in each industry. To see that this is all you are doing,
> replace your notion of a wage plus profits, w(1+r), with simply a wage
> rate w*..
No, that does not make JimT's point. I could have told the same sort
of story with wages being paid out of product, instead of being
advanced.
One way I get equations like:
( [p 1] A + a0 w)(1 + r) = [p 1]
The other way I get equations like:
[p 1] A (1 + r) + a0 w* = [p 1]
where, as is standard in the literature A is a square matrix and
a0 is a row vector.
If JimT means the accounting rate of profits must be zero, he has
confused accounting profits with economic profits.
> then all revenues are paid out.
All revenues are paid out in either case.
> This is similar
> to the economy equilibrium in the small open economy version of the
> Herscher-Ohlin model
There is no need to refer to the HOS model. My example satisfies
the properties of the so-called non-substitution theorem.
> There is no equilibrium condition in the firm...as a price taker the
> firm goes to an external factor market. It doesn't do an ad hoc
> change to accounting prices to equilibrate profit rates, but rather
> enters a market price on iron and sticks to the production process
> with the highest profit rate.
The accounting price in my story is not ad hoc.
Still, there need not be a market price. One should be able to tell
the story either way.
Consider a vertically-integrated firm producing corn. Assume nobody
sells iron on the market; all iron is produced for internal use of
the iron-producing firms. So there is no market price to look at.
The corn-producing firm will have inventories of iron and corn at
any time. What would be a fair price for the owners of the firm
to sell out at? Economists should be able to answer that question.
> For CRS production technology in competitive markets,
> you can only determine factor *intensities*, not factor demands, at
> the firm level.
That is all I need to consider for my point.
> >If one does not consider a different level of the price of
> >iron with each different level of the wage, the second condition
> >is not satisfied. If one does change the price of iron with
> >the wage, as I indicate, the total amount of labor that firms
> >want to hire can be higher at a higher level of wages.
> But those conditions that you refer to have nothing to do with the
> firm problem. If they aren't satified with equality for a given set
> of prices, then one activity is not undertaken.
And one will not have an equilibrium in the labor market where
supply and demand curves intersect.
My point is that labor demand curves, in the intro textbook story
have several properties. They are supposed to apply, among other
cases, when:
o Some of the firms hiring labor are using it to produce
capital goods and some are using it to produce consumption
goods with previously-produced capital goods
And they are supposed to be such that,
o Any point on a labor demand curve can be part of a supply-and-
demand equilibrium for the labor market, at least to a
first-order approximation.
My example shows labor-demand curves cannot be constructed in
my example to satisfy these properties. The market conditions
that JimT talks about are not second-order.
See, for example:
Ian Steedman, "On Input 'Demand Curves'", Cambridge Journal
of Economics, 198?.
> The zero profit conditions consist of two
> equations in three unknowns (price of commodities, wage)...because
> you've set the corn to one (numeraire), the wage and price are
> completely determined by the system. Since you want to take the wage
> as exogenous, you are forced to use a fudge factor (the rate of
> profits) to insure that the system isn't overdetermined.
> So the rate of profits ends up being endogenous.
The above is mistaken. It exhibits a confusion between accounting
and economic profits.
And Keith Ramsay, having read Samuelson's "Summing Up" article, for
example, can see that it is mistaken too.
> >It's justification for the accounting story arises from the
> >determination of the return on investment.
> There is no accounting story to be told. If a price taking firm can
> buy inputs, why invent a nonsense price to generate nonsense profit
> rates?
It is NOT a nonsense price. If JimT understood his own story, he
would know that it is also the price that would be generated on the
iron market for competitive firms if his equilibrium condition were
satisfied for markets arising in an analysis of a (notionally)
vertically-integrated industry.
> >For some reason, JimT has failed to acknowledge that no
> >markets (corn, iron, labor) need be in equilibrium in my
> >analysis. After all, I did not model consumers.
> Again, the block recursive nature of the problem doesn't require
> reference to the demand side for determination of the prices.
My essay Sraffa3.pdf on my website demonstrates that JimT is
mistaken. No markets need be in equilibrium in my analysis. And, yes,
equilibrium prices differ with different levels of a parameter of
the utility function I postulate there.
> >> If the set of prices is such that one activity has a lower rate of
> >> return, that activity is not undertaken in the firm equilibrium.
> >Which is what I say.
> Yes, but there is no reason for the firm to adjust the accounting
> price of iron. There is nothing to proclude an external market for
> iron. You're forcing unnecessary and unjustified structure into the
> firm problem.
It does not matter in my model whether firms are integrated or
not along the (w, p) locus I describe.
I wonder how many times I need to repeat myself.
As for definitions...
As JimT acknowledges, my example is of profit-maximizing competitive
firms.
My example is one of long run equilibrium, but not of any markets
in equilibrium.
> Your model: The textbook example assumes decreasing returns to scale
> after some level of output. Your techology exhibits CRS. As a
> result, a firm will wish to provide an infinite amount of output if
> P>ATC, an indeterminate amount if P=ATC, and no amount (exit) if
> P<ATC.
I think the above is wrong. A standard textbook assumption is of
Constant Returns to Scale, with diminishing marginal returns to
each factor. Because some factors are fixed in quantity (land),
average costs will eventually increase.
"The 'non-substitution theorem' is of particular interest in the
present context since, as was already mentioned, it puts into sharp
relief the role of demand in neoclassical analysis.
The original formulation of the theorem assumes (i) constant returns
to scale, (ii) a single primary factor of production only (homogeneous
labor) and (iii) no joint production, that is, circulating capital
only (see Arrow, 1951, Georgescu-Roegen, 1951, Koopmans, 1951a, and
Samuelson, 1951). The theorem was received with some astonishment by
authors working in the neoclassical tradition since it seemed to
flatly contradict the importance attached to consumer preferences for
the determination of relative prices. As Samuelson wrote: 'From
technology and the interest rate alone, AND COMPLETELY WITHOUT REGARD
TO DEMAND CONSIDERATIONS..., price relations can be accurately
predicted as constants' (1966b, p. 530). This astonishment is all the
more understandable, since several 'classroom' neoclassical models,
for didactical reasons, are based precisely on the set of simplifying
assumptions (i)-(iii) underlying the theorem, WITHOUT however
arriving at the conclusion that demand does not matter.
This latter observation should have raised doubts as to the validity
of the widely held opinion that it is first and foremost the SPECIAL
MODELING OF PRODUCTION on which the theorem hinges. In order for
demand to exert an influence on the price of a good the supply
function must not be horizontal. Then how do neoclassical models that
are subject to constant returns to scale, no joint production, and
homogeneous labor arrive at an upward sloping supply curve? The
upward slope of the supply curve reflects the increase in the relative
price of the productive service which is required in a relatively
high proportion in the production of the good. For example, if the
good under consideration happens to be produced with a relatively
high proportion of labor to 'capital,' that is, a high 'labor
intensity,' then an increase in the demand for the good, that is, a
rightward shift of the demand schedule, would lead to a rise in the
relative price of the good due to an increase in the wage rate relative
to the rate of profit. This change in relative prices of productive
services is ultimately traced back to changes in the relative scarcity
of factors, labor and 'capital,' the endowment of which is assumed to
be given."
-- Heinz D. Kurz and Neri Salvadori, _Theory of Production: A Long-
Period Analysis_, Cambridge University Press, 1995.
> you have imposed an additional condition, which is that
> multiple industries are in long-run competitive equilibrium.
JimT can repeat mistaken claims all he wants.
> Your programming problem doesn't have
> the implications that you want it to... It also has
> no implications about either firm-specific or overall employment
> responses to a change in the wages.
I think I'll stick with Paul Samuelson and other authors of
the peer-reviewed literature. After all, Paul Samuelson has
frequently implied examples like mine can be used to show that
a higher wage can be associated with a cost-minimizing technique
with a higher ratio of labor to net output.
JT
<rv...@see.sig.com> wrote:
>In article <9f2ad7a3.03062...@posting.google.com>,
>ji...@hotmail.com (JT) wrote:
>
>> On Sun, 29 Jun 2003 22:31:30 -0400, Robert Vienneau
>> <rv...@see.sig.com> wrote:
>
>> Your locus of (w,p) are not firm equilibrium conditions. This is
part
>> of economy equilibrium
>
>JimT hasn't phrased his point well. He should say these are part of
>the equilibrium conditions for the sectors within a
vertically-integrated
>industry. (The integration need not be more than notional.)
I don't accept your definition of an industry. There are two distinct
activities, two distinct outputs with distinct prices and hence two
distinct industries. You've already agreed that integration is not a
necessary condition for profit maximization. Your firm is simply
active in two industries. The vertically-integrated firm is simply a
firm that is in active in both industries in such a way that it's
production of iron is chosen to replenish it's inputs for the next
period. I agree with Chris on a point here...this activity is really
only meaningful for a firm optimizing a dynamic objective function.
However, it really doesn't matter for what follows.
>
>> which insures agents have to reason to relocate
>> factors between sectors. They are conditions that insure that
profits
>> are zero in each industry. To see that this is all you are doing,
>> replace your notion of a wage plus profits, w(1+r), with simply a
wage
>> rate w*..
>
>No, that does not make JimT's point. I could have told the same sort
>of story with wages being paid out of product, instead of being
>advanced.
>
>One way I get equations like:
>
> ( [p 1] A + a0 w)(1 + r) = [p 1]
>
>The other way I get equations like:
>
> [p 1] A (1 + r) + a0 w* = [p 1]
>
>where, as is standard in the literature A is a square matrix and
>a0 is a row vector.
>
>If JimT means the accounting rate of profits must be zero, he has
>confused accounting profits with economic profits.
Fine, it's not a detail of any consequence. Your conditions are
simply a version of the standard zero profit conditions with an
arbitary mark-up. I apparently mis-read part of your paper on a quick
glance back. Makes my life easier with things the way they are. We
are refering to zero profit conditions in two industries, which is
what I've been assuming all along.
>
>Still, there need not be a market price. One should be able to tell
>the story either way.
>
>Consider a vertically-integrated firm producing corn. Assume nobody
>sells iron on the market; all iron is produced for internal use of
>the iron-producing firms. So there is no market price to look at.
>The corn-producing firm will have inventories of iron and corn at
>any time. What would be a fair price for the owners of the firm
>to sell out at? Economists should be able to answer that question.
Why make any of these assumptions when we have two industries and no
reason to proclude non-integrated supply chains? You have never
provided a justification for integration. Anyhow, it also doesn't
matter in the bigger picture.
>
>My point is that labor demand curves, in the intro textbook story
>have several properties. They are supposed to apply, among other
>cases, when:
>
> o Some of the firms hiring labor are using it to produce
> capital goods and some are using it to produce consumption
> goods with previously-produced capital goods
>
>And they are supposed to be such that,
>
> o Any point on a labor demand curve can be part of a supply-and-
> demand equilibrium for the labor market, at least to a
> first-order approximation.
Which doesn't imply that any of the other markets are in equilibrium.
Individual firms will be, for the prices they face, but this need not
be consistent with any kind of a broader equilibrium concept. The
second point simply means that the supply curve can cross any point on
the labour demand curve.
>> >It's justification for the accounting story arises from the
>> >determination of the return on investment.
>
>> There is no accounting story to be told. If a price taking firm
can
>> buy inputs, why invent a nonsense price to generate nonsense profit
>> rates?
>
>It is NOT a nonsense price. If JimT understood his own story, he
>would know that it is also the price that would be generated on the
>iron market for competitive firms if his equilibrium condition were
>satisfied for markets arising in an analysis of a (notionally)
>vertically-integrated industry.
Exactly...prices generated by long-run competitive equilibria in two
industries. Thanks for agreeing with me. Vertical integration is a
non-sequitor.
>As for definitions...
>
>As JimT acknowledges, my example is of profit-maximizing competitive
>firms.
>
>My example is one of long run equilibrium, but not of any markets
>in equilibrium.
No. You are using long-run competitive equilibrium conditions for
industries. You've admitted as much. See above.
>> Your model: The textbook example assumes decreasing returns to
scale
>> after some level of output. Your techology exhibits CRS. As a
>> result, a firm will wish to provide an infinite amount of output if
>> P>ATC, an indeterminate amount if P=ATC, and no amount (exit) if
>> P<ATC.
>
>I think the above is wrong. A standard textbook assumption is of
>Constant Returns to Scale, with diminishing marginal returns to
>each factor. Because some factors are fixed in quantity (land),
>average costs will eventually increase.
The point is simply that the marginal cost curve slopes up in the
short-run.
> The original formulation of the theorem assumes (i) constant returns
> to scale, (ii) a single primary factor of production only (homogeneous
> labor) and (iii) no joint production, that is, circulating capital
> only (see Arrow, 1951, Georgescu-Roegen, 1951, Koopmans, 1951a, and
> Samuelson, 1951). The theorem was received with some astonishment by
> authors working in the neoclassical tradition since it seemed to
> flatly contradict the importance attached to consumer preferences for
> the determination of relative prices. As Samuelson wrote: 'From
> technology and the interest rate alone, AND COMPLETELY WITHOUT REGARD
> TO DEMAND CONSIDERATIONS..., price relations can be accurately
> predicted as constants' (1966b, p. 530). This astonishment is all the
> more understandable, since several 'classroom' neoclassical models,
> for didactical reasons, are based precisely on the set of simplifying
> assumptions (i)-(iii) underlying the theorem, WITHOUT however
> arriving at the conclusion that demand does not matter.
Translation: We don't need to know the position of the demand curve,
because in the long-run the supply curve is horizontal. Prices are
nevertheless being determined under the assumption that the demand and
supply curves for the output of the industry are crossing.
>I think I'll stick with Paul Samuelson and other authors of
>the peer-reviewed literature. After all, Paul Samuelson has
>frequently implied examples like mine can be used to show that
>a higher wage can be associated with a cost-minimizing technique
>with a higher ratio of labor to net output.
Fine. I'm not disagreeing with the result. But you have never
illustrated how it contradicts what I think of as the standard
textbook case. Industry or firm labour demand curves are drawn
holding the price of all other inputs and outputs fixed...you aren't
doing that. Your so-called firm equilibrium is really a long-run
competitive equilibrium in two industries, as you've admitted
yourself. These equilibria assume that long-run supply and demand
meet in each industry...hence the determination of prices of both
outputs from the horizonal supply curve. Are you even trying to make
any kind of point with these essays? There is nothing here that isn't
consistent with the standard first year presentation.
JT
I agree with Chris Auld that the problem is essentially a dynamic one,
meaning that your example is nonsense. Let me explain. Stockpiling
corn and iron for future production involves an opportunity cost in
the current period, namely the revenue that could have been
established by selling it at the time it was produced. You haven't
established that this is optimal behaviour on the firm's part because
you haven't laid out a dynamic objective function for the firm. Yet
one more reason to dismiss your claims to a model where a dynamic
considerations are unimportant. [Actually, I'm guessing this is where
your profit rates are coming into play...however, this means that you
are imposing an additional *dynamic* equilibrium condition.]
You've already agreed that a price taking firm will never switch to
the more labour intensive method for producing either good in response
to a change in the labour market, so no controversy there...the unit
factor requirements are thus well behaved in terms of the wage.
You've also shown than when the wage increases, the feedbacks between
markets result in higher unit labour requirements in one of the
industries (and for the representative firm in your ridiculous
definition of an integrated industry). However, you've failed to show
anything about overall employment. To do this, you need market demand
for each industry. Let a(w,p) denote the unit labour requirement for
the iron industry and b(w,p) denote the unit labour requirement for
the corn industry. To establish labour demand at the industry level,
you require gross demand for output of that industry. Let I(w,p,X)
denote demand for iron, where X is a vector of unspecified exogenous
parameters. Labour demand is then given by a(w,p)I(w,p,X). Corn
industry demand for labour is found in a similar fashion.
Now let's consider why your title is wrong, ignoring that it's not
clear that it's relevent to the textbook case. Prices and thus unit
labour requirements were determined by competitive equilibrium
conditions in each industry. These are essentially supply
considerations...competition among suppliers drives profits to zero,
resulting in (when we combine the two industries) a unique set of
prices and a labour requirement for a single unit of output in each
industry. To close the model and establish employment in each
industry, we need to know how much of each good is produced, which
requires making reference to market demand conditions (the long-run
industry supply curve is horizontal), which will include both consumer
demand and demand by firms for inputs for future production. Adding
the labour-demand curves for the two industries yields the labour
demand at this set of prices for the two industries. What I have
established so far is a relationship between the wage and total labour
demanded by producers LD(w). To close the model we need a model of
labour supply LS(w) to establish a unique value of employment and the
wage rate. So the wage rate and employment *are* determined by supply
and demand. [If you pay close attention you'll notice that I've
back-pedalled on a few claims I made earlier about the nature of
industry labour demand. All I can say is fire away!] I'm still not
completely comfortable calling LD(w) a labour demand curve. However,
the system is closed through a serious of supply and demand
considerations. Off the top of my head I'm not sure what the slope
properties of the LD(w) function are.