Minimum Wages Needn't Cause Unemployment
Robert Vienneau
1.0 INTRODUCTION
This long post presents an example in which higher wages are associated
with a higher quantity demanded of labor. The exact numeric values used
are obviously unreasonable. The example, though, is used to make a
point. Those who think the demand curve for labor *must* slope down
should answer the following question: what are your assumptions?
2.0 DATA ON TECHNOLOGY
Consider a very simple economy that produces a single consumption
good, corn, from inputs of labor, steel, and (seed) corn. All production
processes in this example require a year to complete. Only one
production process is known for producing corn. This process requires
the following inputs to be available at the beginning of the year for
each bushel corn produced and available at the end of the year:
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Steel is also produced in this economy. Two processes are known for
producing steel:
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
Apparently, inputs of corn and steel can be traded off in producing steel.
The process that uses less corn and more steel, however, also requires
a greater quantity of labor input.
3.0 QUANTITY FLOWS
The example is constructed by comparing equilibrium prices associated
with stationary states for producing a net output of 1,000 bushels corn.
Two stationary states are possible, corresponding to the two techniques
for producing steel. A technique is a combination of one steel-producing
process and the corn-producing process. The techniques are named after
the process used in producing steel. Table 3 shows the quantity flows for
a stationary state in which the alpha technique is used. Table 4 shows
the corresponding quantity flows for the beta technique.
TABLE 3: QUANTITY FLOWS FOR THE ALPHA TECHNIQUE
INPUTS STEEL INDUSTRY CORN INDUSTRY
Labor 71.80 Person-Years 1000 Person-Years
Steel 130.1 Tons 241.6 Tons
Corn 3.551 Bushels 204.0 Bushels
OUTPUTS 371.6 Tons Steel 1208 Bushels Corn
TABLE 4: QUANTITY FLOWS FOR THE BETA TECHNIQUE
INPUTS STEEL INDUSTRY CORN INDUSTRY
Labor 9.752 Person-Years 1042 Person-Years
Steel 38.69 Tons 251.6 Tons
Corn 45.26 Bushels 212.5 Bushels
OUTPUTS 290.3 Tons Steel 1258 Bushels Corn
Notice that 1072 person-years are employed per year when the
alpha technique is used to produce a net output of 1,000 bushels
corn. 1052 person-years are employed under the beta technique.
Hence, the alpha technique is the more labor-intensive technique
for producing corn.
4.0 PRICES
The argument proceeds by determining which technique is
cost-minimizing at equilibrium prices. In this context, equilibria
have the following properties:
o The corn-producing process is operated, and at least one of
of the steel-producing processes is operated.
o The cost of inputs for each process in operation, including
interest charges, does not exceed revenues.
o No process can be used to obtain pure economic profits.
I assume that steel and corn inputs are paid for at the beginning
of the year. Labor, although hired at the beginning of the year,
is paid out of the product at the end of the year.
4.1 INITIAL EQUILIBRIUM PRICES
Suppose wages are $3,347 per person year, the price of steel
is $6,013 per ton, and the price of corn is $10,000 per bushel. Also,
let the rate of interest be 150%. Consider the costs and revenues
for the steel industry if the beta technique is used. Table 5 shows
the relevant calculations.
TABLE 5: COSTS AND REVENUES FOR THE STEEL INDUSTRY
Cost of producing steel for the beta technique
= ( 38.69 x $6013 + 45.26 x $10000 )( 1 + 1.5 ) + 9.752 x $3347
= $1,746,000
Revenues for the steel industry using the beta technique
= 290.3 x $6013 = 1,746,000
Notice that the costs incurred in the steel industry equal the revenues
obtained. Thus, the cost of operating the beta process does not exceed
the revenues. Furthermore, no pure economic profits are obtained by
operating the beta process.
Now consider the costs and revenues in the corn industry. Table
6 shows that here too, the costs do not exceed revenues, and no
pure economic profits are obtained.
TABLE 6: COSTS AND REVENUES FOR THE CORN INDUSTRY
Cost of producing corn for the beta technique
= ( 251.6 x $6013 + 212.5 x $10000 )( 1 + 1.5 ) + 1042 x $3347
= $12,580,000
Revenues for the corn industry using the beta technique
= 1258 x $10000 = 12,580,000
I have not yet shown the prices under consideration are
equilibrium prices. I also need to show that the alpha process
for producing steel cannot be used to obtain pure economic
profits at these prices. Accordingly, Table 7 shows the cost
of operating the alpha process.
TABLE 7: COSTS FOR OPERATING THE ALPHA PROCESS
Cost of the alpha process per ton steel produced
= ( 0.35 x $6013 + 0.0095553 x $10000 )( 1 + 1.5 ) + 0.1932 x $3347
= $6147
Notice that the cost of producing a ton of steel with the alpha
process is $134 more than the price of the steel produced. Thus,
the alpha process will not be used at these prices, and these prices
are equilibrium prices.
4.2 ANOTHER SET OF PRICES
Next, consider higher wages, $5,864 per person-year. This cannot
be an equilibrium wage if the price of steel, the price of corn, and
the interest rate are unchanged from above. At this set of prices,
all processes will cost more than the revenue they bring in. No
process will be operated.
Accordingly, consider a different set of commodity prices and
interest rate for this wage. First, suppose the price of steel
is $4,487 per ton, and the price of corn is $10,000 per bushel.
The rate of interest is 98.9%. It turns out these are not equilibrium
prices, but the reason why is instructive. Tables 8 and 9 show
the costs and revenues in the steel and corn industries, respectively,
if the beta technique is operated. The costs of each process
comprising the beta technique do not exceed the revenues. Nor
is any pure economic profit earned in operating these processes.
TABLE 8: NEW COSTS AND REVENUES FOR THE STEEL INDUSTRY
Cost of producing steel for the beta technique
= ( 38.69 x $4487 + 45.26 x $10000 )( 1 + 0.989 ) + 9.752 x $5864
= $1,303,000
Revenues for the steel industry using the beta technique
= 290.3 x $4487 = 1,303,000
TABLE 9: NEW COSTS AND REVENUES FOR THE CORN INDUSTRY
Cost of producing corn for the beta technique
= ( 251.6 x $4487 + 212.5 x $10000 )( 1 + 0.989 ) + 1042 x $5864
= $12,580,000
Revenues for the corn industry using the beta technique
= 1258 x $10000 = 12,580,000
Why, then, are these not equilibrium prices? The answer lies
in examining the costs of operating the alpha process, as shown in
Table 10. Notice that the cost of producing a ton of steel with
the alpha technique is less than the price of steel. Hence, pure
economic profits can be earned at these prices by producing steel
with the alpha process. Firms will tend to operate the cheapest
known process at going prices.
TABLE 10: NEW COSTS FOR OPERATING THE ALPHA PROCESS
Cost of the alpha process per ton steel produced
= ( 0.35 x $4487 + 0.0095553 x $10000 )( 1 + 0.989 ) + 0.1932 x $5864
= $4447
4.3 FINAL EQUILIBRIUM PRICES
Accordingly, consider a different set of prices of outputs and
interest rates corresponding to a wage of $5,864 per person-year.
Since pure economic profits were available at an interest rate of
98.9%, the equilibrium rate of interest would be slightly higher,
namely 100%. The price of steel is $4,414 per ton, and the price of
corn is $10,000 per bushel.
These are equilibrium prices, and the alpha technique would be
adopted at these prices. Tables 11 and 12 show that costs do not
exceed revenues for any processes in the alpha technique. Nor are
pure economic profits available in any process. Table 13 shows
the cost of producing steel with the beta process exceeds its price.
So the beta technique will not be adopted.
TABLE 11: FINAL COSTS AND REVENUES FOR THE STEEL INDUSTRY
Cost of producing steel for the alpha technique
= ( 130.1 x $4414 + 3.551 x $10000 )( 1 + 1 ) + 71.8 x $5864
= $1,640,000
Revenues for the steel industry using the alpha technique
= 371.6 x $4414 = 1,640,000
TABLE 12: FINAL COSTS AND REVENUES FOR THE CORN INDUSTRY
Cost of producing corn for the alpha technique
= ( 241.6 x $4414 + 204 x $10000 )( 1 + 1 ) + 1000 x $5864
= $12,080,000
Revenues for the corn industry using the alpha technique
= 1208 x $10000 = 12,080,000
TABLE 13: NEW COSTS FOR OPERATING THE BETA PROCESS
Cost of the beta process per ton steel produced
= ( 0.13329 x $4414 + 0.1559 x $10000 )( 1 + 1 ) + 0.033594 x $5864
= $4492
5.0 CONCLUSIONS
Table 14 summarizes the results of these calculations for this
example. Clearly it is possible for cost-minimizing firms to prefer
to adopt a more labor-intensive process at a higher wage. This is
a matter of logic.
TABLE 14: LABOR USED TO PRODUCE NET OUTPUT
OF 1,000 BUSHELS CORN
Wage Equilibrium Labor Employed
$3,347 1052 person-years
$5,864 1072 person-years
Those who do not think that this possibility ever occurs in
the real world have failed to face a challenge for decades now.
What are the special case assumptions adopted so as to rule out the
possibility illustrated in the example? Furthermore, why should
a special-case model be preferred to the more general model? The
general model for analyzing the choice of technique does not imply
a lower quantity of labor will be demanded at a higher wage.
From long experience, I know that some are likely to make logical
mistakes at this point. So I'll conclude with a few observations. The
effect illustrated in the example can arise when there are many more
processes to choose from. In fact, it can arise when the cost-minimizing
technique varies continuously with the wage. It does not depend
on there only being one process for some industry. It can arise in
models with more than two goods being produced. It does not depend
on the existence of a produced good that is used either directly or
indirectly in the production of all goods. (Both steel and corn have
this property in the example.) It can arise if there are different types
of labor, non-produced commodities used in production ("land"),
and capital-goods that last more than one production cycle ("fixed
capital" or "machinery"). I gather that numeric examples with
reasonable values are easier to construct, in some sense, if there
are more produced goods. At least, more degrees of freedom arise.
Consequently, incorrect answers to my question are assumptions
that more goods are produced, more techniques are available,
different types of labor exist, etc. These assumptions are simply
insufficient to imply the conclusion that higher wages are
associated with a lower quantity demanded of labor.
The final questions posed by this example are a matter of the
sociology of knowledge. Similar examples have been available
in the literature for over three decades. Many economists,
including specialists in labor economics, seem to be unaware of
this possibility. Why do so many economists have logically
mistaken beliefs about their subject? Why do they continue to
teach exploded dogma?
--
Robert Vienneau
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n o Whether strength of body or of mind, or wisdom,
@ c or virtue, are always found...in proportion to
d . the power or wealth of a man [is] a question
r e fit perhaps to be discussed by slaves in the
e p hearing of their masters, but highly unbecoming
a a to reasonable and free men in search of the
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SUSUPPLY
Okay, maybe I was unfair to Robert Vienneau. He may not be intellectually
dishonest. It appears that he really is "that obtuse".
Witness the title of this thread: "Minimum Wages Needn’t Cause Unemployment",
and the first sentence of his post:
"This long post presents an example in which higher wages are associated with a
higher quantity demanded of labor."
It should be obvious that the two things are not on the same topic.
First, the thread title is correct, but you don’t need the tortured logic of
Robert to explain why. It is simple. If the market wage rate for unskilled
labor is above the mandated minimum wage then the mandate is moot. That is, no
unemployment effect. Employers will find no takers if they offer the minimum
wage.
Second, just rearrange Robert’s opening sentence thus: "A higher quantity
demanded of labor" is "associated" with "higher wages".
Duh! Does Robert think any competent economist would disagree with that
sentence?
Which makes this from Robert laughable:
"Why do so many economists have logically mistaken beliefs about their subject?
Why do they continue to teach exploded dogma?"
They don’t, Robert. What goes over your head, cannot be labeled "exploded
dogma".
Patrick
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
4-May-98 Minimum Wages Needn't Cause.. by Robert Vien...@see.sig.
> 1.0 INTRODUCTION
>
> This long post presents an example in which higher wages are associated
> with a higher quantity demanded of labor. The exact numeric values used
> are obviously unreasonable. The example, though, is used to make a
> point. Those who think the demand curve for labor *must* slope down
> should answer the following question: what are your assumptions?
And the answer would be:
1) firms are price takers
2) all other prices are fixed
How reasonable those assumptions are in any particular
application is a separate question, obviously.
-- Bill
d...@temple.edu
I only skimmed the post. If it is arguing that capital-enhancing
(labor-saving) growth increases wages, well that's been known for a long
time.
Note: it's unfair to use this to criticize demand curves, which are
drawn for a given level of technology.
Dan
in Philly
Robert Vienneau
> I only skimmed the post. If it is arguing that capital-enhancing
> (labor-saving) growth increases wages, well that's been known for a long
> time.
It is not arguing that.
> Note: it's unfair to use this to criticize demand curves, which are
> drawn for a given level of technology.
The example does assume a given level of technology. Technology is
specified by a set of techniques. The number of techniques is found
by multiplying together the number of processes known in each industry.
Try again.
Robert Vienneau
In article <354d4d5e....@news.blarg.net>, wa...@blarg.net wrote:
> He's right.
>
> Simply set the minimum wage so low that every worker, no matter how
> marginal, can be relied on to do work that is worth more than the
> minimum wage.
>
> Then the minimum wage won't cause unemployment.
This response fails to note that the post to which it is supposedly
answering shows the analytical framework used above to be unfounded.
I wrote:
> > Table 14 summarizes the results of these calculations for this
> > example. Clearly it is possible for cost-minimizing firms to prefer
> > to adopt a more labor-intensive process at a higher wage. This is
> > a matter of logic.
> >
> >
> > TABLE 14: LABOR USED TO PRODUCE NET OUTPUT
> > OF 1,000 BUSHELS CORN
> >
> > Wage Equilibrium Labor Employed
> >
> > $3,347 1052 person-years
> > $5,864 1072 person-years
Suppose $3,347 per year is a market-clearing wage. Suppose a law sets
the minimum wage at $5,864 per year. The example shows that there may
be a greater quantity of labor demanded at this wage. Once again, this
wage could be *higher* than a market-clearing wage.
Robert Vienneau
In article <QpHnVqe00...@andrew.cmu.edu>, William B Vogt
<wili...@andrew.cmu.edu> wrote:
> Excerpts from netnews.talk.politics.libertarian:
> 4-May-98 Minimum Wages Needn't Cause.. by Robert Vien...@see.sig.
> > 1.0 INTRODUCTION
> > This long post presents an example in which higher wages are associated
> > with a higher quantity demanded of labor. The exact numeric values used
> > are obviously unreasonable. The example, though, is used to make a
> > point. Those who think the demand curve for labor *must* slope down
> > should answer the following question: what are your assumptions?
> And the answer would be:
> 1) firms are price takers
This assumption is consistent with my example.
> 2) all other prices are fixed
Assume there are no pure economic profits available at the lower
wage in my example. Now consider the higher wage, while leaving the
prices of steel and corn unchanged. Then the rate of return will be
different in the two industries of steel-making and corn-making. In
other words, pure economic profits will be available.
> How reasonable those assumptions are in any particular
> application is a separate question, obviously.
The application suggested by the thread title is a consideration
of different wages for unskilled labor economy-wide. William
seems to be claiming that a demand curve for labor is drawn on
the assumption that firms tend to leave hundred-dollar bills lying
on the sidewalk. Maybe he ought to try to find assumptions more
compatible with mainstream economics, if he is trying to defend
the exposed logical errors in their textbooks.
Christopher Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>> > The example, though, is used to make a
>> > point. Those who think the demand curve for labor *must* slope down
>> > should answer the following question: what are your assumptions?
>> 2) all other prices are fixed
>Assume there are no pure economic profits available at the lower
>wage in my example. Now consider the higher wage, while leaving the
>prices of steel and corn unchanged. Then the rate of return will be
>different in the two industries of steel-making and corn-making. In
>other words, pure economic profits will be available.
>> How reasonable those assumptions are in any particular
>> application is a separate question, obviously.
>The application suggested by the thread title is a consideration
>of different wages for unskilled labor economy-wide.
Which is a claim about comparative statics in general equilibrium,
whereas labor demand curves are derived in partial equilibrium,
which is, I think, what William was pointing out. When all other
prices are held equal, labor demand curves slope down, even in
Robert's model. In general equilibrium, the argument here runs,
the rate of return on capital and wages are simultaneously
determined and an increase in the minimum wage may increase the
interest rate. It is then possible that the net effect is an
increase in labor demanded. This is an interesting argument, but
it is not technically a claim that labor demand curves slope up.
Empirically: 1) labor demand curves slope down and 2) it is
exceedingly unlikely that changes in the minimum wage have
anything but a vanishingly small impact on the interest rate. If
the widely disputed claim that increases in the minimum wage have
no or positive effects on employment holds, I don't think anyone
would seriously suggest that this is the mechanism generating that
result.
[ Followups to sci.econ. ]
--
Professor Chris Auld au...@acs.ucalgary.ca
Economics, University of Calgary (403)220-4098
Calgary, Alberta, Canada <URL:http://jerry.ss.ucalgary.ca>
Markku Stenborg ®
On Tue, 5 May 1998 12:04:06 -0400, William B Vogt
<wili...@andrew.cmu.edu> wrote:
> Excerpts from netnews.talk.politics.libertarian:
> 4-May-98 Minimum Wages Needn't Cause.. by Robert Vien...@see.sig.
>
> > 1.0 INTRODUCTION
> >
> > This long post presents an example in which higher wages are associated
> > with a higher quantity demanded of labor. The exact numeric values used
> > are obviously unreasonable. The example, though, is used to make a
> > point. Those who think the demand curve for labor *must* slope down
> > should answer the following question: what are your assumptions?
>
> And the answer would be:
> 1) firms are price takers
> 2) all other prices are fixed
>
> How reasonable those assumptions are in any particular
> application is a separate question, obviously.
Nope.
If demand curve for labor is "the marginal willingness to pay for
labor" or is a monotonic function of it: Demand for labor must slope
down if the value of marginal product of labor is diminishing at that
level of labor used, ie, the last unit of labor produces less ouput
times its selling price than the previous unit of labor.
In any event, it has nothing to do w/ 1) and 2) above.
--
© Markku Stenborg
OFC & Turku Biz School
ROT13ed for the hell of it:
zne...@hgh.sv <- out-of-order for the time being
znexxh....@svabsp.sv
JMH
Robert Vienneau wrote:
>
> In article <QpHnVqe00...@andrew.cmu.edu>, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
>
> > Excerpts from netnews.talk.politics.libertarian:
> > 4-May-98 Minimum Wages Needn't Cause.. by Robert Vien...@see.sig.
>
>
> > > This long post presents an example in which higher wages are associated
> > > with a higher quantity demanded of labor. The exact numeric values used
> > > are obviously unreasonable. The example, though, is used to make a
> > > point. Those who think the demand curve for labor *must* slope down
> > > should answer the following question: what are your assumptions?
>
> > 1) firms are price takers
>
>
>
> wage in my example. Now consider the higher wage, while leaving the
> prices of steel and corn unchanged. Then the rate of return will be
> different in the two industries of steel-making and corn-making. In
> other words, pure economic profits will be available.
How the pure economic profits? Are you assuming that
the minimum rate of return being earned in the post
wage increase period defines the market rate?
JMH
Robert Vienneau
In article <6ioqhn$o...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >> > The example, though, is used to make a
> >> > point. Those who think the demand curve for labor *must* slope down
> >> > should answer the following question: what are your assumptions?
> >> 2) all other prices are fixed
> >Assume there are no pure economic profits available at the lower
> >wage in my example. Now consider the higher wage, while leaving the
> >prices of steel and corn unchanged. Then the rate of return will be
> >different in the two industries of steel-making and corn-making. In
> >other words, pure economic profits will be available.
> >> How reasonable those assumptions are in any particular
> >> application is a separate question, obviously.
> >The application suggested by the thread title is a consideration
> >of different wages for unskilled labor economy-wide.
> Which is a claim about comparative statics in general equilibrium,
Ok. If one accepts mainstream economics, one should agree that that
is an appropriate framework to begin analyzing minimum wages.
> whereas labor demand curves are derived in partial equilibrium,
> which is, I think, what William was pointing out.
There is another, partial equilibrium reading of my example. Consider
my example to be an analysis of a vertically-integrated firm
producing corn. The firm takes the price of the output, corn,
and the wages of labor as givens. The firm choses what
technique it wants to use to produce corn, if any.
The price of steel is a matter of the firm's internal accounting.
The firm will set this accounting price such that the firm is making
the same rate of return in steel-production and corn-production.
My example shows that, for the two levels of wages analyzed, the
cost-minimizing vertically-integrated firm will prefer a more
labor-intensive technique at a higher wage. Given the output,
the firm will employ more labor at the higher wage.
I guess Chris would say one would be reverting back to a general
equilibrium argument if one wanted to analyze whether the firm
would continue producing corn at these prices. Such an analysis
would compare the bookkeeping price of steel to the market price,
if any, and the return achievable by the firm to what's possible
in other industries.
> When all other
> prices are held equal, labor demand curves slope down, even in
> Robert's model.
Given the above interpretation, I don't think so. By the way, that
interpretation has also been available in the literature for quite
some time.
So care to try again?
> In general equilibrium, the argument here runs,
> the rate of return on capital and wages are simultaneously
> determined and an increase in the minimum wage may increase the
^^^^^^^^
> interest rate.
I assume Chris means "decrease the interest rate." I would try to
avoid this wording - I don't think I'm always successful - which
suggests a causal process operating through time. Wording like
Chris' is susceptible to an argument of Joan Robinson's about the
differences between historical time and logical time. I try to
avoid this argument by talking about how "higher wages are
associated with a higher quantity demanded of labor."
Otherwise, I have no comment on Chris' summary.
> It is then possible that the net effect is an
> increase in labor demanded. This is an interesting argument,
That's progress, I guess. Have you examined the paper at
http://csf.Colorado.EDU/pkt/pktauthors/Vienneau.Robert/Sraffa3.pdf
If so, do you think I was quoting Blaug fairly? I did not mean to be
as harsh as sometimes I think I ended up being.
Also, notice that the argument I am presenting in this thread is
not about difficulties in creating price or quantity indices
across heterogeneous goods. This suggests to me that there are
plausible alternative accounts one can construct about the CCC, other
than a story I have often seen suggested. That depreciated story is
that the CCC was exclusively about how to create an index for capital
to use as an argument in an aggregated production function.
If one wants to use empirical data to decide between a model
illustrated by my example and some other model, it would be
helpful if one could articulate a logically-consistent alternative
in which the conclusions follow from the assumptions. My comments
about Joan Robinson might suggest why I don't attempt to apply
the model illustrated by my example directly to empirical data.
I wore my tie from the "Jerry Garcia collection" to work today. When
I pointed this out to one of my co-workers, he jokingly suggested I
should be drug-tested.
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
5-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> The application suggested by the thread title is a consideration
> of different wages for unskilled labor economy-wide. William
> seems to be claiming that a demand curve for labor is drawn on
> the assumption that firms tend to leave hundred-dollar bills lying
> on the sidewalk. Maybe he ought to try to find assumptions more
> compatible with mainstream economics, if he is trying to defend
> the exposed logical errors in their textbooks.
Labor demand curves *must* slope down.
To get this result, one must assume that:
1) firms are price takers
2) all other prices are fixed
3) firms profit maximize in their
choices of inputs and outputs
Observe:
A firm's profits are:
p*y - w*x
y = output
x = inputs (including labor)
p = price of output
w = prices of inputs
* = vector (or scalar) multiplication
Let (p1,w1) and (p2,w2) be two different sets
of input and output prices. Let (y1,x1) and
(y2,x2) be the associated maximizing input
demands and output supplies. Then profit
maximization implies:
p1*y1 - w1*x1 > p1*y2 - w1*x2
p2*y2 - w2*x2 > p2*y1 - w2*x1
Note: there is no ascii character for greater
than or equal to, so I use >.
Rewrite the inequalities:
p1*(y1-y2) - w1*(x1-x2) > 0
p2*(y2-y1) - w2*(x2-x1) > 0
Add the inequalities:
(p1-p2)*(y1-y2) - (w1-w2)*(x1-x2) > 0
This must be true for any two sets of prices
(p1,w1), (p2,w2).
Now, let's consider two sets of prices which
differ only in that the price of labor is higher
in the second (let's say by 1 unit). Let's denote
the elements of x1 and x2 corresponding to labor
as l1 and l2. Then the inequality says:
(0)*(y1-y2) - (-1)*(l1-l2) > 0
--OR--
l1 > l2
So, when the price of labor is higher (w2), the demand
for labor is lower (l2). Thus labor demand curves *must*
slope down.
The above argument is essentially identical to one you
can find in Varian (1984) _Microeconomic Analysis_,
2nd ed. NY: WW Norton. pg. 58.
The simplicity of the argument should be a tip-off to
its generality.
Labor demand curves are a notional concept in the
neoclassical theory of the firm. They are defined
as being the relationship between the firm's optimal
choice of labor and the price of labor, holding all
other prices constant.
The different result you get in your example arises
because other prices are not constant. In the example,
the steel industry changes from process beta to the
more labor intensive process alpha, even though the
price of labor has risen. Let's see why they do this
(mapping back into my notation).
First Set of Prices:
Raw Normalized
p = 6013 1
wsteel = 15032.5 2.5
wcorn = 25000 4.16
wlabor = 3347 0.56
Second Set of Prices:
Raw Normalized
p = 4414 1
wsteel = 8828 2
wcorn = 20000 4.53
wlabor = 5864 1.33
In both cases, I have multiplied the prices of
steel and corn through by the interest rate, to
make the example compatible with my notation.
First, let us notice that this example does not
involve only a change in the price of labor (as
a counterexample to the thesis that the labor
demand curve slopes downward would have to). All
three input prices change.
Recall that process beta uses less steel, more corn,
and less labor than does alpha. In the second set
of prices, the price of input steel falls, input corn
rises, and input labor rises. The firm adopts the
process alpha because the price changes to steel
and corn favor alpha more than the price change to
labor favors beta.
In more standard economic terminology, corn is such
a strong substitute for labor and steel such a strong
complement that the increase in the price of corn and
decrease in price of steel causes the steel industry
to increase its consumption of labor, even though
labor's price has also risen.
So, the example does not falsify the thesis that
labor demand curves slope downwards. It is merely
completely irrelevant to the thesis.
My guess is that those evil labor economists teaching
"exploded dogma" would be more receptive to changing
their nefarious practices were their critics to
obtain a rudimentary grasp of the dogma they are
purporting to explode.
-- Bill
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
6-May-98 Re: Minimum Wages Needn't C.. by Markku Stenborg @bottom
> On Tue, 5 May 1998 12:04:06 -0400, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
[when does labor demand slope down?]
> > And the answer would be:
> > 1) firms are price takers
> > 2) all other prices are fixed
> >
> > How reasonable those assumptions are in any particular
> > application is a separate question, obviously.
>
> Nope.
>
> If demand curve for labor is "the marginal willingness to pay for
> labor" or is a monotonic function of it: Demand for labor must slope
> down if the value of marginal product of labor is diminishing at that
> level of labor used, ie, the last unit of labor produces less ouput
> times its selling price than the previous unit of labor.
>
> In any event, it has nothing to do w/ 1) and 2) above.
Nope. See my other post today. The fact that labor demand
slopes down is easily derived from price-taking, profit-maximizing
behavior. It is, of course, true that the marginal product of
labor is diminishing at any optimal level of labor demand
(by the second order conditions for a maximum). So, both the
decreasing marginal product of labor and the downward slope
of the labor demand curve are caused by the price-taking,
profit-maximizing assumptions, just as I said.
The difference between our two statements is as follows.
From your claim, someone might get the idea that labor
demand *could* slope up if there was some place in the
production function where the marginal product of labor
was increasing. No such thing can happen. Labor demand
always slopes down, even if the marginal product of labor
is rising some places and falling others.
-- Bill
Markku Stenborg ®
> Excerpts from netnews.talk.politics.libertarian:
> 6-May-98 Re: Minimum Wages Needn't C.. by Markku Stenborg
@bottom
[snip]
> > If demand curve for labor is "the marginal willingness to pay for
> > labor" or is a monotonic function of it: Demand for labor must slope
> > down if the value of marginal product of labor is diminishing at that
> > level of labor used, ie, the last unit of labor produces less ouput
> > times its selling price than the previous unit of labor.
> >
> > In any event, it has nothing to do w/ 1) and 2) above.
>
> Nope. See my other post today. The fact that labor demand
> slopes down is easily derived from price-taking, profit-maximizing
> behavior. It is, of course, true that the marginal product of
Yes, it *can* be derived, but it *needn't*. Downward-sloping input
demand is more fundamental property than profit maximization, let
alone price-taking.
First, your characterization is silent on firms that are not price
takers, ie, on any firm that has any mkt power whatsoever. For
instance, the firm could be an "atom" on local labor mkts, so that it
cannot take the wage rate as given.
Second, not all firms max profits, eg, due to agency problems b/w
owners and managers. For instance, the manager's could be interested
in building empires, and thus hire in excess of profit max level of
labor.
Still these firms have downward sloping labor demand near equilibrium.
The concept "demand curve" could be interpreted in (at least) two
ways.
First, it could be your "true" marginal willingness to pay. In this
case, it would be something like the marginal productivity of labor
times output price times the effect this has on the firm's objective
function; the last term is identical to 1 for profit-max price-taking
firms.
Second, it could be the total effect changes in wage-rate lead in
amount of labor hired. For instance, the firm could have long-term
contracts with its labor, and it could provide insurance to workers
against fluctuations in wage rate, output price and in productivity by
promising to hire L amount of labor at W for T periods. Then its
observed behavior on labor mkts differs from its marginal willingness
to pay as the market wage changes, even ceteris paribus.
> labor is diminishing at any optimal level of labor demand
> (by the second order conditions for a maximum). So, both the
> decreasing marginal product of labor and the downward slope
> of the labor demand curve are caused by the price-taking,
> profit-maximizing assumptions, just as I said.
Yep, and something like this generalizes to any (next to all) economic
behavior w/ price-setting and objectives other than pure profit max.
> The difference between our two statements is as follows.
> From your claim, someone might get the idea that labor
> demand *could* slope up if there was some place in the
> production function where the marginal product of labor
> was increasing. No such thing can happen. Labor demand
OK; no economic agent would want to operate on the increasing part of
the MPL curve, so that the demand for labor could be defined as the
downward-sloping part of MPL.
> always slopes down, even if the marginal product of labor
> is rising some places and falling others.
--
William B Vogt
Excerpts from netnews.talk.politics.libertarian: 5-May-98 Re: Minimum
Wages Needn't C.. by Christopher Au...@acs.uca
> >of different wages for unskilled labor economy-wide.
>
> which is, I think, what William was pointing out.
Not quite. The exogenous variables of a GE model are preferences,
endowments, and technology. So, the only comparative statics
that can be done are on preferences, endowments, and technology.
What Mr Vienneau does in his example is not a comparative statics
exercise, since there can be no comparative statics on an
endogenous variable (price of labor). What he does (if we grant,
arguendo, that he has revealed equilibrium prices) is to exhibit
two different equilibria of a GE model, one of which has both a
higher price and higher transacted quantity of labor. The higher
price and quantity of labor in the second equilibrium
arises (of course) from a shift in the labor demand curve of
the steel industry due to changes in the *other* input prices
of the steel industry, not from a movement along it.
> When all other
> prices are held equal, labor demand curves slope down, even in
> Robert's model. In general equilibrium, the argument here runs,
> the rate of return on capital and wages are simultaneously
> determined and an increase in the minimum wage may increase the
> interest rate. It is then possible that the net effect is an
> increase in labor demanded. This is an interesting argument, but
> it is not technically a claim that labor demand curves slope up.
I think the difference is more than "technical." It confuses
(simultaneously) notional and equilibrium relationships,
shifts in and movements along a demand curve, and
partial and general equilibrium. (Although, I'm not sure it
is even right to describe labor demand curves as a partial
equilibrium object ---- they are merely an output of the
firm's maximization problem, not of any equilibrium interaction
at all.)
> Empirically: 1) labor demand curves slope down and 2) it is
> exceedingly unlikely that changes in the minimum wage have
> anything but a vanishingly small impact on the interest rate. If
> the widely disputed claim that increases in the minimum wage have
> no or positive effects on employment holds, I don't think anyone
> would seriously suggest that this is the mechanism generating that
> result.
Yes, it is strange to criticize the conventional wisdom that
minimum wages cause unemployment by noting that that wisdom
comes from partial equilibrium analysis. To make this criticism
empirically relevant, you would have to believe that increasing
the wages of the small number of people at the minimum wage
has important feedback effects on either the aggregate demand
for (all? most?) minimum-wage-worker-employing industries or
that it has important feedback effects on the price of other
inputs to (all? most?) minimum-wage-worker-employing industries.
The criticisms that I know of embody more fundamental
attacks on the neoclassical framework, since they involve
failures of information assumptions or of price-taking
behavior.
-- Bill
SUSUPPLY
In a refreshing change for this newsgroup, William B Vogt (obviously not a play
economist) uses fundamental economic reasoning to produce:
>What Mr Vienneau does in his example.... is to exhibit
>two different equilibria of a GE model, one of which has both a
>higher price and higher transacted quantity of labor. The higher
>price and quantity of labor in the second equilibrium
>arises (of course) from a shift in the labor demand curve of
>the steel industry due to changes in the *other* input prices
>of the steel industry, not from a movement along it.
Yes, that was what I thought his error was too. However, with Robert one can
never be sure of much. I also agree wholeheartedly with this from your earlier
post:
"So, the example [of Vienneau] does not falsify the thesis that
labor demand curves slope downwards. It is merely
completely irrelevant to the thesis.
"My guess is that those evil labor economists teaching
'exploded dogma' would be more receptive to changing
their nefarious practices were their critics to
obtain a rudimentary grasp of the dogma they are
purporting to explode."
Thanks for expending the time and effort to explode nonsense.
Patrick
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
7-May-98 Re: Minimum Wages Needn't C.. by Markku Stenborg @bottom
> On Wed, 6 May 1998 15:09:28 -0400, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
>
> > Excerpts from netnews.talk.politics.libertarian:
> > 6-May-98 Re: Minimum Wages Needn't C.. by Markku Stenborg
> @bottom
> > Nope. See my other post today. The fact that labor demand
> > slopes down is easily derived from price-taking, profit-maximizing
> > behavior. It is, of course, true that the marginal product of
>
> Yes, it *can* be derived, but it *needn't*. Downward-sloping input
> demand is more fundamental property than profit maximization, let
> alone price-taking.
And it is a *less* fundamental property than decreasing marginal
product (as you admit at the end of your post).
> First, your characterization is silent on firms that are not price
> takers, ie, on any firm that has any mkt power whatsoever. For
> instance, the firm could be an "atom" on local labor mkts, so that it
> cannot take the wage rate as given.
A firm w/ market power in the labor market has no labor
demand curve. To handle a firm with market power in the
output market, you just replace profit-max with cost-min,
in which case the result *still* follows only from the
optimization assumption and not from the marginal product
of labor. (Do you really see this as something other than
a detail?) I don't know exactly how the argument would
go if the firm had market power in another input market
(and I don't care enough to think about it), but my guess
is that the result still follows from the optimization
assumption.
> Second, not all firms max profits, eg, due to agency problems b/w
> owners and managers. For instance, the manager's could be interested
> in building empires, and thus hire in excess of profit max level of
> labor.
>
> Still these firms have downward sloping labor demand near equilibrium.
Shrug. Depends on the utility function you specify. For example,
- (w-l)^2 as a utility function yields upward-sloping labor
demand. I do take your point, sort of, though. The downward-
sloping nature of input demand curves is a property of the
optimization assumption, and the property still follows for
some optimization problems. Do you know of a minimal set
of requirements on the objective function to get the result?
> The concept "demand curve" could be interpreted in (at least) two
> ways.
>
> First, it could be your "true" marginal willingness to pay. In this
> case, it would be something like the marginal productivity of labor
> times output price times the effect this has on the firm's objective
> function; the last term is identical to 1 for profit-max price-taking
> firms.
>
> Second, it could be the total effect changes in wage-rate lead in
> amount of labor hired. For instance, the firm could have long-term
> contracts with its labor, and it could provide insurance to workers
> against fluctuations in wage rate, output price and in productivity by
> promising to hire L amount of labor at W for T periods. Then its
> observed behavior on labor mkts differs from its marginal willingness
> to pay as the market wage changes, even ceteris paribus.
I don't agree either that demand curve has multiple interpretations
or that either of the two above is a valid interpretation. Demand
curve is the relationship between the optimal quantity of some
input and its (exogenously fixed) price, holding other prices (and
sometimes other things) fixed.
Of course, this is an argument over definitions, not a substantive
point.
> > labor is diminishing at any optimal level of labor demand
> > (by the second order conditions for a maximum). So, both the
> > decreasing marginal product of labor and the downward slope
> > of the labor demand curve are caused by the price-taking,
> > profit-maximizing assumptions, just as I said.
>
> Yep, and something like this generalizes to any (next to all) economic
> behavior w/ price-setting and objectives other than pure profit max.
See above. I still don't agree, but our positions are rapidly
converging. (And I'll bet we both walk away thinking we have
"won.")
>
> > The difference between our two statements is as follows.
> > From your claim, someone might get the idea that labor
> > demand *could* slope up if there was some place in the
> > production function where the marginal product of labor
> > was increasing. No such thing can happen. Labor demand
>
> OK; no economic agent would want to operate on the increasing part of
> the MPL curve, so that the demand for labor could be defined as the
> downward-sloping part of MPL.
Right, except I think you want marginal value product instead of
marginal product and assuming an objective function
reasonably like profit-max.
-- Bill
jim blair
Christopher Auld wrote:
> When all other
> prices are held equal, labor demand curves slope down, even in
> Robert's model. In general equilibrium, the argument here runs,
> the rate of return on capital and wages are simultaneously
> determined and an increase in the minimum wage may increase the
> interest rate. ...
> Empirically: 1) labor demand curves slope down and 2) it is
> exceedingly unlikely that changes in the minimum wage have
> anything but a vanishingly small impact on the interest rate.
Hi,
This is a variation of an earlier example that Robert Vienneau posted.
It
contains the same unrealistic assumptions as before-- or am I just not
understanding it?
First, is the assumption that people can be shifted from making steel
to growing corn with a constant level of productivity? Like there
is no skill involved in farming? When the company changes from ALPHA
to BETA, does it transfer steel makers to the farm? Or does it fire
them and hire farmers? Either way, if the price of steel drops by
73% while the price of corn remains constant, it would be reasonable
to make less steel and more corn. Even if wages were unchanged.
Next, the fall in the "interest rate" from 150% to 98.9%. Is that
unrelated to the change in wages? Last time the claim was that
raising wages CAUSED a fall in "interest" (which was taken to mean
return on investment). Are these two changes now independent?
Finally, are you talking only about the wages of THIS company, or
about wages in the entire economy? If only THIS company, the why
"minimum wages" in the title? Is this analysis intended to have
implications for a national legal minimum wage?
If wages increase by 75% in your example, but production remains
little changed, you must be considering only this company: nation
wide this would be very inflationary. Right?
So your example says that if steel prices and interest rates both
fall substantially while corn prices remain unchanged, a company
that both makes steel and grows corn (and pays the same wages to
farmers and steel workers) will make less steel and grow more corn.
And the firm does not make any "pure economic profit" either way.
Or does your example say that "interest rate" (profits?) will fall
if wages are raised and employment increased, with no productivity
gains?
--
,,,,,,,
_______________ooo___(_O O_)___ooo_______________
(_)
jim blair (jeb...@facstaff.wisc.edu) For a good time call
http://www.geocities.com/capitolhill/4834
Christopher Auld
[ I have simply removed all newsgroups but sci.econ, since Robert
chose to ignore my setting of followups. ]
Robert Vienneau <rv...@see.sig.com> wrote:
>> Which is a claim about comparative statics in general equilibrium,
>Ok. If one accepts mainstream economics, one should agree that that
>is an appropriate framework to begin analyzing minimum wages.
Well, of course this isn't the point: I think we have agreed that
your first example did not, as claimed, show that labor demand
curves can slope up. Nor do I necessarily think that this sort of
GE frameork is appropriate to exploring the effects of a minimum
wage which impacts only a small fraction of workers.
Now, Robert reinterprets his model and claims it
> shows that, for the two levels of wages analyzed, the
>cost-minimizing vertically-integrated firm will prefer a more
>labor-intensive technique at a higher wage. Given the output,
>the firm will employ more labor at the higher wage.
Such behavior necessarily violates cost-minimization (and therefore
profit maximization). Once we abandon cost-minimization anything
can happen, so the result (if correct) isn't interesting. Note too
that Robert's claim is even stronger than a claim that labor demand
curves can slope up: he claims that _conditional_ labour demand
curves slope up.
>I guess Chris would say one would be reverting back to a general
>equilibrium argument if one wanted to analyze whether the firm
I don't think I would claim that analyzing how one firm behaves
in response to price changes is a "general equilibrium argument."
>I wore my tie from the "Jerry Garcia collection" to work today. When
>I pointed this out to one of my co-workers, he jokingly suggested I
>should be drug-tested.
Jerry Garcia used drugs?
JC Cooper
William B Vogt wrote in message ...
Would any of you care to let us in on what companies you manage?
When all else fails, play DEAD!
(Deflect, Evade, Attack, Divert)
JC Cooper
Mayor
Gnat Flats, Texas
JMH
William B Vogt wrote:
> I think the difference is more than "technical." It confuses
> (simultaneously) notional and equilibrium relationships,
> shifts in and movements along a demand curve, and
> partial and general equilibrium. (Although, I'm not sure it
> is even right to describe labor demand curves as a partial
> equilibrium object ---- they are merely an output of the
> firm's maximization problem, not of any equilibrium interaction
> at all.)
Doesn't that (not the distinction between shifts in and movements
along but the "merely output" of maximization activities) imply that
no input demand curve is properly decribed in partial equalibrium
terms?
JMH
Robert Vienneau
In article <6itclq$9...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >> Which is a claim about comparative statics in general equilibrium,
> >Ok. If one accepts mainstream economics, one should agree that that
> >is an appropriate framework to begin analyzing minimum wages.
> Well, of course this isn't the point: I think we have agreed that
> your first example did not, as claimed, show that labor demand
> curves can slope up.
I did not agree. But I'm aware that one could complete my example
with intertemporal utility-maximization. In the overlapping
generations framework I used in my paper, one can vary a parameter
in the utility function of a representative agent to obtain
the different equilibria in my example. So your statement is
defensible. One should be aware that this "general equilibrium"
is closer to the Walras (corrected) or Lucas models than it
is to the Arrow-Debreu model.
> Now, Robert reinterprets his model and claims it
> > shows that, for the two levels of wages analyzed, the
> >cost-minimizing vertically-integrated firm will prefer a more
> >labor-intensive technique at a higher wage. Given the output,
> >the firm will employ more labor at the higher wage.
> Such behavior necessarily violates cost-minimization (and therefore
> profit maximization).
How is my numerical example not consistent with cost minimization?
I have difficulty in understanding what you think is a general
equilibrium argument.
...
> Jerry Garcia used drugs?
Would he ever have worn a tie?
Robert Vienneau
In article <cpI_LKm00...@andrew.cmu.edu>, William B Vogt
<wili...@andrew.cmu.edu> wrote:
> Labor demand curves *must* slope down.
> To get this result, one must assume that:
> 1) firms are price takers
> 2) all other prices are fixed
> 3) firms profit maximize in their
> choices of inputs and outputs
[ valid proof in inapplicable setting - deleted ]
I suggest the use of <= for "less than or equal" and >= for "greater
than or equal".
William's response and Varian's textbook illustrate what, in my
opinion, is a deficiency in graduate education. Economists tend
to be taught a bunch of mathematics. But they don't tend to be
taught about the alternative settings of different models, about
the different logical structures of the models, nor about how the
models arose in debates among economists. I also don't think
economists learn much about the institutional structures of
different economies. One might think of economics as a discussion
among various parties. As a consequence of these deficiencies,
I think many economists graduate ill-prepared to continue
the discussion well.
Examples of some economists that have continued interesting
discussions include Frank Hahn, Deidre McClosky, and E. Roy
Weintraub - to name some economists with which I don't necessary
agree.
> The simplicity of the argument should be a tip-off to
> its generality.
Nope.
By the way, the theorem and proof are also in section 3.5 of
Debreu (1959). In section 3.4, Debreu defines "an equilibrium
production of the ... producer relative to [the price system]."
I think I'll help William out. I'll here give a set of sufficient
conditions that answer my challenge: "Those who think the demand
curve for labor *must* slope down should answer the following
question: what are your assumptions?"
Consider a simple economy capable of producing various quantities
of n consumer goods with prices p. Suppose there are a number of
non-increasing returns to scale processes available for producing
consumer goods. These processes have the property that they all
produce their outputs instantaneously. None of the m inputs into
these processes are among the consumer goods produced. The inputs
are also all non-produced goods. These inputs are something like
different qualities of land, although we might call some of
them "labor." Total endowments and the distribution of endowments
among the agents in this economy are given. Their prices are w.
Make William's three assumptions.
Consider the question of which factors are free (have a price
wj of zero) and which have positive prices. The answer is
found by solving the model. Consider a factor that is free
for some consumer price vector p. Suppose that the endowment
of this factor is decreased, while all other endowments are
unchanged. Then the factor price wj either remains zero or
becomes positive. In some sense, prices are scarcity indices. I
believe it is also the case that as an endowment of a factor
with a positive price is decreased at given consumer prices p,
its factor price wj will either remain constant or increase.
(Hmm, I seem to have failed to use a wording consistent with my
earlier comments to Mr. Auld.)
These properties of the model are explained in a linear
programming context in the appendix to chapter VI in
Luigi Pasinetti's _Lectures on the Theory of Production_ (1977).
Prices are not scarcity indices in my example. Obviously,
I don't think my example fits into the above structure.
Suppose neoclassical theory is thought to imply that prices
are scarcity indices. Suppose one takes substitution relations
as fundamental to neoclassical theory. Then, I think,
neoclassical theory only makes sense in a multicommodity
model if production is timeless, in some sense. It cannot
handle the existence of intermediate goods, of produced
goods that are further used in producing other goods. I think
the above model abstracts from crucial properties of advanced
industrial economies.
Samuelson, in _Joan Robinson and Modern Economics_ (edited by
G. R. Feiwel, 1989), provides an interesting example of the
effects on neoclassical theory of allowing production to
take time. He labels labor the sole input into a production
process which requires more than two periods to complete. So
there are several inputs of labor, distinguished by the time
in which they enter the production process. Samuelson denotes
the wage of all labor by a single scalar. He considers what
technique the cost-minimizing firm will adopt. Keep in mind
that only wages are varied, not the prices of any other inputs.
Lo and behold, Samuelson concludes that a more labor-intensive
technique may be preferred at a higher wage. If the level of
output is taken as given, a higher quantity of labor may be
demanded at a higher wage. Samuelson allows for continuous
variation in coefficients of production and labels his example
"neoclassical."
Samuelson's example relates to his earlier work and to some
work by Tatsuo Hatta:
T. Hatta, "Capital Perversity" in _The New Palgrave:
Capital Theory_ (1990)
T. Hatta, "The paradox in capital theory and complementarity
of inputs," _Review of Economic Studies_, V. 43, pp. 127-42,
1976.
The examples in these works could be said to be "Austrian,"
assuming one accepts Bohm-Bawerk's capital theory as Austrian.
For some reason, William failed to comment on my claims about
different rates of return prevailing in the two industries under
his theories. Maybe this is because the rate of return doesn't
make much sense in the timeless model outlined above.
I didn't check the numbers in William's further calculations
with my numerical example.
I suggest that William might want to try to understand the
so-called non-substitution theorem. Pasinetti provides a
clearer explanation than Varian does.
"Joan Robinson...came on a tour of American universities and was
invited to give a lecture at Columbia University. The year 1975
had been proclaimed 'Woman's Year,' and many American economists
expected the Swedish Royal Academy would seize that opportunity
to award the Nobel Memorial Prize in Economics to Joan Robinson...
She delivered her lecture in a crowded hall at Columbia to a
huge audience of enthusiastic and roaring students, and to a group
of numerous but rather silent members of the teaching staff. I
remember Al Eichner being amazed and impressed by the contrast.
Many years later I noticed that that impression still remained:
in his biographical essay on Joan Robinson, in which he describes
the polemical exchanges with American neoclassical economists,
he presents the latter as fighting back 'with the one weapon
left to them: private scorn and public silence.'"
-- Luigi L. Pasinetti, "At the Source of Alfred Eichner's
Post-Keynesian Economics: A Personal Note," in _The
Megacorp & Macrodynamics: Essays in Memory of Alfred
Eichner_, edited by William Milberg, M. E. Sharpe, 1992.
Markku Stenborg ®
> Excerpts from netnews.talk.politics.libertarian:
> 7-May-98 Re: Minimum Wages Needn't C.. by Markku Stenborg
@bottom
[snip]
> > Yes, it *can* be derived, but it *needn't*. Downward-sloping input
> > demand is more fundamental property than profit maximization, let
> > alone price-taking.
>
> And it is a *less* fundamental property than decreasing marginal
> product (as you admit at the end of your post).
Yes.
> > First, your characterization is silent on firms that are not price
> > takers, ie, on any firm that has any mkt power whatsoever. For
> > instance, the firm could be an "atom" on local labor mkts, so that it
> > cannot take the wage rate as given.
>
> A firm w/ market power in the labor market has no labor
> demand curve. To handle a firm with market power in the
Yes, I was too haste to post that as an example.
But the atom-on-local-labor-mkt firm still has some marginal
willingness-to-pay for labor, and some derived mapping of wages W and
amount of labor L bought L(W;.) st dL/dW =< 0 that sorta looks like a
demand curve. As, eg, regular textbook monopoly firm has a derived
supply mapping P(Q;MC,.) w/ dP/dQ >= 0.
Anyways, the firm could have some mkt power on some other mkts, and
still have downward-sloping labor demand.
> output market, you just replace profit-max with cost-min,
> in which case the result *still* follows only from the
> optimization assumption and not from the marginal product
> of labor. (Do you really see this as something other than
> a detail?) I don't know exactly how the argument would
OK; economic optimization leads the firm to operate on the downward
sloping part of the marginal willingess-to-pay schedule.
> go if the firm had market power in another input market
> (and I don't care enough to think about it), but my guess
> is that the result still follows from the optimization
> assumption.
Yes, it does, as I think I sorta implied in my earlier post: near
equilibrium, w/ or w/o price taking, w/ or w/o profit maximization,
labor demand must slope down (save, perhaps, some peculiar cases, eg,
if the objective of the firm puts a huge weight on the welfare of its
labor).
> > Second, not all firms max profits, eg, due to agency problems b/w
> > owners and managers. For instance, the manager's could be interested
> > in building empires, and thus hire in excess of profit max level of
> > labor.
> >
> > Still these firms have downward sloping labor demand near equilibrium.
>
> Shrug. Depends on the utility function you specify. For example,
> - (w-l)^2 as a utility function yields upward-sloping labor
> demand. I do take your point, sort of, though. The downward-
> sloping nature of input demand curves is a property of the
> optimization assumption, and the property still follows for
> some optimization problems. Do you know of a minimal set
> of requirements on the objective function to get the result?
Nope. Must be some limit on the weights of terms in the firm's
objective fn, I suppose.
[snip]
> I don't agree either that demand curve has multiple interpretations
> or that either of the two above is a valid interpretation. Demand
> curve is the relationship between the optimal quantity of some
> input and its (exogenously fixed) price, holding other prices (and
> sometimes other things) fixed.
This is my 1st interpretation above, using other words. Marginal
willingness to pay is deduced from the optimization problem: Max
Objective Fn wrt Control Variables st Constraints. So I think we are
in next to total agreement, just using different words?
> Of course, this is an argument over definitions, not a substantive
> point.
Yep, in many cases.
But the nicety of demand = optimal quantity bought at different prices
ceteris paribus sorta brokes down or becomes (partially) irrelevant in
more complicated cases where the mkts are incomplete or there are bigb
enough imperfections. There is a nice paper illustrating this (among
others issues) by Bulow and Klemperer, I think, in JPE around '92-'94.
Second "but" comes from reading Rob's posts, where he seems [I don't
claim he commits this mistake, I haven't read his post that carefully]
to confuse statements concerning two quite different concepts:
downward-sloping marginal willingness to pay for labor on one hand,
and, on the other hand, the quite usual possibility in GE that there
is an equilibrium where both the wage and the amount of labour hired
are higher than in some other equilibrium.
[snip]
> > OK; no economic agent would want to operate on the increasing part of
> > the MPL curve, so that the demand for labor could be defined as the
> > downward-sloping part of MPL.
>
> Right, except I think you want marginal value product instead of
> marginal product and assuming an objective function
> reasonably like profit-max.
Exactomundo.
d...@temple.edu
> > Note: it's unfair to use this to criticize demand curves, which are
> > drawn for a given level of technology.
> The example does assume a given level of technology. Technology is
> specified by a set of techniques. The number of techniques is found
> by multiplying together the number of processes known in each industry.
> Robert Vienneau
But a demand curve only applies to the technology in use - as soon as
you use a different technology you get a new, different demand curve.
Dan
in Philly
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
7-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> In article <cpI_LKm00...@andrew.cmu.edu>, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
>
> > Labor demand curves *must* slope down.
>
> > To get this result, one must assume that:
>
> > 1) firms are price takers
> > 2) all other prices are fixed
> > 3) firms profit maximize in their
> > choices of inputs and outputs
>
> [ valid proof in inapplicable setting - deleted ]
This is, of course, a complete capitulation. Everything
afterwards is merely noise. Labor demand curves
*must* slope down.
Mr Vienneau's other points must amount to claims that
labor demand curves are not relevant to some purpose
or another, obviously irrelevant to the point at hand.
> By the way, the theorem and proof are also in section 3.5 of
> Debreu (1959). In section 3.4, Debreu defines "an equilibrium
> production of the ... producer relative to [the price system]."
>
> I think I'll help William out. I'll here give a set of sufficient
> conditions that answer my challenge: "Those who think the demand
> curve for labor *must* slope down should answer the following
> question: what are your assumptions?"
Shrug. I've given them. You have agreed that they are
right. Neither "help" nor any further analysis are
necessary, unless of course to see if even weaker assumptions
are possible (elsewhere in the thread).
> For some reason, William failed to comment on my claims about
> different rates of return prevailing in the two industries under
> his theories. Maybe this is because the rate of return doesn't
> make much sense in the timeless model outlined above.
Or, it may be that the comment was irrelevant.
-- Bill
_______________________________________________________________
| |
| William B. Vogt Assistant Professor |
| |
| H. John Heinz III School ph: (412) 268-1843 |
| of Public Policy and Management fx: (412) 268-7902 |
| Carnegie Mellon University wili...@andrew.cmu.edu |
|_______________________________________________________________|
Christopher Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>(Christopher Auld) wrote:
>> Well, of course this isn't the point: I think we have agreed that
>> your first example did not, as claimed, show that labor demand
>> curves can slope up.
>I did not agree. But I'm aware that one could complete my example
>with intertemporal utility-maximization.
Relevance?
> In the overlapping
>generations framework I used in my paper, one can vary a parameter
>in the utility function of a representative agent to obtain
>the different equilibria in my example. So your statement is
>defensible.
This is simply incoherent. My point was that Robert did not show
that labor demand curves slope down. It did not depend on "varying
parameters in the utility function." It was more than "defensible:"
it is true as a matter of sheer logic.
>> Such behavior necessarily violates cost-minimization (and therefore
>> profit maximization).
>How is my numerical example not consistent with cost minimization?
Hiring more of an input at a higher price to produce a given output
for a price-taking firm is axiomatically impossible. The firm you
postulate is therefore not minimizing costs.
>I have difficulty in understanding what you think is a general
>equilibrium argument.
For the general case, please see any microeconomics textbook. Here, it
is certainly not the case that analyzing how a firm responds to
exogenous shocks in the input prices it faces is a "general
equilibrium argument."
Christopher Auld
I wrote:
>This is simply incoherent. My point was that Robert did not show
>that labor demand curves slope down.
Of course, I meant "up."
SUSUPPLY
In response to Robert Vienneau’s most recent posts we have this from
Christopher Auld:
"This is simply incoherent. My point was that Robert did not show
that labor demand curves slope [up]. It did not depend on "varying parameters
in the utility function." It was more than "defensible:" it is true as a
matter of sheer logic."
and this from William B Vogt:
"This is, of course, a complete capitulation. Everything
afterwards is merely noise."
Do we see a pattern being repeated by the resourceful Mr. Vienneau?
Patrick
Robert Vienneau
> > > Note: it's unfair to use this to criticize demand curves, which are
> > > drawn for a given level of technology.
> > The example does assume a given level of technology. Technology is
> > specified by a set of techniques. The number of techniques is found
> > by multiplying together the number of processes known in each industry.
> But a demand curve only applies to the technology in use - as soon as
> you use a different technology you get a new, different demand curve.
Dan,
I have no idea what you are trying to say. My characterization of
a technology is standard. It's consistent with what Joan Robinson
called a book of blueprints. It's also been referred to as the
MIT mathematical programming approach. The assumption is that all
pages in the book are assumed to be known to the relevant agents.
The agents choose which page they want to be on.
Robert Vienneau
Hi Chris,
In article <6ivo55$j...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >(Christopher Auld) wrote:
> >> Well, of course this isn't the point: I think we have agreed that
> >> your first example did not, as claimed, show that labor demand
> >> curves can slope up.
> >I did not agree. But I'm aware that one could complete my example
> >with intertemporal utility-maximization.
> Relevance?
Your reading is that I was presenting a general equilibrium argument.
Adding intertemporal utility-maximization shows how to complete the
example to better support your prior statement.
> > In the overlapping
> >generations framework I used in my paper, one can vary a parameter
> >in the utility function of a representative agent to obtain
> >the different equilibria in my example. So your statement is
> >defensible.
> This is simply incoherent.
Are you withdrawing your comment that my example was "a claim about
comparative statics in general equilibrium"? Or do you not see how
the above supports your position?
Interested bystanders are invited to examine the paper:
ftp://csf.colorado.edu/econ/authors/Vienneau.Robert/Sraffa3.pdf
> My point was that Robert did not show
> that labor demand curves [could?] slope [up].
Your point did not only dismiss that interpretation; it also
offered an alternative explanation. I don't know why you should
reasonably object to my agreement that your alternative explanation
is defensible.
Look at my first post in this thread. The only place I explicitly
talk about a labor demand function or curve is in a question. The
question remains. What is the logic that mainstream economists
think lies behind a decreasing demand function for labor? I have yet
to see a clear and correct answer to this question.
> It did not depend on "varying
> parameters in the utility function."
I would think a mainstream economist would want to include utility
maximization somewhere in a general equilibrium model. Chris is
correct in thinking that there are other ways of understanding
my example. But he was the one calling on a general equilibrium
understanding.
> It was more than "defensible:"
> it is true as a matter of sheer logic.
See below.
> >> Such behavior necessarily violates cost-minimization (and therefore
> >> profit maximization).
>
> >How is my numerical example not consistent with cost minimization?
> Hiring more of an input at a higher price to produce a given output
> for a price-taking firm is axiomatically impossible. The firm you
> postulate is therefore not minimizing costs.
Wrong. Please show where the error lies. Your answer is not responsive
to the question. It merely reiterates your previous statement.
You could also take a look at the Samuelson and Hatta references I gave
elsewhere on this thread. Why are they in error?
> >I have difficulty in understanding what you think is a general
> >equilibrium argument.
> For the general case, please see any microeconomics textbook.
Uh, I've clearly examined micro textbooks before. Once again,
this answer is not responsive. But I don't think of this as
a main point of contention.
> Here, it
> is certainly not the case that analyzing how a firm responds to
> exogenous shocks in the input prices it faces is a "general
> equilibrium argument."
Comparing rates of return for firms across (vertically integrated)
industries seems to me to be a general equilibrium element in an
economics argument. Once again, you don't seem to have a consistent
position.
Personally, I don't understand this dismissal of specific numerical
examples as a manifestation of reasonable arguments. A proved theorem
cannot have numerical counterexamples.
Robert Vienneau
In article <UpInmom00...@andrew.cmu.edu>, William B Vogt
<wili...@andrew.cmu.edu> wrote:
> [Robert Vienneau writes:]
> > In article <cpI_LKm00...@andrew.cmu.edu>, William B Vogt
> > <wili...@andrew.cmu.edu> wrote:
> > > Labor demand curves *must* slope down.
> > > To get this result, one must assume that:
> > > 1) firms are price takers
> > > 2) all other prices are fixed
> > > 3) firms profit maximize in their
> > > choices of inputs and outputs
> > [ valid proof in inapplicable setting - deleted ]
> This is, of course, a complete capitulation.
Except for the minor little inconvience that I pointed out that
Samuelson and Hatta have shown your assumptions do not imply
your conclusions.
> Everything
> afterwards is merely noise. Labor demand curves
> *must* slope down.
You claimed that the setting of your proof was general. I claimed
that neoclassical economics, as you were presented it, did not
make sense when production takes time and intermediate goods
are produced. If I am correct, you have not shown that "labor
demand curves *must* slope down. I was hoping for another response.
> Mr Vienneau's other points must amount to claims that
> labor demand curves are not relevant to some purpose
> or another, obviously irrelevant to the point at hand.
It seems to be William's consistent opinion that expression of
incomprehension is an argument.
My example shows that a firm may may adopt a more labor-intensive
technique at a higher wage. Changes in all prices other
than the wage are determined by the change in the wage. The
question is how is this compatible with William's proof? The
answer is that the possibility demonstrated by my example is
not compatible.
> > I think I'll help William out. I'll here give a set of sufficient
> > conditions that answer my challenge: "Those who think the demand
> > curve for labor *must* slope down should answer the following
> > question: what are your assumptions?"
> Shrug. I've given them.
Nope.Your conditions were not sufficient. For example, you did not
make it clear that all inputs into production were unproduced. Is it
really your belief that every worker in America is producing consumer
goods directly? That brokers don't advice customers of chances
to improve their rate of return?
By the way, it occurs to me that William's further clarification
of my example in his response was in error. He assumed that the
own rates of interest of steel and corn were equal, I think. This is
not generally true in the setting of his proof.
JMH
Robert Vienneau wrote:
>
> In article <355327...@temple.edu>, d...@temple.edu wrote:
>
> > > > Note: it's unfair to use this to criticize demand curves, which are
> > > > drawn for a given level of technology.
>
> > > The example does assume a given level of technology. Technology is
> > > specified by a set of techniques. The number of techniques is found
> > > by multiplying together the number of processes known in each industry.
>
> > But a demand curve only applies to the technology in use - as soon as
> > you use a different technology you get a new, different demand curve.
>
> Dan,
>
> I have no idea what you are trying to say. My characterization of
> a technology is standard. It's consistent with what Joan Robinson
> called a book of blueprints. It's also been referred to as the
> MIT mathematical programming approach. The assumption is that all
> pages in the book are assumed to be known to the relevant agents.
> The agents choose which page they want to be on.
I think what is being said here is that as each agent chooses
the page of production he's on he is defining a particular
demand curve. When they change the page they move to an
entirely different location on the labor demand function
which produces an entirely different demand curve. When
the technology changes you not talking about a movement
along some given demand curve but a movement along a demand
surface.
JMH
SUSUPPLY
Forrest Vienneau, morphing into Professor Irwin Corey, responds to William
Vogt:
"You claimed that the setting of your proof was general. I claimed
that neoclassical economics, as you were presented it, did not
make sense when production takes time and intermediate goods
are produced. If I am correct, you have not shown that "labor
demand curves *must* slope down. I was hoping for another response."
"It seems to be William's consistent opinion that expression of
incomprehension is an argument.
"My example shows that a firm may may adopt a more labor-intensive technique at
a higher wage. Changes in all prices other than the wage are determined by the
change in the wage. The question is how is this compatible with William's
proof? The
answer is that the possibility demonstrated by my example is
not compatible."
"Nope.Your conditions were not sufficient. For example, you did not make it
clear that all inputs into production were unproduced. Is it really your belief
that every worker in America is producing consumergoods directly? That brokers
don't advice customers of chances to improve their rate of return?
"By the way, it occurs to me that William's further clarification
of my example in his response was in error. He assumed that the
own rates of interest of steel and corn were equal, I think. This is
not generally true in the setting of his proof."
And back to Forrest for:
"Dan,
"I have no idea what you are trying to say. My characterization of
a technology is standard. It's consistent with what Joan Robinson
called a book of blueprints. It's also been referred to as the
MIT mathematical programming approach. The assumption is that all pages in the
book are assumed to be known to the relevant agents. The agents choose which
page they want to be on."
Then back into Irwin, for Chris Auld:
"Your reading is that I was presenting a general equilibrium argument. Adding
intertemporal utility-maximization shows how to complete the example to better
support your prior statement."
And back into Forrest, in the same post:
"Look at my first post in this thread. The only place I explicitly
talk about a labor demand function or curve is in a question. The
question remains. What is the logic that mainstream economists
think lies behind a decreasing demand function for labor? I have yet to see a
clear and correct answer to this question."
My question for the adults is: Are we having fun yet, fellas?
Patrick
Christopher Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>Are you withdrawing your comment that my example was "a claim about
>comparative statics in general equilibrium"? Or do you not see how
>the above supports your position?
Once again, my point was that your example did not show that
labor demand curves slope up. You were comparing different
equilibria with different wages and interest rates, whereas
a labor demand schedule gives a firm's optimal labor input as
the wage alone varies.
>Look at my first post in this thread. The only place I explicitly
>talk about a labor demand function or curve is in a question. The
>question remains. What is the logic that mainstream economists
>think lies behind a decreasing demand function for labor? I have yet
>to see a clear and correct answer to this question.
Which is confusing. William already paraphrased the standard
explanation. What is it you think to be "incorrect" about it?
>I would think a mainstream economist would want to include utility
>maximization somewhere in a general equilibrium model. Chris is
>correct in thinking that there are other ways of understanding
>my example. But he was the one calling on a general equilibrium
>understanding.
I meant "general equilibrium" in the sense that your model includes
interactions between multiple markets. I agree that full GE model
would also need to include utility maximization. But, again, this
isn't the point.
>> Hiring more of an input at a higher price to produce a given output
>> for a price-taking firm is axiomatically impossible. The firm you
>> postulate is therefore not minimizing costs.
>Wrong. Please show where the error lies. Your answer is not responsive
>to the question. It merely reiterates your previous statement.
I don't know where the error lies; I suspect with the "the firm
sets the accounting price of steel to equalize returns" assumption,
but that is just a hunch. Conditional input demand schedules cannot
slope up. Robert's example does not work out a profit-maximizing
firm's optimization problem. If he would like to formally write
down the firm's problem and show that the result he claims holds,
I would be interested to see that.
>Comparing rates of return for firms across (vertically integrated)
>industries seems to me to be a general equilibrium element in an
>economics argument. Once again, you don't seem to have a consistent
>position.
No, once again Robert is engaging is revisionist history. He
claimed his example can be interpreted as a an analysis of how
_one_ firm responds to exogenous changes in wages. That is in
no sense a "general equilibrium" argument, even if that one
firm "compares rates of return across industries." As William
has correctly chided me for, it isn't even really a partial
equilibrium argument.
>Personally, I don't understand this dismissal of specific numerical
>examples as a manifestation of reasonable arguments. A proved theorem
>cannot have numerical counterexamples.
Again: Robert has not shown that the example he gives is actually
how a profit-maximizing firm responds to changes in prices.
Robert Vienneau
> Robert Vienneau wrote:
> > In article <355327...@temple.edu>, d...@temple.edu wrote:
> > > But a demand curve only applies to the technology in use - as soon as
> > > you use a different technology you get a new, different demand curve.
> > I have no idea what you are trying to say. My characterization of
> > a technology is standard. It's consistent with what Joan Robinson
> > called a book of blueprints. It's also been referred to as the
> > MIT mathematical programming approach. The assumption is that all
> > pages in the book are assumed to be known to the relevant agents.
> > The agents choose which page they want to be on.
> I think what is being said here is that as each agent chooses
> the page of production he's on he is defining a particular
> demand curve. When they change the page they move to an
> entirely different location on the labor demand function
> which produces an entirely different demand curve. When
> the technology changes you not talking about a movement
> along some given demand curve but a movement along a demand
> surface.
John,
The neoclassical economist, assuming competive conditions, no
information problems, etc., would describe every point on a
labor demand function as equating the wage and the value of the
marginal product of labor, in some sense. Different points on
the labor demand function have different values of the marginal
product of labor. Given a choice of technique, the firm will
choose the technique to minimize costs. Different points on
the labor demand function will generally be associated with
different coefficients of production. That is, different points
on the labor demand function will be associated with different
pages in Joan Robinson's book of blueprints.
I still don't think Dan's comment makes any sense.
By the way, in my favorite modeling technique the value of
the marginal product of labor is only defined up to an
interval bounded by left-hand and right-hand derivatives.
James "jim" McCown
Robert Vienneau <rv...@see.sig.com> wrote in article
<rvien-03059...@ua2-p44.dreamscape.com>...
> 1.0 INTRODUCTION
>
> This long post presents an example in which higher wages are
associated
> with a higher quantity demanded of labor. The exact numeric values used
> are obviously unreasonable. The example, though, is used to make a
> point. Those who think the demand curve for labor *must* slope down
> should answer the following question: what are your assumptions?
After reading this essay, instead of answering a question, I have to ask
one. Are your equilibrium real interest rates of 100% and 150% supported by
the empirical facts, Robert? It is obvious that your model is not robust to
this assumption because that is what results in the process with higher
material inputs and less labor being the more expensive of the two
processes.
Try this exercise again with more realistic real rates of about 3%. Then
see what your demand curve for labor is.
Robert Vienneau
In article <6j3rhi$4ve$1...@gte1.gte.net>, "James \"jim\" McCown"
<James....@gte.net> wrote:
> After reading this essay, instead of answering a question, I have to ask
> one.
That's right - you dodge the question of what is a logically consistent
theory in which the dogmatic conclusions of neoclassical economists
follows from their assumptions.
> Are your equilibrium real interest rates of 100% and 150% supported by
> the empirical facts, Robert? It is obvious that your model is not robust to
^^^^^^^
> this assumption because that is what results in the process with higher
> material inputs and less labor being the more expensive of the two
> processes.
You misspelled "erroneous".
Paul Samuelson addressed your misconception long ago. If this bothers
you, translate my "year" to "decade". Workers can be paid more often
in models like this, and examples can still be created with the
illustrated property.
> Try this exercise again with more realistic real rates of about 3%. Then
> see what your demand curve for labor is.
Shall I try it again with a million goods being produced?
JMH
The confusion here is that the demand function and the demand
curve are two different constructions. The demand curve is a
trace of the demand function in a two diminsional space, price
and quantity. When you change "pages" you are discussing a
different demand curve. If you then connect the dots observed
you are not drawing a demand curve but more likely drawing some
view of a supply curve. That would be the case if the supply
could be held fixed and the dots were the equilibirum intersection
of supply and demand curves.
One can disagree with neoclassical economics but if one is
going to talk about supply and demand curves they must, IMO,
be talking in marginal terms. If the margins defining the
curves are price and quantity then any other change necessarily
refers to a shift of the curve and not movement along the curve.
In cases where both a shift and a movement are considered it's
much more difficult to make any sensible statments about
the slope of the curves. In short you'd have to bring in some
analogous decomposition as Slutski did in consumer theory and
determine what the sign of the substitution effect was. I think
what other's have been arguing here is that the sign is unabiguosly
negative.
JMH
James "jim" McCown
> In article <6j3rhi$4ve$1...@gte1.gte.net>, "James \"jim\" McCown"
> <James....@gte.net> wrote:
>
> > After reading this essay, instead of answering a question, I have to
ask
> > one.
>
> That's right - you dodge the question of what is a logically consistent
> theory in which the dogmatic conclusions of neoclassical economists
> follows from their assumptions.
No, you're dodging the question of whether or not your model can be
supported by the empirical facts.
> > Are your equilibrium real interest rates of 100% and 150% supported by
> > the empirical facts, Robert? It is obvious that your model is not
robust to
> ^^^^^^^
> > this assumption because that is what results in the process with higher
> > material inputs and less labor being the more expensive of the two
> > processes.
>
> You misspelled "erroneous".
>
> Paul Samuelson addressed your misconception long ago. If this bothers
> you, translate my "year" to "decade". Workers can be paid more often
> in models like this, and examples can still be created with the
> illustrated property.
Your model is not robust to the assumption of the length of the time
period. You are assigning the higher cost to the process with higher
material inputs and less labor because you are assuming that the employer
must pay for the materials in advance and pay for the labor afterwards.
That assumption may be reasonable for a period of one year but not for a
decade. Production cycles for most products are shorter than that. Even if
we did assume a decade-long production cycle, you would still end up with
real interest rates that are unrealistically high.
> > Try this exercise again with more realistic real rates of about 3%.
Then
> > see what your demand curve for labor is.
>
> Shall I try it again with a million goods being produced?
Non sequitur.
SUSUPPLY
JMH, responding to the latest Vienneauvian sophistry, wrote:
>The confusion here is that the demand function and the demand
>curve are two different constructions. The demand curve is a
>trace of the demand function in a two diminsional space, price
>and quantity. When you change "pages" you are discussing a
>different demand curve.
Absolutely correct; two dimensions.
>If you then connect the dots observed
>you are not drawing a demand curve but more likely drawing some
>view of a supply curve. That would be the case if the supply
>could be held fixed and the dots were the equilibirum intersection
>of supply and demand curves.
That would do it. Succinctly put, congratulations.
>One can disagree with neoclassical economics but if one is
>going to talk about supply and demand curves they must, IMO,
>be talking in marginal terms. If the margins defining the
>curves are price and quantity then any other change necessarily
>refers to a shift of the curve and not movement along the curve.
I wonder if Robert still thinks he hasn't heard a coherent explanation?
Patrick
Robert Vienneau
In article <6j4gup$huh$1...@gte1.gte.net>, "James \"jim\" McCown"
<James....@gte.net> wrote:
> Robert Vienneau <rv...@see.sig.com> wrote
> > That's right - you dodge the question of what is a logically consistent
> > theory in which the dogmatic conclusions of neoclassical economists
> > follows from their assumptions.
> No, you're dodging the question of whether or not your model can be
> supported by the empirical facts.
You seem to be having problems with logic. There is a general model
of the choice of technique. I give an exposition of this model in
Appendix A of my paper that I've mentioned elsewhere in this thread.
My example shows one possible behavior that's consistent with the
assumptions of this model. If one accepts this model and one wants
to assert that the illustrated type of behavior does not occur, one
must add additional assumptions to rule out this behavior.
The resulting model would be a special-case of the more general
model. Consider two models, A and B. The axioms of A are a subset
of the axioms of B. Then B is a special case of A.
Furthermore, if one is a neoclassical economist, one should prefer
axioms that are consistent with "methodological individualism."
The general model is consistent with a correction of the models
proposed by neoclassical economists between 1870 and the 1920s. It
is also consistent with multicommodity generalizations of Solow's
growth model and Lucas approach to macroeconomics.
So the challenge for economists is either
a) Reject the above models and propose an alternative
Or
b) List your special case assumptions that are compatible
with methodological individualism and are reasonably
general enough to be defended.
Nobody has been able to do (b) in 30 years of trying.
As far as empirical work goes, the burden is on the neoclassical
economist to argue for the special case. Furthermore, I have
said on previous threads that I think the interesting empirical
questions are in other directions - for example, deciding between
different theories of distribution.
[...]
> Your model is not robust to the assumption of the length of the time
> period. You are assigning the higher cost to the process with higher
> material inputs and less labor because you are assuming that the employer
> must pay for the materials in advance and pay for the labor afterwards.
It makes no difference. Rework my example under the assumption that
wages are advanced, just like the material costs. Only use a wage
of $1,339 = $3,347/( 1 + 1.5 ) for the initial equilibrium prices.
Use a wage of $2,932 = $5,864/( 1 + 1 ) for the final equilibrium
prices.
[Further mistaken and beside-the-point comments deleted.]
> > > Try this exercise again with more realistic real rates of about 3%.
> > > Then see what your demand curve for labor is.
> > Shall I try it again with a million goods being produced?
> Non sequitur.
How are changes in the convexity of the factor-price curve for
a given technique limited by the number of goods in the model?
How are the maximum number of switch points limited by the goods
in the model? In an example with more goods, wouldn't it be easier
to locate two switch points at rates of interest below, say, 5%?
If you don't understand the jargon, I suggest you need to look at
the literature to correct your logic.
Robert Vienneau
John,
I think you're mistaken. The marginal product of labor is varied
by changing pages on Joan Robinson's book of blueprints. The marginal
product of labor varies along a two dimensional labor demand curve
in wage-employment space. Therefore, the labor demand curve is not
drawn for a given page, but by varying the page. And least that's
my story.
Robert Vienneau
John,
I think you're mistaken. The marginal product of labor is varied
by changing pages on Joan Robinson's book of blueprints. The marginal
product of labor varies along a two dimensional labor demand curve
in wage-employment space. Therefore, the labor demand curve is not
drawn for a given page, but by varying the page. At least that's
Robert Vienneau
1.0 INTRODUCTION
This long post presents my previous example as a problem in the
theory of the firm. In this example, higher wages are associated
with a higher quantity demanded of labor. The exact numeric values used
are not claimed to be reasonable. The example, though, is used to make a
point. Those who think the demand curve for labor *must* slope down
should answer the following question: what are your assumptions?
2.0 DATA ON TECHNOLOGY
Recall that I am considering a vertically integrated firm that produces
a single consumption good, corn, from inputs of labor, steel, and (seed)
corn. Since the firm is vertically integrated, the firm also produces
steel and corn used in the production processes adopted. The firm
produces the produced inputs used in the production of the steel and
corn used directly in the production of the final output, corn. And so
on.
Assume all production processes known by the firm in this example
require a year to complete. Only one production process is known for
producing corn. This process requires the following inputs to be
available at the beginning of the year for each bushel corn produced
and available at the end of the year:
TABLE 1: INPUTS REQUIRED PER BUSHEL CORN PRODUCED
0.82816 Person-years
0.2 Tons steel
0.16889 Bushels corn
Steel is also produced by this firm for its own needs. Two processes
are known for producing steel:
TABLE 2: INPUTS REQUIRED PER TON STEEL PRODUCED
Process Alpha Process Beta
0.19321 Person-Years 0.033594 Person-Years
0.35 Tons Steel 0.13329 Tons Steel
0.0095553 Bushels Corn 0.15590 Bushels Corn
Apparently, inputs of corn and steel can be traded off in producing steel.
The process that uses less corn and more steel, however, also requires
a greater quantity of labor input.
I assume all processes available for production exhibit constant returns
to scale.
3.0 QUANTITY FLOWS
3.1 STATIONARY STATES
The example is constructed by comparing equilibrium prices associated
with stationary states for producing a net output of 1,000 bushels corn.
Two stationary states are possible, corresponding to the two techniques
for producing steel. A technique is a combination of one steel-producing
process and the corn-producing process. The techniques are named after
the process used in producing steel. Table 3 shows the quantity flows for
a stationary state in which the alpha technique is used. Table 4 shows
the corresponding quantity flows for the beta technique.
TABLE 3: QUANTITY FLOWS FOR THE ALPHA TECHNIQUE
INPUTS STEEL INDUSTRY CORN INDUSTRY
Labor 71.80 Person-Years 1000 Person-Years
Steel 130.1 Tons 241.6 Tons
Corn 3.551 Bushels 204.0 Bushels
OUTPUTS 371.6 Tons Steel 1208 Bushels Corn
TABLE 4: QUANTITY FLOWS FOR THE BETA TECHNIQUE
INPUTS STEEL INDUSTRY CORN INDUSTRY
Labor 9.752 Person-Years 1042 Person-Years
Steel 38.69 Tons 251.6 Tons
Corn 45.26 Bushels 212.5 Bushels
OUTPUTS 290.3 Tons Steel 1258 Bushels Corn
Notice that 1072 person-years are employed per year when the
alpha technique is used to produce a net output of 1,000 bushels
corn. 1052 person-years are employed under the beta technique.
Hence, the alpha technique is the more labor-intensive technique
for producing corn.
3.2 VERTICAL INTEGRATION FOR THE ALPHA TECHNIQUE
I only present a detailed analysis of quantity flows for a
vertically-integrated firm using the alpha technique. A
parallel analysis is possible for the beta technique.
Accordingly, consider a firm using the alpha technique
to produce 1,000 bushels of wheat for sale at the end of 1998.
As shown in Table 5, this year's output is the result of the
use of labor, steel, and corn purchased at the start of 1998.
(I later assume that the labor hired to work during a year
is paid at the end of the year.) One should note that the steel
and corn inputs used in 1998 are themselves produced by
production processes occurring in 1997. The processes used
in 1997 are specified with the choice of the alpha technique.
Table 5 shows that the production of 1,000 bushels of corn with
the alpha technique for consumption at the end of 1998 requires
that 828.2 person-years be hired in 1998 and 178.5 person-years be
hired in 1997. The alpha technique also requires that 103.8 tons
of steel and 30.4 bushels of corn be available at the beginning of
1997.
TABLE 5: TWO YEAR'S INPUTS FOR PRODUCING CORN
INPUTS INPUTS OUTPUT
USED IN USED IN AT END
1997 1998 OF 1998
828.2 Person-yrs 1000 Bushels
38.6 Person-yrs 200 Tons
70 Tons
1.91 Bushels
139.9 Person-yrs 168.89 Bushels
33.78 Tons
28.52 Bushels
One cannot stop with Table 5. The vertically integrated
firm using the alpha technique will itself produce the steel
and corn used in 1997. Accordingly, Table 6 extends Table 5
to make it clear that vertical integration for this technology
requires an infinite series of inputs. Those checking my
arithmetic should generate this table keeping track of many
more digits than is shown in the precision used in the table.
Also, finite precision sums of sorted numbers are more
accurate from smallest to largest than from largest to
smallest.
TABLE 6: INPUTS USED WITH ALPHA TECHNIQUE TO PRODUCE
1000 BUSHELS FOR CONSUMPTION AT END OF 1998
YEAR LABOR STEEL CORN
1998 828.2 Person-yrs 200 Tons 168.9 Bushels
1997 178.5 Person-yrs 103.8 Tons 30.43 Bushels
1996 45.26 Person-yrs 42.41 Tons 6.132 Bushels
1995 13.27 Person-yrs 16.07 Tons 1.441 Bushels
1994 4.298 Person-yrs 5.913 Tons 0.3969 Bushels
1993 1.471 Person-yrs 2.149 Tons 0.1235 Bushels
1992 0.5165 Person-yrs 0.7768 Tons 0.04139 Bushels
1991 0.1844 Person-yrs 0.2801 Tons 0.01441 Bushels
.
.
.
SUM 1072 Person-yrs 372 Tons 208 Bushels
Notice that labor is the only non-produced input in Table 6.
Table 7 presents the labor inputs for the firm when the alpha
technique is used in a stationary state. Each row in the table
represents dated labor inputs required to produce 1,000 bushels
corn available for consumption at the end of the year in which
the row terminates. How much labor is used in 1998? The
answer is found by summing the 1998 column in the table.
The 1072 person-years used in 1998 are broken down into
labor being used to produce corn for consumption at the end
of 1998, 1999, 2000, etc.
TABLE 7: LABOR INPUTS FOR THE ALPHA TECHNIQUE
... 1993 1994 1995 1996 1997 1998 1999 2000
.
.
.
... 13.27 45.26 178.5 828.2
... 4.298 13.27 45.26 178.5 828.2
... 1.471 4.298 13.27 45.26 178.5 828.2
... 0.516 1.471 4.298 13.27 45.26 178.5 828.2
... 0.184 0.516 1.471 4.298 13.27 45.26 178.5 828.2
... 0.184 0.516 1.471 4.298 13.27 45.26 ...
... 0.184 0.516 1.471 4.298 13.27 ...
.
.
.
One could go through the same sort of analysis for the
beta technique. Table 8 presents the table for beta corresponding
to Table 6 for alpha.
TABLE 8: INPUTS USED WITH BETA TECHNIQUE TO PRODUCE
1000 BUSHELS FOR CONSUMPTION AT END OF 1998
YEAR LABOR STEEL CORN
1998 828.2 Person-yrs 200 Tons 168.9 Bushels
1997 146.6 Person-yrs 60.44 Tons 59.70 Bushels
1996 51.47 Person-yrs 20.00 Tons 19.51 Bushels
1995 16.83 Person-yrs 6.566 Tons 6.412 Bushels
1994 5.530 Person-yrs 2.158 Tons 2.107 Bushels
1993 1.817 Person-yrs 0.7089 Tons 0.6921 Bushels
1992 0.5970 Person-yrs 0.2489 Tons 0.2274 Bushels
1991 0.1967 Person-yrs 0.07866 Tons 0.07722 Bushels
.
.
.
SUM 1052 Person-yrs 290 Tons 258 Bushels
4.0 PRICES
The argument proceeds by determining which technique is
cost-minimizing at equilibrium prices. In this context, equilibria
have the following properties:
o The firm produces corn by a vertically-integrated technique
o The cost of inputs for each technique in operation, including
interest charges, does not exceed revenues.
o No technique can be used to obtain pure economic profits.
Labor, although hired at the beginning of the year, is paid out of
the product at the end of the year.
I assume that the firm regards the price of corn as given on the
market. In fact, I treat the price of corn throughout as a constant,
$10,000 per bushel. Since the firm is assumed to produce 1,000
bushels, the firm's revenues are $10,000,000. I also assume the
firm takes the prices of all non-produced inputs as givens. In
this example, labor is the only non-produced input. Thus, I
assume the wage is given.
Since I am only considering equilibria, in which the firm
cannot make pure economic profits, I regard the rate of interest
as an endogeneous variable.
4.1 INITIAL EQUILIBRIUM PRICES
Suppose wages are $3,347 per person year. Let the rate of interest
be 150%. Consider the costs for each technique. Table 9 shows
the relevant calculations. (I calculated the infinite sums by use of
the procedure explained in Section 5.1.)
TABLE 9: COSTS OF THE TWO TECHNIQUES AT INITIAL PRICES
Cost of alpha technique
= [ 828.2 + 178.5 x (1 + 1.5) + 45.3 x (2.5^2)
+ 13.2 x (2.5^3) + ... ] x $3,347
= $11,112,000
Cost of beta technique
= [ 828.2 + 146.6 x (1 + 1.5) + 51.5 x (2.5^2)
+ 16.8 x (2.5^3) + ... ] x $3,347
= $10,000,000
Note the beta technique is cheaper at these prices. Thus, the
cost-minimizing firm will prefer to adopt the beta technique at this
wage. Also notice that the costs of operating the beta technique are
equal to the revenues obtained from selling the produced corn. That
is, these prices are indeed an equilibrium in which no pure economic
profits can be obtained.
4.2 FINAL EQUILIBRIUM PRICES
Next, consider higher wages, $5,864 per person-year. The equilibrium
rate of interest is consequently lower, namely 100%. Table 10 shows
the costs of the two techniques at these prices. As expected, the
alpha technique is cheaper, does not cost more than revenues, and
does not earn pure economic profits.
TABLE 10: COSTS OF THE TWO TECHNIQUES AT FINAL PRICES
Cost of alpha technique
= [ 828.2 + 178.5 x (1 + 1) + 45.3 x 4 + 13.2 x 8 + ... ] x $5,864
= $10,000,000
Cost of beta technique
= [ 828.2 + 146.6 x (1 + 1) + 51.5 x 4 + 16.8 x 8 + ... ] x $5,864
= $10,086,000
Thus, the firm being analyzed would adopt a more labor-intensive
technique, namely the alpha technique, at the higher wages of the
two levels examined.
5.0 COMMENTS
5.1 A MATHEMATICAL ASIDE
I here show how to calculate the inifinite sum used in
determining costs in Section 4. These calculations are explained
only for the alpha technique. Consider the following matrix:
+- -+
| 0.35 0.2 |
A = | |
| 0.0095553 0.16889 |
+- -+
The first column corresponds to steel production for the alpha
technique, and the second column corresponds to corn production.
The first element of each row shows the amount of steel required
to produce a unit output for the process corresponding to the
respective columns. The second element is the coefficient of
production for corn. Labor requirements per unit output are
specified by the following row vector:
a0 = [ 0.19321 0.82816 ]
These data are sometimes called Leontief input-output matrices.
Gross outputs are given by the column vector q where the
transpose of q is specified below.
q' = [ 0 1,000 ]
Dated labor inputs, shown in Section 3.2, can be derived from
these vectors and matrices:
l0 = a0 q = a0 I q
l1 = a0 A q
l2 = a0 (A^2) q
.
.
.
In general,
ln = a0 (A^n) q
where ln is the amount of labor employed in the nth year before
the year in which the quantity specified by q is to be produced.
Let w be the wage and r the rate of interest. Then the cost of
operating this technique is:
Cost = a0 I q w + a0 A q w ( 1 + r ) + a0 (A^2) q w (1 + r)^2 + ...
= a0 { I + (1 + r) A + [(1 + r) A]^2 + ... } q w
The expression in the brackets {} is a matrix version of a geometric
series. A closed-form expression for the sum is closely analogous
to the scalar version:
= a0 [ I - (1 + r) A ]^(-1) q w
It is left as a (difficult) exercise for the reader to determine why this
sum can be assumed to converge in this application and how one
can be sure the inverse exists.
5.1 A NOTE ON (SOME OF) THE LITERATURE
This post has shown how to transform the technology in my
example to a different representation. Consider a production
function mapping an infinite dimensional vector of dated
labor inputs into corn output:
y = f( l0, l1, l2, ... )
One can view the techniques my example as showing the value
of y for two points in the domain of this function. I claim that
one can construct examples with the interesting property of
my example for a completely specified f, but I have never seen
an easily understood example.
Rather, I am aware of work by Samuelson and Hatta, in seperate
papers, arguing for this claim. The difference is that they prefer
production functions mapping finite dimensional dated labor
vectors into corn output, for example:
y = f( l0, l1, l2 )
Assuming certain smoothness properties, the following
conditions hold for a optimum:
w = p df/dl0
w (1 +r) = p df/dl1
w (1 +r)^2 = p df/dl2
Both Samuelson and Hatta think the sort of perverse
behavior I am highlighting in my example is consistent
with typical "neoclassical" smoothness assumptions.
6.0 CONCLUSIONS
I have shown in this long note a case of a cost-minimizing firm
that adopts a more labor-intensive technique at a higher wage.
SUSUPPLY
Barricading himself in his fantasy world, Robert Vienneau writes:
>If you don't understand the jargon, I suggest you need to look at
>the literature to correct your logic.
Robert is, of course, back to being Prof. Irwin Corey. That is his only hope
of salvaging anything from his farce.
Patrick
JMH
Robert Vienneau wrote:
>
> John,
>
> I think you're mistaken. The marginal product of labor is varied
> by changing pages on Joan Robinson's book of blueprints. The marginal
> product of labor varies along a two dimensional labor demand curve
> in wage-employment space. Therefore, the labor demand curve is not
> my story.
Rob, I don't think what I said is incompatible with your response.
The marginal product product of labor on two labor demand curves
is different and the higher curve will reflect a higher MP for
a given quantity of labor employed. This, however, doesn't really
have much to do with the slope of the two curves.
What you are doing when you talk of changing from one page to
another in Joan's book is to jump from one labor demand curve
to another. The labor demand curve in the wage-employment space
is Q = D(p|const(*)), where const(*) means all other independent
variables are held constant. In other words we don't get to change
pages.
Now, I will say that one can define other labor demand curves
and they're not invalid per se. Such curves are, I think, non-
traditional even in a classical economics sense.
Also, I think what you're doing is a bit more relevant in
a general equalibrium type setting where noting is assumed
fixed. But then in the Walrasian auction process there
really aren't supply and demand curves in the sense above,
there are merely quantities available all of which must go.
And, btw, just for clarification, I don't happen to buy into
the view that traditional demand curves *always* slope down.
When one talks about the three stages of production Stage I
is associated with an upward sloping labor demand curve. I
also think that there are cases where external economies of
scale might result in an upward sloping demand curve (but don't
ask me to prove this as it's basically an intuitive view, not
a formal result, and I don't really do economics these days).
JMH
Robert Vienneau
In article <6j1vj4$l...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >Look at my first post in this thread. The only place I explicitly
> >talk about a labor demand function or curve is in a question. The
> >question remains. What is the logic that mainstream economists
> >think lies behind a decreasing demand function for labor? I have yet
> >to see a clear and correct answer to this question.
> Which is confusing. William already paraphrased the standard
> explanation. What is it you think to be "incorrect" about it?
William was unclear in his statement of assumptions. Also, what
are goods, especially labor? What is a price, especially wages?
Maybe you economists ought to argue a little more with one
another so as to agree on a common story. Do Dan and John agree
with William?
[...]
> I don't know where the error lies; I suspect with the "the firm
> sets the accounting price of steel to equalize returns" assumption,
> but that is just a hunch.
I nowise accept that that statement is in error. However, I have now
accepted your challenge to more formally model the firm. I have
presented my analysis in a third formulation so as to avoid
arguing about the production of steel. That is, I have
transformed my presentation of the technology so the presence
of steel and seed corn is no longer apparent.
> ...As William
> has correctly chided me for, it isn't even really a partial
> equilibrium argument.
You did notice that my Debreu quote used the word "equilibrium"
in characterizing the firm's choice of technology?
sam laurie
central Florida,
west of Lake Okeechobee. The project is the creation of inventor Jacque
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for most of his 80+ years has been designing innovative social and
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for the benefit of all humankind. A core concept is that of a
Resource-Based Economy.
This is truly a unique and idealistic project, worthy of your
consideration.
The Venus Project website is located at http://www.nas.com/venus
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
8-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> In article <UpInmom00...@andrew.cmu.edu>, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
>
> > [Robert Vienneau writes:]
>
> > > In article <cpI_LKm00...@andrew.cmu.edu>, William B Vogt
> > > <wili...@andrew.cmu.edu> wrote:
>
> > > > Labor demand curves *must* slope down.
>
> > > > To get this result, one must assume that:
>
> > > > 1) firms are price takers
> > > > 2) all other prices are fixed
> > > > 3) firms profit maximize in their
> > > > choices of inputs and outputs
>
> > > [ valid proof in inapplicable setting - deleted ]
>
> > This is, of course, a complete capitulation.
>
> Except for the minor little inconvience that I pointed out that
> Samuelson and Hatta have shown your assumption do not imply
> your conclusions.
I express incomprehension. (see below)
> > Everything
> > afterwards is merely noise. Labor demand curves
> > *must* slope down.
>
> You claimed that the setting of your proof was general.
> I claimed
> that neoclassical economics, as you were presented it, did not
> make sense when production takes time and intermediate goods
> are produced. If I am correct, you have not shown that "labor
> demand curves *must* slope down. I was hoping for another response.
I express incomprehension. (see below)
> > Mr Vienneau's other points must amount to claims that
> > labor demand curves are not relevant to some purpose
> > or another, obviously irrelevant to the point at hand.
>
> It seems to be William's consistent opinion that expression of
> incomprehension is an argument.
Not at all. Expression of incomprehension is expression of
incomprehension.
The original challenge was to produce assumptions under
which labor demand curves slope down.
I have provided a definition of labor demand curves. I have
provided a set of assumptions. I have proved that, under
those assumptions, labor demand curves must slope down. None
of this has been disputed by anyone.
The challenge has been met.
I express incomprehension at your current position. This
position appears to be that I have not met the challenge,
although all of the steps above (which together obviously
suffice to meet the challenge) are correct.
To summarize. The posted argument is an argument. The
posted expressions of incomprehension are expressions of
incomprehension. I have no further argument to make, nor
can I have one --- the argument is unchallenged and has
been described as valid by, for example, Mr Vienneau.
> My example shows that a firm may may adopt a more labor-intensive
> technique at a higher wage. Changes in all prices other
> than the wage are determined by the change in the wage. The
> question is how is this compatible with William's proof? The
> answer is that the possibility demonstrated by my example is
> not compatible.
Except that I showed, in detail, how it was compatible. This
argument also has not been challenged at all.
> > > I think I'll help William out. I'll here give a set of sufficient
> > > conditions that answer my challenge: "Those who think the demand
> > > curve for labor *must* slope down should answer the following
> > > question: what are your assumptions?"
>
> > Shrug. I've given them.
>
> Nope. Your conditions were not sufficient.
Yet the argument remains unchallenged and
Mr Vienneau desribes it as valid.
> For example, you did not
> make it clear that all inputs into production were unproduced.
Right, I didn't make it clear that all inputs into
production were unproduced. And I didn't do this because . . .
the assumptions I *did* make were sufficient, without that
additional one, i.e. I did not assume that all inputs into
production were unproduced.
> By the way, it occurs to me that William's further clarification
> of my example in his response was in error. He assumed that the
> own rates of interest of steel and corn were equal, I think. This is
> not generally true in the setting of his proof.
There is no such error.
The equality of interest rates across goods is a feature of
Mr Vienneau's example. It is the case, obviously, that my claim
remains true in, and the framework I posted can handle, the
case in which interest rates differ for different goods.
IOW, the framework can be used to model Mr Vienneau's special
case. As I pointed out, it is also applicable more generally.
-- Bill
Christopher Auld
>> >question remains. What is the logic that mainstream economists
>> >think lies behind a decreasing demand function for labor? I have yet
>> >to see a clear and correct answer to this question.
>
>> Which is confusing. William already paraphrased the standard
>> explanation. What is it you think to be "incorrect" about it?
>
>William was unclear in his statement of assumptions.
Then look it up in Varian.
>Also, what
>are goods, especially labor? What is a price, especially wages?
Both questions have clear answers given the mathematical framework.
If Robert wants to challenge those assumptions, he is of course free,
but that is quite different from claiming the assumptions are unclear.
>> I don't know where the error lies; I suspect with the "the firm
>> sets the accounting price of steel to equalize returns" assumption,
>> but that is just a hunch.
>I nowise accept that that statement is in error. However, I have now
>accepted your challenge to more formally model the firm.
Robert has simply demonstrated he doesn't understand what a labor
demand schedule is. We want to analyse the response of a firm to
changes in the wage rate it must pay. We cannot allow the interest
rate to vary as well while doing so! Robert always bristles when
anyone suggests he actually try to understand the basics of
neoclassical microeconomics before jumping into critiques thereof,
yet it invariably becomes obvious that that is a necessary first
step for him to make any coherent and sensible statements on these
matters. My statement is not in error: conditional input demand
schedules cannot slope up, and Robert's attempted demonstration
otherwise fails on very basic conceptual grounds.
>> ...As William
>> has correctly chided me for, it isn't even really a partial
>> equilibrium argument.
>You did notice that my Debreu quote used the word "equilibrium"
>in characterizing the firm's choice of technology?
He is using the word in a different sense than "partial equilibrium"
usually denotes. That phrase refers to equibirium prices and
quantities in a market, holding other prices fixed. When we say
an agent has reached "equilibrium," as in the firm here, we mean
that the agent has no incentive to change its decisions. Deriving
labor demand schedules does not require determining labor market
equilibria, and is therefore not really partial equilibrium argument.
Robert Vienneau
Hi Chris,
The crossposting is to ensure William gets a chance to see this.
In article <6j7if8$b...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >William was unclear in his statement of assumptions.
> Then look it up in Varian.
Nonresponsive. Besides, I did. I find Varian unclear, especially compared
to Debreu.
> >Also, what
> >are goods, especially labor? What is a price, especially wages?
> Both questions have clear answers given the mathematical framework.
Nonresponsive. Why don't you answer the question to help out anybody
following along? What is the mathematical framework? Give an
interesting interpretation in this context. I have a response you might
find interesting, if you have in mind what I think you should have
in mind.
> If Robert wants to challenge those assumptions, he is of course free,
> but that is quite different from claiming the assumptions are unclear.
It's certainly unclear how the interpretation of the mathematical
framework I have in mind can apply to any capitalist economy. But
that is indeed a different argument.
> >> I don't know where the error lies; I suspect with the "the firm
> >> sets the accounting price of steel to equalize returns" assumption,
> >> but that is just a hunch.
> >I nowise accept that that statement is in error. However, I have now
> >accepted your challenge to more formally model the firm.
> Robert has simply demonstrated he doesn't understand what a labor
> demand schedule is.
Nope. Where have I asserted in this thread that labor demand curves
slope up?
What I have done, in a response to William, is shown a framework where
traditional substitution behavior makes sense. For some reason, nobody
else has been willing to accept *all* of the assumptions of that
framework. I'll furthermore claim that this view of substitution lies
behind the idea of a labor demand curve. William's or Varian's or
Debreu's proof helps substantiate this claim. I don't know why economists
here are so unwilling to articulate their views.
Sometimes it helps to repeat things for clarity. I claim that the
logical foundation behind a monotone non-increasing labor demand curve
is the view that the cost-minimizing firm will choose to substitute
relatively less expensive factors for relatively more expensive factors
in the production of consumer goods. My example shows this is not a
necessary consequence of cost-minimization in a traditional framework. I
cannot see how anybody can argue against this last statement.
Consider a general framework in which firms produce intermediate goods
which are themselves used as further inputs into production. There
is no reason to assume that substitution behavior correctly characterizes
this framework, in some sense.
> We want to analyse the response of a firm to
> changes in the wage rate it must pay.
What do you mean "we"? I want to analyze the technique chosen by
a firm at different wages under the equilibrium condition that
the firm cannot earn pure economic profits. I also assume cost
minimizing behavior. Do you still dispute that I do not assume
cost minimization?
> We cannot allow the interest
> rate to vary as well while doing so!
Why not? We need to either let the interest rate or the price of
non-produced inputs other than labor vary to answer my question. I am
willing to accept that all other exogeneous prices of inputs are
constant. Thus, I get a characterization of the amount of
labor employed by a vertically-integrated firm at different wages,
given the price of all other inputs, the price of the goods produced
by the firm, and the amount of goods produced by the firm.
I assume you know about the distinction between short run and
long run cost curves. Do you know of any related distinction
between short run and long run labor demand curves? (This is
not a test where I claim to be sure of the answer. In fact, I'm
not sure I have an answer.)
> Robert always bristles when
> anyone suggests he actually try to understand the basics of
> neoclassical microeconomics before jumping into critiques thereof,
> yet it invariably becomes obvious that that is a necessary first
> step for him to make any coherent and sensible statements on these
> matters.
And you don't seem to make an effort to understand the critiques.
Do you really think those reading along would think you are more
willing to fairly examine my favorite arguments than I am to
examine neoclassical economics? You keep on reading me as
asserting things I do not. Like so -
> My statement is not in error: conditional input demand
> schedules cannot slope up, and Robert's attempted demonstration
> otherwise fails on very basic conceptual grounds.
> >> ...As William
> >> has correctly chided me for, it isn't even really a partial
> >> equilibrium argument.
> >You did notice that my Debreu quote used the word "equilibrium"
> >in characterizing the firm's choice of technology?
> He is using the word in a different sense than "partial equilibrium"
> usually denotes.
Would you say that it is reasonable to talk about equilibrium in
this context? Are we talking about general equilibrium? I don't
think so, not at this point. Nevertheless, I understand your point:
> That phrase refers to equibirium prices and
> quantities in a market, holding other prices fixed. When we say
> an agent has reached "equilibrium," as in the firm here, we mean
> that the agent has no incentive to change its decisions.
That's why one must allow the interest rate to change when
characterizing an equilibrium of the firm at different wages.
> Deriving
> labor demand schedules does not require determining labor market
> equilibria, and is therefore not really partial equilibrium argument.
You did notice I am silent on supply in my example, as presented in
this thread. So I'm not considering equilibria in a market either.
In another post, William B Vogt <wili...@andrew.cmu.edu> wrote:
> I have provided a definition of labor demand curves. I have
> provided a set of assumptions. I have proved that, under
> those assumptions, labor demand curves must slope down. None
> of this has been disputed by anyone.
I dispute it. I dispute you have stated all of your assumptions.
> > My example shows that a firm may may adopt a more labor-intensive
> > technique at a higher wage. Changes in all prices other
> > than the wage are determined by the change in the wage. The
> > question is how is this compatible with William's proof? The
> > answer is that the possibility demonstrated by my example is
> > not compatible.
> Except that I showed, in detail, how it was compatible. This
> argument also has not been challenged at all.
Your argument was that I varied the price of another input in my
example, namely steel. It is now clear that the only input that
a vertically-integrated firm buys on the market in my example is
labor.
I suggest you read Burmeister, for example, the following to better
understand my example and possible responses:
E. Burmeister, "Sraffa, Labor Theories of Value, and the Economics
of Real Wage Determination," _Journal of Political Economy_,
V. 92, pp. 508-26, 1984.
If you do, you should also check out Kurz and Salvadori's 1987
response. I cannot remember if Burmeister had a counter-response;
I think he did.
I agree that, given my example, you are justified in assuming equal
own-rates of interest for the initial prices. I question whether you
are so justified in the same assumption for final prices, given
your position.
Robert Vienneau
In article <rvien-11059...@ua1-b18.dreamscape.com>,
rv...@see.sig.com (Robert Vienneau) wrote:
> I agree that, given my example, you are justified in assuming equal
> own-rates of interest for the initial prices. I question whether you
> are so justified in the same assumption for final prices, given
> your position.
On second thought, I withdraw the objection.
Robert Vienneau
> minimizing behavior. Do you still dispute that I do not assume
> cost minimization?
I should have written, "Do you still dispute that I assume
cost minimization?"
SUSUPPLY
Robert Vienneau responds to Chris Auld:
"Nonresponsive. Why don't you answer the question to help out anybody
following along? What is the mathematical framework? Give an
interesting interpretation in this context. I have a response you might
find interesting, if you have in mind what I think you should have
in mind."
Well, let’s first remember that this concern for "helping out anybody following
along" is from the same guy who told Jim McCown:
"If you don't understand the jargon, I suggest you need to look at the
literature to correct your logic."
More importantly, I think I have solved the riddle of what is going on with
Vienneau. It is said that men talk to exchange information while women talk to
establish relationships. Ergo, Mr. Vienneau is actually a woman. Not just any
woman, but one who understands almost nothing about economics, and enjoys
public humiliation--and keeps coming back for more. Who else could it be but:
Hillary Rodham Vienneau.
Patrick
Christopher Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>Nope. Where have I asserted in this thread that labor demand curves
>slope up?
You have repeatedly asserted that you have shown that labor demand
curves, and conditional labor demand curves, can slope up. As I've
repeatedly pointed out, you have done no such thing.
>Sometimes it helps to repeat things for clarity. I claim that the
>logical foundation behind a monotone non-increasing labor demand curve
>is the view that the cost-minimizing firm will choose to substitute
>relatively less expensive factors for relatively more expensive factors
>in the production of consumer goods.
Consider a price-taking firm which hires one input and which has a concave
production function. Does it have a downward-sloping labor demand schedule?
>My example shows this is not a
>necessary consequence of cost-minimization in a traditional framework. I
>cannot see how anybody can argue against this last statement.
Because it's flagrantly wrong. Your example changes two prices, not
just the price of labor. When both those prices change, labor does
not become the "relatively less expensive factor," generating your
result. Downward-sloping conditional input demand schedules are a
necessary result of cost-minimizing behavior.
>> We want to analyse the response of a firm to
>> changes in the wage rate it must pay.
>What do you mean "we"? I want to analyze the technique chosen by
>a firm at different wages under the equilibrium condition that
>the firm cannot earn pure economic profits.
Then you are not talking about a labor demand schedule.
> I also assume cost
>minimizing behavior. Do you still dispute that I do not assume
>cost minimization?
In your first reinterpretation of your model, you claimed the interest
rate changes as a matter of internal accounting on the firm's part. I
maintain that that firm is not exhibiting cost-minimizing behavior. In
the next iteration, you allow the interest rate the firm faces externally
to vary endogenously. The firm is now behaving consistently with
cost-minimization, but the example does not show that labor demand or
conditional labor demand schedules can slope up.
>> We cannot allow the interest
>> rate to vary as well while doing so!
>Why not?
Because we are then no longer discussing labor demand schedules. How
deep do you intend to dig yourself into this hole, Rob?
--
SUSUPPLY
Chris Auld asks Hillary:
>How
>deep do you intend to dig yourself into this hole, Rob?
Well, given that it seems to be his one comparative advantage, probably quite a
bit deeper.
Patrick
JC Cooper
William B Vogt wrote in message ...
>Excerpts from netnews.talk.politics.libertarian:
>8-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
>
>> In article <UpInmom00...@andrew.cmu.edu>, William B Vogt
>> <wili...@andrew.cmu.edu> wrote:
>>
>> > [Robert Vienneau writes:]
>>
>> > > In article <cpI_LKm00...@andrew.cmu.edu>, William B Vogt
>I have provided a definition of labor demand curves. I have
>provided a set of assumptions. I have proved that, under
>those assumptions, labor demand curves must slope down. None
>of this has been disputed by anyone.
>
>The challenge has been met.
>
>I express incomprehension at your current position. This
>position appears to be that I have not met the challenge,
>although all of the steps above (which together obviously
>suffice to meet the challenge) are correct.
>
>To summarize. The posted argument is an argument. The
>posted expressions of incomprehension are expressions of
>incomprehension. I have no further argument to make, nor
>can I have one --- the argument is unchallenged and has
>been described as valid by, for example, Mr Vienneau.
>
>> My example shows that a firm may may adopt a more labor-intensive
>> technique at a higher wage. Changes in all prices other
>> than the wage are determined by the change in the wage. The
>> question is how is this compatible with William's proof? The
>> answer is that the possibility demonstrated by my example is
>> not compatible.
>
>Except that I showed, in detail, how it was compatible. This
>argument also has not been challenged at all.
>
Did I miss it, or is the reason you fine theorists have failed to answer my
question is, you have never been in the real world and managed a company?
One of the biggest problems with this country now is that the government
will take a 1st year graduate and put him in a position to tell me how best
to run my business that I have spent 54 years learning while doing. The only
thing that looks the same on paper as it does at the source is poo poo.
When all else fails, play DEAD!
(Deflect, Evade, Attack, Divert)
JC Cooper
Mayor
Gnat Flats, Texas
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
12-May-98 Re: Minimum Wages Needn't C.. by "JC Cooper"@wcnet.net
> Did I miss it, or is the reason you fine theorists have failed to answer my
> question is, you have never been in the real world and managed a company?
>
> One of the biggest problems with this country now is that the government
> will take a 1st year graduate and put him in a position to tell me how best
> to run my business that I have spent 54 years learning while doing. The only
> thing that looks the same on paper as it does at the source is poo poo.
>
> When all else fails, play DEAD!
> (Deflect, Evade, Attack, Divert)
>
> JC Cooper
> Mayor
> Gnat Flats, Texas
I missed your previous post. I, for one, have never
managed any company. This is relevant to the present
discussion, how?
-- Bill
William B Vogt
Excerpts from netnews.sci.econ: 12-May-98
Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> What I have done, in a response to William, is shown a framework where
> traditional substitution behavior makes sense.
> For some reason, nobody
> else has been willing to accept *all* of the assumptions of that
> framework. I'll furthermore claim that this view of substitution lies
> behind the idea of a labor demand curve. William's or Varian's or
> Debreu's proof helps substantiate this claim. I don't know why economists
> here are so unwilling to articulate their views.
Their views on what? Substitution causes input demand curves
to slope down. However, proving that input demand curves slope
down does not require any detailed analysis of substitution,
so that it naturally has not come up.
> Sometimes it helps to repeat things for clarity. I claim that the
> logical foundation behind a monotone non-increasing labor demand curve
> is the view that the cost-minimizing firm will choose to substitute
> relatively less expensive factors for relatively more expensive factors
> in the production of consumer goods. My example shows this is not a
> necessary consequence of cost-minimization in a traditional framework. I
> cannot see how anybody can argue against this last statement.
The first statement is true. The second statement is false, as I
have detailed many posts ago.
> > We want to analyse the response of a firm to
> > changes in the wage rate it must pay.
>
> What do you mean "we"? I want to analyze the technique chosen by
> a firm at different wages under the equilibrium condition that
> the firm cannot earn pure economic profits. I also assume cost
> minimizing behavior. Do you still dispute that I do not assume
> cost minimization?
Analyzing the technique chosen by firms at different price
vectors is an entirely coherent activity. However, it is not
possible to conclude from such an analysis that input demand
curves don't slope down. This is so for either and both of the
following two reasons:
1. Input demand curves do slope down.
2. The object produced by the comparison of the choice
of techniques under two different price vectors which
differ in more than one element is not an input demand
curve.
This is now at least the third repetition of these facts. In
past posts, they have been proved. The proofs remain
unchallenged.
> > We cannot allow the interest
> > rate to vary as well while doing so!
>
> Why not? We need to either let the interest rate or the price of
> non-produced inputs other than labor vary to answer my question. I am
> willing to accept that all other exogeneous prices of inputs are
> constant.
What Mr Vienneau is willing to accept is entirely beside the
point. The challenge was to post the assumptions under which
labor demand curves slope down.
> I assume you know about the distinction between short run and
> long run cost curves. Do you know of any related distinction
> between short run and long run labor demand curves? (This is
> not a test where I claim to be sure of the answer. In fact, I'm
> not sure I have an answer.)
Yes, there is such a distinction. Long-run input demand
curves are optimal input combinations when the firm may
change all inputs. Short-run input demand curves are
optimal input combinations when the firm must keep some
of the inputs at a fixed, prespecified level. As an aside,
the LR-SR distinction in economics depends heavily on
context for its definition --- the definition I just gave
is relevant for the context: neoclassical theory of the firm,
and not for other contexts. As another aside, both LR and
SR input demand curves must slope down, by exactly the
same argument as before.
> In another post, William B Vogt <wili...@andrew.cmu.edu> wrote:
>
> > I have provided a definition of labor demand curves. I have
> > provided a set of assumptions. I have proved that, under
> > those assumptions, labor demand curves must slope down. None
> > of this has been disputed by anyone.
>
> I dispute it. I dispute you have stated all of your assumptions.
So dispute it. Find the error in the reasoning. Exhibit the
hidden assumption. Show how the proof fails to hold in the
absense of the hidden assumption.
The assumptions are:
1) firms choose output and inputs to profit maximize
2) firms take prices as given
3) all prices other than the price of labor are fixed
The result is: the quantity of labor demanded is nonincreasing
in the wage rate.
As a couple of people have pointed out, the result follows
under *weaker* assumptions than the ones I have given.
> > > My example shows that a firm may may adopt a more labor-intensive
> > > technique at a higher wage. Changes in all prices other
> > > than the wage are determined by the change in the wage. The
> > > question is how is this compatible with William's proof? The
> > > answer is that the possibility demonstrated by my example is
> > > not compatible.
>
> > Except that I showed, in detail, how it was compatible. This
> > argument also has not been challenged at all.
>
> Your argument was that I varied the price of another input in my
> example, namely steel. It is now clear that the only input that
> a vertically-integrated firm buys on the market in my example is
> labor.
In both examples, the price of labor and the price of
steel change. Integrating the firm only serves to
make this fact slightly less transparent. (Mr Auld
takes this up elsewhere)
In any event, it is not incumbent on me to uncover the
error in each and every alleged counterexample Mr Vienneau
cooks up. I provided a proof that labor demand curves
slope down.
> I suggest you read Burmeister, for example, the following to better
> understand my example and possible responses:
>
> E. Burmeister, "Sraffa, Labor Theories of Value, and the Economics
> of Real Wage Determination," _Journal of Political Economy_,
> V. 92, pp. 508-26, 1984.
I just skimmed it and can see no relevance to the present
context. The principle similarity seems to be that you
both use Leontief production technologies.
-- Bill
William B Vogt
Sorry not to respond more quickly, missed
your post.
Excerpts from netnews.sci.econ:
7-May-98 Re: Minimum Wages Needn't C.. by J...@erols.com
> William B Vogt wrote:
>
> > I think the difference is more than "technical." It confuses
> > (simultaneously) notional and equilibrium relationships,
> > shifts in and movements along a demand curve, and
> > partial and general equilibrium. (Although, I'm not sure it
> > is even right to describe labor demand curves as a partial
> > equilibrium object ---- they are merely an output of the
> > firm's maximization problem, not of any equilibrium interaction
> > at all.)
>
> Doesn't that (not the distinction between shifts in and movements
> along but the "merely output" of maximization activities) imply that
> no input demand curve is properly decribed in partial equalibrium
> terms?
Yes. Input demand curves are part of the neoclassical theory
of the firm. Partial equilibrium analysis is the determination
of P and Q for one market (holding prices in all other markets
constant). At least this is my take on standard usage. So
input demand curves can serve as an input to partial equilibrium
analysis (ie they are the D-curve in the labor market), but they
are not determined in partial equilibrium --- they are fixed
in partial equilibrium.
-- Bill
William B Vogt
Sorry to take so long to respond, somehow I
missed your post.
Excerpts from netnews.sci.econ: 8-May-98
Re: Minimum Wages Needn't C.. by Markku Stenborg @bottom
[snip large amounts of agreement]
> Second "but" comes from reading Rob's posts, where he seems [I don't
> claim he commits this mistake, I haven't read his post that carefully]
> to confuse statements concerning two quite different concepts:
> downward-sloping marginal willingness to pay for labor on one hand,
> and, on the other hand, the quite usual possibility in GE that there
> is an equilibrium where both the wage and the amount of labour hired
> are higher than in some other equilibrium.
Yes, I think this is precisely the mistake he is making. However,
he seems not to agree.
-- Bill
JC Cooper
William B Vogt wrote in message ...
>Excerpts from netnews.talk.politics.libertarian:
I think the heading is Minimum wages needn't cause unemployment, isn't it.
When one actually manages a company, a set minimum wage can and does cause
the unemployment of some and in the real world, when the minimum wage goes
up, you have to give everyone else in the company an equal raise for reasons
you probably would not understand.
Robert Vienneau
In article <6j9v7f$m...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
Chris continues to refuse to respond to questions for some reason
or another. For example:
[> > >Also, what ]
[> > >are goods, especially labor? What is a price, especially wages? ]
[> ]
[> > Both questions have clear answers given the mathematical framework. ]
[> ]
[> Nonresponsive. Why don't you answer the question to help out anybody ]
[> following along? What is the mathematical framework? Give an ]
[> interesting interpretation in this context. ]
No response here.
> >Nope. Where have I asserted in this thread that labor demand curves
> >slope up?
> You have repeatedly asserted that you have shown that labor demand
> curves, and conditional labor demand curves, can slope up.
You're just making crap up. If I have repeatedly asserted this in
this thread, why can't you quote me saying so?
> As I've
> repeatedly pointed out, you have done no such thing.
> >Sometimes it helps to repeat things for clarity. I claim that the
> >logical foundation behind a monotone non-increasing labor demand curve
> >is the view that the cost-minimizing firm will choose to substitute
> >relatively less expensive factors for relatively more expensive factors
> >in the production of consumer goods.
> Consider a price-taking firm which hires one input and which has a concave
> production function. Does it have a downward-sloping labor demand schedule?
And the relevance of this question for my example is...? Keep in mind
the use of symbols in William's/Varian's/Debreu's example, particularly
Debreu's.
> >My example shows this is not a
> >necessary consequence of cost-minimization in a traditional framework. I
> >cannot see how anybody can argue against this last statement.
> Because it's flagrantly wrong. Your example changes two prices, not
> just the price of labor.
What are you talking about? The price of which two goods changes?
> When both those prices change, labor does
> not become the "relatively less expensive factor," generating your
> result. Downward-sloping conditional input demand schedules are a
> necessary result of cost-minimizing behavior.
[> > Consider a general framework in which firms produce intermediate goods ]
[> > which are themselves used as further inputs into production. There ]
[> > is no reason to assume that substitution behavior correctly characterizes ]
[> > this framework, in some sense. ]
No response here.
> >> We want to analyse the response of a firm to
> >> changes in the wage rate it must pay.
> >What do you mean "we"? I want to analyze the technique chosen by
> >a firm at different wages under the equilibrium condition that
> >the firm cannot earn pure economic profits.
> Then you are not talking about a labor demand schedule.
I am discussing the logic that might or might not lie behind
a labor demand schedule.
> > I also assume cost
> >minimizing behavior. Do you still dispute that I do not assume
> >cost minimization?
>
> In your first reinterpretation of your model, you claimed the interest
> rate changes as a matter of internal accounting on the firm's part.
That is, the interest rate changes endogeneously.
> I
> maintain that that firm is not exhibiting cost-minimizing behavior.
You can maintain mistaken logic all you want. Perhaps you might want
to outline an alternative accounting convention?
> In
> the next iteration, you allow the interest rate the firm faces externally
> to vary endogenously. The firm is now behaving consistently with
> cost-minimization, but the example does not show that labor demand or
> conditional labor demand schedules can slope up.
If the textbook treatment of labor demand curves is as you say, why
do econ 101 presentations typically contain the usual mistaken argument
on the thread topic?
sam laurie
SUSUPPLY
For Chris Auld’s edification (and the others whose time has been wasted on this
thread), I first reproduce this sequence:
Vienneau:
"Nope. Where have I asserted in this thread that labor demand curves slope up?"
Chris Auld:
"You have repeatedly asserted that you have shown that labor demand curves, and
conditional labor demand curves, can slope up."
Vienneau:
"You're just making crap up. If I have repeatedly asserted this in this thread,
why can't you quote me saying so?"
I’ve experienced this gambit from Robert before. He keeps it in reserve for
when he really needs an exit strategy. It is somewhat akin to Miss Piggy’s:
"Moi?". In the post that started this thread (May 4th) Robert Vienneau wrote:
"This long post presents an example in which higher wages are associated
with a higher quantity demanded of labor. The exact numeric values used
are obviously unreasonable. The example, though, is used to make a
point. Those who think the demand curve for labor *must* slope down
should answer the following question: what are your assumptions?"
Any normal person would read that last sentence as taking the position that
demand curves for labor could slope up. It is of course, a logical assumption,
except when dealing with Robert Vienneau. Attempting to bait him into
explicitly stating HIS assumptions, I wrote:
"Second, just rearrange Robert’s opening sentence thus: ‘A higher quantity
demanded of labor’ is ‘associated’ with ‘higher wages’.
"Duh! Does Robert think any competent economist would disagree with that
sentence?"
Well, as the competent economists who have been participating on this thread
well know, the opposite of my sentence is more likely true. That was the bait.
Robert didn’t go for it, because then he wouldn’t have been able to continue
his "playing an economist". If Robert had responded that his phrase, "a higher
quantity demanded of labor" is usually associated with movement along a demand
curve, while I was really saying, "higher demand" is associated with higher
wages (a curve expanded outward or rightward). Then I was going to point out
to him that his example implies different demand curves, not movement along a
single curve.
In case the mayor from Texas is reading, this is a real business-world
phenomenon. As someone who is a businessman, and not an academic, I have one
"demand for labor" in my specialty construction business when I am repairing
concrete floors in a privately owned warehouse. I have a very different demand
for labor when I am working on an Interstate highway, and am bound by
Davis-Bacon prevailing wage laws. In fact, I usually do hire more people at a
higher wage in the latter case, but I am not moving along a single demand curve
when I do so.
At any rate, an e-mail correspondent—who, like me, finds Vienneau both
entertaining and bizarre—informs me:
"The unfortunate thing is that Robbie actually might be somewhat
right. He's copying stuff out of the Cambridge Capital Controversy where in
capital theory, there are a lot of strange equilibrium results and the
assumptions needed to make things work out nicely really aren't pretty.
However, in my opinion (in an example taken from Mark Blaug), the "factor
perversity" Venal talks about is about as interesting as the case of the
"Giffen Good" in demand theory. Well no, less interesting, but about as
empirically important."
What makes Robert tick is a question probably better suited for a "sci.psych"
newsgroup, though in his book, "The Shadow of Keynes", Harry Johnson makes some
pointed comments about the motivations of the Cambridge personalities that may
be relevant.
Patrick
Frank Mayer
JC Cooper wrote:
>
> I think the heading is Minimum wages needn't cause unemployment, isn't it.
> When one actually manages a company, a set minimum wage can and does cause
> the unemployment of some and in the real world, when the minimum wage goes
> up, you have to give everyone else in the company an equal raise for reasons
> you probably would not understand.
Maybe we do understand. If you've read the messages in the thread you
know they unanimously disagree with the thinking behind the heading --
except for those from one person who is making full use of the "play
DEAD" strategy you recommend.
Read before posting, Mr. Mayor.
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
12-May-98 Re: Minimum Wages Needn't C.. by "JC Cooper"@wcnet.net
> >I missed your previous post. I, for one, have never
> >managed any company. This is relevant to the present
> >discussion, how?
> >
> >
> >-- Bill
> I think the heading is Minimum wages needn't cause unemployment, isn't it.
> When one actually manages a company, a set minimum wage can and does cause
> the unemployment of some and in the real world, when the minimum wage goes
> up, you have to give everyone else in the company an equal raise
> for reasons you probably would not understand.
Well, although the heading is about min wages, the actual
topic under discussion is something quite different, and
the question of my probable ignorance on the topic you
mention just isn't relevant to it.
-- Bill
Christopher Auld
>[> Nonresponsive. Why don't you answer the question to help out anybody ]
>[> following along? What is the mathematical framework? Give an ]
>[> interesting interpretation in this context. ]
>No response here.
Asked and answered. If Rob has an objection, he should simply stop
being coy and state it.
>> >Nope. Where have I asserted in this thread that labor demand curves
>> >slope up?
>
>> You have repeatedly asserted that you have shown that labor demand
>> curves, and conditional labor demand curves, can slope up.
>
>You're just making crap up. If I have repeatedly asserted this in
>this thread, why can't you quote me saying so?
This is simply bizarre. Fine, I'll waste time and drag out quotes.
Let's start with the introduction to the post Rob keeps spamming across
the internet:
>point. Those who think the demand curve for labor *must* slope down
>should answer the following question: what are your assumptions?
Is this not a statement Rob is about to show that labor demand curves
needn't slope down? But let's continue. How about:
>of different wages for unskilled labor economy-wide. William
>seems to be claiming that a demand curve for labor is drawn on
>the assumption that firms tend to leave hundred-dollar bills lying
>on the sidewalk. Maybe he ought to try to find assumptions more
and continue with:
>You claimed that the setting of your proof was general. I claimed
>that neoclassical economics, as you were presented it, did not
>make sense when production takes time and intermediate goods
>are produced. If I am correct, you have not shown that "labor
>demand curves *must* slope down. I was hoping for another response.
and more directly:
>> Well, of course this isn't the point: I think we have agreed that
>> your first example did not, as claimed, show that labor demand
>> curves can slope up.
>I did not agree.
or how about:
>There is another, partial equilibrium reading of my example. Consider
>my example to be an analysis of a vertically-integrated firm
>producing corn. The firm takes the price of the output, corn,
>and the wages of labor as givens. The firm choses what
>technique it wants to use to produce corn, if any.
>The price of steel is a matter of the firm's internal accounting.
>The firm will set this accounting price such that the firm is making
>the same rate of return in steel-production and corn-production.
>My example shows that, for the two levels of wages analyzed, the
>cost-minimizing vertically-integrated firm will prefer a more
>labor-intensive technique at a higher wage. Given the output,
>the firm will employ more labor at the higher wage.
and, finally, directly, explicitly:
>> When all other
>> prices are held equal, labor demand curves slope down, even in
>> Robert's model.
>Given the above interpretation, I don't think so.
I don't take kindly to being accused of "making up crap," Rob. Everyone
following this thread knows what you claimed.
>> >Sometimes it helps to repeat things for clarity. I claim that the
>> >logical foundation behind a monotone non-increasing labor demand curve
>> >is the view that the cost-minimizing firm will choose to substitute
>> >relatively less expensive factors for relatively more expensive factors
>> >in the production of consumer goods.
>
>> Consider a price-taking firm which hires one input and which has a concave
>> production function. Does it have a downward-sloping labor demand schedule?
>
>And the relevance of this question for my example is...?
That substitution is not "the" foundation of downward-sloping demand curves
for labor. It is the foundation for downward-sloping conditional demand
curves for labor, but since you merrily confuse the two concepts I suppose
that distinction is lost on you.
>> Because it's flagrantly wrong. Your example changes two prices, not
>> just the price of labor.
>What are you talking about? The price of which two goods changes?
The interest rate is a price, Rob.
>> Then you are not talking about a labor demand schedule.
>I am discussing the logic that might or might not lie behind
>a labor demand schedule.
No, you're not. What part of "you're changing more than just the wage"
is so difficult to understand?" Suppose we could write the demand
schedule as a smooth function of the wage and the interest rate. You
are showing that is is possible that:
d L ( w, r(w) ) \partial L \partial L dr
--------------- = ---------- + ---------- -- >0,
dw \partial w \partial r dw
where r(w) encapsulates the zero-profits condition. This has _nothing_
to do with the "logic ... behind a labor demand schedule." Only the first
term on the RHS is the labor demand schedule, and you haven't shown that
term can be positive. You are, rather, showing that when more than one
price changes it is possible that a higher wage is associated with higher
quantity demanded for labor.
>> I
>> maintain that that firm is not exhibiting cost-minimizing behavior.
>
>You can maintain mistaken logic all you want. Perhaps you might want
>to outline an alternative accounting convention?
If the 'accounting convention' the firm chooses causes it to fail to
exhibit cost-minimizing input choices, the firm is no longer acting
in accord with cost-minimizization, is it Rob? Can you write out the
firm's cost minimization problem solely in terms of non-artificial prices
and quantities and show that changing the wage and wage alone increases
the amount of labor hired? My "logic" is not mistaken: Rob just
doesn't understand basic microeconomics.
>> In
>> the next iteration, you allow the interest rate the firm faces externally
>> to vary endogenously. The firm is now behaving consistently with
>> cost-minimization, but the example does not show that labor demand or
>> conditional labor demand schedules can slope up.
>If the textbook treatment of labor demand curves is as you say, why
>do econ 101 presentations typically contain the usual mistaken argument
>on the thread topic?
You haven't shown the 101 presentation is wrong. You don't understand
basic methodology and have several distinct concepts quite confused.
Frank Mayer
Robert Vienneau wrote:
> (Christopher Auld) wrote:
> > You have repeatedly asserted that you have shown that labor demand
> > curves, and conditional labor demand curves, can slope up.
>
> You're just making crap up. If I have repeatedly asserted this in
> this thread, why can't you quote me saying so?
This ought to be simple enough to straighten out:
Robert, do you believe that labor demand curves can slope up? A simple
yes/no answer will suffice. No need for further explanation at this
point.
---------------
Robert Vienneau wrote:
>William B Vogt <wili...@andrew.cmu.edu> wrote:
>> I have proved that, under
>> those assumptions, labor demand curves must slope down. None
>> of this has been disputed by anyone.
>I dispute it. I dispute you have stated all of your assumptions.
----
Robert Vienneau wrote:
>(Christopher Auld) wrote:
>> When all other
>> prices are held equal, labor demand curves slope down, even in
>> Robert's model.
> Given the above interpretation, I don't think so.
----
Robert Vienneau wrote:
> Those who think the demand curve for labor *must* slope down
> should answer the following question: what are your assumptions?
... among several other examples.
But maybe in all these cases Robert didn't even mean to *imply* that
labor demand curves actually could slope up, and only meant to challenge
us to clarify our understanding of why they must slope down.
jim blair
JC Cooper wrote:
>Did I miss it, or is the reason you fine theorists have failed to answer my
>question is, you have never been in the real world and managed a company?
Hi,
I think the point here is that this example has no connection to
reality.
Aside from such minor factors as switching production between steel and
corn and paying steel workers and corn farmers equal wages (once a
year!),
this example varies several parameters at the same time (price of steel,
interest rates and wages) to conclude that this firm will hire more
people to make about the same amount of total product (depending on the
steel-to-corn conversion factor) and pay them 75% higher wages, because
this will CAUSE interest rates to drop about one third.
This is intended to offer us insights on the national federal minimum
wage law?
But notice that in the world of Robert Vienneau, while wages rising
cause
interest rates to fall, there is no connection between wages and
productivity.
Hey, if you want a "concrete example" of rising wages being "associated
with" increased employment, I will give you TWO: one theoretical and one
real.
Theory: a company doubles wages. At the same time a new production
technique
GAMMA quintuples worker productivity. The company cuts the price of
their
product by 10% which expands their sales ten times. So they double their
workforce at twice the old wage. If Robert Vienneau can use examples
that vary several parameters at once....
Actual case: I read about it in the newspapers, so it must be true ;-).
A guy named Jack offered to walk dogs for 50 cents an hour. Very few dog
owners were interested. So he changed his name to Jacques, and raised is
rate to $5 an hour. So many people wanted him to walk their dog that he
was soon hiring assistants and started a franchise. (this was in
Mahattan
or maybe Beverly Hills--one of those places where they have more dollars
than cents)
So these two examples, like that of Robert Vienneau, show that a higher
legal minimum wage can result in higher employment.
--
,,,,,,,
_______________ooo___(_O O_)___ooo_______________
(_)
jim blair (jeb...@facstaff.wisc.edu) For a good time call
http://www.geocities.com/capitolhill/4834
JC Cooper
William B Vogt wrote in message ...
Well put.
Robert Vienneau
William B Vogt <wili...@andrew.cmu.edu> wrote (not in this order):
> Robert Vienneau:
> > William B Vogt <wili...@andrew.cmu.edu> wrote:
> > > I have provided a definition of labor demand curves. I have
> > > provided a set of assumptions. I have proved that, under
> > > those assumptions, labor demand curves must slope down. None
> > > of this has been disputed by anyone.
> > I dispute it. I dispute you have stated all of your assumptions.
> So dispute it. Find the error in the reasoning.
I have. But I'll repeat myself.
> Exhibit the
> hidden assumption. Show how the proof fails to hold in the
> absense of the hidden assumption.
> The assumptions are:
> 1) firms choose output and inputs to profit maximize
> 2) firms take prices as given
> 3) all prices other than the price of labor are fixed
> The result is: the quantity of labor demanded is nonincreasing
> in the wage rate.
A mathematical proof draws logical connections between some
uninterpreted symbols. Formal mathematics operates entirely on
the level of syntax. For all it matters to the validity of a proof,
the symbols could stand for beer mugs, chairs, and tables.
My question is why do you want to call some symbol in your
proof "labor" and another symbol "wages"?
I have pointed out an interpretation where your proof makes sense.
All the inputs hired by the firm are hired at the same time. There
are no inputs produced by labor at an earlier date. If there were
any such produced inputs, the vertically integrated firm would have
hired at least two inputs that could reasonably be called labor. These
inputs would be distinguished by the dates in which they enter into
the process of production. Then a variation in wages would imply
a variation in the price of at least two inputs. Your proof would
be inapplicable. My interpretation that all the inputs considered
in your proof are hired at the same date as the output is produced
is further supported by the fact that you don't explicitly say
anything about present value calculations.
Since dated labor quantities are different inputs in your symbols,
my example has an infinite number of inputs. The above has merely
rephrased some points in prior posts.
There is a different interpretation of your symbols, which I have
been trying to get somebody to offer, that is Debreu's intertemporal
equilibrium. I think this should have been obvious, but apparently
it wasn't. In the case of Debreu's intertemporal equilibrium, physically
identical goods offered for sale at different dates are treated as
different commodities. The prices of all commodities refer to one point
in time. Commodities are all traded on forward markets. At the beginning
of time, where endowments are given, all agents enter contracts to
deliver certain goods and services on various dates in the future.
The payments, however, are all made instantaneously.
Under this interpretation, your proof compares equilibria of
the firm - in the very limited theory of the firm treated in our
discussion - that faces some odd circumstances. All prices are the
same in the two equilibria, except the price of one particular dated
labor quantity. This, too, is inapplicable to my example.
The forward prices in an intertemporal equilibrium can be mapped
into perfectly anticipated spot prices. One can use either these
spot prices or the forward prices to determine own-rates of interest
for each good. Own rates of interest will generally be different
for different goods. Likewise, the spot prices of a given good
will generally be different at different times. Suppose one takes
initial endowments of goods as given and imposes the condition
of stationary relative spot prices - that is, equal own rates
of interest. Then the model is generally overdetermined and
inconsistent. Walras made this mistake. I haven't been taking
endowments as given in my example. Therefore, my example is
not yet explicitly about intertemporal equilibria.
My example compares two locations on a so-called factor-price
frontier. I gave you a reference to a discussion of this sort
of example, with the usual result:
> > I suggest you read Burmeister, for example, the following to better
> > understand my example and possible responses:
> > E. Burmeister, "Sraffa, Labor Theories of Value, and the Economics
> > of Real Wage Determination," _Journal of Political Economy_,
> > V. 92, pp. 508-26, 1984.
> I just skimmed it and can see no relevance to the present
> context. The principle similarity seems to be that you
> both use Leontief production technologies.
As I recall, Burmeister argues that comparisons of points on
a so-called factor price frontier are irrelevant. Economically
meaningful questions are about intertemporal equilibria paths
from points with given endowments. I think he asserts that
examples like mine have no bearing on such paths, though in his
1980? book he has something about some regularity condition that
I don't understand.
This is a standard reaction to examples like mine - that
the Arrow-Debreu model is untouched. But, as I have pointed out
to you before, under certain conditions an Arrow-Debreu equilibrium
path will approach equilibria like those in my example as
saddle-point limits.
I think something like the above should be common knowledge to
those well-trained in economic theory. Economists I admire have
expressed doubts that the Arrow-Debreu model is an adequate
answer to certain objections to neoclassical economic theory.
But these different rates of return will all converge towards
the same in the long run, under the conditions stated.
This explains why Joan Robinson declared that she was confused
when she asked what the most general modern theory of value and
distribution was and received the answer that it was intertemporal
theory. For the intertemporal model does not represent a
long-run position in the classical sense with a uniform rate of
profit; in fact, a peculiar type of such a position emerges only
as the terminal state, as we now know, according to the turn-pike
propositions.
-- Bertram Schefold, "Joint Production, Intertemporal Preferences,
and Long-period Equilibrium," first published in _Political
Economy. Studies in the Surplus Approach_, V. 6, pp. 139-63,
1990.
Joan Robinson remarked that she could never make intertemporal theory
stand up long enough to knock it down.
-- Harvey Gram, "The role of perfect foresight in Krishna
Bharadwaj's critique of demand and supply equilibrium-based
theory," in _The Classical Tradition in Economic Thought_,
(edited by I. H. Rima), Edward Elgar, 1995.
P. Garegnani has also expressed objections along these lines, and has
tried to relate examples like mine to his objections. I find his
arguments too impressionistic to be convincing to one not already
convinced on this point.
Now for the novel part. Bertram Schefold has recently shown how to
relate a concrete example like mine to the Arrow-Debreu model. He
has constructed a numerical example where an Arrow-Debreu equilibrium
path starts at a stationary state like one technique in my example
and approaches a stationary state like the other. Along such a
path, both the wage and employment can tend to increase together. A
couple of Schefold relevant Schefold papers are:
B. Schefold, "Classical Theory and intertemporal Equilibrium",
Chapter 18 in _Normal Prices, Technical Change and Accumulation_,
Macmillan, 1997.
B. Schefold, "Paradoxes of Capital and Counterintuitive Changes
of Distribution in an Intertemporal Equilibrium Model", July
1996, available at:
http://wwwwiwi.uni-frankfurt.de/professoren/schefold/schefold.html
I have not fully absorbed these papers - in fact haven't even
fully read them yet. Nevertheless, I think they are an important
move in ongoing debates. I also think questions about how this
behavior relates to uniqueness and stability concerns might be
important.
Robert Vienneau
In article <3559F7B6.27BF@spam_me_not.com>, frank@spam_me_not.com wrote
(in opposite order):
> But maybe in all these cases Robert didn't even mean to *imply* that
> labor demand curves actually could slope up, and only meant to challenge
> us to clarify our understanding of why they must slope down.
Exactly. A claim that upward-sloping labor demand curves can exist is
not a precondition for demonstrating mistakes in reasoning of those who
assert that downward-sloping labor demand curves are a necessary consequence
of optimizing behavior.
Chris's response to the one case where he says I "explicitly" (Chris'
word) asserted labor-demand curves can slope up was mistaken. The use
of "explicitly" suggest Chris was aware at some level of consciousness
that his other quotes did not solidly support his point.
> Robert, do you believe that labor demand curves can slope up? A simple
> yes/no answer will suffice. [...]
I think a neoclassical economist might find it reasonable to describe
my example as illustrating the logical possibility of upward-sloping
conditional labor demand curves.
At every point along a labor-demand curve, the firms being aggregated
would be in equilibrium. That is, if the prices given in drawing the
curve did, in fact, hold, the firms would not want to change their
decision to hire the amount of labor shown.
Chris Auld seems to want to think of a labor demand curve as part of
an analysis in a partial equilibrium setting. The X axis shows
quantity flows - employment - in this case. The idea is if a
supply curve intersected the labor-demand curve at any given point
on the labor demand curve, there would be no forces in the labor
market tending to drive the wage away from its value at that point.
So that wage could be expected to last for some time. Thus, all
the dated quantities of labor in my example would be hired at the
same wage.
Now there are no other inputs hired from the market by the vertically
integrated firm in my example. So objections that one must not allow
the prices of any inputs other than labor to vary in my example are
irrelevant. In the jargon, a netput vector describing either technique
would contain no non-zero quantities of steel.
I have already shown that, given cost minimization, the level
of output, and the price of the good being produced; a comparison at the
two wages considered in my example of a vertically-integrated firm in
equilibrium implies the adoption of a more labor-intensive technique at
the higher wage. This is the way I prefer to describe my example. But
another reasonable way to describe this conclusion might be that a
conditional labor demand curve slopes up. The reader may recall that a
discussion of conditional labor demand curves under that label was
introduced into this thread by Chris Auld.
SUSUPPLY
Frank Mayer asks a simple question of Hillary Rodham Vienneau (HRV, hereafter):
"Robert, do you believe that labor demand curves can slope up? A simple
yes/no answer will suffice. No need for further explanation at this
point."
HRV, completely in character, responds with….a five paragraph "further
explanation".
In those five paragraphs we find HRV admitting:
"I think a neoclassical economist might find it reasonable to describe
my example as illustrating the logical possibility of upward-sloping
conditional labor demand curves." And also:
"But another reasonable way to describe this conclusion might be that a
conditional labor demand curve slopes up."
Now, let us revisit the reason Frank Mayer asked HRV the question in the first
place:
"You're just making crap up. If I have repeatedly asserted this in this thread,
why can't you quote me saying so?"
So, HRV has quickly gone from accusing Chris Auld of "just making crap up", to
his drawing "reasonable" conclusions. Obviously, HRV believes in diversity.
Will the next post from HRV be under a new thread title? "Minimum Wages Must
Cause Unemployment".
Patrick
Christopher Auld
Robert Vienneau <rv...@see.sig.com> backpedals furiously:
>Chris's response to the one case where he says I "explicitly" (Chris'
>word) asserted labor-demand curves can slope up was mistaken. The use
>of "explicitly" suggest Chris was aware at some level of consciousness
>that his other quotes did not solidly support his point.
So when I said labor demand curves slope down in the example and Rob
replied "I do not agree," he was not asserting that he thought he
had shown otherwise? Please do explain your curious use of declarative
English sentences, Rob.
>I think a neoclassical economist might find it reasonable to describe
>my example as illustrating the logical possibility of upward-sloping
>conditional labor demand curves.
I think several neoclassical economists have demonstrated quite clearly
that this is not the case. I think any economist who agreed with Rob's
interpretation of his example should have their degree stripped from them.
Which part of "when more than one price changes, it's not a labor demand
curve" is so very difficult for you to grasp, Rob?
>Chris Auld seems to want to think of a labor demand curve as part of
>an analysis in a partial equilibrium setting. The X axis shows
>quantity flows - employment - in this case. The idea is if a
>supply curve....
No. A labor demand curve gives the profit-maximizing amount of labor
hired for a given firm at various wage rates, all else equal. As I
explicitly said, it doesn't rely on partial equilibrium in the labor
market.
>Now there are no other inputs hired from the market by the vertically
>integrated firm in my example. So objections that one must not allow
>the prices of any inputs other than labor to vary in my example are
>irrelevant.
Not if we want to discuss labor demand curves. What Rob wants to
discuss might be an interesting exercise (particularly if we were
in 1965), but it has absolutely nothing to do with the "logic
underlying labor demand curves." Labor demand curves still exist
in a dynamic setting: change the price of labor at some date t and
t alone.
>I have already shown that, given cost minimization, the level
>of output, and the price of the good being produced; a comparison at the
>two wages considered in my example of a vertically-integrated firm in
>equilibrium implies the adoption of a more labor-intensive technique at
>the higher wage.
Let's rewrite this accurately:
>I have already shown that, given cost minimization, the level
>of output, and the price of the good being produced; a comparison of
>two different price vectors with different wages and interest rates
>considered in my example of a vertically-integrated firm in
>equilibrium implies the adoption of a more labor-intensive technique at
>the the price vector which has a higher wage rate.
Which doesn't show that:
>another reasonable way to describe this conclusion might be that a
>conditional labor demand curve slopes up.
Conditional labor demand curves do not slope up.
>The reader may recall that a
>discussion of conditional labor demand curves under that label was
>introduced into this thread by Chris Auld.
Rob randomly applies the caveat "for a given output" and therefore
it is never clear whether he is talking about labor demand curves or
conditional labor demand curves. When he does invoke that caveat, he
is talking about the latter regardless of what "label" he wants to
apply to the concept.
--
Professor Chris Auld au...@acs.ucalgary.ca
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
14-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> > Robert Vienneau:
> > The assumptions are:
> > 1) firms choose output and inputs to profit maximize
> > 2) firms take prices as given
> > 3) all prices other than the price of labor are fixed
>
> > The result is: the quantity of labor demanded is nonincreasing
> > in the wage rate.
>
> A mathematical proof draws logical connections between some
> uninterpreted symbols. Formal mathematics operates entirely on
> the level of syntax. For all it matters to the validity of a proof,
> the symbols could stand for beer mugs, chairs, and tables.
>
> My question is why do you want to call some symbol in your
> proof "labor" and another symbol "wages"?
Because I am interested, in general at least, in modelling
objects in the real world, namely labor and wages.
> I have pointed out an interpretation where your proof makes sense.
> All the inputs hired by the firm are hired at the same time. There
> are no inputs produced by labor at an earlier date. If there were
> any such produced inputs, the vertically integrated firm would have
> hired at least two inputs that could reasonably be called labor. These
> inputs would be distinguished by the dates in which they enter into
> the process of production. Then a variation in wages would imply
> a variation in the price of at least two inputs. Your proof would
> be inapplicable. My interpretation that all the inputs considered
> in your proof are hired at the same date as the output is produced
> is further supported by the fact that you don't explicitly say
> anything about present value calculations.
This is all a diversion. As you know, the goods in neoclassical
models can be indexed both by their physical characteristics and
by their dates and by their locations and (in stochastic settings)
by their "state." So, the proof applies to a variation in the
wage of one type of labor at one time at one location.
Either interpretation is just fine. One beauty of the neoclassical
framework is that it appies to static cases (the interpretation
you prefer above), to dynamic cases, to case differentiated by
location, and to stochastic cases. In short, I have not assumed
a static model. Furthermore, NPV calculations only make sense
under fairly restrictive assumptions (the interest rate is the
same for all goods); whereas, the framework of my proof makes
sense in more general cases (e.g. when the interest rate is
different for different goods).
> Since dated labor quantities are different inputs in your symbols,
> my example has an infinite number of inputs. The above has merely
> rephrased some points in prior posts.
First, if what you say in the quoted paragraph is true, it
utterly devastates your position, since labor demand curves
are defined by changing one and not an infinite number of
prices.
Second, your example has a static interpretation (and I mapped
your example into the static neoclassical framework long ago).
The fact that you choose to call it dynamic is beside the point.
> There is a different interpretation of your symbols, which I have
> been trying to get somebody to offer, that is Debreu's intertemporal
> equilibrium. I think this should have been obvious, but apparently
> it wasn't. In the case of Debreu's intertemporal equilibrium, physically
> identical goods offered for sale at different dates are treated as
> different commodities. The prices of all commodities refer to one point
> in time. Commodities are all traded on forward markets. At the beginning
> of time, where endowments are given, all agents enter contracts to
> deliver certain goods and services on various dates in the future.
> The payments, however, are all made instantaneously.
See, you do know it.
> Under this interpretation, your proof compares equilibria of
> the firm - in the very limited theory of the firm treated in our
> discussion - that faces some odd circumstances. All prices are the
> same in the two equilibria, except the price of one particular dated
^^^^^^^^^^^^^^
> labor quantity.
We don't compare equilibria in the neoclassical theory of the
firm, we compare the firm's response to different price
vectors.
> This, too, is inapplicable to my example.
I express incomprehension. The challenge was to exhibit
assumptions under which labor demand curves slope down.
This has been done. I went further and showed exactly
why your example fails to be a counterexample.
> The forward prices in an intertemporal equilibrium can be mapped
> into perfectly anticipated spot prices. One can use either these
> spot prices or the forward prices to determine own-rates of interest
> for each good. Own rates of interest will generally be different
> for different goods. Likewise, the spot prices of a given good
> will generally be different at different times. Suppose one takes
> initial endowments of goods as given and imposes the condition
> of stationary relative spot prices - that is, equal own rates
> of interest. Then the model is generally overdetermined and
> inconsistent. Walras made this mistake. I haven't been taking
> endowments as given in my example. Therefore, my example is
> not yet explicitly about intertemporal equilibria.
Mr Vienneau's posts are chock full of seemingly irrelevant
text, which day after dreary day never ever connect to
any point under discussion.
Again, this is so obviously irrelevant that one is left gasping.
> Economists I admire have
> expressed doubts that the Arrow-Debreu model is an adequate
> answer to certain objections to neoclassical economic theory.
This statement is so utterly vague that I expect absolutely
everyone will agree with it. Maybe you should now declare
victory, or Vietnamize the war or something.
Could be. Relevance?
-- Bill
SUSUPPLY
William B Vogt encourages Hillary Rodham Vienneau with sweet nothings:
>This is all a diversion.....
>First, if what you say in the quoted paragraph is true, it
>utterly devastates your position....
>See, you do know it....
>I express incomprehension....
>Mr Vienneau's posts are chock full of seemingly irrelevant
>text, which day after dreary day never ever connect to
>any point under discussion....
>Again, this is so obviously irrelevant that one is left gasping....
>This statement is so utterly vague that I expect absolutely
>everyone will agree with it. Maybe you should now declare
>victory, or Vietnamize the war or something.
Bill,
I think Vienneau loves it when you talk that way.
Patrick
Robert Vienneau
In article <6jf88o$r...@ds2.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:
> So when I said labor demand curves slope down in the example and Rob
> replied "I do not agree," he was not asserting that he thought he
> had shown otherwise? Please do explain your curious use of declarative
> English sentences, Rob.
Apropos of nothing in particular, Chris wrote, "I think we have agreed
that your first example did not, as claimed, show that labor demand
curves can slope up." I responded, "I did not agree." This, of course,
is not an assertion that labor demand curves can slope up. It is an
assertion that I do not agree with Chris' summary of the discussion.
That's as close as I can come in this thread to Chris' supposed direct
quote.
The point at issue has been how to apply neoclassical concepts to
my example. Chris has continually had difficulty here, and I have
tried to get him to say something sensible. Now when I characterize
his interpretation as reasonable (for a neoclassical economist), Chris
says he should have his degree revoked. Of course, I also draw the
logical conclusion that, if Chris were consistent, he would describe
a (long run?) conditional labor demand curve as sloping up in my example.
[> > At every point along a labor-demand curve, the firms being aggregated ]
[> > would be in equilibrium. That is, if the prices given in drawing the ]
[> > curve did, in fact, hold, the firms would not want to change their ]
[> > decision to hire the amount of labor shown. ]
> >Chris Auld seems to want to think of a labor demand curve as part of
> >an analysis in a partial equilibrium setting. The X axis shows
> >quantity flows - employment - in this case. The idea is if a
> >supply curve [ intersected the labor-demand curve at any given point ]
[> > on the labor demand curve, there would be no forces in the labor ]
[> > market tending to drive the wage away from its value at that point. ]
[> > So that wage could be expected to last for some time. Thus, all ]
[> > the dated quantities of labor in my example would be hired at the ]
[> > same wage. ]
> No.
It's difficult to fathom what Chris thinks he's disagreeing with here.
> A labor demand curve gives the profit-maximizing amount of labor
> hired for a given firm at various wage rates,
That's a reasonable summary of the paragraph Chris deleted.
> all else equal.
That's not contradicted above.
> As I
> explicitly said, it doesn't rely on partial equilibrium in the labor
> market.
So Chris doesn't think equilibria in the labor market traced by
shifting the labor supply function while holding the labor demand
function constant would draw a labor demand function? Or now does
he want to insert his firm into a general equilibrium setting?
> >Now there are no other inputs hired from the market by the vertically
> >integrated firm in my example. So objections that one must not allow
> >the prices of any inputs other than labor to vary in my example are
> >irrelevant.
> Not if we want to discuss labor demand curves. [stupidity deleted]
> Labor demand curves still exist
> in a dynamic setting: change the price of labor at some date t and
> t alone.
So does Chris think I am varying two prices in my example, as he
has previously said? Three? A countably infinite number of prices?
Recall I have tried several times to get Chris to clarify what he
means by "labor" and "wages". And what does Chris imagine the interest
rate is a price of?
> >I have already shown that, given cost minimization, the level
> >of output, and the price of the good being produced; a comparison at the
> >two wages considered in my example of a vertically-integrated firm in
> >equilibrium implies the adoption of a more labor-intensive technique at
> >the higher wage.
>
> Let's rewrite this accurately:
>
> I have already shown that, given cost minimization, the level
> of output, and the price of the good being produced; a comparison of
> two different price vectors with different wages and interest rates
> considered in my example of a vertically-integrated firm in
> equilibrium implies the adoption of a more labor-intensive technique at
> the the price vector which has a higher wage rate.
> Which doesn't show that:
> >another reasonable way to describe this conclusion might be that a
> >conditional labor demand curve slopes up.
Once again, consider the two techniques in my example in the dated
labor quantities representation. Let the price of the corn finally
produced be given. Consider different level of wages. At each wage,
determine the internal rate of return for some technique, say, alpha.
Using that rate of interest, determine which technique has a cheaper
present value. Repeat this calculation for the internal rate of
return of beta.
For a wage between zero and a maximum, both calculations will yield
the same conclusion about which technique is cheaper. The cheaper
technique will be more labor-intensive at the higher of the two
levels of wages I mentioned in my example.
For the firm to actually be profit-maximizing when choosing that
technique, the rate of interest faced by the firm must match the
one used for its calculations of the internal rate of return.
But this is implicit in the assumption that the profit-maximizing
firm will want to produce some finite quantity of corn at the wages
being examined.
> >The reader may recall that a
> >discussion of conditional labor demand curves under that label was
> >introduced into this thread by Chris Auld.
> Rob randomly applies the caveat "for a given output" and therefore
> it is never clear whether he is talking about labor demand curves or
> conditional labor demand curves. When he does invoke that caveat, he
> is talking about the latter regardless of what "label" he wants to
> apply to the concept.
But Chris' "accurate" rewording includes "given...the level of output."
An uncharitable reader might say Chris is conceding that conditional
labor demand curves slope up.
Robert Vienneau
In article <kpKpgi200...@andrew.cmu.edu>, William B Vogt
<wili...@andrew.cmu.edu> wrote:
> Excerpts from netnews.talk.politics.libertarian:
> 14-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> > My question is why do you want to call some symbol in your
> > proof "labor" and another symbol "wages"?
> Because I am interested, in general at least, in modelling
> objects in the real world, namely labor and wages.
My turn. I express incomprehension. Your model is either of all
consumer goods being produced directly and exclusively from unproduced
natural reasources and labor or of intertemporal equilibrium.
Neither model seems applicable to the U.S. economy.
Are you aware of Hahn's opinion of the purpose of the Arrow-Debreu
model? It's not to describe economies at some level of abstraction,
but a thought experiment illustrating a case under which markets
behave ideally, in some sense which I think of little interest.
Anyways you're very vague about how to map those objects into your
symbols. In fact, I had to state two different set of assumptions
to add on to yours in order for your proof to make sense.
> > I have pointed out an interpretation where your proof makes sense.
> > All the inputs hired by the firm are hired at the same time. There
> > are no inputs produced by labor at an earlier date. [...]
> > My interpretation that all the inputs considered
> > in your proof are hired at the same date as the output is produced
> > is further supported by the fact that you don't explicitly say
> > anything about present value calculations.
> This is all a diversion.
Do you agree that I have stated one set of additional sufficient
assumptions for your proof?
> As you know, the goods in neoclassical
> models can be indexed both by their physical characteristics and
> by their dates...
> So, the proof applies to a variation in the
> wage of one type of labor at one time at one location.
And that's a statement of another set of additional sufficient
assumptions for your proof.
> Either interpretation is just fine. One beauty of the neoclassical
> framework is that it appies to static cases (the interpretation
> you prefer above), to dynamic cases, to case differentiated by
> location, and to stochastic cases. In short, I have not assumed
> a static model. Furthermore, NPV calculations only make sense
> under fairly restrictive assumptions (the interest rate is the
> same for all goods); whereas, the framework of my proof makes
> sense in more general cases (e.g. when the interest rate is
> different for different goods).
That's open to debate.
> > Since dated labor quantities are different inputs in your symbols,
> > my example has an infinite number of inputs. The above has merely
> > rephrased some points in prior posts.
> First, if what you say in the quoted paragraph is true, it
> utterly devastates your position, since labor demand curves
> are defined by changing one and not an infinite number of
> prices.
Sometimes they are, where prices are defined as in the Arrow-Debreu
model. What do you think neoclassical economists between
1870 and Lindahl and Hayek's 1920's formulation of intertemporal
equilibrium meant by factor demand functions?
So when you teach introductory economics, you don't give the
usual argument about why minimum wages higher than a market-clearing
wage lead to unemployment? You're clear about what you're
claiming when drawing labor supply and demand curves?
> Second, your example has a static interpretation (and I mapped
> your example into the static neoclassical framework long ago).
The labels "static" and "dynamic" are yours.
> The fact that you choose to call it dynamic is beside the point.
The fact that it doesn't fit into the "static" framework is part of
the point.
> > There is a different interpretation of your symbols, [...]
> > that is Debreu's intertemporal
> > equilibrium.[...] The prices of all commodities refer to one point
> > in time. Commodities are all traded on forward markets. At the beginning
> > of time, where endowments are given, all agents enter contracts to
> > deliver certain goods and services on various dates in the future.
> > The payments, however, are all made instantaneously.
>
> See, you do know it.
>
> > Under this interpretation, your proof compares equilibria of
^^^^^^^^^^^^^
> > the firm - in the very limited theory of the firm treated in our
^^^^^^^^
> > discussion - that faces some odd circumstances. All prices are the
> > same in the two equilibria, except the price of one particular dated
> ^^^^^^^^^^^^^^
>
> > labor quantity.
> We don't compare equilibria in the neoclassical theory of the
> firm, we compare the firm's response to different price
> vectors.
Whatever. I long ago quoted Debreu's "equilibrium production of the
jth producer relative to p."
> > This, too, is inapplicable to my example.
> I express incomprehension. The challenge was to exhibit
> assumptions under which labor demand curves slope down.
> This has been done.
And, I agree that if you had stated all of your assumptions, your
conclusion was true.
[...]
> > I have not fully absorbed these papers - in fact haven't even
> > fully read them yet. Nevertheless, I think they are an important
> > move in ongoing debates. I also think questions about how this
> > behavior relates to uniqueness and stability concerns might be
> > important.
>
> Could be. Relevance?
Motivation for my example. To point out one discussion about
how my example relates to intertemporal equilibrium. To point
out that your and Markku's understanding of my example seems
flawed. To inform the reader of contemporary debates over
the adequacy of the theory of employment in the setting of the
Arrow-Debreu equilibrium model. To wonder about an equilibrium
where prices and quantities change endogeneously. To question
whether substitution behavior characterizes the Arrow-Debreu
model. To wonder if some sort of long period labor demand curve
might, indeed, slope up.
William B Vogt
Excerpts from netnews.talk.politics.libertarian:
15-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> In article <kpKpgi200...@andrew.cmu.edu>, William B Vogt
> <wili...@andrew.cmu.edu> wrote:
>
> > Excerpts from netnews.talk.politics.libertarian:
> > 14-May-98 Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
>
> > > My question is why do you want to call some symbol in your
> > > proof "labor" and another symbol "wages"?
>
> > Because I am interested, in general at least, in modelling
> > objects in the real world, namely labor and wages.
>
> My turn. I express incomprehension. Your model is either of all
> consumer goods being produced directly and exclusively from unproduced
> natural reasources and labor or of intertemporal equilibrium.
> Neither model seems applicable to the U.S. economy.
What model? Labor demand is one building block
which can be used in a number of models. I haven't
given a model, since, for the umpteenth time, labor
demand is not defined in the context of any particular
market model, it is defined in the context of a single
firm facing fixed prices --- where those prices come
from is a topic which may be modelled in many different
ways.
> Are you aware of Hahn's opinion of the purpose of the Arrow-Debreu
> model? It's not to describe economies at some level of abstraction,
> but a thought experiment illustrating a case under which markets
> behave ideally, in some sense which I think of little interest.
Yes, I heard him speak on a related issue. His articulated
view was that UK and US economists differ on whether or not
neoclassical theory should be taken as an approximation to
observed reality, and whether predictive power is a useful
criterion in evaluating theory. He argued for the UK position, and I
was not persuaded. Though I don't recall the substance of his
position well at all, I *think* it revolved around
the usual "I don't think the assumptions are satisfied" -
type statements.
> Anyways you're very vague about how to map those objects into your
> symbols. In fact, I had to state two different set of assumptions
> to add on to yours in order for your proof to make sense.
Rubbish. Mathematics "makes sense" on its own terms. Whether
there is a practical application for any particular mathematical
object is a separate quesion. The assumptions I gave were
sufficient, no extra ones are needed. You have yet to do anything
other than repetatively assert the contrary.
> > > I have pointed out an interpretation where your proof makes sense.
> > > All the inputs hired by the firm are hired at the same time. There
> > > are no inputs produced by labor at an earlier date. [...]
> > > My interpretation that all the inputs considered
> > > in your proof are hired at the same date as the output is produced
> > > is further supported by the fact that you don't explicitly say
> > > anything about present value calculations.
>
> > This is all a diversion.
>
> Do you agree that I have stated one set of additional sufficient
> assumptions for your proof?
I neither agree nor disagree.
> > As you know, the goods in neoclassical
> > models can be indexed both by their physical characteristics and
> > by their dates...
> > So, the proof applies to a variation in the
> > wage of one type of labor at one time at one location.
>
> And that's a statement of another set of additional sufficient
> assumptions for your proof.
More rubbish. You are evincing an inability to tell the
difference between the truth of an abstract proposition
and the mapping between the proposition and observed
reality.
> > > Since dated labor quantities are different inputs in your symbols,
> > > my example has an infinite number of inputs. The above has merely
> > > rephrased some points in prior posts.
>
> > First, if what you say in the quoted paragraph is true, it
> > utterly devastates your position, since labor demand curves
> > are defined by changing one and not an infinite number of
> > prices.
>
> Sometimes they are, where prices are defined as in the Arrow-Debreu
> model. What do you think neoclassical economists between
> 1870 and Lindahl and Hayek's 1920's formulation of intertemporal
> equilibrium meant by factor demand functions?
No idea.
> So when you teach introductory economics, you don't give the
> usual argument about why minimum wages higher than a market-clearing
> wage lead to unemployment? You're clear about what you're
> claiming when drawing labor supply and demand curves?
Yes, I am always clear about what assumptions I am making.
No, none of this is at all relevant to the point at hand.
> > Second, your example has a static interpretation (and I mapped
> > your example into the static neoclassical framework long ago).
>
> The labels "static" and "dynamic" are yours.
>
> > The fact that you choose to call it dynamic is beside the point.
>
> The fact that it doesn't fit into the "static" framework is part of
> the point.
Endless, repetative assertion without argument is not convincing.
I mapped the example into the static framework. You ignored
it.
> > We don't compare equilibria in the neoclassical theory of the
> > firm, we compare the firm's response to different price
> > vectors.
>
> Whatever. I long ago quoted Debreu's "equilibrium production of the
> jth producer relative to p."
1959 != 1998. Furthermore, I have not read Debreu recently
enough to recall context. I bet that "equilibrium relative
to p" != "equilibrium", however. I'd even wager that
"equilibrium relative to p" is what is currently called
the neoclassical theory of the firm (it sure sounds like
it).
> > > This, too, is inapplicable to my example.
>
> > I express incomprehension. The challenge was to exhibit
> > assumptions under which labor demand curves slope down.
> > This has been done.
>
> And, I agree that if you had stated all of your assumptions, your
> conclusion was true.
I stated all of my assumptions. Again, endless repetition is
a poor substitute for argument. If you think there is a
missing assumption, prove it.
> > > I have not fully absorbed these papers - in fact haven't even
> > > fully read them yet. Nevertheless, I think they are an important
> > > move in ongoing debates. I also think questions about how this
> > > behavior relates to uniqueness and stability concerns might be
> > > important.
> >
> > Could be. Relevance?
>
> Motivation for my example. To point out one discussion about
> how my example relates to intertemporal equilibrium. To point
> out that your and Markku's understanding of my example seems
> flawed. To inform the reader of contemporary debates over
> the adequacy of the theory of employment in the setting of the
> Arrow-Debreu equilibrium model. To wonder about an equilibrium
> where prices and quantities change endogeneously. To question
> whether substitution behavior characterizes the Arrow-Debreu
> model. To wonder if some sort of long period labor demand curve
> might, indeed, slope up.
Except for the last sentence, this is an admission of
the irrelevance of the point. The last sentence is merely
a cloud of gas, since "some sort of long period labor demand
curve" is safely undefined.
-- Bill
Robert Vienneau
William B Vogt <wili...@andrew.cmu.edu> wrote:
> Robert Vienneau:
> > William B Vogt <wili...@andrew.cmu.edu> wrote:
> > > Robert Vienneau:
> > > > My question is why do you want to call some symbol in your
> > > > proof "labor" and another symbol "wages"?
> > > Because I am interested, in general at least, in modelling
> > > objects in the real world, namely labor and wages.
> > My turn. I express incomprehension. Your model is either of all
> > consumer goods being produced directly and exclusively from unproduced
> > natural reasources and labor or of intertemporal equilibrium.
> > Neither model seems applicable to the U.S. economy.
> What model? Labor demand is one building block
> which can be used in a number of models. I haven't
> given a model, since, for the umpteenth time, labor
> demand is not defined in the context of any particular
> market model, it is defined in the context of a single
> firm facing fixed prices --- where those prices come
> from is a topic which may be modelled in many different
> ways.
My example can be viewed as of a single firm facing given
prices. My example is a building block which can be used in
a number of models. I've mentioned two.
One is of an equilibrium in an overlapping generations framework in
which population, tastes, and technology are given. One can consider
different values of a parameter in the utility function. The
equilibrium in which profit-maximizing firms adopt one of the
techniques in my example is thereby transformed to an equilibrium
in which profit-maximizing firms adopt the other technique. I
brought this up to show how my example can serve as a building
block in a comparative statics exercise, in contradiction to your
apparent belief that this cannot be done:
"The exogenous variables of a GE model are preferences,
endowments, and technology. So, the only comparative statics
that can be done are on preferences, endowments, and technology.
What Mr Vienneau does in his example is not a comparative statics
exercise, since there can be no comparative statics on an
endogenous variable (price of labor)."
The other model I mentioned was Schefold's claim that one can construct
an intertemporal equilibrium path leading from one equilibrium of
the firm like one of those in my example to the other equilibrium
of the firm in my example. This use of my example as a building
block in another model is another contradiction of your and Markku's
misinterpretation of my example:
Markku:
"Second "but" comes from reading Rob's posts, where he seems [I don't
claim he commits this mistake, I haven't read his post that carefully]
to confuse statements concerning two quite different concepts:
downward-sloping marginal willingness to pay for labor on one hand,
and, on the other hand, the quite usual possibility in GE that there
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
is an equilibrium where both the wage and the amount of labour hired
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
are higher than in some other equilibrium."
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (Underlining mine - RV)
William:
Yes, I think this is precisely the mistake he is making. However,
he seems not to agree.
Markku's characterization is mistaken. My posts show that I
am quite aware that "labor demand is one building block
which can be used in a number of models." Furthermore, in both my
detailed expositions of my example in this thread I mentioned
neither the supply of labor nor the demand for consumer goods.
> More rubbish. You are evincing an inability to tell the
> difference between the truth of an abstract proposition
> and the mapping between the proposition and observed
> reality.
The terms "wages" and "employment" should not appear with any meaning
in the abstract propositions in your proof. The use of these
terms in a meaningful way requires a mapping between the terms in your
proof and something like a model in the sense used in meta-mathematics.
I did not bring up anything about "reality." Your insistence
that these terms relate to "reality," while refusing to elucidate
any possible relationship, is neither persuasive nor consistent.
> > > > Since dated labor quantities are different inputs in your symbols,
> > > > my example has an infinite number of inputs. The above has merely
> > > > rephrased some points in prior posts.
> > > First, if what you say in the quoted paragraph is true, it
> > > utterly devastates your position, since labor demand curves
> > > are defined by changing one and not an infinite number of
> > > prices.
> > Sometimes they are, where prices are defined as in the Arrow-Debreu
> > model. What do you think neoclassical economists between
> > 1870 and Lindahl and Hayek's 1920's formulation of intertemporal
> > equilibrium meant by factor demand functions?
> No idea.
I don't claim to be sure about this as a matter of history. But
suppose prices were such that the quantity supplied was equal to
the quantity demanded in all (spot) markets. Further suppose
endowments of produced goods were adjusted to this level of
production. As I understand it, neoclassical economists of that era and
many today would say there existed no endogenous forces tending to
change prices and quantities. That means the wages in this
equilibrium would persist.
This lack of endogeneous forces to change quantities implies that,
under competitive conditions, the same rate of normal profits or interest
would be earned in all industries. This, then, is a condition of the
equilibrium of the firm considered in constructing a long-period
labor demand function.
> > > Second, your example has a static interpretation (and I mapped
> > > your example into the static neoclassical framework long ago).
> > The labels "static" and "dynamic" are yours.
> > > The fact that you choose to call it dynamic is beside the point.
> > The fact that it doesn't fit into the "static" framework is part of
> > the point.
> Endless, repetative assertion without argument is not convincing.
> I mapped the example into the static framework. You ignored
> it.
I don't see why you are arguing. We are agreed that my example, as I
presented it, is not an example consistent with what you are calling
the static framework, are we not? And my presentation of how to
represent the techniques in my example with dated labor quantities
is partially an answer to your mapping. That is, I showed how
to correctly relate my example to netput vectors.
> > > We don't compare equilibria in the neoclassical theory of the
> > > firm, we compare the firm's response to different price
> > > vectors.
> > Whatever. I long ago quoted Debreu's "equilibrium production of the
> > jth producer relative to p."
> 1959 != 1998.
Relevance?
> Furthermore, I have not read Debreu recently
> enough to recall context. I bet that "equilibrium relative
> to p" != "equilibrium", however. I'd even wager that
> "equilibrium relative to p" is what is currently called
> the neoclassical theory of the firm (it sure sounds like
> it).
And how is my example not an equilibrium of the firm?
> > > > I have not fully absorbed these papers - in fact haven't even
> > > > fully read them yet. Nevertheless, I think they are an important
> > > > move in ongoing debates. I also think questions about how this
> > > > behavior relates to uniqueness and stability concerns might be
> > > > important.
> > > Could be. Relevance?
> > Motivation for my example. To point out one discussion about
> > how my example relates to intertemporal equilibrium. To point
> > out that your and Markku's understanding of my example seems
> > flawed. To inform the reader of contemporary debates over
> > the adequacy of the theory of employment in the setting of the
> > Arrow-Debreu equilibrium model. To wonder about an equilibrium
> > where prices and quantities change endogeneously. To question
> > whether substitution behavior characterizes the Arrow-Debreu
> > model. To wonder if some sort of long period labor demand curve
> > might, indeed, slope up.
> Except for the last sentence, this is an admission of
> the irrelevance of the point. The last sentence is merely
> a cloud of gas, since "some sort of long period labor demand
> curve" is safely undefined.
In neoclassical theory under competitive conditions, the wage
equals the value of the marginal product of labor along the
labor demand curve. In the long period, the rate of interest
is given when defining the value of the marginal product of
labor (if the wage is not given). Unless the labor demand
curve is horizontal, wages will be different at different
locations on the labor demand curve. Therefore, the rate of
interest, too, will be different at different locations on the
labor demand function. Consider my example in the dated labor
quantities representation.
"It would thus appear that the assumption of a 'neoclassical
technology', i.e. one which excludes reswitching and perverse
Wicksell effects, is necessary not for the existence of an
intertemporal equilibrium but for the possibility of
interpreting it as the explanation of distribution in a
long-period equilibrium by affording the possibility of a
transition towards it..."
The essential point of the criticism concerns the factor demand
curves. The discovery that factor demand curves may be positively
sloped in the relevant range, not negatively as is necessary for
stability, have not impressed neoclassical theorists that much
because, they say, sufficiently general proofs for stability are
not available anyway, not even in pure exchange economics...
Convincing conditions of sufficient generality which ensure a
well-behaved technology have not been proposed. We therefore should
not seek for those special assumptions under which the neoclassical
theory might work but for a different theory of distribution and
employment..."
-- Bertram Schefold
The coherence of neoclassical theory has been challenged. The response
of many economists seems to be to support misrepresentations of the
challenge by a refusal to examine the literature, even to the extent
of denying the existence of the most contemporary literature.
It is my opinion that wages and employment are not determined by the
interaction of supply and demand in the labor market, even in a
general equilibrium sense.
JMH
Robert Vienneau wrote:
. . .
> In neoclassical theory under competitive conditions, the wage
> equals the value of the marginal product of labor along the
> labor demand curve. In the long period, the rate of interest
> is given when defining the value of the marginal product of
> labor (if the wage is not given). Unless the labor demand
> curve is horizontal, wages will be different at different
> locations on the labor demand curve. Therefore, the rate of
> interest, too, will be different at different locations on the
> labor demand function. Consider my example in the dated labor
> quantities representation.
I think this is incorrect Rob.
At all points on the labor demand curve the wage (and quantity)
differs. At all points on the labor demand curve the interest
rate is held constant so not all points on the labor demand
curve will be equilibrium points and so will not be selected
by the firm.
If you allow the interest rate to change then you are
jumping from one demand curve to another.
JMH
jim blair
Frank Mayer wrote:
>
> Robert, do you believe that labor demand curves can slope up? A simple
> yes/no answer will suffice. No need for further explanation at this
> point.
Hi,
Actual case: I read about it in the newspapers, so it must be true ;-).
A guy named Jack offered to walk dogs for 50 cents an hour. Very few dog
owners were interested. So he changed his name to Jacques, and raised is
rate to $5 an hour. So many people wanted him to walk their dog that he
was soon hiring assistants and started a franchise. (this was in
Mahattan
or maybe Beverly Hills--one of those places where they have more dollars
than cents)
So this example, like that of Robert Vienneau, shows that a higher
legal minimum wage can result in higher employment!!
William B Vogt
Excerpts from netnews.sci.econ: 18-May-98
> William B Vogt <wili...@andrew.cmu.edu> wrote:
>
> > Robert Vienneau:
>
> > > William B Vogt <wili...@andrew.cmu.edu> wrote:
>
> > > > Robert Vienneau:
>
> > > > > My question is why do you want to call some symbol in your
> > > > > proof "labor" and another symbol "wages"?
>
> > > > Because I am interested, in general at least, in modelling
> > > > objects in the real world, namely labor and wages.
>
> > > My turn. I express incomprehension. Your model is either of all
> > > consumer goods being produced directly and exclusively from unproduced
> > > natural reasources and labor or of intertemporal equilibrium.
> > > Neither model seems applicable to the U.S. economy.
>
> > What model? Labor demand is one building block
> > which can be used in a number of models. I haven't
> > given a model, since, for the umpteenth time, labor
> > demand is not defined in the context of any particular
> > market model, it is defined in the context of a single
> > firm facing fixed prices --- where those prices come
> > from is a topic which may be modelled in many different
> > ways.
>
> My example can be viewed as of a single firm facing given
> prices. My example is a building block which can be used in
> a number of models. I've mentioned two.
So what? Do you now claim that the statements "All labor
demand curves are building blocks" is equivalent to the
statement "All building blocks are labor demand curves?"
I suspect you have lost track of the point.
> One is of an equilibrium in an overlapping generations framework in
> which population, tastes, and technology are given. One can consider
> different values of a parameter in the utility function. The
> equilibrium in which profit-maximizing firms adopt one of the
> techniques in my example is thereby transformed to an equilibrium
> in which profit-maximizing firms adopt the other technique. I
> brought this up to show how my example can serve as a building
> block in a comparative statics exercise, in contradiction to your
> apparent belief that this cannot be done:
>
> "The exogenous variables of a GE model are preferences,
> endowments, and technology. So, the only comparative statics
> that can be done are on preferences, endowments, and technology.
> What Mr Vienneau does in his example is not a comparative statics
> exercise, since there can be no comparative statics on an
> endogenous variable (price of labor)."
What you did is not a comparative statics exercise.
What you did is not an analysis of a labor demand curve.
Your errors arise from a lack of understanding of
definitions. Given that you don't understand the definitions
of the words most economists use, the fact that you believe
plainly true statements to be false can be understood.
Do you have any argument at all in support of your assertion
that Marku's characterization is mistaken?
> > More rubbish. You are evincing an inability to tell the
> > difference between the truth of an abstract proposition
> > and the mapping between the proposition and observed
> > reality.
>
> The terms "wages" and "employment" should not appear with any meaning
> in the abstract propositions in your proof. The use of these
> terms in a meaningful way requires a mapping between the terms in your
> proof and something like a model in the sense used in meta-mathematics.
> I did not bring up anything about "reality." Your insistence
> that these terms relate to "reality," while refusing to elucidate
> any possible relationship, is neither persuasive nor consistent.
Labor demand curves *must* slope down. This is true
under the follwing assumptions:
1. Prices are fixed from the point of view of the firm
2. Firm's profit maximize
3. The only price varied in the construction of the labor
demand curve is the price of labor.
Everything in the above has a precise mathematical definition.
Using those definitions, the statement is true, and I have
posted a proof, which is *still* not disputed.
The proof is correct, hence both persuasive and consistent.
I have, of course, at no time "[insisted] that these terms
relate to 'reality'" I have, of course, repeatedly, explicitly,
and carefully expressed the view that the truth of the proposition
that labor demand curves slope down exists independently of
observed reality. I have repeatedly pointed out that any
relevance of this fact to the real world is a separate matter.
Finally, although I did bring up reality, it was absolutely,
postively, unambiguously, and obviously NOT as part of any
argument of mine for the truth of the proposition that labor
demand curves slope down. It was in response to your (irrelevant)
question as to my motivation in examining the statement
"labor demand curves *must* slope down."
So, I partially retract what I said. It could be that you
can't tell the difference between the truth of an abstract
proposition and the question of its applicability to observed
reality or it could be that you think my motives are
relevant to the truth of propositions I post proofs of.
> I don't see why you are arguing. We are agreed that my example, as I
> presented it, is not an example consistent with what you are calling
> the static framework, are we not?
No. You must have misread what I said. I said *if* you are
right about this (changing and infinite # of prices),
it vitiates your position.
> And my presentation of how to
> represent the techniques in my example with dated labor quantities
> is partially an answer to your mapping. That is, I showed how
> to correctly relate my example to netput vectors.
I don't recall you doing so. Your example clearly fits the
standard static framework. *You* choose to interpret it
as representing an endlessly repeated sequence of essentially
static choices by the firm. Prices do not change between periods.
Production technology does not change between periods.
There is no dependence of future returns of the firm on present
decisions by the firm. Since there is nothing in your
example to make the firm's problem interestingly dynamic, and
since all the behavior of the firm is summarized by the static
model, the model is static.
> > > > We don't compare equilibria in the neoclassical theory of the
> > > > firm, we compare the firm's response to different price
> > > > vectors.
>
> > > Whatever. I long ago quoted Debreu's "equilibrium production of the
> > > jth producer relative to p."
>
> > 1959 != 1998.
>
> Relevance?
>
> > Furthermore, I have not read Debreu recently
> > enough to recall context. I bet that "equilibrium relative
> > to p" != "equilibrium", however. I'd even wager that
> > "equilibrium relative to p" is what is currently called
> > the neoclassical theory of the firm (it sure sounds like
> > it).
>
> And how is my example not an equilibrium of the firm?
Labor demand curves are derived from (what is commonly
called) the neoclassical theory of the firm. This theory
involves comparing the behavior of firms at different
(fixed from their perspective) price vectors. Labor demand
curves, in particular, are derived by moving only the price
of labor, keeping other prices fixed.
When you move more than one price, and examine the reaction
of the firm, you are not tracing out a labor demand curve.
Equilibrium analysis, whether partial or general, involves
"solving" for prices and quantities.
It may be that Debreu used a different notational convention
to distinguish between the two things. However, it is not
currently the notational convention to call the neoclassical
theory of the firm "equilibrium of the firm ..."
Regardless of the notation, it is clear enough that the two
concepts are distinct. Your example, regarded only as a
theory of the behavior of the firm, moves more than one
price. Your example (if we ignore the incoherence involved
in performing comparative statics by moving endogenous
variables), regarded as a comparative statics exercise on only
the price of labor, is an equilibrium analysis and, therefore,
not relevant to the question of labor demand curves. Either
way, your example is not relevant to labor demand curves. It
is only by chattering back and forth between the two
interpretations and periodically emitting fog that any
appearance of a contradiction to the fact of labor demand
curves' downward slope is created.
> The coherence of neoclassical theory has been challenged. The response
> of many economists seems to be to support misrepresentations of the
> challenge by a refusal to examine the literature, even to the extent
> of denying the existence of the most contemporary literature.
This becomes tiring. Although the "coherence" of neoclassical
theory has been challenged, it has been challenged (here) in
a way which demonstrates a lack of understanding of key
concepts under challenge.
The statement "labor demand curves *must* slope down," (under
the assumptions I posted) is not a statement on which
reasonable disagreement is possible. It is true the way
statements like "stricly monotonic functions of the reals
into the reals are invertible on their range" or
"the rational numbers are dense in the reals" are true. And,
like the statements about the reals, their applicability
to any particular situation is a separate issue.
-- Bill
Robert Vienneau
No. I claim that your statement "Labor demand is one building
block which can be used in a number of models" does not provide
a characteristic of your analysis that distinguishes it from
mine.
> > One is of an equilibrium in an overlapping generations framework in
> > which population, tastes, and technology are given. One can consider
> > different values of a parameter in the utility function. The
> > equilibrium in which profit-maximizing firms adopt one of the
> > techniques in my example is thereby transformed to an equilibrium
> > in which profit-maximizing firms adopt the other technique. I
> > brought this up to show how my example can serve as a building
> > block in a comparative statics exercise, ...
> What you did is not a comparative statics exercise.
Non-responsive.
How is what I am outling above not a comparative statics
excerise? One takes the population as given in an overlapping
generations framework. One takes the technology as given in
my example. Dated quantities of corn are the only consumer
goods in the example. Consumers maximize utility, including
intertemporally. Firms maximize profits or, equivalently,
minimize costs. Given technology and preferences, I solve
for equilibrium prices and quantities. I then consider
variations in a parameter in the utility function used
to specify preferences. I consider how one equilibrium
varies due to this variation in preferences. I find
a region where both wages and the quantity of labor the
firms want to hire increase together as this parameter varies.
(When I talk about variation here, I am only talking about
shapes of certain mathematical functions, not movements
in time.) As I have pointed out before, a full presentation
of this analysis is at:
ftp://csf.colorado.edu/econ/authors/Vienneau.Robert/Sraffa3.pdf
> What you did is not an analysis of a labor demand curve.
Whatever. Please explain how a long run labor demand curve can
be anything but horizontal at a wage equal to the value of the
marginal product of labor, as determined by the given interest
rate. Note that if the wage is above this value, the firms will
be making losses, and being profit-maximizing, will not choose
to produce or hire any workers. If the wage is below this
value, profit-maximizing firms will be making pure economic
profits. Therefore the firms will prefer to expand production
above any finite value and will hire an infinite number of
workers at any lower wage.
The question is also addressed to you, John Hall, if you choose
to answer. If I am permitted to allow the interest rate to
vary, I don't see any problem of characterizing my analysis
as characterizing two points on a conditional labor demand
curve. I do see a problem if I extend my example to
characterize vertically integrated firms producing more
than one type of consumption good and am restricted to
considering all non-numeraire prices of consumption goods
as fixed.
> Your errors arise from a lack of understanding of
> definitions.
No. My "errors" arise from understanding that there is no
coherent long run neoclassical theory of value and distribution.
> > The other model I mentioned was Schefold's claim that one can construct
> > an intertemporal equilibrium path leading from one equilibrium of
> > the firm like one of those in my example to the other equilibrium
> > of the firm in my example. This use of my example as a building
> > block in another model is another contradiction of your and Markku's
> > misinterpretation of my example:
> > Markku:
> > "Second "but" comes from reading Rob's posts, where he seems [I don't
> > claim he commits this mistake, I haven't read his post that carefully]
> > to confuse statements concerning two quite different concepts:
> > downward-sloping marginal willingness to pay for labor on one hand,
> > and, on the other hand, the quite usual possibility in GE that there
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> > is an equilibrium where both the wage and the amount of labour hired
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> > are higher than in some other equilibrium."
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (Underlining mine - RV)
> > William:
> > Yes, I think this is precisely the mistake he is making. However,
> > he seems not to agree.
> > Markku's characterization is mistaken...
> Do you have any argument at all in support of your assertion
> that Marku's characterization is mistaken?
Yes. I understand Markku to be referring to multiple equilibria in
some sort of general equilibrium model. My argument against this
characterization of my example is quoted in your post, namely the
outline of two uses of my example. Keep on pretending it is not there
all you like.
> > > More rubbish. You are evincing an inability to tell the
> > > difference between the truth of an abstract proposition
> > > and the mapping between the proposition and observed
> > > reality.
> > The terms "wages" and "employment" should not appear with any meaning
> > in the abstract propositions in your proof. The use of these
> > terms in a meaningful way requires a mapping between the terms in your
> > proof and something like a model in the sense used in meta-mathematics.
> > I did not bring up anything about "reality." Your insistence
> > that these terms relate to "reality," while refusing to elucidate
> > any possible relationship, is neither persuasive nor consistent.
> Labor demand curves *must* slope down. This is true
> under the follwing assumptions:
> 1. Prices are fixed from the point of view of the firm
> 2. Firm's profit maximize
> 3. The only price varied in the construction of the labor
> demand curve is the price of labor.
> Everything in the above has a precise mathematical definition.
Oh, so your proof relies on additional assumptions? But of
course, I outlined two sets of definitions where your proof
holds. (Labor is one of a set of non-produced inputs used
to directly produce only consumer goods and intertemporal
equilibrium.) Perhaps you might want to clarify what you understand
meta-mathematicans to mean by "truth" or what you mean by
definitions.
> Using those definitions, the statement is true, and I have
> posted a proof, which is *still* not disputed.
Your point?
> The proof is correct, hence both persuasive and consistent.
Your confusion that I have been criticizing your proof by
saying it does not relate to "reality" is what is unpersuasive.
> I have, of course, at no time "[insisted] that these terms
> relate to 'reality'" I have, of course, repeatedly, explicitly,
> and carefully expressed the view that the truth of the proposition
> that labor demand curves slope down exists independently of
> observed reality. I have repeatedly pointed out that any
> relevance of this fact to the real world is a separate matter.
This addresses no point I made.
> Finally, although I did bring up reality, it was absolutely,
> postively, unambiguously, and obviously NOT as part of any
> argument of mine for the truth of the proposition that labor
> demand curves slope down.
Right, you were making an irrelevant comment.
> It was in response to your (irrelevant)
> question as to my motivation in examining the statement
> "labor demand curves *must* slope down."
I agree you misread me as asking about motivation, not
meaning.
> So, I partially retract what I said. It could be that you
> can't tell the difference between the truth of an abstract
> proposition and the question of its applicability to observed
> reality or it could be that you think my motives are
> relevant to the truth of propositions I post proofs of.
Or it could be I have a different understanding of conventional
views about the truth of logical propositions.
> > I don't see why you are arguing. We are agreed that my example, as I
> > presented it, is not an example consistent with what you are calling
> > the static framework, are we not?
> No. You must have misread what I said. I said *if* you are
> right about this (changing an infinite # of prices),
> it vitiates your position.
I like your willingness to take a definition position on what
components of netput vectors can be non-zero in my example. You
do remember that you politely answered my query about whether
there was a concept of long-run labor demand curves in neoclassical
theory?
> > And my presentation of how to
> > represent the techniques in my example with dated labor quantities
> > is partially an answer to your mapping. That is, I showed how
> > to correctly relate my example to netput vectors.
> I don't recall you doing so. Your example clearly fits the
> standard static framework. *You* choose to interpret it
> as representing an endlessly repeated sequence of essentially
> static choices by the firm.
Maybe you should research what are netput vectors in intertemporal
equilibrium some more. Intermediate goods that are produced only
to be used in further production do not have nonzero values in
a "production plan". I don't think goods used exclusively as
produced means of production need to be placeholders in netput
vectors. Thus dated quantities of steel in my example do not
have "prices" in the formal theory which can be interpreted as an
intertemporal equilibrium. A "production plan" is jargon introduced by
Debreu in the usual interpretations of his formalism.
> Prices do not change between periods.
> Production technology does not change between periods.
> There is no dependence of future returns of the firm on present
> decisions by the firm. Since there is nothing in your
> example to make the firm's problem interestingly dynamic, and
> since all the behavior of the firm is summarized by the static
> model, the model is static.
So you retract your charactization of that presentation of my model
as being "dynamic"?
> > > > > We don't compare equilibria in the neoclassical theory of the
> > > > > firm, we compare the firm's response to different price
> > > > > vectors.
> > > > Whatever. I long ago quoted Debreu's "equilibrium production of the
> > > > jth producer relative to p."
> > > Furthermore, I have not read Debreu recently
> > > enough to recall context. I bet that "equilibrium relative
> > > to p" != "equilibrium", however. I'd even wager that
> > > "equilibrium relative to p" is what is currently called
> > > the neoclassical theory of the firm (it sure sounds like
> > > it).
> > And how is my example not an equilibrium of the firm?
> Labor demand curves are derived from (what is commonly
> called) the neoclassical theory of the firm. This theory
> involves comparing the behavior of firms at different
> (fixed from their perspective) price vectors.
Nonresponsive.
> Labor demand
> curves, in particular, are derived by moving only the price
> of labor, keeping other prices fixed.
Whatever. Continually nonresponsive.
> When you move more than one price, and examine the reaction
> of the firm, you are not tracing out a labor demand curve.
Are you claiming that the interest rate is a price? Do you
want to answer the question that Chris has not yet answered -
What is the interest rate the price of?
[Blah, blah, blah]
> > The coherence of neoclassical theory has been challenged. The response
> > of many economists seems to be to support misrepresentations of the
> > challenge by a refusal to examine the literature, even to the extent
> > of denying the existence of the most contemporary literature.
> This becomes tiring. Although the "coherence" of neoclassical
> theory has been challenged, it has been challenged (here) in
> a way which demonstrates a lack of understanding of key
> concepts under challenge.
And it has been "answered" by evasion and misrepresentation of
the challenge.
> The statement "labor demand curves *must* slope down," (under
> the assumptions I posted) is not a statement on which
> reasonable disagreement is possible. It is true the way
> statements like ...
> "the rational numbers are dense in the reals" are true.
It hardly helps to make an analogy to a statement where it
is not clear what it means for the statement to be true. For
example, Godel took a platonic interpretation of math, and
it is traditional in metamathematics to use models to
explain meaning.
Under what assumptions must long run labor demand curves slope
down?
> And,
> like the statements about the reals, their applicability
> to any particular situation is a separate issue.
Relevance?
Markku Stenborg ®
On Tue, 19 May 1998 12:44:25 -0700, jim blair
<jeb...@facstaff.wisc.edu> wrote:
[snip]
> So this example, like that of Robert Vienneau, shows that a higher
> legal minimum wage can result in higher employment!!
Umm, your fine example shows that a fancy foreign name can result in
higher employment.
--
© Markku Stenborg
OFC & Turku Biz School
ROT13ed for the hell of it:
zne...@hgh.sv <- out-of-order for the time being
znexxh....@svabsp.sv
Markku Stenborg ®
On Tue, 19 May 1998 16:10:24 -0400, William B Vogt
<wili...@andrew.cmu.edu> wrote:
[snip]
> Labor demand curves *must* slope down. This is true
> under the follwing assumptions:
>
> 1. Prices are fixed from the point of view of the firm
> 2. Firm's profit maximize
> 3. The only price varied in the construction of the labor
> demand curve is the price of labor.
Just in case: Labor demand curves *must* slope down even under much
less restrictive assumptions. 1 and 2 are far from necessary conds and
3 is just the defn of partial derivative. All that we need is that
firms have some idea of cost minimization and do not consume labor per
se but uses it as a factor of production (or, I guess, do not put too
much weight on labor consumption).
If 1 above is not true, the firm obviously does not have a demand
curve -- the *defn* of demand curve requires that the firm only
passively reacts to wage-rate and is not able to affect it at all. But
even if the firm can influence the wage rate, it will still have some
mapping L(w;Q,K,.) relating amount of labor hired L to the wage w (and
to output Q, capital K, etc) st dL/dw < 0, where d denotes partial
derivative.
[snip]
Charles Stewart
<posted & e-mailed, was `Minimum Wages Needn't Cause Unemployment'>
Robert Vienneau <rv...@see.sig.com> wrote:
> William B Vogt <wili...@andrew.cmu.edu> wrote:
>> Robert Vienneau <rv...@see.sig.com> wrote:
>>> The terms "wages" and "employment" should not appear with any
>>> meaning in the abstract propositions in your proof. The use of
>>> these terms in a meaningful way requires a mapping between the
>>> terms in your proof and something like a model in the sense used
>>> in meta-mathematics. I did not bring up anything about "reality."
>>> Your insistence that these terms relate to "reality," while
>>> refusing to elucidate any possible relationship, is neither
>>> persuasive nor consistent.
>> Labor demand curves *must* slope down. This is true under the
>> follwing assumptions:
>> 1. Prices are fixed from the point of view of the firm
>> 2. Firm's profit maximize
>> 3. The only price varied in the construction of the labor
>> demand curve is the price of labor.
>> Everything in the above has a precise mathematical definition.
> Oh, so your proof relies on additional assumptions? But of course, I
> outlined two sets of definitions where your proof holds. (Labor is
> one of a set of non-produced inputs used to directly produce only
> consumer goods and intertemporal equilibrium.) Perhaps you might
> want to clarify what you understand meta-mathematicans to mean by
> "truth" or what you mean by definitions.
As I am having difficulty following this argument, would it be
possible to confirm that my summary of the debate is broadly correct:
1. William has provided an informal argument to show that the labour
demand curve must slope down;
2. Robert responded by saying that for this argument to count as
proof, it is necessary to provide two things:
- a plausible model in which the standard reformulation of the
cited assumptions are true;
- a demonstration that the argument can be formalised in the model.
3. William responded by naming a model from an economics text book in
which the proof can be carried out;
4. Robert countered by saying that whilst his second criteria is
satisfied by this model, his first is not, since he claims that he can
provide plausible situations which violate the model's own assumptions.
Thus he claims that William has not `made clear his additional
assumptions';
5. Robert then goes on to provide two models which he claims are more
plausible, in which the cited assumptions are validated, but in which
the proof cannot be carried out. Both of these are models which
validate his original example.
If (2) above is a correct characterisation of Robert's original
objection, then it seems to me that he is justified in making the
demand for William to `make clear his additional assumptions'.
William's appeal to mathematical certainties do presuppose a
mathematical level of precision.
My difficulties come with the last three points:
- My interest in economics is amateur, and I cannot immediately
summon to my awareness a random example from a random textbook. Would
it be possible for William to provide an explicit account of the model
he mentioned, and for Robert to say what he objected to in it;
- Jim Blair has objected to Robert's example on the grounds that it
is not plausible, and I find his objection compelling: even if Robert
is right that different points on the demand curve could be associated
with different interest rates, a 150% variation in interest rates
should not arise from a small variation in the price of labour.
If Robert's example is implausible, then the failure of a model to
validate it is not much of a failure at all;
- If I remember rightly, Markku appears at one point to have
endorsed Robert's criticisms of the textbook model, but hinted that
they can be repaired in a model in which William's argument can go
through. If this is so, then surely he should provide the details of
such an account.
I'm sorry if I am asking people to repeat themselves; it has been
difficult to follow all of the things people have said in this tangled
thread.
Charles
Markku Stenborg ®
On 20 May 1998 10:31:16 GMT, worc...@sable.ox.ac.uk (Charles Stewart)
wrote:
[snip]
> - If I remember rightly, Markku appears at one point to have
> endorsed Robert's criticisms of the textbook model, but hinted that
> they can be repaired in a model in which William's argument can go
> through. If this is so, then surely he should provide the details of
> such an account.
I'm not sure I'm reading this (and the stuff snipped) as you intend.
Anyways, my view is something as follows:
Firms use labor as factors of production. The demand for labor is thus
derived demand in econ jargon. That is, a firm hires labor not b/c it
wants to consume labor -- eg, to have people hanging around -- but in
order to produce whatever it wishes to produce. (Consumer's demand is
often not derived but direct demand to satisfy some wants and needs.)
The marginal benefit of labor to the firm is then the added value the
labor produces to the firm, ie, the extra output a small increase in
labor generates times the price this output is sold. The marginal cost
of labor is the wage (+ whatever taxes and other costs there are). In
equilibrium, the firm will want to hire labor L st its MB(L) = MC(L).
Equilibrium or not, the economically relevant part of the marginal
benefit of labor must always the slope down: the higher the (marginal)
price of labor, the less labor the firm wants to hire, ceteris
paribus. Along the upward-sloping part of the marginal benefit for
labor, the firm would increase the profits by hiring one more worker
and paying slightly more to every worker.
The reason for this is the following. Along the labor demand curve,
only the price of labor is changing, and everything else remains
constant, including the costs and amounts of other factors of
production and all the prices. Since nothing happens to the price of
the output or to any cost (other than wage), the firm will want to
produce exactly as it did before the miniscule increase in wage but it
will want to shift to less labor intensive production method, ie, to
reduce the amount of labor hired.
Strictly speaking, only firms with no mkt power whatsoever on labor
mkts have labor demands. Must firms have at least some power to
influence wages, and do not have labor demand curves. However, also
these firms have something that looks pretty much like labor demand,
and also this more general animal must always slope down on
economically relevant domains.
Charles Stewart
Markku Stenborg ® <real.a...@bottom.of.msg> wrote:
>On 20 May 1998 10:31:16 GMT, worc...@sable.ox.ac.uk (Charles Stewart)
>wrote:
>> - If I remember rightly, Markku appears at one point to have
>> endorsed Robert's criticisms of the textbook model, but hinted that
>> they can be repaired in a model in which William's argument can go
>> through. If this is so, then surely he should provide the details of
>> such an account.
<snip>
> Equilibrium or not, the economically relevant part of the marginal
> benefit of labor must always the slope down: the higher the (marginal)
> price of labor, the less labor the firm wants to hire, ceteris
> paribus. Along the upward-sloping part of the marginal benefit for
> labor, the firm would increase the profits by hiring one more worker
> and paying slightly more to every worker.
> The reason for this is the following. Along the labor demand curve,
> only the price of labor is changing, and everything else remains
> constant, including the costs and amounts of other factors of
> production and all the prices. Since nothing happens to the price of
> the output or to any cost (other than wage), the firm will want to
> produce exactly as it did before the miniscule increase in wage but it
> will want to shift to less labor intensive production method, ie, to
> reduce the amount of labor hired.
As I recall, Robert's objection to the standard account was based upon
his claim that `substitutivity' fails in this example. As I am not
sure I have a sure grasp of the content of his objection, I didn't
outline this idea in my last post. I will have a go here, though:
1. We must make a distinction between the demand schedule of an
individual firm, and the aggregate demand curve. For the sake of
argument, let us also assume that the decisions made by any particular
individual firm will not affect the aggregate curve;
2. Robert agrees that if we examine the demand schedule of a given
firm, then the demand schedule will slope down. However he does not
agree that the aggregate curve must slope down, due to his
anti-substitutivity argument;
3. I can see an argument to this end as follows: let the demand
curve be d(x), where x is the amount of labour demanded, and d(x) is
its unit price. Let X be a function from the set of individual firms
to the amount of labour they demand. A hypothetical situation in
which there is demand x, will be composed of some such X (where the
sum of the values of X across all firms equals x);
4. Now let us assume that for a subset of firms, X does not
represent an equilibrium position. Then they will profit by changing
the amount they demand, an instance of substitution, leading to a new
function X' representing the demands made by the individual firms.
This will be associated with a new demand level x', which we shall
assume to be different from x;
5. The claim of substitutivity is that the value of the curve d at
x' can be obtained by adding up the prices paid by the individual
firms. Since the individual demand schedules slope down (ie. are
monotone non-increasing), so must the function d;
6. Robert's objection, if I understand him rightly, is that this
does not follow. Although an individual firm's change will not affect
the collection of relevant prices taken by the market, a change
adequate to induce a change from x to x' may well do so.
This appears to be a plausible position, consistent with the `local
substitutivity' of part 4 (and so not contradicting the assumption
that `Prices are fixed from the point of view of the firm'), but
inconsistent with the `global substitutivity' of part 5. If William's
argument against Robert's example depends upon global substitutivity,
then it appears that he owes an explanation of why it must hold.
Charles
William B Vogt
I have whittled down the discussion greatly. In particular,
the discussion beginning with Mr Vienneau's question
"why do you want to call some symbol..." which I took to
be a question about my motives and which he now claims
was not has been deleted. I have also deleted all the
discussion arising from various speculations as to the
precise error Mr Vienneau is making, since it is now clear
that that discussion has been unproductive. Finally,
some discussion could be snipped since it arose from
an error of mine (see below).
Excerpts from netnews.sci.econ: 20-May-98
Re: Minimum Wages Needn't C.. by Robert Vien...@see.sig.
> William B Vogt <wili...@andrew.cmu.edu> wrote:
> > > One is of an equilibrium in an overlapping generations framework in
> > > which population, tastes, and technology are given. One can consider
> > > different values of a parameter in the utility function. The
> > > equilibrium in which profit-maximizing firms adopt one of the
> > > techniques in my example is thereby transformed to an equilibrium
> > > in which profit-maximizing firms adopt the other technique. I
> > > brought this up to show how my example can serve as a building
> > > block in a comparative statics exercise, ...
>
> > What you did is not a comparative statics exercise.
>
> Non-responsive.
>
> How is what I am outling above not a comparative statics
> excerise?
What you are outlining is. The example is not.
> > What you did is not an analysis of a labor demand curve.
>
> Whatever. Please explain how a long run labor demand curve can
> be anything but horizontal at a wage equal to the value of the
> marginal product of labor, as determined by the given interest
> rate. Note that if the wage is above this value, the firms will
> be making losses, and being profit-maximizing, will not choose
> to produce or hire any workers. If the wage is below this
> value, profit-maximizing firms will be making pure economic
> profits. Therefore the firms will prefer to expand production
> above any finite value and will hire an infinite number of
> workers at any lower wage.
Whatever. This is all irrelevant to the claim that what
you did is not an analysis of a labor demand curve.
> > > > More rubbish. You are evincing an inability to tell the
> > > > difference between the truth of an abstract proposition
> > > > and the mapping between the proposition and observed
> > > > reality.
>
> > > The terms "wages" and "employment" should not appear with any meaning
> > > in the abstract propositions in your proof. The use of these
> > > terms in a meaningful way requires a mapping between the terms in your
> > > proof and something like a model in the sense used in meta-mathematics.
> > > I did not bring up anything about "reality." Your insistence
> > > that these terms relate to "reality," while refusing to elucidate
> > > any possible relationship, is neither persuasive nor consistent.
>
> > Labor demand curves *must* slope down. This is true
> > under the follwing assumptions:
>
> > 1. Prices are fixed from the point of view of the firm
> > 2. Firm's profit maximize
> > 3. The only price varied in the construction of the labor
> > demand curve is the price of labor.
>
> > Everything in the above has a precise mathematical definition.
>
> Oh, so your proof relies on additional assumptions?
No, it does not.
> But of
> course, I outlined two sets of definitions where your proof
> holds. (Labor is one of a set of non-produced inputs used
> to directly produce only consumer goods and intertemporal
> equilibrium.) Perhaps you might want to clarify what you understand
> meta-mathematicans to mean by "truth" or what you mean by
> definitions.
Don't know what a meta-mathematician is.
> > Using those definitions, the statement is true, and I have
> > posted a proof, which is *still* not disputed.
>
> Your point?
Labor demand curves slope down under the assumptions I gave.
> > The proof is correct, hence both persuasive and consistent.
>
> Your confusion that I have been criticizing your proof by
> saying it does not relate to "reality" is what is unpersuasive.
What would a persuasive confusion look like?
> > So, I partially retract what I said. It could be that you
> > can't tell the difference between the truth of an abstract
> > proposition and the question of its applicability to observed
> > reality or it could be that you think my motives are
> > relevant to the truth of propositions I post proofs of.
>
> Or it could be I have a different understanding of conventional
> views about the truth of logical propositions.
Great. And you feel no obligation to advertise this fact
before engaging people in discussions where such differences
are likely to cause confusion? Perhaps you could sketch
the points of departure of your view from the conventional
one?
> > I don't recall you doing so. Your example clearly fits the
> > standard static framework. *You* choose to interpret it
> > as representing an endlessly repeated sequence of essentially
> > static choices by the firm.
>
> Maybe you should research what are netput vectors in intertemporal
> equilibrium some more. Intermediate goods that are produced only
> to be used in further production do not have nonzero values in
> a "production plan". I don't think goods used exclusively as
> produced means of production need to be placeholders in netput
> vectors. Thus dated quantities of steel in my example do not
> have "prices" in the formal theory which can be interpreted as an
> intertemporal equilibrium. A "production plan" is jargon introduced by
> Debreu in the usual interpretations of his formalism.
Whether they "need" to be so represented is irrelevant. I
choose to so represent them in demonstrating that your example
maps into the standard neoclassical static framework and that
it fails to be a counterexample.
> > Prices do not change between periods.
> > Production technology does not change between periods.
> > There is no dependence of future returns of the firm on present
> > decisions by the firm. Since there is nothing in your
> > example to make the firm's problem interestingly dynamic, and
> > since all the behavior of the firm is summarized by the static
> > model, the model is static.
>
> So you retract your charactization of that presentation of my model
> as being "dynamic"?
If I said that your example is dynamic in any meaningful sense,
I misspoke. Your model has the trappings of dynamism without
any dynamic content, as I have argued several times. It is presented
as if it were dynamic; whereas, it is not essentially dynamic.
> > > > > > We don't compare equilibria in the neoclassical theory of the
> > > > > > firm, we compare the firm's response to different price
> > > > > > vectors.
>
> > > > > Whatever. I long ago quoted Debreu's "equilibrium production of the
> > > > > jth producer relative to p."
>
> > > > Furthermore, I have not read Debreu recently
> > > > enough to recall context. I bet that "equilibrium relative
> > > > to p" != "equilibrium", however. I'd even wager that
> > > > "equilibrium relative to p" is what is currently called
> > > > the neoclassical theory of the firm (it sure sounds like
> > > > it).
>
> > > And how is my example not an equilibrium of the firm?
>
> > Labor demand curves are derived from (what is commonly
> > called) the neoclassical theory of the firm. This theory
> > involves comparing the behavior of firms at different
> > (fixed from their perspective) price vectors.
>
> Nonresponsive.
I retract the statement "We don't compare . . ." I badly
misread Mr Vienneau's post (several posts ago). I'll restore
it:
> Under this interpretation, your proof compares equilibria of
> the firm - in the very limited theory of the firm treated in our
> discussion - that faces some odd circumstances. All prices are the
> same in the two equilibria, except the price of one particular dated
> labor quantity.
I now agree that the substance of the above is correct. The
proof I offered, interpreted in a dynamic context, is about
changing the price of a single, dated good. However, the
proof suffices to produce the same result (labor demand
curves slope down) with the price of labor changing by the
same amount at all dates, as long as long run profit max
is adequately characterized by profit max in each period.
(as is true, for example, in Mr Vienneau's example).
Furthermore, I don't see anything "odd" at all about taking
a partial derivative.
> Are you claiming that the interest rate is a price? Do you
> want to answer the question that Chris has not yet answered -
> What is the interest rate the price of?
Interest rates are not prices, they are (related to) price
ratios of commodities which differ only in time. Of course,
you can't change an interest rate without changing a price,
so (if I had to guess) Chris was probably being slightly
sloppy --- a slight sloppiness which is common and, in most
contexts, harmless.
> > > The coherence of neoclassical theory has been challenged. The response
> > > of many economists seems to be to support misrepresentations of the
> > > challenge by a refusal to examine the literature, even to the extent
> > > of denying the existence of the most contemporary literature.
>
> > This becomes tiring. Although the "coherence" of neoclassical
> > theory has been challenged, it has been challenged (here) in
> > a way which demonstrates a lack of understanding of key
> > concepts under challenge.
>
> And it has been "answered" by evasion and misrepresentation of
> the challenge.
Not true. The challenge you issued was to produce some assumptions.
They were produced, along with an argument for their sufficiency,
and a discussion of why the posted example were not a contradiction
to their sufficiency.
> > The statement "labor demand curves *must* slope down," (under
> > the assumptions I posted) is not a statement on which
> > reasonable disagreement is possible. It is true the way
> > statements like ...
> > "the rational numbers are dense in the reals" are true.
>
> It hardly helps to make an analogy to a statement where it
> is not clear what it means for the statement to be true. For
> example, Godel took a platonic interpretation of math, and
> it is traditional in metamathematics to use models to
> explain meaning.
In what way is it not clear what the statement means?
-- Bill
_______________________________________________________________
| |
| William B. Vogt Assistant Professor |
| |
| H. John Heinz III School ph: (412) 268-1843 |
| of Public Policy and Management fx: (412) 268-7902 |
| Carnegie Mellon University wili...@andrew.cmu.edu |
|_______________________________________________________________|
William B Vogt
Excerpts from netnews.sci.econ: 20-May-98 Need labour demand curves s..
by Charles Ste...@sable.ox
>
> Robert Vienneau <rv...@see.sig.com> wrote:
>
> >>> The terms "wages" and "employment" should not appear with any
> >>> meaning in the abstract propositions in your proof. The use of
> >>> these terms in a meaningful way requires a mapping between the
> >>> terms in your proof and something like a model in the sense used
> >>> in meta-mathematics. I did not bring up anything about "reality."
> >>> Your insistence that these terms relate to "reality," while
> >>> refusing to elucidate any possible relationship, is neither
> >>> persuasive nor consistent.
>
> >> Labor demand curves *must* slope down. This is true under the
> >> follwing assumptions:
>
> >> 1. Prices are fixed from the point of view of the firm
> >> 2. Firm's profit maximize
> >> 3. The only price varied in the construction of the labor
> >> demand curve is the price of labor.
>
> >> Everything in the above has a precise mathematical definition.
>
> > Oh, so your proof relies on additional assumptions? But of course, I
> > outlined two sets of definitions where your proof holds. (Labor is
> > one of a set of non-produced inputs used to directly produce only
> > consumer goods and intertemporal equilibrium.) Perhaps you might
> > want to clarify what you understand meta-mathematicans to mean by
> > "truth" or what you mean by definitions.
>
> possible to confirm that my summary of the debate is broadly correct:
>
> 1. William has provided an informal argument to show that the labour
> demand curve must slope down;
No, it was formal. You'll have to go back through the thread
to find it --- it is a minor modification of a formal argument
in Varian's book, _Microeconomic Analysis_.
> 2. Robert responded by saying that for this argument to count as
> proof, it is necessary to provide two things:
> - a plausible model in which the standard reformulation of the
> cited assumptions are true;
> - a demonstration that the argument can be formalised in the model.
> 3. William responded by naming a model from an economics text book in
> which the proof can be carried out;
> 4. Robert countered by saying that whilst his second criteria is
> satisfied by this model, his first is not, since he claims that he can
> provide plausible situations which violate the model's own assumptions.
> Thus he claims that William has not `made clear his additional
> assumptions';
Can you clarify what you mean by this? What does the first
requirement mean?
> 5. Robert then goes on to provide two models which he claims are more
> plausible, in which the cited assumptions are validated, but in which
> the proof cannot be carried out. Both of these are models which
> validate his original example.
Except that he has not done this. His example changes more than
one price! This I also explained, with detailed calculations
early on in the discussion.
To be clear, I showed that under a set of assumptions a conclusion
follws, and that in Mr Vienneau's example the assumptions are
not satisfied.
> If (2) above is a correct characterisation of Robert's original
> objection, then it seems to me that he is justified in making the
> demand for William to `make clear his additional assumptions'.
> William's appeal to mathematical certainties do presuppose a
> mathematical level of precision.
Again, I don't know what you mean here.
> My difficulties come with the last three points:
> - My interest in economics is amateur, and I cannot immediately
> summon to my awareness a random example from a random textbook. Would
> it be possible for William to provide an explicit account of the model
> he mentioned, and for Robert to say what he objected to in it;
The proof is in my post of May 6th. The explanation that
the example was not a couterexample was also in that post.
Vienneau's response was to delete all of that.
We have been arguing, since that time, over what I see as
tangential issues.
To summarize the discussion (and a bit of motivation):
The post thread title is about minimum wages and unemployment.
The ususal economic argument that minimum wages cause
unemployment makes use of supply and demand. Demand slopes
down, supply slopes up, and their intersection is the equilibrium
price. A minimum wage, if set above the equilibrium price,
causes unemployment (more quantity supplied than demanded).
There are a number of assumptions lying behind the sketch I
gave; hence, a number of ways to attack the conclusion.
For whatever reason, Mr Vienneau chooses to attack this usual
description of minimum wages causing unemployment by challenging
the idea that the demand curve for labor slopes down. His
challenge is that there are stronger assumptions necessary
to prove this fact than economists admit, and he claims that
his example reveals this to be the case. I have disagreed,
provided what I claim are sufficient assumptions, have offered
a proof, and have explained why his example is not a couterexample
to the proof.
The rest of the discussion has been on a wide variety of tangential
issues.
As an aside, I do agree that Mr Vienneau's example is a step
towards a model in which minimum wages do not cause unemployment,
and there are other such models. I don't agree that Mr Vienneau's
example has much to do with labor demand curves.
-- Bill
Robert Vienneau
William,
I think I'll only provide cryptic comments on the philosophy
of math. Basically, the axiomatic approach I think you are
adopting operates only on the level of syntax. A traditional
approach to semantics is through the use of models. For example,
one could define the reals through a collection of axioms
including, say, the archimedean property. Or one could construct
the reals from the rationals as Dedekind cuts or as equivalence
classes of Cauchy-convergent series of rational numbers. This
latter approach is an example of the use of models. I believe
that when considering properties of sets indexed by real
numbers, such as whether one wants to assume the axiom of choice,
some contemporary mathematicians think one might still be able
to provide convincing arguments, about which sets of axioms should
be adopted, through the use of models. Perhaps somebody might
be willing to explain the difference between Russell's and
Hilbert's program.
I don't think I need to whole-heartedly adopt any position here to
justify my continued request for you to provide objects in a model to
which your proof applies. I know you now accept that the Arrow-Debreu
model of intertemporal equilibrium is one such model, a position
I also outlined.
William B Vogt wrote:
> Robert Vien...@see.sig.
> > William B Vogt <wili...@andrew.cmu.edu> wrote:
> > > > One is of an equilibrium in an overlapping generations framework in
> > > > which population, tastes, and technology are given. One can consider
> > > > different values of a parameter in the utility function. The
> > > > equilibrium in which profit-maximizing firms adopt one of the
> > > > techniques in my example is thereby transformed to an equilibrium
> > > > in which profit-maximizing firms adopt the other technique. I
> > > > brought this up to show how my example can serve as a building
> > > > block in a comparative statics exercise, ...
> > > What you did is not a comparative statics exercise.
> > How is what I am outling above not a comparative statics
> > excerise?
> What you are outlining is.
Exactly what I was trying to say. I could stop here, but, typically,
I will go on.
> The example is not.
I can see how a neoclassical economist would say so. However,
some economists have recently proposed an interesting reading of
the classical economists. Classical economists include Adam Smith
and David Ricardo, for instance. This reading sees a distinctive
core theory of value in classical economics. This theory of value
takes the level and composition of output, the technology, and
wages as given. One then determines from this data "natural prices"
or "prices of production." My example can be seen as a comparative
statics exercise in that theory of value - although I can also
see the point of refusing to use that label, and also "general
equilibrium", in this context.
Those who read the classicals in this way typically think that
this core theory of value should be supplemented with analyses
on a lower level of abstraction of the interactions between the
data given in the theory of value. For example, increased wages
might lead to different conventions about what commodities are
necessities and what are luxuries, thereby also influencing
the composition of output. The classical theory of value is
open to different theories extending it, some of which could
be "softer" than is typical of modern mainstream economics.
Developments along these lines might then lead to closer cooperation
between economists and other researchers in the social
sciences.
I have seen some who understand this view joke that Neoclassical
Economics is an acronym for "Near-Enough-to-Obscure" Classical
Economics.
> If I said that your example is dynamic in any meaningful sense,
> I misspoke.
Actually, you assigned to me the view that my example was dynamic,
although I never discussed the distinction between statics
and dynamics.
> Your model has the trappings of dynamism without
> any dynamic content, as I have argued several times. It is presented
> as if it were dynamic; whereas, it is not essentially dynamic.
Later William wrote:
> > Under this interpretation, your proof compares equilibria of
> > the firm - in the very limited theory of the firm treated in our
> > discussion - that faces some odd circumstances. All prices are the
> > same in the two equilibria, except the price of one particular dated
> > labor quantity.
> I now agree that the substance of the above is correct. The
> proof I offered, interpreted in a dynamic context, is about
> changing the price of a single, dated good.
Evidently William thinks of the Arrow-Debreu model of intertemporal
equilibrium, or some extension of it, as an exemplar of "dynamic"
economic analysis. This is interesting rhetoric. Generally, "dynamics"
sounds like a better thing than "statics". So if one could assign
my example to illustrate a "static" analysis of some distant past
and William's idea of "dynamic" analysis to contemporary theory,
one has managed to insinuate economics is progressing. I don't know
that this is William's view, but if it is, it is vastly mistaken.
First, it is trivial to extend my example to treat a given constant
rate of growth of the employed labor force. The output of the
steel and corn industries - or, more generally, all industries -
will be growing at the same rate. This extension can be used to
examine generalizations of Harrod's warranted and natural growth
model, e.g. through the Cambridge equation. This extension can
also be used to demonstrate difficulties in extending Solow's
growth model to multiple commodities. So, even from a neoclassical
perspective, my example easily accomodates some well-known analyses
usually thought to be dynamic. Since Solow's model underlies
some contemporary work in mainstream economics, known under the rubric
of the "New Growth Theory," these analyses are of contemporary interest.
More interestingly, the interpretation mentioned above of my example
as illustrating the rebirth of classical economics also leads to
a view of how to extend it dynamically. One could treat the
coefficients of production characterizing the various techniques
as growing smaller, usually along paths decaying exponentially.
Typically, the rates of decay will differ among the different
coefficients. One can then determine how the solution levels
of operation of the processes and relative "natural prices" change
over time.
Looking outside the core theory of classical value, one then
asks how market prices would be attracted to these natural
prices. This attraction is sometimes referred to as a "gravitational"
process, using a metaphor from Adam Smith. One might analogously
ask how orbits are determined given some sort of given movement
of the center of gravity of the solar system. From this perspective,
the Arrow-Debreu model of intertemporal equilibrium is a very
constricted model of a classical process of gravitational attraction
of market prices to natural prices. The only difficulty is the
Arrow-Debreu model suffers from the unnecessary special case
restrictions of assuming continuous full employment, an unchanging
value of the capital stock, always correct foresight, etc.
I have not read the literature - I'm not sure if _Marx and
Non-Equilibrium Economics_ (edited by A. Freeman and G. Carchedi)
counts - but apparently there are formal models of classical
gravitational processes that have been very recently developed. (By the
way, the assumption of full employment of the labor force is
not a necessary property of the classical core theory of value. Say's law
is one of those many ideas the Classical economists adopted
in addition to their value theory.) From the perspective
outlined here, my example better relates to broader dynamical
analyses than constipated Arrow-Debreu equilibrium paths.
I know some will ask, "What does this have to do with labor
demand curves?" I personally don't understand - perhaps
some might think I should stop there - this objection
to expositions of the broader background behind a debate.
(It guess it is hard to get this sort of history in a
peer-reviewed journal article in the natural sciences.)
Nevertheless, I think it relevant. One characteristic of
the neoclassical revolution was the extension of supply and
demand analysis to the theory of natural prices or, in
Marshall's terminology, long run normal prices. The claim
is that early generations of neoclassical economists
continued the method of focusing on long-run prices,
while adopting a different theoretical structure. This
structure emphasizes the supposedly ever-active principle
of substitution in consumption and production.
The point of examples like mine is to show that the neoclassicals
failed to find a rational foundation for their long run
analysis of factor markets:
"[Bharadwaj] is not objecting to the fact that gravitation
towards a natural position will take time or that the terms
'short-period' and 'long-period' might be used in a discussion
of how an economy 'accomodate[s] fresh observations of
economic phenomena...' She is objecting, rather, to the
idea that the *only* difference between a short-period and
a long-period equilibrium, that is to say, the only difference
that a [Demand and Supply Equilibrium] DSE-based theory credits
to the classical distinction between 'market' and 'natural'
values is the *extent* or *degree* to which the principle
of substitution in response to price changes has come into play.
Indeed, a recurring theme in Bharadwaj's essays concerns the
enervating effect of this one idea, which, of course, many
economists would regard as the whole basis for their claim to
be engaging in a scientific, and peculiarly economic approach
to the various social problems with which they are concerned."
-- Harvey Gram
Needless to say, I don't think classical economics required
an all-encompassing principle of substitution. More shortly,
economics need not be about the allocation of scarce resources
among alternative ends.
Again, the question is why should long-run factor demand curves
slope down, on neoclassical principles? Or perhaps what I should
have asked for is a demonstration that long period supply and demand
analysis has the implications assumed without argument in many
mistaken textbook treatments. (Opinions?) These questions are not
answered by the Arrow-Debreu equilibrium model. Rather I would
like to see an analysis of production in a model where:
(a) Some goods produced with the assistance of labor are used
in a later stage in production, rather than as consumption
goods.
(b) Firms would persist in hiring the same amount of labor-hours
and producing the same amount of goods if the prices they
are assumed to face in drawing factor demand curves did,
in fact, persist over many time periods.
The first requirement (a) is that the model be sufficiently general
to address my sort of example. My claim is also that endowments
of produced commodities would not be given data in a full model
with factor-demand curves derived under these conditions.
I think even William will agree nobody has met this challenge
with a formal model. William might object that the parameters
of my challenge were never clear. However, I have repeatedly
asked for an answer along these lines. I think all I've received
is confused and vague handwaving.
From this perspective, the emphasis on intertemporal and temporary
equilibrium is a step backward. Mainstream economists should
recognize the failure of neoclassical economics to analyze
long-run theory.
> > > This becomes tiring. Although the "coherence" of neoclassical
> > > theory has been challenged, it has been challenged (here) in
> > > a way which demonstrates a lack of understanding of key
> > > concepts under challenge.
> > And it has been "answered" by evasion and misrepresentation of
> > the challenge.
> Not true. The challenge you issued was to produce some assumptions.
> They were produced, along with an argument for their sufficiency,
> and a discussion of why the posted example were not a contradiction
> to their sufficiency.
I think the relationship of my challenge to an increasing literature
produced over three decades should lead one to wonder whether my
challenge has been adequately addressed. Of course, some might say
that my frequent repetitions of these themes is an idiosyncrasy all
my own. This seems a weird belief, given that my references easily
demonstrate the existence of a school of thought with similar
beliefs. Furthermore, this school's analysis, if accepted, casts at
least two centuries of economics in a new light. Surely that should
lead to at least some proper representation in mainstream teaching?
Robert Vienneau
In article <6jubdk$j0a$1...@news.ox.ac.uk>, worc...@sable.ox.ac.uk (Charles
Stewart) wrote:
> As I am having difficulty following this argument, would it be
> possible to confirm that my summary of the debate is broadly correct:
I think it important to emphasize that my initial post contained
a specific numerical example illustrating possible consequences
of maximizing behavior in the theory of production. Whatever I
say, such examples pose a challenge to make sense of.
In the give and take of argument, we each seem to have ended up making
assertions about what conclusions others should draw if they understood
their own position like those making the assertions understand the
others' positions to be. Nobody seems too pleased with how others
understand their views. Given this rhetoric, difficulty in following
the discussion is quite natural.
> 1. William has provided an informal argument to show that the labour
> demand curve must slope down;
I agree with William that he has provided a formal proof of something.
I don't think that William ever provided a formal proof that his theorem
applied to my example. Rather, he showed that the antecedents of his
informally-stated theorem were not satisfied by my example because I
varied more than one price.
> 2. Robert responded by saying that for this argument to count as
> proof, it is necessary to provide two things:
> - a plausible model in which the standard reformulation of the
> cited assumptions are true;
> - a demonstration that the argument can be formalised in the model.
I agree, except I don't emphasize plausibility. The first request I
understand to be asking for a clarification of the meaning of the
terms in William's proof.
> 3. William responded by naming a model from an economics text book in
> which the proof can be carried out;
I think I first named the model, Arrow-Debreu intertemporal equilibrium,
and provided an explanation of it. William and I agree that his proof
can be carried out in that model, I think.
> 4. Robert countered by saying that whilst his second criteria is
> satisfied by this model, his first is not, since he claims that he can
> provide plausible situations which violate the model's own assumptions.
> Thus he claims that William has not `made clear his additional
> assumptions';
I would say I want to see an analysis of labor demand curves in a
setting which can be reasonably described as a long run theory.
> 5. Robert then goes on to provide two models which he claims are more
> plausible, in which the cited assumptions are validated, but in which
> the proof cannot be carried out. Both of these are models which
> validate his original example.
I'm not going to agree or disagree with this.
> If (2) above is a correct characterisation of Robert's original
> objection, then it seems to me that he is justified in making the
> demand for William to `make clear his additional assumptions'.
> William's appeal to mathematical certainties do presuppose a
> mathematical level of precision.
> My difficulties come with the last three points:
> - My interest in economics is amateur, and I cannot immediately
> summon to my awareness a random example from a random textbook. Would
> it be possible for William to provide an explicit account of the model
> he mentioned, and for Robert to say what he objected to in it;
Anybody want to have a shot at this?
> - Jim Blair has objected to Robert's example on the grounds that it
> is not plausible, and I find his objection compelling: even if Robert
> is right that different points on the demand curve could be associated
> with different interest rates, a 150% variation in interest rates
> should not arise from a small variation in the price of labour.
I don't find this plausibility argument convincing. Nor do I think it
particularly relevant. Nevertheless, I'll address it. I think I already
partially addressed it in my comments to Jim McCown (?).
The question is how are the results in my example generated? Could
one reasonably expect the "perverse" results to occur at more
reasonable interest rates.
First, I take the wage as exogeneous in my example. I also treat
corn as a numeraire. I also take the composition and level of net
output as given. The level of operation of each process, all other
prices, and the interest rate are endogeneous variables which I
solve for.
Quantities and the price system can be considered seperately. Prices
and the interest rate are found as a function of the wage. (I
actually find it easier to solve for the wage and prices as
a function of the wage and invert.) Anyways, each technique
allows one to find a function relating the wage and the interest
rate, say r( alpha, w ). Refer to this function as the wage-rate
of interest curve for the technique. Cost minimization can be
shown to imply that the preferred technique at given w is
the one with the highest r. Call the (outer) envelope curve
the wage-rate of interest frontier.
Under fairly general assumptions in circulating capital models,
each wage rate of profit must slope down in w-r space and intersect
the wage and interest rate axis at finite values. Nothing further
can be said in the general n-good case. Convexity can change along
a wage-rate of profits curve for a given technique.
Now consider the wage-rate of interest curves for two techniques.
In a multiple good model, they can intersect many times. The
maximum number of intersections, if I remeber correctly, is
the total number of goods used in the techniques. The intersection
at the highest w - therefore, lowest r - is nonperverse. The
second intersection is perverse. Other intersections can also
be perverse. So the question becomes can these perverse
intersections occur on the frontier at low interest rates?
If so, an example like mine can be constructed by comparing
wages slightly lower and slightly higher than the wage at the
perverse switch point. One can make these wages as close as
one wishes, thereby restricting the variation in the interest
rate in the example to as small a value as one wants.
I limited my example to 2 produced goods in which the processes used
to produce the same good use the same 2 goods as produced means
of production. This limitation imposes special restrictions. The
wage-rate of interest curves for each technique cannot change
convexity throughout the first quadrant. The convexity of the
curves must be the same for all techniques. There can be at
most two intersections of the wage-rate of interest curves
for two techniques. I don't see that these restrictions imply
that the perverse intersection must be at an unreasonably high
interest rate. They did make my task of finding a numerical
example more difficult. I did what I could. I also wanted to
compare wages sufficiently far apart that difference in cost
between the two techniques was obviously more than round-off
error resulting from performing my calculations with finite
precision.
These limitations are removed when considering models with more
goods. Therefore I consider it easier to find numerical examples
in models with more goods, in some sense. Of course, it's also
more difficult to actually carry out the calculations.
Given my understanding, I find objections based on the implausibility
of the interest rates in my example ill-founded.
jim blair
William B Vogt wrote: (to Robert Vienneau)
....
> First, if what you say in the quoted paragraph is true, it
> utterly devastates your position, since labor demand curves
> are defined by changing one and not an infinite number of
> prices.
Hi,
I also initially accused him of changing several things at once
to get his result. Specifically both wages and "interest rates"
(in addition to the price of steel relative to corn). But I have
since realized that by "interest rate" he means not what most would
mean by that term: he means more nearly "return on investment"
And he thinks the increase in wages CAUSES the drop in "interest
rates" that his model needs, so to him this is not changing two
DIFFERENT variables at once.
The problem that I have with his model (well ONE problem I have ;-)
is that there is no empirical evidence, or logical reason, to think
that higher wages are the cause of lower interest rates or lower
return on investment. Or that these two are even related. Quite
the contrary, the industries that pay the highest wages are also
the ones that make the highest returns for their investors.
And my attempts to related federal minimum wage increases to
decreases in interest rates have indicated that if there is
ANY relationship it is in the OTHER direction.
Look at historic interest rates at:
And at the minimum wage, at:
http://www.geocities.com/capitolhill/4834/mw_t1.gif
and tell me if YOU see any correlation between higher minimum
wage and lower interest.
PS: I will be offline for about a month, and won't be very active on the
net for the rest of the summer. Hope to be back with more of my
insightful posts and comments after the sailing season ends in
September.
Robert Vienneau
a function of the interest rate and invert.) Anyways, each technique
--
William B Vogt
Excerpts from netnews.sci.econ: 21-May-98
> William,
>
> I think I'll only provide cryptic comments on the philosophy
> of math.
I'll note that they were, indeed, cryptic, in particular
on the distinction between a proof being correct and the other,
non-empirical criterion Mr Vienneau claims the proof fails
and which I still do not comprehend.
> William B Vogt wrote:
>
> > Robert Vien...@see.sig.
>
> > > William B Vogt <wili...@andrew.cmu.edu> wrote:
> > > How is what I am outling above not a comparative statics
> > > excerise?
>
> > What you are outlining is.
>
> Exactly what I was trying to say. I could stop here, but, typically,
> I will go on.
Again, I point out that the particular comparative
statics exercise you are outlining will not sweep
out a labor demand curve.
> > The example is not.
>
> I can see how a neoclassical economist would say so. However,
> some economists have recently proposed an interesting reading of
> the classical economists. Classical economists include Adam Smith
> and David Ricardo, for instance. This reading sees a distinctive
> core theory of value in classical economics. This theory of value
> takes the level and composition of output, the technology, and
> wages as given. One then determines from this data "natural prices"
> or "prices of production." My example can be seen as a comparative
> statics exercise in that theory of value - although I can also
> see the point of refusing to use that label, and also "general
> equilibrium", in this context.
>
> Those who read the classicals in this way typically think that
> this core theory of value should be supplemented with analyses
> on a lower level of abstraction of the interactions between the
> data given in the theory of value. For example, increased wages
> might lead to different conventions about what commodities are
> necessities and what are luxuries, thereby also influencing
> the composition of output.
These sorts of effects can be modeled in a neoclassical
framework. Essentially, if there are complementarities
between consumption of a good at dates t and t+j,
consumption early on can increase demand later on, and
if the good is normal, wages up at t ==> consumption up
at t ==> demand up at t+j ==> different later
composition.
I would be very happy to drop the neoclassical framework
if some framework comes along which is superior. But
the enormous flexibility and transparant simplicity of
the neoclassical framework makes me doubt that one will,
at least soon.
(Note: Lots of modern information-theoretic arguments
are arguably not neoclassical, and I am not taking any
position either on whether they are neoclassical or
whether they are superior)
My problem with your example, interpreted as a threat to
neoclassical orthodoxy (which interpretation you clearly
favor), is that it fits instantly into the neoclassical
framework and is easily explained in that framework's
terms.
> The classical theory of value is
> open to different theories extending it, some of which could
> be "softer" than is typical of modern mainstream economics.
> Developments along these lines might then lead to closer cooperation
> between economists and other researchers in the social
> sciences.
You talk as if this is desirable, per se.
> > If I said that your example is dynamic in any meaningful sense,
> > I misspoke.
>
> Actually, you assigned to me the view that my example was dynamic,
> although I never discussed the distinction between statics
> and dynamics.
I also assign to you the view that you know how to spell,
though we have had no discussion about spelling. etc. You
use time and interest rates in your example, if you thought
it was not dynamic, you could have said so.
> > Your model has the trappings of dynamism without
> > any dynamic content, as I have argued several times. It is presented
> > as if it were dynamic; whereas, it is not essentially dynamic.
>
> Later William wrote:
>
> > > Under this interpretation, your proof compares equilibria of
> > > the firm - in the very limited theory of the firm treated in our
> > > discussion - that faces some odd circumstances. All prices are the
> > > same in the two equilibria, except the price of one particular dated
> > > labor quantity.
>
> > I now agree that the substance of the above is correct. The
> > proof I offered, interpreted in a dynamic context, is about
> > changing the price of a single, dated good.
>
> Evidently William thinks of the Arrow-Debreu model of intertemporal
> equilibrium, or some extension of it, as an exemplar of "dynamic"
> economic analysis. This is interesting rhetoric.
I think of it as an example, certainly.
Generally, "dynamics"
> sounds like a better thing than "statics".
To you, perhaps. As you probably have noticed, we have
different tastes in theory. Ceteris paribus, statics sounds
better to me than dynamics. Ceteris paribus, simple sounds
better to me than complicated. Ceteris paribus, strong
assumptions sound better to me than weak. etc. Frankly,
I am paying your model a compliment when I call it static;
though I am not paying it a compliment when I say it has
dynamic trappings.
> So if one could assign
> my example to illustrate a "static" analysis of some distant past
> and William's idea of "dynamic" analysis to contemporary theory,
> one has managed to insinuate economics is progressing. I don't know
> that this is William's view, but if it is, it is vastly mistaken.
Yes, that's it. Standard economic terminology is all a
sinister plot to permit me to call you, your example, and
classical economics nasty names.
I deleted a discussion of how Mr Vienneau claims his example
could be extended to make it interestingly dynamic. The
discussion is irrelevant to the point at hand, and I don't
have time carefully to evaluate the claims.
> Looking outside the core theory of classical value, one then
> asks how market prices would be attracted to these natural
> prices. This attraction is sometimes referred to as a "gravitational"
> process, using a metaphor from Adam Smith. One might analogously
> ask how orbits are determined given some sort of given movement
> of the center of gravity of the solar system. From this perspective,
> the Arrow-Debreu model of intertemporal equilibrium is a very
> constricted model of a classical process of gravitational attraction
> of market prices to natural prices. The only difficulty is the
> Arrow-Debreu model suffers from the unnecessary special case
> restrictions of assuming continuous full employment, an unchanging
> value of the capital stock, always correct foresight, etc.
Other than full employment, I don't see these assumptions in
the A-D framework. There can be as many different capital
goods as you want and their time path is not restricted
by the model. As far as foresight goes, interpreting the
goods as indexed by state space elements, there is *no concept*
of "correct foresight" inherent in the theory. Each agent
can have different opinions about the probabilities of the
different states, and there is not even a machinery for
talking about who is "right." If you are talking about the
time path of prices, however, you are right.
> The point of examples like mine is to show that the neoclassicals
> failed to find a rational foundation for their long run
> analysis of factor markets:
How does it make that point?
> Again, the question is why should long-run factor demand curves
> slope down, on neoclassical principles?
Asked and answered. Same reason SR ones do.
> Or perhaps what I should
> have asked for is a demonstration that long period supply and demand
> analysis has the implications assumed without argument in many
> mistaken textbook treatments. (Opinions?)
What does this mean? You have claimed before that it
is not a reference to any empirical fact. You have claimed
that proving that demand curves are downward sloping
is not enough. What would be?
> These questions are not
> answered by the Arrow-Debreu equilibrium model. Rather I would
> like to see an analysis of production in a model where:
>
> (a) Some goods produced with the assistance of labor are used
> in a later stage in production, rather than as consumption
> goods.
The A-D model, without modification, satisfies this one. Index
goods by time and have production functions with outputs some
number of periods after the inputs are consumed --- then tell
any intervening story of storing intermediate product which
makes you happy.
> (b) Firms would persist in hiring the same amount of labor-hours
> and producing the same amount of goods if the prices they
> are assumed to face in drawing factor demand curves did,
> in fact, persist over many time periods.
This is satisfied by any model without interesting dynamics, ie
no intertemporal linkages in production. It may or may not
be satisfied with more general production technologies.
> The first requirement (a) is that the model be sufficiently general
> to address my sort of example. My claim is also that endowments
> of produced commodities would not be given data in a full model
> with factor-demand curves derived under these conditions.
>
> I think even William will agree nobody has met this challenge
> with a formal model.
Actually, it looks to me like you want some narrow special
case of the A-D model, and you persist in calling the A-D
model not general because it has been developed in more
general cases.
> William might object that the parameters
> of my challenge were never clear. However, I have repeatedly
> asked for an answer along these lines. I think all I've received
> is confused and vague handwaving.
Actually what you have received is precise, formal argument,
replete with explicit definitions, explicit assumptions,
and rigorous arguments. What you have given, conversely,
is reasonably described as confused and vague handwaving.
> > > > This becomes tiring. Although the "coherence" of neoclassical
> > > > theory has been challenged, it has been challenged (here) in
> > > > a way which demonstrates a lack of understanding of key
> > > > concepts under challenge.
>
> > > And it has been "answered" by evasion and misrepresentation of
> > > the challenge.
>
> > Not true. The challenge you issued was to produce some assumptions.
> > They were produced, along with an argument for their sufficiency,
> > and a discussion of why the posted example were not a contradiction
> > to their sufficiency.
>
> I think the relationship of my challenge to an increasing literature
> produced over three decades should lead one to wonder whether my
> challenge has been adequately addressed.
On the contrary. If anything, that the sorts of analysis you
favor are both old and absent from graduate and undergraduate
curricula is surely evidence that they have been adequately
addressed.
> Of course, some might say
> that my frequent repetitions of these themes is an idiosyncrasy all
> my own. This seems a weird belief, given that my references easily
> demonstrate the existence of a school of thought with similar
> beliefs. Furthermore, this school's analysis, if accepted, casts at
> least two centuries of economics in a new light. Surely that should
> lead to at least some proper representation in mainstream teaching?
You state as facts things you have provided no convincing
argument for. The "dogma" that labor demand curves slope
down, for example, is still not "exploded."
-- Bill
Brad Crockett
jim blair wrote:
> A guy named Jack offered to walk dogs for 50 cents an hour. Very few dog
> owners were interested. So he changed his name to Jacques, and raised is
> rate to $5 an hour. So many people wanted him to walk their dog that he
> was soon hiring assistants and started a franchise. (this was in
> Mahattan
> or maybe Beverly Hills--one of those places where they have more dollars
> than cents)
>
> So this example, like that of Robert Vienneau, shows that a higher
> legal minimum wage can result in higher employment!!
Jim, the reason that the consumers took the $5 rate and not the .50 rate
is because the service offered seemed risky at .50. At $5, it seemed
more respectable, and took on value. The change in consumer behaviour
can be explained by the way the product was marketed.
To say that the way this service was priced is an example of how minimum
wages affect unemployment is way too simplistic.
...Brad
Robert Vienneau
A TALE OF TWO MODELS
1.0 ARROW-DEBREU MODEL OF INTERTEMPORAL EQUILIBRIUM
1.1 Commodities and Prices
"Prices" and "commodities" in this model differ from common usage. This
difference must be kept clearly in mind to avoid confusion.
Time is modeled as divided into small discrete intervals, starting
at some given instant. Each interval is referred to as a date. Goods
are distinguished by whatever physical characteristics are relevant
to the agents in the model. For example, there may be several grades
of wheat of concern. Goods physically identical except for
availability at different dates are distinguished as different
commodities. For example, a person-hour expended by a barber in
providing a haircut today and a week from today are different
commodities.
Debreu originally assumed there were only a finite number of
commodities; therefore, time comes to an end at a definite
date. The project of removing this restriction has revealed
some problems. Nevertheless, I'll discuss a model with an
infinite number of time periods below.
There is no money in this model. Prices are a real number in some
arbitrary standard. All (discounted) prices specify how much is paid
or received at the given initial instant at the beginning of time
in the model. These prices have an analogy to futures or forward
markets in that the commodities being paid for can be contracted
to be delivered at any specified date in the future. They differ
from existing futures market in that actually existing futures
markets typically contract for payment to also be made at the
future delivery date; the model prices are paid immediatedly. Forward
markets exist for all commodities for all future dates; no markets
exist at any date other than the initial date and no payments can
be made at any future time.
1.2 Exogeneous Data and Equilibrium Solutions
The given data consists of tastes, technology, and endowments.
Tastes are specified for each agent as follows. One imagines a
set of all possible consumptions plans for the each consumer,
where a consumer is one of two kinds of agents in the model. A
consumption plan is a list of commodities the consumer provides to
firms (e.g. labor services at a specified date, the use for
specified dates of a specified plot of land owned by the agent)
and a list of commodities delivered from the firms to the
consumer (e.g. a specified kind of cereal). Tastes are represented
as preferences defined over the set of consumption plan. These
preferences are assumed to satisfy certain criteria defining
"rationality" (e.g. completeness, reflexitivity, transitivity,
and another property of a complete ordering <=). Given preferences
are also commonly represented by utility functions. So consumers
are utility-maximizers.
The other kind of agent in the model is a firm. Firms face
a given technology. Technology is represented by a set of production
plans, where a production plan is a list of inputs and outputs.
By adopting certain sign conventions, both production and consumption
plans can be represented by netput vectors. For example, a negative
element in a netput vector for a production plan represents an
input; a positive element represents an output (a commodity
produced by the firm). The set of all production plans are assumed
to satisfy certain criteria (e.g. convexity, the set contains the
zero vector). Firms maximize (economic) profits.
Endowments are given as a vector of resources (a point in the
commodity space) owned by each consumer.
Finally, how much of each firm is owned by each consumer is given.
This allows the consumers' budget constraints to include profits
earned by the firm, although in equilibrium all profits are zero.
An "equilibrium of a private ownership economy" is a vector of
prices, a consumption plan chosen by each consumer, and a production
plan chosen by each producer where the consumers have maximized
utility, the firms have maximized profits, and the demand
for every commodity does not exceed the total endowments.
The relationship between equilibria and "efficiency" is clarified
in the first and second welfare theorems. An interesting implication
of "efficiency" in this model is as follows:
"Consider any efficient capital program and its corresponding
profile of prices and own-rates. *At every point of time the value
of the current capital stock at current efficiency prices, discounted
back to the initial time, is a constant* equal to the initial value. This
law of conservation of discounted value of capital (or discounted
Net National Product) reflects, as do the grand laws of conservation
of energy of physics, the maximizing nature of the path."
-- Robert Dorfman, Paul A. Samuelson, and Robert M. Solow,
_Linear Programming and Economic Analysis_, Dover, 1958
(Section 12-2-6).
The model is a symphony with three movements. First, equilibrium
prices are established somehow or other. All agents then make all
their transactions at those prices. All payments are immediate.
Finally, production and consumption occur with commodities
produced, delivered, and consumed at the contracted dates.
The agents pursue their plans and deliver commodities to one another
as contracted for at the initial instant. Unexpected events and any
inability to satisfy contracts are not considered in this exposition
of the model.
1.3 Dynamics Before the Beginning of Time
Equilibria are fixed points of some sort of dynamic process. In
this case, equilibria are the result of a Walrasian tatonnement or
"groping" process occuring in some sort of no-time before the
first date in the model.
A central authority or auctioneer calls out prices. The agents
determine their optimal plans at these prices and inform the
auctioneer of them. The auctioneer determines which goods, if
any, have a positive excess demand. The autioneer raises these
prices and lowers the prices for commodities with excess supplies.
The autioneer then calls out a new set of prices. The process
terminates when a vector of equilibrium prices is found. Commodities
with an excess supply will have prices of zero (free good rule).
No transactions are made, no contracts are entered, and no
production is begun during this process. It is only when
equilibria prices are found that the Arrow-Debreu model of
intertemporal equilibrium begins on the course outlined above.
1.4 Another Pseudo Dynamics
Consider a special case of the Arrow-Debreu model where commodities
consist of the identical n goods distinguished only by the time period
in which they become available. Let p( t, j), j = 1, ..., n; t = 0, 1, ...
be the
prices of these goods at the respective time periods. The own rate of
interest for each good at time t is defined as:
r( t, j ) = [ p( t, j )/p( t + 1, j ) ] - 1
Let r( t ) be the own rate of interest of the numeraire. Consider the
(undiscounted) prices defined with the own rate of interest of the
numeraire:
p'( 0, j ) = p( 0, j )
p'( t + 1, j ) = p'( t, j) [ 1 + r( t ) ]/[ 1 + r( t, j ) ]
Equilibrium in the Arrow-Debreu model is formally equivalent
to equilibrium set out in terms of these undiscounted prices. This
new model would have spot markets at all dates, but no forward
markets.
Under certain assumptions, the undiscounted prices approach
positive limiting values as time increases without bound. Let p( j )
be these prices, where the time index is deleted as being
unneeded. These limiting values are known as "prices of
production" or "natural prices." These are the equilibrium prices
discussed in the model in Section 2 of this essay.
1.5 Getting Into Equilibrium
Consider the above transformation of Arrow-Debreu equilibrium
prices into a succession of dated spot prices. One might think
this transformation would allow a disequilibrium groping process
to occur at each date throughout time, instead of only
before the initial instant. But one would be wrong.
Equilibria are defined by the dynamic processes which generate
them. If a different dynamical process was analyzed along these
lines, the equilibria would not be the Arrow-Debreu equilibria.
It's also unclear how the agents would recognize they were
in an Arrow-Debreu equilibrium. Suppose spot prices were
appropriate to an Arrow-Debreu equilibrium at some date. If one
used unchanged prices to determine investment decisions over the
future, one would find industries making unequal rates of profit
for an Arrow-Debreu equilibrium. Consequently, investment
would flow from the industries with lower rates of return
to the industries with higher rates of return. The economy
would immediately deviate from the Arrow-Debreu equilibria.
Suppose, on the other hand, firms realized prices would
change and used past history to construct forecasts for
determining investment decisions. It is unclear how they
could do this, since future prices are not a function of
observable past variables in the Arrow-Debreu equilibrium.
Rather, they depend on the plans of the agents, which
determine the prices and quantities. An accurate determination
by an agent of future profitability depends on the agent
having some understanding of the theories and plans in the
heads of the other agents in the model. I suppose it is
barely conceivable that if the economy was in
equilibrium, the agents would continue to carry out their
plans so as to keep it in equilibrium. But how could
the economy even approach any equibria? If we are not
in equilibrium today, why would one expect the economy
to be in equilibrium tomorrow?
As another way of understanding this difficulty, suppose
an economy was in an Arrow-Debreu equilibrium at some
date. All spot markets clear. If the agents take this as
a signal to leave quantity flows unchanged, generally the
economy would immediately deviate from Arrow-Debreu
equilibria.
1.6 Factor Demand Curves
In this model, factor demand curves are derived from
profit-maximizing production plans drawn up for given
technology and prices. Consider a price vector in which
the price of labor services of a specified date is set at
different values. It can be show that the firm will
hire no more labor at a higher wage than at a lower
wage. This is what a downward-sloping factor demand
means in this model.
Suppose the firm is on its factor demand curve at a
specified date. Would one expect the firm to hire
the same amount of labor at the same wage at the
next date? The correct answer is, generally no. Labor
at the succeeding date is a different commodity. Its
price, a wage, is generally different from the wage
at the date under consideration. Furthermore, there
is no reason to expect the firm to plan to employ
the same quantity of labor, even if the succeeding
wage was the same. After all, labor demand curves
are derived by considering variations in wages at
a given date.
Consequently, it is not clear that the usual supply
and demand stories in introductory microeconomics
are well-founded in the Arrow-Debreu model of
intertemporal equilibrium.
2.0 THEORY OF PRODUCTION IN LONG PERIOD POSITIONS
2.1 Gravitational Attraction
Equilibria are fixed points of classes of dynamic processes.
The dynamic processes considered in classical economics
have become known as processes of gravitational attraction,
after a metaphor of Adam Smith's. As the number of dates
increases, the agents adjust the endowments of produced
means of production, and relative prices approach stationary
values. An Arrow-Debreu intertemporal equilibrium is
a peculiar special case of such a process.
2.2 Exogeneous Data and Equilibrium Solutions
From the standpoint of the theory of production, the
data for analyzing the limit point of a classical
gravitational process are technology, outputs, and
either the wage or the rate of profits (interest rate).
For this special case, I take net outputs as given and
represent the technology in this section by a single
technique.
Accordingly, let the columns of the n x n matrix
A be the inputs needed for unit outputs of each
industry. That is, a( i, j ) is the amount of the ith
commodity used in the production of one unit
of the jth commodity. Let l be an n element row
vector denoting the quantity of labor employed
directly in each industry.
Net output is expressed by the n element column
vector y, where y( i ) is the net quantity produced
by the ith industry. Gross outputs are denoted by
column vector q. Gross and net outputs are related
as follows:
y = q - A q = ( I - A ) q
Or:
q = [ (I - A)^(-1) ] y
Suppose wages are advanced, and the workers
spend them in the proportions in the n-element
column vector d. Let the wage be w. Then the total
material inputs per unit output of each industry
are given by the matrix A':
A' = A + l d w
Steady state prices are given by the row vector p.
Since relative spot prices are stationary, all commodities
have the same own rate of interest in the limit being
examined here. Let r be that common rate of interest.
Prices must satisfy the following equation:
p A' ( 1 + r ) = p
Or
p A' = [ 1/( 1 + r ) ] p
The distinction between the rate of interest and a price
is analogous to the mathematical distinction between a
scalar function of an eigenvalue of a matrix and an element
of the corresponding eigenvector.
2.3 Labor Demand Curves
In the special case considered above, one can represent
each technique as producing the final output solely with
dated quantities of labor. The amount of labor expended
directly in producing the current year's output is:
v( 0 ) = l q = l [ (I - A)^(-1) ] y
The amount of labor that would need to have been
expended t years in the past, assuming this technique
had been used in the past is:
v( t ) = l ( A^t ) q = l ( A^t ) [ (I - A)^(-1) ] y
The total labor used in producing the output is then:
v( 0 ) + v( 1 ) + v( 2 ) + ...
We want to find how much labor will be hired in a long
period position in a vertically integrated industry per unit
output, given a choice of techniques. The amount of labor,
per unit output for the jth vertically integrated industry, can
be determined for any technique as above, where y is
replaced by the jth column of the identity matrix. This
analysis represents each technique as producing the output
solely by dated labor quantities. Thus, one can take the
price of the final output as given and consider how the
chosen technique is determined for each feasible level of
the wage.
The chosen technique is the cheapest. One procedure for
determining the cheapest technique is as follows. Pick
a technique, say, alpha. Calculate the internal rate of
return, where the internal rate of return is the interest
rate that equates the present value of the costs of labor
inputs to the present value of the outputs. Using this
interest rate, calculate the present value of the dated
labor quantities for each technique. The cheapest
technique found by this method for the model
considered here is independent of the technique
used initially to determine the internal rate of return.
I have shown that the least-cost technique at the
higher of two wages may be more labor-intensive
than the least-cost technique at the lower of the
two wages. That is, a more labor-intensive
technique may be cheaper at a higher wage in
a comparison of long period positions with given
technology.
One might generalize the model to include several
non-produced inputs, like several qualities of labor. The
wages of each one of these kinds of labor would be
exogeneous variables in a classical long period position.
Thus, one could take all wages but one as given. Each
technique can then be represented by inputs consisting
solely of dated quantities of these types of labor. Consider
which techniques are cheaper at two levels of the
remaining wage. Once again, there is no implication that a
technique using this kind of labor less intensively will
necessarily be cheaper at the higher wage. There seems
to be no rational foundation for downward sloping
factor demand functions in this model.
There are other ways of supplementing the model.
One could consider the use of land and other
unproduced commodities. One could assume variations
in returns to scale. One could assume technology that requires
the use of fixed capital, i.e. produced machines and plant
used to produce outputs at several dates. None of these
complications imply downward sloping factor demand
curves. In fact, it seems incoherent and illogical to model
long period equilibria by the intersections of monotonic supply
and demand functions. Interestingly enough, the best classical
economists did not use supply and demand functions
for this purpose. Later work has found fault with the
attempts of the early neoclassical economists to explain
normal prices by supply and demand theories.
(The above model can be combined with various theories of
distribution, of which I know at least three. In some of
these theories, variations of model parameters can lead
to bifurcations of long period equilibria. This finding
suggests gravitational processes can exhibit complex
dynamics.)
3.0 CONCLUSION
Given the structures of the two models, it is unclear
why one would think the Arrow-Debreu model provides
a better basis for empirical work. The prices in the model
would not persist and cannot be associated with averages
over various dates of observed prices. Classical prices of
production seem of greater economic significance.
Furthermore, the classical model has greater room for
incorporating theories reflecting "specific experience"
(Alfred Marshall), for example, in determining wages,
in examining unemployment conditions, and in
modeling innovations in technology.
The introductory economics story of how minimum
wages lead to unemployment is not well-grounded in
either model. This story relies on a model of the labor
market with monotone supply and demand functions.
An equilibrium in this story is supposed to lead to
constancy in wages and employment across dates. Thus,
the labor demand function in this story cannot be
identified with factor demand functions in the Arrow-
Debreu model. If long period equilibria were compatible
with supply and demand theories, they would provide
the rational foundation of the textbook story. But it can
be reasonably said that long period factor demand curves,
if they exist in this theory at all, can slope up.
Understanding what economists teach has been characterized
as "making sense out of complete nonsense."
4.0 AN ANNOTATED, SELECTED, AND OPINIONATED BIBLIOGRAPHY
4.1 General Overviews
Gerard Debreu, _Theory of Value: An Axiomatic Analysis of Economic
Equilibrium_, Yale University Press, 1959.
All well-educated economists have read this book. Contains a
terse and classic exposition of the Arrow-Debreu model. Presents
the theory in terms of set-theoretic mathematics in the style
of Bourbaki.
Piero Sraffa, _Production of Commodities by Means of Commodities:
Prelude to A Critique of Economic Theory_, Cambridge University
Press, 1960.
All well-educated economists have read this book. Contains
the seminal presentation of the modern revival of classical
theory. Has an elegant formal beauty and an architectonic quality.
Kenneth J. Arrow and Frank H. Hahn, _General Competitive Analysis_,
Holden-Day, 1971.
A textbook presentation of the Arrow-Debreu model. I have not
read this book. I should.
Luigi L. Pasinetti, _Lectures on the Theory of Production_, Columbia
University Press, 1977.
A textbook presentation of the circulating-capital special case of
the modern revival of classical theory. An elegant presentation
of the mathematics using matrix algebra.
Heinz D. Kurz and Neri Salvadori, _Theory of Production: A Long-
Period Analysis_, Cambridge University Press, 1995.
An advanced textbook presentation of post-Sraffian theory.
4.2 Recent Debates on the Relationship Between the Two Models
Frank Hahn, "The Neo-Ricardians," _Cambridge Journal of
Economics_, V. 6, pp. 353-374, 1982.
Mistakenly argues that Sraffa's model is a special-case of an
Arrow-Debreu intertemporal equilibrium path. Clarifies
marginal productivity theory, demonstrates that it is
not a theory of distribution, and shows that Sraffa's analysis
of the choice of technique is consistent with it.
G. Dumenil and D. Levy, "The Classicals and the Neoclassicals:
A Rejoinder to Frank Hahn," _Cambridge Journal of Economics_,
V. 9, pp. 327-345, 1985.
Shows that Frank Hahn was arguing against a strawman. Argues
that the Arrow-Debreu model is an uninteresting special case
of a classical gravitational process.
Pierangelo Garegnani, "Sraffa: Classical versus Marginalist
Analysis," in _Essays on Piero Sraffa: Critical Perspectives on
the Revival of Classical Theory_, (edited by Krishna Bharadwaj
and Bertram Schefold), Unwin Hyman, 1990.
Another answer to Frank Hahn examining his errors.
Concentrates on conceptual differences between the two
approaches to value and distribution. Important in
understanding contemporary assessments of the classical
theory of wages and employment.