Re: Replicating A Result In Cohen And Harcort

From: Igor (jjweatherby_at_houston.rr.com)
Date: 11/04/04 

Date: Thu, 04 Nov 2004 23:04:21 GMT

Robert Vienneau wrote:
> In article <XYlid.5004$nD6.1423@fe2.texas.rr.com>, Igor
> <jjweatherby@houston.rr.com> wrote:
>
>
>>Robert Vienneau wrote:
>
>
>
>>>Consider:
>>>
>>> Avi J. Cohen and G.C. Harcourt "Retrospectives: Whatever happened
>>> to the Cambridge Capital Theory Controversy", The Journal of Economic
>>> Perspectives Volume 17 No. 1 Winter 2003. <http://tinyurl.com/6pm6f>
>>>
>>>Figure 2 in that paper illustrates a case of capital-reversing.
>>>
>>>I happen to have a spread*** in which a qualitatively identical
>>>graph is generated, namely the file ChoiceOfTechnique.xls at
>>><http://tinyurl.com/3tcq4>.
>>>
>>>Here's how to generate this graph. Download the spread***. This
>>>spreadsheet consists of a number of worksheets. The one furthest to
>>>the left is called "Intro". On the "Intro" work***, change the
>>>entry in cell F30 to 2.
>>>
>>>Now look at the work*** furthest to the right, called "Numeraire
>>>Industry". Look at the graph starting at cell I94. This is the
>>>desired graph illustrating of capital-reversing, reflected around
>>>a 45 degree line through the origin.
>
>
>
>>>For some reason, some economists, who haven't been taught well,
>>>get excited about phenomena illustrated on the "Numeraire Industry"
>>>graph starting at cell I32. This graph shows that cost-minimizing
>>>firms will want to employ more workers per unit output at a higher
>>>wage around a switch point illustrating capital-reversing.
>
>
>
>>No they get excited when you try to say this INVALIDATES modern
>>economics.
>
>
> Mr. Weatherby doesn't know what he is talking about. It shows the
> neoclassical theory of value and distribution to be mistaken.
>
>
>>It does not it gives the same result that a long run
>>mainstream model would give.
>
>
> The mainstream response to the CCC, as Cohen and Harcourt note,
> was to advocate a very short run General Equilibrium model. Again,
> the Arrow-Debreu model of intertemporal equilibrium is not long
> run.
>
>
>>IN THE LONG RUN, an increase in wages has
>>an indeterminate effect on unemployment. As wages rise in the LONG RUN,
>>firms invest in more capital. That means an increase in labor demand
>>offsetting the initial decrease in employment. NB this assumes holding
>>all non wage factors constant. The long run effects are similar under
>>either model.
>
>
> Mr. Weatherby is mistaken in his "logic". His idea seems to be that
> firms will respond to an increased wage by:
>
> (1) Substituting capital for labor, thereby lowering the ratio
> of labor to output.
> (2) Raising the level of output.
>
> And Mr. Weatherby's poorly expressed objection is that since the
> the combination of these two effects on employment is indeterminate,
> the ultimate result is consistent with my result.
>
> But, once again, Mr. Weatherby does not know what he is talking
> about. The example shows the first effect does not exist.
>
>
>>Where you consistently blunder is saying that this model overturns a
>>SHORT RUN effect. The short run effect of an increase in wages, caused
>>by decreased supply or a price floor, will be less employment. This
>>assumes CAPTIAL IS CONSTANT. The concept of the short run drives
>>diminising returns which is precisely why an increase in the wage leads
>>to a decrease in the employment level.
>
>
> Mr. Weatherby is too ignorant to be able to accurately state
> mainstream theory. Consider this site:
>
> <http://www.courses.rochester.edu/oi/eco223/>

Verifies my argument.

"The Short Run Demand for Labor: (a) A production function is a
technical relationship describing how the rate of output is related to
inputs of labor N, capital K, and possibly other inputs such as energy,
materials, etc. In the short run, when inputs other than labor are
fixed, one can specify a short run production function, X = f(N). What
is the concept of the marginal product of labor, MPn = dX/dN? How is
the marginal product related to the total product X and to the average
product, AP?

(b) Demand by a single competitive firm: A firm will employ an
additional worker if the increment to total revenue, R'(N), exceeds the
increment to total cost. A firm selling output in a competitive product
market faces an infinitely elastic product demand at the market price P.
  Further, if the firm is a price-taker in the labor market, the
increment to total costs is the price of labor given by the wage rate.
Equilibrium is attained when the marginal revenue product of labor, MRP
= R'(N) is equated to the wage rate; MRP = P*(MPn) = W. The demand
curve for labor by a single firm will be downward sloping if there are
diminishing returns; i.e. if MP is inversely related to employment,
dMP/dN < 0. The position of the labor demand curve depends on the price
of the product P and the properties of the production function, f(N)
which in the short run is a function of the supply of the fixed input.

(c) Demand by the Industry: A set of firms that produce the same
product, say frozen pies X, constitutes an industry. The price of pies
P is inversely related to the output of pies, P = P(X) with P'(X) < 0.
The short run equilibrium of the frozen pies industry is described by
two equations. First, the MRP of labor in producing pies is equated to
the wage rate of labor. Given the number of firms in the pies industry,
the labor demands by all of the firms determines output X which, in
turn, determines the product price. This forms the second equilibrium
condition, namely, the output of pies equals the amount demanded. These
two equations jointly determine {N,P}, labor demand N and product price
for pies P. The labor demand curve for the industry is downward sloping
for two reasons. Each firm in the industry confronts diminishing
returns. An increase in employment expands output whose price P has to
be reduced to clear the market. "

"3.3 Long Run Demand for Labor: Employment is determined in the long
run in two steps. First, each firm demands labor and capital to
minimize the total cost of a given rate of output. This is accomplished
by equating the marginal rate of substitution of capital for labor to
the relative prices of the two inputs; MRS = (MPn/MPk) = w/r. Here r
stands for the price of capital. From this cost minimization problem,
one can derive a constant output demand for each input; N = N(w,r:X) and
K = K(w,r:X). In the second step, the long run marginal cost of output
is equated to the price of the product which in turn depends on the
output rate; LRMC = P = P(X). "

In the long run when returns are equalized an increase in capital
increases labor demand. This is the same argument given. CAN YOU READ?

Now read what the page says about your favorite study Card and Krueger.
"In 1996, David Card and Alan Krueger published Myth and Measurement:
The New Economics of the Minimum Wage. They concluded that "...contrary
to received wisdom, minimum wage increases do not appear to have any
adverse effects on employment." A policy that can raise the wages of
those at the bottom of the wage ladder with no job losses is remarkable.
  It rivals a perpetual motion machine or alchemy. Myth and Measurement
elicited a number of studies which questioned its empirical evidence.
Further, as Stigler and Burkhauser have pointed out, the minimum wage is
not the right policy instrument to combat poverty. Finally, employers
will respond to a wage floor not only by changing the level of
employment but also the other components of the job package. The debate
over the New Economics has largely ignored the impact of the minimum
wage on these other margins of an employment relation. "

DID YOU READ THIS? I would read things before you post them and find out
they say the opposite of what you thought.

>
> Apparently, the University of Rochester students correctly learn
> that J. R. Hicks' (mistaken) Theory of Wages was an important
> statement of the mainstream theory. And that theory develops
> downward-sloping labor demand curves in the long run, not the
> short run. For example, here's a quote from Hicks (which I
> get second-hand):
>
> "One of the cooperating factors - capital - is, at any
> particular moment, largely incorporated in goods of a certain
> degree of durability [...] If the capital is at present
> invested in durable goods, the change in conduct which
> follows from the change in relative profitability cannot
> immediately be realised. At the moment, only a small portion
> of the total supply of capital is 'free' - available for
> investment in new forms - and although this portion will be
> reinvested in ways more appropriate to the new situation,
> that in itself may make very little difference to the demand
> for labour [...]

Hicks says capital is fixed for a period of time.

In the short period, therefore, it is
> reasonable to expect that the demand for labour will
> be very inelastic, since the possibility of adjusting the
> organization of industry to a changed level of wages is
> relatively small [...]

This is an argument that labor demand is not responsive to wages in the
short run. NB this has not been empirically verified. However, this is
not incosistent with mainstream analysis. It simply assumes that labor
demand is inelastic or perfectly inelastic. Something that is easily
incorporated in the model. This just says firms operate in an inelastic
region or that labor demand curves are very steep but downward sloping
or vertical. This does not say a labor demand curve can have a positive
slope.

>Since the whole conception of marginal
> productivity depends upon the variability of industrial methods,
> little advantage seems to be gained from the attempt which is
> sometimes made to define a 'short period marginal product' the
> additional product due to a small increase in the quantity of
> labour, when not only the quantity, but also the form, of the
> cooperating capital is supposed unchanged. It is very doubtful
> if this conception can be given any precise meaning which is
> capable of useful application."
> -- J. R. Hicks (1932)
>

No where does he say anything about a long run effect. Only that in the
short run that labor demand may be inelastic and a wage change may have
little efffect. Hicks is arguing the short run is hard to define. This
says nothing about long run effects.

> And here's an economist that knows the traditional mainstream argument
> against minimum wages is a long-run theory:
>
> "Why would this effect occur a year after the minimum wage
> increase rather than right away? ... when the minimum wage increases,
> employers take time to adjust their methods of production. That is
> to say, it takes time for fast-food joints to buy new burger-flipping
> machinery that requires one teenager to operate rather than two."
> -- David Henderson,
> <http://www.davidrhenderson.com/articles/1098_minimumwageplus.html>
>
> Unfortunately, the mainstream argument is mistaken. I have proven that.
>

You can not even read what is written. This says the theory states that
the loss in employment is a short run effect. Lets add the piece of the
quotation you cut " Second, low-wage jobs turn over quickly, so
employers who don't like firing (i.e., most of them) tend to wait for
turnover and attrition to do the job for them." This clearly says it
takes a while for the business to react. Rather than fire they wait for
people to quit and do not rehire. 1 year does not mean long run. Long
run means time to CHANGE CAPITAL. The quotation clearly says that in one
year capital will not change. "it takes time for fast-food joints to buy
new burger-flipping
> machinery that requires one teenager to operate rather than two."

This clearly says in one year the firm can still be in the SHORT run
because capitial is still fixed. The argument is that the short run is
not a calendar time frame. It is how long it takes to CHANGE CAPITAL.
The argument in this quotation is exactly what I said. Employment will
drop in the short run due to diminishing returns in the long run
diminishing returns do not exist. Henderson is arguing 1 year may very
possibly be the SHORT RUN.

It does seem that Henderson may be of the belief that the increase in
productivity may not be enough to offset the negative effect of the
increased wage. I do not know if he is speaking from an empirical
standpoint or not. This is an assumption long run theory may or may not
support. It depends on the increase in productivity due to the new
capital. Henderson may be making an assumption that the theory says is
unclear.

To recap under a Cobb Douglas production function the MPL will be

\alpha L^{\alpha-1}K^{\beta}

The solution will imply that

MPL/w = MPK/r where r is the RENTAL rate or Price of capital.

The implication is holding labor constant increasing capital decreases
MPK in order to bring equality after an increase in wages. Looking at
MPL it is CLEAR that an increase in capital increases MPL.

Since in the short run W= PMPL. This will mean more labor hired at the
CURRENT wage. If the increase in MPL is small due to a low beta or a
small increase in capital in equilibrium the amount of labor hired will
be less than the amount hired before the increase in wages. A large beta
or a large increase in capital will mean more labor hired. So it depends
on how much capital is substituted and the size of beta. If the effect
of substitution is rather small then it will lead to a long run decrease
in employment. If there is a large substitution of capital it could mean
an increase in employment.

This effect also depends on the elasticity of labor demand. If labor
demand is very elastic than the short run effect of a minimum wage would
be devastating. It would take an extermely large increase in capital to
offset this. If demand is inelastic an increase in the wage would only
have a small impact on short run employment. This is the argument you
posted from Hicks. Contrary to your belief Hicks is not arguing that the
labor supply labor demand framework is wrong only that labor demand is
likely to be inelastic so the wage causes little to no change in hiring.
This is consistent with a perfectly inelastic or nearly perfectly
inelastic labor demand curve. In the long run a small increase in
capital could increase employment. Henderson may be making the
assumption that labor demand is highly elastic. I can not say this was a
short piece written for an audience of non-economists so his analysis is
not in depth.

The elasticity argument is also a big contention among economist. Is
labor demand inelastic or elastic. Is supply elastic or inelastic. This
is difficult to obtain because the model does not quite fit the
macroeconomy. I think it is appropiate analysis for a single market.
Even then labor is not homogenous but you have less error. In the macro
sense it is very inappropiate because markets may vary largely in
elasticity. The demand for burger flippers may be very inelastic while
the demand for sales clerks may be elastic. This would mean policies
would affect the two markets differently. A minimum wage for burger
flippers would not decrease employment much and in the long run might
have a slightly positive effect on employment as the increase in capital
increased productivity. A minimum wage for sales clerks would like have
a negative impact in the long and short run. So the elasticity of demand
is extermely important and may vary among workers.

>
>>IN THE LONG RUN DIMINISHING
>>RETUNRS DO NOT EXIST. This is because capital can change. If you can
>>supply the new worker with capital there is no reason to assume
>>diminishing returns. This means in the long run, all bets are off and
>>the prediction may not hold. The short run is a period of time where
>>capital can not change. YOUR MODEL HAS NO SHORT RUN IMPLICATIONS.
>
>
> Simply untrue. Even if a model is long run, it may have short run
> implications. Some authors to read about disputes about the short
> run implications of the Cambridge Capital Controversy are Michael
> Mandler, Fabio Petri, and Bertram Schefold, for example.
>

Your model has no short run implications because if you fix capital then
the marginal product of labor is independent of workers hired. So it
says nothing about how workers will be hired if the process can not change.

>
>>IT IS
>>A LONG RUN MODEL. You have not found anything extremely exiting or even
>>interesting. It predicts what mainstream economist already predict.
>
>
> That's right. It predicts results the mainstream economist Paul
> Samuelson well knows. Unfortunately, most mainstream economists, such as
> John Weatherby, are simply ignorant of correct - that is, post-Sraffian -
> price theory.
>

It is a result every mainstream economist knows well. As the Rochester
site shows that the solution for a long run when capital is changed
differs from the short run. The feedback effect is an increase in
capital will increase productivity of and demand for labor.

>
>>... Even some of the best
>>texts have simplifications that lead to misconceptions in them. A
>>otherwise very good textbook on the market actually states there is a
>>law of supply...
>
>

>
>>A misconception that occurred when the author was
>>obviously trying to omit some material about rare cases and make the
>>subject a bit easier to learn.
>
>
> This isn't about what is incorrectly considered "rare".

This was a comment about one misconception from one textbook. What is
considered rare? I was refering to a downward sloping supply curve. That
is why cases contrary to the mistaken law of supply are rare. There are
few if any decreasing cost industries.

> The neoclassical theory of value and distribution is fatally flawed.
> It is getting on near half a century since this has been demonstrated.
>

So no one uses the models. We use general equilibrium models. Read Cohen
and Harcourt it clearly states that these models give similar results
and that is why the general equilibrium round was said to have solved
the controversy.

You still do not understand the difference between short and long run
and how that changes the analysis of the effect of an increased wage on
employment. The Rochester site is a good start. You need to a little
work past the statements about the long run but the tools are there that
verify the result I obtain in a model you dismissed out of hand. I
assume because you believed that r meant interest rate rather than
rental rate on capital. No assumption about the equality of the two
terms was necessary to solve the model and get an indeterminate result
of the effect of an increase wage on labor employed.

Again Rob you are more guilty of what you accuse mainstream economics
of. You know the alternative theories but are really fuzzy on what
mainstream economics actually says. Cohen and Harcourt was the beginning
of understanding that but you still have serious misconceptions about
what is mainstream economics and what the theory predicts. You are tying
today's economist unfairly to the past. You need to do some reading and
catch up. I mean reading with an open and unbiased mind so you are not
constantly twisting something into something it is not.

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