Upward-Sloping Labor Demand Curves
Robert Vienneau
This post reviews a problem. I then bring some literature to your
attention where this topic is discussed. The question addressed here
is whether it is appropriate or the pratice of economists to
describe a certain effect as an upward-sloping labor demand
curve.
2.0 REVIEW OF THE PROBLEM
Consider a (vertically integrated) firm facing a given technology.
A technology can be thought of as a book of blueprints. Each page
describes one possible technique for making a specified net output.
(The book may contain an uncountably infinite number of pages). I
have previously presented detailed examples in which a
cost-minimizing firm chooses to adopt a more labor-intensive
technique at a higher wage. This is a logical possibility in this
framework.
I claim that this possibility shows as mistaken traditional teaching
about, for example, why a minimum wage causes unemployment. Many
textbooks show that firms will necessarily choose to employ more
labor at a lower wage. This textbook assertion is false.
Some posters have previously gotten angry when I've pointed this
out. The question here is whether the logical possibility I am
describing is properly described as an "upward-sloping labor
demand curve." I have been quite tentative about any such
wording in my last few go-arounds on this topic.
Labor demand curves are constructed given technology, as above.
Each point on the curve is constructed by considering a given
vector of prices, the price vector differing for each point.
I claim the quantity is determined by considering an equilibrium
of the firm for each price vector:
"Given the price system p, the jth producer chooses his
production set Y(j) so as to maximize his profit. The resulting
action is called an equilibrium production of the jth producer
relative to p."
-- Gerard Debreu, _Theory of Value_, 1959, p. 43.
I think that this implies, in a long run context, that the firm
is on the so-called factor-price frontier. Prices other than
the wage and the interest rate are functions of the wage on
the factor-price frontier. A higher wage is associated with
a lower interest rate and different commodity prices.
Others insist that a labor demand curve can be drawn only by
varying only the wage, given other prices and the interest rate.
In a long period context and the sort of technology I normally
consider, it would be logically inconsistent to draw a
labor-demand curve with any (non-zero) slope at all.
3.0 SOME LITERATURE
I now summarize some literature that discusses these points.
3.1 Antonella Stirati
Some economists are quite aware of the argument that there is no
logical basis for the neoclassical theory of a long-run necessarily
downward-sloping labor demand curve. Some summarize the results
of this argument without talking about upward-sloping labor
demand curves. As an example, consider Antonella Stirati:
"The idea of an inverse relation between wages and employment is
central to the marginalist or neoclassical wage theory. In that
context it depends on the possibility of substitution between
production factors (direct substitution) and consumer goods
(indirect substitution) following changes in distribution. It is
argued that when, for example, the labor supply increases, the
fall in wages due to competition among workers will make it
advantageous for employers to use more labour-intensive production
techniques, and this, other things being equal, will bring an
increase in employment (and vice versa if wages rise).
[Footnote 15:] Recently economists have tended to construct
'short-period' demand curves for labour, which assume given
equipment, rather than the type of substitution described
in the text - based on a change in production methods and in
the type of machinery used - which takes a longer time to
carry out. This way of dealing with the demand for labour,
however, meets the following problems, described by Hicks:
'one of the cooperating factors - capital - is, at any
particular moment, largely incorporated in goods of a certain
degree of durability [...] the change in conduct which
follows from the change in relative profitability cannot
immediately be realised. [...] 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 [...] 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' (Hicks, 1932, pp. 19-21).
In addition, it is argued that (in the same situation) a drop in
wages will reduce the prices of those goods whose production
requires relatively more labour. On the basis of the marginalist
theory of consumer behavior this will lead to an increase in demand
for such goods compared to those whose production is less labour-
intensive. This will result in increased employment in the economy
as a whole.
[Footnote 16:] Both of these substitution mechanisms are subject
to serious difficulties and criticisms, which I shall not go into
here; suffice it to mention that both direct and indirect
mechanisms fail because, as was shown by Sraffa and then during
the 1960s in the debate on capital theory, relative prices do not
necessarily change in the direction predicted by marginalist
theory following variations in distribution: if wages fall the
prices of more labour-intensive products may actually go up
rather than down, and the more labour-intensive techniques may
become *less* advantageous. The marginalist theory of demand
also meets serious problems in demonstrating that changes in
relative prices really do lead to substitution in consumption
favoring goods whose relative price has fallen; on the latter
point see Kirman, 1989.
If these arguments are accompanied by the idea that competition means
unlimited downward flexibility of wages when there is unemployment,
we have a tendency for the labour market to adjust automatically
towards full employment.
[Footnore 17:] Of course, downward sloping labour demand curves
and wage flexibility ensure a tendency to the full employment of
labour only if there are no obstacles to the adjustment of
investments to full employment savings, such as persistent
rigidities in the interest rate.
-- Antonella Stirati, _The Theory of Wages in Classical
Economics_, Edward Elgar, 1994.
This book is translated from Italian and based on a successful PhD
thesis supervised by P. Garegnani. Stirati's position seems to be
be that the Classical economists did not describe wages and
employment as ultimately determined by supply and demand, and that
their theory can be reconstructed in a logically consistent manner.
3.2 Bertram Schefold
The German economist Bertram Schefold mentions factor demand curves
with positive slope:
"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, "Joint Production, Intertemporal Preferences,
and Long-Period Equilibirum," _Political Economy: Studies in
the Surplus Approach_, V. 6, 1990, pp. 162-163.
3.3 J. E. Woods
J. E. Woods has presented implications for microeconomics of a
correct analysis of the choice of technique:
"In this section, I discuss some implications for microeconomics
of the theory of the choice of technique derived above. To be
specific, I shall concentrate on the relationship between the
quantity of an input used in an industry and its price. This
analysis will be conducted within the simplest possible
framework...Any negative conclusions drawn from such a model
apply a fortiori to more general systems...I consider, first
of all, four numerical examples."
-- J. E. Woods, _The Production of Commodities: An Introduction
to Sraffa_, Humanities Press, 1990.
The examples rely on an analysis of the cost-minimizing choice
of technique in a long run position. They show that the sectoral
use of a produced input need not be inversely related to its
price, that the direction of this association can be dependent
on the choice of a numeraire, and that the sectoral use of a
produced input may not even be an unique function of its price.
Furthmore, the amount of labor employed may not be an inverse
function of the wage, either in a given sector or in the economy
as a whole. Woods' detailed analysis of his examples does not
refer to these relations between input uses and prices as
"demand curves." He does use this expression in summarizing his
findings, though:
"The main conclusion to be drawn from this section is a
negative one: there is not necessarily an inverse monotonic
relation between the cost-minimizing quantity of an input
and its price. This has been demonstrated with respect to
produced commodities...and non-produced inputs...Thus, the
proposition that the cost-minimizing quantity of an input is
inversely related to its price is invalid. It might have
been presupposed that the failure of this proposition could
be attributed to the possibilities of reswitching and
recurrence...Yet the proposition fails in models where there
is no reswitching...Apparently 'perverse' results can be
obtained in 'reasonable' technologies. Clearly, the failure
of the proposition has nothing to do with reswitching or
recurrence.
The theory developed in this chapter relates to choice of
technique, i.e. a whole set of input coefficients, rather
than of a particular input coefficient...In so far as it
relies on the proposition, traditional theory can be
criticized on the basis of the conclusions drawn from the
examples and the discussion above. In particular, the
notion of substitution - which seems to rely on changes
in input quantities being in the opposite direction to
the respective price changes - is called into question.
Though this section has been devoted to microeconomic
implications of the theory of choice of technique, it is
appropriate to conclude with a brief discussion of a
macroeconomic implication, especially as it arises from
the same analysis. Figures 6.17a-6.17c can be interpreted
as demand curves for labour. The relation between l(2)
and w(2) is a microeconomic demand curve for labour, that
of the second industry. The relation between v(2) and
w(2) can be interpreted as a macroeconomic demand curve
for labour, which would occur if there were a net output
of only the second commodity. In Figure 6.17a, both the
sectoral and aggregate demand curves for labour are
downward-sloping; in Figure 6.17b, the aggregate demand
curve is downward-sloping while the sectoral demand curve
is upward-sloping. In a two-sector, three process model,
the aggregate demand curve is necessarily downward-sloping
in the absence of reswitching. I have shown in Figure 6.17c
that the aggregate demand curve is not downward-sloping in
the presence of reswitching: indeed, like the sectoral
demand curve, it is not even monotonic. Reswitching is
sufficient, not necessary, for the aggregate demand curve
for labour not to be downward-sloping: to see this,
consider Figure 6.18...
In Figure 6.17b, it was shown that the sectoral demand curve
for labour was not necessarily downward-sloping, even in the
abscence of reswitching and recurrence of techniques. In
Figure 6.18b, is has been shown that this negative conclusion
can be extended to the aggregate demand curve for labour. Of
course, this raises doubts about the validity of the
aggregate demand curve for labour as traditionally employed
in the macroeconomic models."
3.4 Ian Steedman
In an earlier paper, Ian Steedman never describes the relationship
between input use and prices constructed from the analysis of the
choice of technique as "factor demand curves." Yet he is clear that
these results call the traditional teaching into question:
"Introduction
During the capital theory debates of the 1960s and early 1970s,
attention was naturally centered on the relations between
capital-labor ratios (or capital-output ratios) and the rate of
interest in the economy as whole, or at the vertically integrated
sector level. It was always *implicit* in the results of those
debates, however, that input use per unit of output need not be
related to relative prices in the 'conventional' way even at the
level of the individual process. Yet it seems that these 'micro'
implications of the capital theory debate have not always been
fully recognized by those working in particular 'microeconomic'
fields. Thus labour economics, for example, appears to have felt
little influence from those capital theory debates, as if these
latter concerned *only* the 'demand for value capital.' The
purpose of this paper is to render quite explicit the implications
of the use of produced means of production for direct input
demands, at the firm and industry levels, and to relate those
implications to conventional results concerning the 'downward
sloping demand curve' for any input. It will emerge that the
presence of produced inputs has significant implications for such
'demand curves' even when the rate of interest is zero.
1. Three examples
It will be shown in this section, by means of three simple examples,
that input use need not be inversely related to the corresponding
'price', even at the direct industry level. Since each model
presupposes the existence of constant returns to scale, our focus
will be, more specifically, on the relation between input use
*per unit of output* and the 'price', a relation which is, of
course, an inverse one in the conventional theory of production."
-- Ian Steedman, "On Input 'Demand Curves,'" _Cambridge Journal
of Economics_, V. 9, pp. 165-172, 1985.
And
"It has been shown that the cost-minimising use of an input,
per unit of output, need not be inversely related to the 'price'
of that input. It has also been seen that these results are
not logically inconsistent with the conventional proof that
the 'own price demand curve' for an input (for given output)
is always downward sloping. Rather, this latter result is
revealed to be a partial equilibrium result which has no
bearing on long-period analysis, where its conditions of
application never obtain."
-- p. 170
Steedman summarizes a widely used "proof" that labor demand curves
are downward-sloping and explains why it is inapplicable:
"The conventional analysis of the cost-minimising choice of the
inputs used to produce a given output is both simple and powerful;
it does not depend on such strong assumptions as differentiability
or even convexity of the (physically specified) isoquants. Let x
be a column vector of inputs, both produced and primary; and let
pi be the corresponding row vector of prices, wage rates, etc.
Let x* be a solution to the problem of minimizing pi . x
subject to producing a given output and let ( x* + deltax*)
be a solution when pi changes to (pi + deltapi ). By the very
meaning of minimisation, pi x* <= pi (x* + deltax* ) and
(pi + deltapi) (x* + deltax*) <= (pi + deltapi) x*. But these
two weak inequalities entail that
deltapi deltax* <= 0. (1)
Relation (1) is not in any significant sense a specifically
'neoclassical' result; it is a logical implication of cost
minimisation and that is that. The next step in the conventional
analysis is then to point out, correctly, that if deltapi(j)
is the only non-zero element of deltapi then, from (1),
deltax*( j ) deltapi( j ) <= 0. (2)
The amount of any input used to produce a given output is a
non-increasing function of its price (wage, etc.). But if (1)
is correct and (2) follows validly from (1), how could our
three examples all exhibit an input use, per unit of output,
which was positively related to the corresponding 'price'?
The answer is, of course, very simple; whilst (1) is always
satisfied in our examples, (2) is simply irrelevant (*not*
invalid) because it is never the case, in those examples,
that one *can* change just one input price. The step from (1)
to (2) involves not only raising pi(j) relative to all the
other elements of pi, but also keeping all (pi(i)/pi(k)) -
i /= j /= k - constant. In general, *this simply cannot be
done whilst remaining on the wage-interest rate frontier or
the appropriate wage-rent frontier*. If one stays on the
appropriate frontier - that is, if one considers only
long-period value and distribution constellations - then, in
general, the step from (1) to (2) cannot be made. (2) is still
logically valid, of course, but is completely irrelevant...
In brief, if we only compare positions on the wage-rent-interest
rate frontier then, in production models in which means of
produced means of production are employed and input proportions
differ as between productive processes, relations such as (2)
simply have no place, for (2) is derived under conditions
which *cannot* be satisfied (except by a fluke). Whilst (1)
holds good in any competitive, cost-minimizing economy, (2) is
a partial equilibrium result which *has no application* to
long-period comparisons. It is to be hoped that this way of
presenting matters will help those thoroughly drilled in the
argument leading up to relation (2) to accept more easily,
Pasinetti's statements to the effect that input quantity
ratios and input price ratios are not systematically related."
-- p. 167-168 (notation changed due to ASCII limitations
and an obvious error corrected.)
Steedman documents that economists have discussed long-period
labor demand curves:
"Hicks, for example, has written that 'In the short period...
it is reasonable to expect that the demand for labour will be
very inelastic...but if time is allowed the elasticity grows
very considerably' (1968, p. 20). This is the standard view of
contemporary labour economists: thus Bellante and Jackson, for
example, state that 'the long-run demand curve for labour is
more elastic than the short-run demand curve' (1979, p. 29)
and Ehrenberg and Smith confirm that 'the demand for labour
is more elastic in the long-run than in the short-run' (1984,
p. 93)."
Steedman is amusing on the logical inconsistency mentioned in my review
of the problem:
"...our findings about long-period input 'demand curves' are
a particular expression of Sraffa's famous critique of partial
equilibrium analysis (1925, 1926). If his arguments continue
to be ignored in (much) practice, one must remember that they
are not yet sixty years old!"
Steedman distinguishes his analysis from general equilibrium:
"There remarks clearly imply the need to go beyond the usual
partial equilibrium analysis of the demand for inputs, *whether
in its short-run or its long-run form*. It is just this need
to go beyond partial equilibrium analysis that our examples
were intended to illustrate. It does not follow, of course,
that one must have recourse to a 'full neoclassical general
equilibrium' - indeed our point has already been made in terms
of long-period positions alone. It is sufficient to compare
positions on the wage-rent-interest-rate frontier to show that
input use and 'price' need not be inversely related; one does
not need to 'close the system' in any way. Our point, then, is
not identical to the general equilibrium one that changes in
the data have complicated consequences for the endogeneous
variables"
4.0 CONCLUSION
This limited literature survey shows some economists are aware
that the neoclassical theory of input demand curves is without
convincing logical foundation. Some economists are willing to
occassionally describe the Cambridge argument as showing the
logical possibility of upward-sloping input demand curves. The
point is that a technique that uses an input more intensively
may be cost-minimizing at a higher price for that input, given
altered prices for all other prices that vary endogeneously
with the given input's price in a comparison of long run
positions.
The semantic question does not alter the logic of the case. In
a comparison of equilibria of the firm, one may find a higher
price of an input is associated with a choice of a technique
that uses that input more intensively. Consequently, a higher
wage may be associated with a desire of firms to employ more
labor, given technology.
Some of those who understand this argument have indicated the
need for theories that explain wages and employment on a
basis other than supply and demand. There has even been
work developing such theories by placing Keynes in a setting
related to Classical economics.
--
Robert Vienneau
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@ c or virtue, are always found...in proportion to
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John J Weatherby
>
> Labor demand curves are constructed given technology, as above.
> Each point on the curve is constructed by considering a given
> vector of prices, the price vector differing for each point.
> I claim the quantity is determined by considering an equilibrium
> of the firm for each price vector:
order conditions. Your confusion comes from think in two dimensions only. To
find cost min./profit max. combinations the systems of equations given by
FOC's are solved. Therefore both of your statements are correct. Not just
one.
>
> "Given the price system p, the jth producer chooses his
> production set Y(j) so as to maximize his profit. The resulting
> action is called an equilibrium production of the jth producer
> relative to p."
> -- Gerard Debreu, _Theory of Value_, 1959, p. 43.
>
> I think that this implies, in a long run context, that the firm
> is on the so-called factor-price frontier. Prices other than
> the wage and the interest rate are functions of the wage on
> the factor-price frontier. A higher wage is associated with
> a lower interest rate and different commodity prices.
Again you are only tinking in two dimension. This is a static statment it
does not show the comparitve statics. This hold everything else constant.
This is the cost min/ profit max. output at current r and w if r or w
changes these isoquants shift. Just because r rises doesn't mean w
decreases.
>
> Others insist that a labor demand curve can be drawn only by
> varying only the wage, given other prices and the interest rate.
> In a long period context and the sort of technology I normally
> consider, it would be logically inconsistent to draw a
> labor-demand curve with any (non-zero) slope at all.
>
Even with constant returns to scale the MPL (marginal product of labor) is
decreasing as labor increase. Look back to FOC of profit you see MPL= the
real wage. As L increases MPL decreases. The real wage must drop to justify
hiring more labor.
> In addition, it is argued that (in the same situation) a drop in
> wages will reduce the prices of those goods whose production
> requires relatively more labour. On the basis of the marginalist
> theory of consumer behavior this will lead to an increase in demand
> for such goods compared to those whose production is less labour-
> intensive. This will result in increased employment in the economy
> as a whole.
Shooting yourself in the foot over a misunderstanding. This says as wages
drops employment rises. Downward sloping demand.
> [Footnore 17:] Of course, downward sloping labour demand curves
> and wage flexibility ensure a tendency to the full employment of
> labour only if there are no obstacles to the adjustment of
> investments to full employment savings, such as persistent
> rigidities in the interest rate.
>
> -- Antonella Stirati, _The Theory of Wages in Classical
> Economics_, Edward Elgar, 1994.
>
> This book is translated from Italian and based on a successful PhD
> thesis supervised by P. Garegnani. Stirati's position seems to be
> be that the Classical economists did not describe wages and
> employment as ultimately determined by supply and demand, and that
> their theory can be reconstructed in a logically consistent manner.
>
What Stirati is reforming to price and wage inflexiblity presented by
nominal rigidities. This if true supports the Keynesian argument that
markets may be slow to adjust but gives no proof to upward sloping demand or
even any implication of 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...
Proof where. May I bring your attention to relevant range. Second this
assumes some sort of very wierd nonconvex technology. Theoretically it may
exist but has ever seen it. Might as well chase UFO's.
>
> 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..."
What does he propose to replace it with? Convincing conditions of sufficent
generality? Ok just ignore the emprical work of the past 50 yrs. Sure sounds
good now.
> -- Bertram Schefold, "Joint Production, Intertemporal Preferences,
> and Long-Period Equilibirum," _Political Economy: Studies in
> the Surplus Approach_, V. 6, 1990, pp. 162-163.
>
Has anyone else ever heard of this journal?
> The examples rely on an analysis of the cost-minimizing choice
> of technique in a long run position. They show that the sectoral
> use of a produced input need not be inversely related to its
> price, that the direction of this association can be dependent
> on the choice of a numeraire, and that the sectoral use of a
> produced input may not even be an unique function of its price.
> Furthmore, the amount of labor employed may not be an inverse
> function of the wage, either in a given sector or in the economy
> as a whole. Woods' detailed analysis of his examples does not
> refer to these relations between input uses and prices as
> "demand curves." He does use this expression in summarizing his
> findings, though:
Of course you won't finding totaly negitive sloped demand curves here there
is the possibility of fixed porportion technology (Leontiff functions). In
this case labor demand is infinitely sloped (perfectly inelastic) because it
can only be used in fixed proportions to capital. If you want to include
these and the possibility of perfectly elastic labor demand. Sure you don't
always have negative slopes, but if it isn't zero or infinity it is
negative.
>
> "The main conclusion to be drawn from this section is a
> negative one: there is not necessarily an inverse monotonic
> relation between the cost-minimizing quantity of an input
> and its price.
See above note.
>
> The theory developed in this chapter relates to choice of
> technique, i.e. a whole set of input coefficients, rather
> than of a particular input coefficient...In so far as it
> relies on the proposition, traditional theory can be
> criticized on the basis of the conclusions drawn from the
> examples and the discussion above. In particular, the
> notion of substitution - which seems to rely on changes
> in input quantities being in the opposite direction to
> the respective price changes - is called into question.
The notion of substitution is not called into question. It allows for fixed
porportion technology that has an infinite slope. Yet you would have to be
Trotsky to believe it exist in the aggregate. I don't even think most
micro-economist use it much. It mostly used for comp questions so that get
you out of the calculus mode catch your off guard and make you think rather
than blindly apply the calculus.
> Steedman is amusing on the logical inconsistency mentioned in my review
What logical inconsistency. You need to read the whole paper or the whole
book not just skim for paragraphs that support your postion.
> "...our findings about long-period input 'demand curves' are
> a particular expression of Sraffa's famous critique of partial
> equilibrium analysis (1925, 1926). If his arguments continue
> to be ignored in (much) practice, one must remember that they
> are not yet sixty years old!"
What are there findings what was Sraffa's findings?
> of long-period positions alone. It is sufficient to compare
> positions on the wage-rent-interest-rate frontier to show that
> input use and 'price' need not be inversely related; one does
> not need to 'close the system' in any way. Our point, then, is
> not identical to the general equilibrium one that changes in
> the data have complicated consequences for the endogeneous
> variables"
>
Again highly therotical can't determine they are always negatively because
Leontiff functions could exist. Again you would have better luck finding a
UFO
> This limited literature survey shows some economists are aware
> that the neoclassical theory of input demand curves is without
> convincing logical foundation.
No it says that there might be cases where the demand curve is not always
negatively sloping. i.e. Leontiff
There is convincing logical evidence just take FOC of the profit function
and assuming decreasing MPL. The second derivate of profit with respect to
labor is less than zero.
I suppose if you assume some wonder machine changes this anything could
happen.
Again you will have better luck proving Monica Lewisky is realy an alien
leader trading technology with the US in exchange for much needed human
bodily fluids.
Some economists are willing to
> occassionally describe the Cambridge argument as showing the
> logical possibility of upward-sloping input demand curves. The
> point is that a technique that uses an input more intensively
> may be cost-minimizing at a higher price for that input, given
> altered prices for all other prices that vary endogeneously
> with the given input's price in a comparison of long run
> positions.
>
Sorry still doesn't work even if this a wonder input and a company will use
this input exclusively regardless of the wage rate, there is still
diminishing marginal product. The only way that can conceivably be denied is
with Leontiff technology. Even at that it MPL falls to at any level above
the fixed porpotion.
One more clarifing comment you seem to associate the need for upward sloping
supply curves to invalidate classical macro. This is not the way to do it.
Check out John Taylor, or Copper and John, or Greg Mankiw's work. The reason
they argue that neoclassical economic is not valid is not because
diminishing marginal product doesn't exist not because the demand for labor
may not always be negatively slope rather because there real and nominal
rigidities that keep the economy from immediately adjusting. Just a couple
of examples, staggered wage contracts make wages slow to adjust, There are
cost associated with change prices(relabing, reprint catalogues, flyers,
menu) that make firms slow to adjust, or there are coordination failures.
Just because you don't buy RBC doesn't mean you have to jump to extremes to
disprove it. There are better ways.
John J Weatherby
Robert Vienneau
[...]
John,
You just do not understand. I happen to have some long essays that
explain this stuff slowly. I'll present three.
I have a number of interesting examples of an effect. Sometimes
economists mistakenly think that these examples use fixed coefficients
of production (Leontief production functions). I assume constant returns
to scale, a widely used assumption in neoclassical theory. I also
assume at least two processes are available for producing at least one
commodity. These processes use the same set of inputs { steel,
corn, labor } for producing the output, but exhibit different
coefficients of production. So I do not assume constant coefficients.
An interesting aspect of this approach is that any continuously
differentiable well-behaved neoclassical production function can
be approximated arbitrarily closely by linear combinations of
processes like those in my examples. I think a geometric illustration
of two-dimensional isoquants might convince undecided readers of
this point.
Accordingly, consider isoquants of two different processes
for producing gross outputs of some commodity. Let X1 and X2
represent the quantities of inputs. The output produced by
a single process is given by a function of the form:
min( X1/a1, X2/a2 )
where a1 and a2, the coefficients of production, are given
parameters for a process, but vary between processes. The two
diagrams below show isoquants for each process.
/|\
| | |
| | | |
| | .______________ | | | |
| | | | | |
| | | | | .______
| | X2 | | |
X2 | ._________________ | | .__________
| | |
| | ._______________
| |
+--------------------> +-------------------->
X1 X1
The points of the L-shaped isoquants lie along a ray through
the origin with the equation X2 = ( a2/a1) X1.
A firm with these processes available does not need to
choose one or the other for producing all output. The firm
can choose a linear combination. In this case, an isoquant
would then look something like the following:
/|\
| |
| |
| .
| .
| .
| .
X2 | .__________
|
|
|
+-------------------->
X1
An isoquant with linear combinations of pairs of three processes
might look like so:
/|\
| |
| |
| .A
| .
| .
| .
X2 | +
| . B
| .____________
|
+-------------------->
X1
Note that by increasing the number of processes, the resulting isoquants
could be arbitrary close to a smooth curve with slopes of the linear
combinations varying for each pair. Also note that there's an
optimization process underlying the construction of these isoquants.
A nonoptimal choice for the firm would be to produce the same level
as shown in the above isoquant along a line connecting A and B.
I cannot draw hyperplanes in N dimensions. I hope the reader can
see, however, that this approximation approach applies to smooth
neoclassical production functions with N arguments, each argument
representing another input.
There are differences between production functions with differentiable
isoquants and these approximations which are not differentiable
at a finite number of points. There's a theorem, whose proof
I haven't thoroughly studied, that asserts something like the following:
Given a smooth, differentiable production function for one
commodity that is basic in all techniques, reswitching of techniques
cannot occur. (A commodity is basic iff it is used either directly or
indirectly in the production of each produced commodity. For example,
if iron is used in producing steel and steel is used in producing
cars, then iron is used indirectly in producing cars.)
Reswitching and capital reversing are different phenomena. Reswitching
is sufficient but not necessary for capital reversing. The point of
my examples is often a corollary of capital reversing - what might be
called labor reversing. The hypotheses of the theorem seem not to be
sufficient to rule out capital reversing. Anybody thinking otherwise
could probably get a proof published.
There's also a question about whether the assumption of the existence
of a basic good is needed. I don't think neoclassical economists should
be happy relying on this assumption. If no good is basic, the
reduction of a circulating capital example to inputs consisting solely
of quantities of dated labor will result in a finite sequence. It seems
both capital-reversing and reswitching are possible with smooth
production functions in this case. At least Paul Samuelson believes
that, and he's probably still quite cautious about drawing conclusions
about these matters.
References:
Tatsuo Hatta, "Capital Perversity", _The New Palgrave: Capital
Theory_, 1990.
Tatsuo Hatta, "The Paradox in Capital Theory and Complementarity
of Inputs", _Review of Economic Studies_, V. 43, pp. 127-42, 1976.
Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and Modern
Economic Theory_ (edited by G. R. Feiwel), New York University Press,
1989.
V. Walsh and H. Gram, _Classical and Neoclassical Theories of
General Equilibrium: Historical Origins and Mathematical Structure_,
Oxford University Press, 1980.
Robert Vienneau
This essay outlines some tools for analyzing the choice of
technique in long run positions. It shows that these tools apply
to continuously differentiable production functions and other
production functions with variable coefficients of production.
The choice of technique is a microeconomic problem. The solution
does not use any price or quantity indices. Nor does it use any
methods of aggregation.
This essay also discusses some consequences of this analysis,
namely that certain traditional beliefs of neoclassical economists
are false. It shows that long run prices, especially factor prices,
are not scarcity indices. This conclusion can be substantiated
even when reswitching does not occur on the wage-interest rate
frontier. Nor does this conclusion rely on any particular method
of aggregating capital.
The argument of this essay is based on the Cambridge Capital
Controversy (CCC). Some economists assert that the CCC was
exclusively about how to measure or aggregate capital. The argument
of this essay demonstrates that these economists are mistaken.
2.0 REPRESENTATION OF TECHNOLOGY
2.1 Production Processes
Consider the following production function:
Qj = fj( L0j, X1j, X2j, ..., Xnj ) (1)
where Qj is the amount of the jth commodity available at the
end of a production cycle, L0j is the quantity of labor required
as input, and Xij is the quantity of the ith commodity used in
producing Qj units of the jth commodity.
Assume constant returns to scale. Then the production function
can be written as in Equation 2:
Qj = Qj fj( a0j, a1j, a2j, ..., anj ) (2)
where a0j is the amount of labor used to produce one unit of the
jth commodity, and aij is the amount of the ith commodity used to
produce one unit of the jth commodity. The production function
can also be represented as in Equation 3:
1 = fj( a0j, a1j, a2j, ..., anj ) (3)
The arguments of this represention of the production function
are known as "coefficients of production." They are not fixed,
and the above is not necessarily a Leontief production function.
Display 3 defines a relation for the coefficients of production.
Formally, a relation is a set of ordered tuples:
{ ( a0j( k ), a1j( k ), ..., anj( k ) ) | k is an element of Kj } (4)
where Kj is an index set. Kj could be continuous. Sometimes it
might be convenient to use a multidimensional index set. This
representation of the production possibilities available to an
industry is completely general for constant-returns-to-scale,
circulating capital technologies.
A tuple in the set in Display 4 characterizes a process for
producing the jth commodity.
An example illustrates how to handle continuously differentiable
production functions. Consider the Cobb-Douglas production function:
Q = c L^( alpha ) X^( 1 - alpha ) (5)
Equation 6 gives this function for unit output:
1 = c a0^( alpha ) a1^( 1 - alpha ) (6)
Equation 6 implicitly defines a function relating the coefficients of
production. One parametric representation of this function is given
in Display 7:
{ ( a0( k ), a1( k ) ) | a0 = k^( ( 1 - alpha )/alpha ),
a1 = 1/( c0 k ), k > 0 } (7)
2.2 A Technique
Consider an economy in which n commodities can be produced. In other
words, at least one process is known for producing each of n commodities.
A technique is constructed by selecting one process for producing
each commodity. A technique is represented by the row matrix
a0 = [ a01, a02, ..., a0n ] (8)
and the square matrix:
a11 a12 ... a1n
A = a21 a22 ... a2n (9)
. . . .
. . . .
. . . .
an1 an2 ... ann
Each element of a0 shows possible direct labor inputs per unit output
for an industry. Each column of A shows the material inputs per unit output
for an industry. a0 and A are known as the Leontief input-output matrix.
The processes define Leontief production functions if and only if only
one process is known for each industry. In that case, only one technique
is known.
The number of techniques is the product of the number of processes
defined for each industry. An uncountably infinite number of techniques
exist if the processes in at least one industry form a continuum, for
instance, if they are defined by a continuously differentiable production
function.
Thus, this representation of techniques does not assume Leontief
production functions. It is a convenient representation for using
certain mathematical programming techniques (Dorfman, Samuelson, and
Solow, 1958; Pasinetti, 1977).
3.0 DEFINITION OF A LONG RUN POSITION
The analysis is based on an examination of long run positions of
an economy. A long run position satisfies the following criteria:
o There exists a level of operation of the processes comprising
the chosen technique(s) such that all inputs used up in
production can be replaced from the gross outputs, and a
non-negative quantity of each good remains. In other words,
the economy can be in, at least, a self-reproducing state.
o The processes comprising the technique(s) in use are operated
at a level to satisfy the requirements for use of the economy.
In other words, the processes produce the quantities of the
different commodities in demand for consumption and investment.
o Relative (spot) prices are stationary.
o For each process comprising the adopted technique(s), the cost of
inputs, including wages and interest charges, does not exceed the
revenues generated by that process.
o No pure economic profits can be earned by operating any process
at the prices, wage, and interest rate for a long run position.
A (possibly non-unique) technique satisfying these requirements is
said to be a cost-minimizing technique (Kurz and Salvadori, 1995).
4.0 CHOICE OF TECHNIQUE
Equation 10 will be satisfied for prices of commodities in an
economy in a long run position:
p A ( 1 + r ) + a0 w = p (10)
where p is a row vector of prices, w is the wage, and r is the
interest rate. It follows that
p [ I - ( 1 + r ) A ] = a0 w (11)
Or,
p = a0 [ I - ( 1 + r ) A ]^(-1) w (12)
The matrix inverse exists for all interest rates between zero and a
maximum. This existence follows from the assumption that processes
comprising the technique can be operated at a level such that the
economy can generate a surplus.
Let e be the column vector defining the numeraire. By definition,
p e = 1 (13)
Hence, Equation 14 follows:
p e = a0 [ I - ( 1 + r ) A ]^(-1) e w (14)
Or,
1 = a0 [ I - ( 1 + r ) A ]^(-1) e w (15)
Or
1
w = ------------------------------- (16)
a0 [ I - ( 1 + r ) A ]^(-1) e
Equation 16 expresses the wage as a function of the interest rate,
given a technique. This function can be called the wage-interest rate
curve for a technique. The wage-interest rate curve expresses the
wage as a decreasing function of the interest rate. Assume that there
exists at least one commodity that is used either directly or indirectly
in the production of all other commodities. Then there exists a maximum
wage, corresponding to an interest rate of zero. Likewise, there exists
a maximum interest rate, corresponding to a wage of zero. When all
commodities are used directly or indirectly in the production of each
commodity, the maximum interest rate is related to the maximum eigenvalue
of the matrix A.
The wage-interest rate curves for every technique can be displayed on
the same graph. Figure 1 is an example for three techniques. The
wage-interest rate curves shown for the three techniques are continuous
curves, although they cannot be drawn as such due to limitations of ASCII.
Their shapes reflect the lack of any restrictions on concavity in the
n-commodity case.
KEY
/|\
+ xxxx Alpha Technique Wage-Interest Rate Curve
| % .... Beta Technique Wage-Interest Rate Curve
y2 + % %%%% Gamma Technique Wage-Interest Rate Curve
|. %
| . %
y1 + . %
|x . %
| x . %
| x . %
w1 + + %
| .x %
| . x %
| . +
Wage | . % x
( w ) | + x
| % . x
| % . x
w2 + % +
| % x .
| % x .
O +---------+------+-------------+----+---+---------------------+---->
r1 r3 r2 R
Interest Rate ( r )
FIGURE 1: AN EXAMPLE OF THE CHOICE OF TECHNIQUE
The cost minimizing technique, given the interest rate, maximizes the
wage. Equivalently, the cost-minimizing technique maximizes the interest
rate, given the wage. In the example, the gamma technique is cost
minimizing between an interest rate of zero and r3. Alpha is cost
minimizing between an interest rate of r3 and r2. Beta is cost minimizing
between r2 and R. Interest rates, such as r2 and r3, where two or more
techniques are cost minimizing are called "switch points."
Consider the frontier formed by the outer envelope of the wage-interest
rate curves in Figure 1. Up to the interest rate r3, this frontier consists
of the wage-interest rate curve for the gamma technique. The frontier
consists of the curve for the alpha technique between r3 and r2. And
so on. This frontier can be called the wage-interest rate frontier. It
has also been called the "efficiency frontier" and, somewhat misleadingly
the "factor-price frontier." In some sense, the construction of the
wage-interest rate frontier completes the analysis of the choice of
technique in long run positions.
5.0 NONGENERALITY OF TRADITIONAL BELIEFS
5.1 Definition of Reswitching
Reswitching occurs when a technique is cost-minimizing at two interest
rates, with at least one other technique being cost minimizing at some
interest rate inbetween. Reswitching is also sometimes called
double-switching. Figure 2 illustrates. The alpha technique is cost
minimizing between the interest rates r1 and r2. The beta technique is
cost-minimizing for interest rates less than r1 and greater than r2.
KEY
/|\
| xxxxxx Alpha Technique Wage-Interest Rate Curve
| ...... Beta Technique Wage-Interest Rate Curve
y2 +
|.
| .
y1 + .
|x .
| x .
| x .
w1 + +
| .x
| . x
| . x
Wage | . x
( w ) | . x
| . x
| . x
w2 + +
| x .
| x .
O +---------+-------------------------+---+---------------------+---->
r1 r2
Interest Rate ( r )
FIGURE 2: A RESWITCHING EXAMPLE
5.2 Reswitching and Capital Reversing
Economists have traditionally believed that higher interest charges
are associated with firms choosing to adopt less capital-intensive
techniques. In other words, economists have traditionally believed in
the existence of an inverse, monotonic relationship between the interest
rate and total capital per worker. The logical possibility of reswitching
shows this traditional belief is without foundation. The lack of
generality of such a relationship is true for *all reasonable measures
or indices of capital*.
Net output per worker for a given technique is shown by the intercept
on the wage axis of the wage-interest rate curve for that technique. In
Figure 2, y1 is the value of net output per worker when the alpha
technique is used, and y2 is the value of net output per worker when
the beta technique is chosen. Consider the switch point at the interest
rate r1. Interest charges per worker are ( y1 - w1 ) for the alpha
technique at this point. Similarly, interest charges per worker are
( y2 - w1 ) for the beta technique here. Notice that interest charges
per worker are larger for the beta technique. Since the interest rate is,
by assumption, the same, the value of capital per worker must be larger
for the beta technique at the interest rate r1. This is true for
any measure of capital in which interest charges, at a given rate of
interest, are larger when there is more capital. Surely this is a
reasonable requirement. Hence, a lower interest rate is associated with
the choice of a more capital-intensive technique around the switch
point at r = r1.
By parallel reasoning, a lower interest rate is associated with the
choice of a less capital-intensive technique at the switch point r = r2.
Hence, the beliefs that the interest rate is a scarcity index for capital,
that lower interest rates are associated with the adoption of more
capital-intensive techniques, are unfounded. This claim holds for all
measures of capital per worker. The phenomenon illustrated by the switch
point at r = r2 is known as "reverse capital deepening" or "capital
reversing". Reswitching is sufficient for capital reversing, but not
necessary.
5.3 Capital Reversing without Reswitching
Figure 1, presented above with the analysis of the choice of technique,
illustrates capital reversing without reswitching. Notice that the
switch point at an interest rate of r2 is "perverse" from the traditional
standpoint. This switch point is an instance of capital reversing. But
reswitching does not occur in Figure 1 along the frontier.
I typically present examples of capital reversing by emphasizing
behavior around a "perverse" switch point. The structure of the
theory allows such examples to be presented by considering only
the two techniques that are cost minimizing at the switch point. The
wage-interest rate curves for any number of other (unmentioned)
techniques might appear elsewhere on the frontier. There can even
be a continuum of techniques. For example, if the techniques
are constructed from continuously differentiable production functions,
a continuum of techniques *will* appear on the frontier. The literature
does not contain any theorem asserting capital reversing cannot occur
in this case, as far as I am aware. It seems quite possible to me.
(There does exist a theorem that reswitching cannot occur if there
exists a continuously differentiable production function for a
commodity that is used either directly or indirectly in the production
of all other commodities. Since reswitching is not necessary for
capital reversing, this theorem does not seem relevant to this
discussion. Apparently, the condition that there be a commodity that
enters into the production of all other commodities is necessary
for the conclusion of the theorem. If no such commodity exists,
the technology can be represented as a function relating output
to, exclusively, a finite number of quantities of dated labor inputs.
Paul Samuelson asserts that reswitching is possible in this
Wicksell-Austrian case. Not surprisingly, capital reversing also
seems to be possible.)
5.4 Perversity without Aggregating Capital
Consider a "perverse" switch point, that is, one at which capital
reversing occurs. Around such a switch point, a lower interest rate
is associated with a choice of a technique with lower interest charges
per worker. A lower interest rate is also associated here with
lower output per worker. This last observation has been used to
discuss capital reversing, while cleverly avoiding arguments about
indices and aggregate measures of capital (Hatta, 1976; Hatta, 1990;
Samuelson, 1989).
Around a perverse switch point, higher wages are associated with
the choice of a technique which yields lower output per worker. Hence,
around a perverse switch point, higher wages are associated with the
cost-minimizing choice of a more labor-intensive technique. Therefore,
the belief that wages are a scarcity index for labor, that higher
wages will induce rational firms to substitute relatively less
labor-intensive techniques for more labor-intensive techniques, is
unfounded. The demonstration of this lack of foundation of the
neoclassical theory of value and distribution does not require
*any* aggregate measure or index of capital.
6.0 REFERENCES
Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, _Linear
Programming and Economic Analysis_, Dover Publications, 1958.
Tatsuo Hatta, "The Paradox in Capital Theory and Complementarity
of Inputs," _Review of Economic Studies_, V. 43, pp. 127-42, 1976.
Tatsuo Hatta, "Capital Perversity," in _The New Palgrave: Capital
Theory_, (edited by John Eatwell, Murray Milgate, and Peter Newman),
Macmillan Press, 1990.
Heinz D. Kurz and Neri Salvadori, _Theory of Production: A
Long-Period Analysis_, Cambridge University Press, 1995.
Luigi L. Pasinetti, _Lectures on the Theory of Production_, Columbia
University Press, 1977.
Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and Modern
Economic Theory_ (edited by G. R. Feiwel), New York University Press,
1989.
--
Robert Vienneau
This long post presents an example in which higher wages are associated
with firms choosing to employ more workers per unit output produced. The
exact numeric values used are obviously unreasonable. The example, though,
is used to make a point. Those who think the demand curve for labor *must*
slope down should answer the following question: what are your assumptions?
Some further points might help clarify the question. The example
illustrates behavior that is possible under some maximizing frameworks.
Those who accept one of these frameworks, but reject the possibility
of this behavior occuring in existing economies must accept the
existence of additional special case assumptions. Those adopting this
position should clearly state their assumptions, ad hoc as they may be.
They might also try to give some rationale for why one should be
interested in this special case. If one does not accept any maximizing
model that could produce the illustrated behavior in the general case,
but does accept the use of mathematical models of maximization in
economics, one should outline an alternative model. The models in
which I am especially interested, although not exclusively so, are
those of steady state or long run prices. Along such an equilibrium
path, the needs for specific quantities of capital goods will have
been foreseen and the structure of capital goods will have been
adapted to production. I question whether equilibria of this sort
can be explained by the intersections of monotone long run supply
and demand curves. Some economists have also raised this question:
"How can classical-Keynesian economists show that there is no
tendency towards a long-period equilibrium in order to establish
the principle of effective demand in the short, medium, and long
terms? The only possible way is to attempt to show that selected
premises underlying neoclassical theory are untenable. Specifically,
it must be shown that under ideal conditions, i.e. perfect
competition and absence of disturbing elements like uncertainty
and money, one or more markets do not function properly so that,
even in the long run, no tendency towards full employment exists:
the problem is *not* about possible market failures, but about
principles.
This task has been accomplished by the capital-theory debate, the
main economic implications of which are set out in Garegnani (1970),
Kurz (1985) and Pasinetti (1974, pp. 132-42; 1977, pp. 169-77);
a comprehensive and easily understandable presentation of the crucial
issues is Harcourt (1972).
The capital-theory debate has revealed that, *if production is
conceived of as a social process*, i.e. if there is 'production
of commodities by means of commodities' (and labor) (implying the
existence of heterogeneous capital goods), it is impossible to
measure capital independently of income distribution since
relative prices depend upon the conditions of production *and*
upon the profit rate (or a hierarchy of profit rates); a
physical measure of capital independent of value and distribution
and consequently a marginal product of capital simply cannot
be conceived of. As a consequence, no regular (downward-sloping)
associations between profit rates, on the one hand, and capital
and output per worker and the capital-output ratio, on the other
hand, exist. These relationships are, in fact, totally irregular.
Since the 'capital market' does not function in the neoclassical
sense and since factor markets are supposed to be interrelated,
regular *long-period* relationships between 'factor prices' and
'factor quantities' cannot exist in general, i.e. there are no
'factor markets' at all if the long run is considered. This is
the main result of the capital-theory debate...
...The fact that there are no regular relationships between 'factor
prices' and 'factor quantities' is extremely damaging for equilibrium
theory: the market cannot produce a tendency towards some postulated
long-period equilibrium to solve the central economic problems, i.e.
value, distribution and employment. This clears the way for classical-
Keynesian political economy. For instance, it may be argued that
effective demand always governs the level of employment.
Hence the position an economist takes up with respect to the
capital-theory debate is of decisive importance. Accepting its results
is tantamount to adopting the classical-Keynesian view of economic
and social events which is set out in chapters 3 and 4 *and* the
underlying third-way vision of society in general (chapter 2).
Rejecting the capital-theoretic results, however, implicitly amounts
to accepting the existence of factor markets which are supposed to
solve the problems of distribution and employment in the *long* run
although there may be short-run disturbances; implicitly this
means accepting liberal social philosophy (chapter 2). Hence it is
wrong to minimize the importance of the capital-theory debate as
some Keynesian Fundamentalists and Robinsonians do (chapter 1, pp.
1-6) since the debate is linked up with the fundamental question of
the functioning of the socioeconomic system and with the essence of
society itself...
...Fundamentally, all these difficulties for the individualistic
marginal productivity theory arise because of the *social nature*
of the process of production: output results from a common effort;
individual producers or entire sectors of production exercise
complementary functions; to co-ordinate these co-operation is
required. Since production is a social phenomenon proper (a set
of relationships between individuals and society), long-period
distribution, price formation and employment determination are
also social processes (chapter 4, pp. 142-204). If production is
conceived of as a social process 'the marginal product of a
factor (or alternatively the marginal cost of a product) would
not merely be hard to find - it just would not be there to be
found' (Sraffa 1960, p. v).
...These references to the history of the capital-theoretic discussion
show that it is a discussion about fundamentals. The basic question is
whether there are regular relationships between 'factor prices' and
'factor quantities' or not, i.e. normally functioning factor markets.
Examining this question seriously will inevitably shape an economist's
vision in a decisive way. The capital-theoretic debate is a theoretic
watershed dividing two different views of looking at socioeconomic
phenomena, i.e. neoclassical equilibrium theory which emphasizes
behavior and classical-Keynesian political economy which starts from
the functioning of the socioeconomic system, the question being which
approach is more appropriate to tackle fundamental socioeconomic
problems, such as value, distribution and employment. Therefore, as
Geoffrey Harcourt was one of the first to perceive, the Cambridge
controversies are 'not merely about the measurement of capital...but
about the scientific status of neoclassical (equilibrium) theory'
(Dixon 1988, pp. 251-2)...
-- Heinrich Bortis, _Institutions, Behavior and Economic Theory:
A Contribution to Classical-Keynesian Political Economy_,
Cambridge University Press, 1997, pp. 282-293.
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.
3.1 AN ALTERNATIVE REPRESENTATION OF TECHNOLOGY
Net output in any year can also be represented as produced solely
by inputs of dated labor quantities. In this representation, no quantities
of steel need to be explicitly shown. Thus, endogeneous changes of
the price of steel in the analysis in section 4 can provide no objection
to any inferences one may want to draw from my initial question.
I only present a detailed analysis of the reduction of quantity flows
to dated labor inputs for 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 when summing 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 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 9 shows
the relevant calculations.
TABLE 9: 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
10 shows that here too, the costs do not exceed revenues, and no
pure economic profits are obtained.
TABLE 10: 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 11 shows the cost
of operating the alpha process.
TABLE 11: 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 12 and 13 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 12: 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 13: 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 14. 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 14: 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 15 and 16 show that costs do not
exceed revenues for any processes in the alpha technique. Nor are
pure economic profits available in any process. Table 17 shows
the cost of producing steel with the beta process exceeds its price.
So the beta technique will not be adopted.
TABLE 15: 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 16: 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 17: 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 18 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 18: 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 less-labor intensive technique will be adopted at a higher wage.
What, then, is the rational basis for assuming downward-sloping
labor demand curves?
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 choice of a less labor-intensive technique.
Paul Samuelson seems to accept the generality of models in which
the effect illustrated by the numerical example can arise:
"Something precious I gained from Robinson's work and that of her
colleagues working in the Sraffian tradition. As I have described
elsewhere, prior to 1952 when Joan began her last phase of capital
research, I operated under an important misapprehension concerning
the curvature properties of a general Fisher-von Neumann technology.
What I learned from Joan Robinson was more than she taught. I learned,
not that the general differentiable neoclassical model was special
and wrong but that a general neoclassical technology does not
necessarily involve a higher steady-state output when the interest
rate is lower. I had thought that such a property generalized from
the simplest one-sector Ramsey-Solow parable to the most general
Fisher case. That was a subtle error and, even before the 1960
Sraffa book on input-output, Joan Robinson's 1956 explorations in
_Accumulation of Capital_ alerted me to the subtle complexities of
general neoclassicism.
These complexities have naught to do with *finiteness* of the number
of alternative activities, and naught to do with the phenomenon in
which, to produce a good like steel you need directly or indirectly
to use steel itself as an input. In other words, what is wrong and
special in the simplest neoclassical or Austrian parables can be
completely divorced from the basic critique of marginalism that Sraffa
was ultimately aiming at when he began in the 1920s to compose his
classic: Sraffa (1960). To drive home this fundamental truth, I
shall illustrate with the most general Wicksell-Austrian case that
involves time-phasing of labor with no production of any good by means
of itself as a raw material.
As in the 1893-1906 works of Knut Wicksell, translated in Wicksell
(1934, Volume I), let corn now be producible by combining labor
yesterday, labor day-before-yesterday, etc):
Q( t ) = f( L(t - 1), L(t - 2), ..., L(t - T) ) = f( L ) (1)
Q = f( L(1), L(2), ..., L(T) ) in steady states (2)
Q = L(1) * f( 1, L(2)/L(1), ..., L(T)/L(1) ),
1st-homogeneous and concave (3)
Q = L(1) * del f( L )/del L(1) + ...
+ L(T) * del f( L )/del L(T), Euler's theorem (4)
del f/del L( j ) = fj( L ),
del del f/(del L(i) * del L(j) ) = fij( L )
exist for L >= 0 (5)
fj > 0, (z1, ..., zT)[ fij( L ) ](z1, ..., zT)' < 0
for zj <> b*L( j ) > 0 (6)
[Symbols are somewhat changed because of ASCII limitations - RLV ]
Nothing could be more neoclassical than (1)-(6). *If* it obtained
in the real world, a Sraffian critique could not get off the ground.
Yet it can involve (a) the qualitative phenomena much like
'reswitching', (b) so-called perverse 'Wicksell effects', (c) a
locus between steady-state *per capita* consumption and the interest
rate, a( i, c ) locus, which is *not* necessarily monotonically
negative once we get away from very low i rates. This cannot
happen for the 2-period case where T = 2. But for T >= 3, all
these 'pathologies' can occur, and there is really nothing
pathological about them. No matter how much they occur, the marginal
productivity doctrine does directly apply here to the general
equilibrium solution of the problem of the distribution of income...
...This monotone relation between (W/Pj, i ) was obscurely glimsped
by Thunen and other classicists and by Wicksell and other
neoclassicists. But the *factor-price trade-off frontier* did not
explicitly surface in the modern literature until 1953, as in
R. Sheppard (1953), P. Samuelson (1953), and D. Champernowne (1954).
One can prove it to be well-behaved for (1)-(3), or any
convex-technology case, by modern duality theory. Before Robinson
(1956), I wrongly took for granted that a similar monotone-decreasing
relation between ( i, Q/( L(1) + ... + L(T) ) ) must also follow
from mere concavity - just as does the relation
- del del C(t + 1)/( del C( t ) )^2 = del i(t)/del C(t) > 0. But
this blythe expectation is simply wrong! I refer readers to my
summing up on reswitching: Samuelson (1966).
I realize that there are many economists who tired of Robinson's
repeated critiques of capital theory as tedious and sterile naggings.
I cannot agree. Beyond the effect of rallying the spirits of
economists disliking the market order, these Robinson-Sraffa-
Pasinetti-Garegnani contributions deepen our understanding of how a
time-phased competitive microsystem works."
-- Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and
Modern Economic Theory_ (edited by G. R. Feiwel), New York
University Press, 1989.
Some comments may help clarify some implications of the above quote.
Under reswitching, the same choice of technique (or coefficients of
production) can be associated with widely different distributions of
income between interest and wages. Thus, Samuelson is implying that
the "marginal productivity doctrine" does not imply that the
distribution of income is determined by the technology and the
chosen technique. If the interest rate i is higher in a steady
state, the real wage W/Pj will be lower. Samuelson accepts that.
Since output per worker, Q/( L(1) + ... + L(T) ), need not be
lower with a higher i, the labor-intensity, ( L(1) + ... + L(T) )/Q
of the cost-minimizing technique can be lower with a lower real wage
in a comparison of steady-states.
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?
SUSUPPLY
>John,
>
>You just do not understand. I happen to have some long essays that
>explain this stuff slowly. I'll present three.
>
No foolin'?
Bill Vogt not having been heard from in almost a year, I guess Robert figures
the coast is clear.
Patrick
John J Weatherby
> 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?
Diminsihing marginal product of labor. P = p*X(k,l) - w*l(p,w,r) - r*k
FOC
[l] dx/dl*P - w = 0
THis implies dx/dl = w/p The marginal product of labor equals the real wage
rate.
assumptions neccesary
dx/dl > 0
Xll < 0
As labor rises ouput rises at a decreasing rate. That means with more
labor the marginal product of labor (dx/dl) decreases. In order for labor to
increase the wage must fall.
This is inherent in labor deamand curves. Whether you use Samuelson's
comparitive statics methods or Ronald Jones' linear programing mehtods it
still holds.
The labor demand curve slopes downward becuase MPL decreases as labor
increases and factors are paid (in real terms) their marginal products.
The only way to get an upward sloping supply curve is to have marginal
product of labor increasing. This is stupid to assume. If it were true you
could grow enough food to feed the whole world in one flower pot by just
apply more labor. Obviously this can't happen.
Second the assumption that outputs can be one hundred percent recycled
into inputs again is absdurd. One of your post uses this assumption to get
its conclusion. If this were ture we would not use any more natural
resources than we use now. Firms would recycle everything that was discarded
and use this for its inputs.
This assumption means you can take my waste products and a few other peoples
and rebuild a cow because we ate beef. Sluaghter that cow and sell it at the
grocery store. Absurd. Yes some things can be recycled for inputs, but an
economy being able to reproduce itself with no new inputs violates the laws
of physics and chemistry as well as economics.
Christopher Auld
>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?
As has been pointed out to Rob many times before, he continually misuses
basic terminology. It is easy to miss the point given Rob's, let us say,
penchant for longwindedness, but his argument amounts to the following:
The markets for labour and capital are related -- a change in one market
will change conditions in the other, and these effects will then feedback.
Labour demand curves are partial equilibrium concepts, that is, they consider
changes in one market holding all else equal. Since this feedback mechanism
exists, the 'all else equal' assumption may lead to misleading conclusions.
In particular, an increase in the wage rate imposed outside the system _may_
have the counterintuitive effect of increasing labour demanded. It is
worth noting that this reasoning, contrary to Rob's continual snide
suggestions to the contrary, is well known to professional economists.
The problem is twofold. First, the empirical relevance of the effect with
respect to minimum wages is at best highly questionable: small changes in
the compensation of the lowest paid two percent of labour the force are
unlikely to change the interest rate enough to produce a perverse effect in
labour market outcomes. So posting (and posting, and posting, and posting...)
the same story whenever the subject comes up is simply a waste of time -- if
minimum wages do increase or fail to decrease observed employment levels,
the mechanism generating that result is not the one Rob is so enamored
with.
Second, Rob continually misuses basic economic terminology. He has not
shown labour demand curves slope up -- in theory, these objects *must*
slope down. The object he shows may slope up simply isn't a labour demand
curve. Mathematically, and assuming some standard regularity conditions
(Rob usually assumes non-differentiability of many of his functions for
some reason I've never quite been able to understand), we have:
r rate of return on capital
w wage rate
L = L(w, r) the firm's demand for labour function
0 = f(w, r) a general way of stating the equilibrium
relationships between the labour and capital
markets, sometimes the "factor price frontier."
[ Note here: by *definition*, the firm's labour demand schedule is the
relationship between L and w holding all else constant: it's slope at
any point is the partial derivative of L with respect to w. ]
That last relationship can be rewritten (under some more assumptions, which
Rob implicitly assumes to hold):
r = r(w).
Collapsing the equilibrium condition into the firm's labour demand function,
L = L(w, r(w)).
Essentially, Rob shows that it can be the case that
dL \partial L \partial L \partial r
-- = ---------- + ---------- ---------- > 0.
dw \partial w \partial r \partial w
He then claims he's shown that labour demand curves can slope up. He hasn't:
the first term on the right hand side of the equation above is, by definition,
the slope of the firm's labour demand schedule. This term is negative, even
in Rob's model. The *total* derivative with respect to the wage rate does not
represent the firm's labour demand schedule by definition. This is not a quibble
over semantics, as Rob claimed earlier in the week: the term "labour demand
schedule" is well-defined and relates to a specific mathematical object. Rob
might as well claim that pi equals 6, as long as one defines pi as twice three.
He'd be quite right, but hindering rather than furthering understanding and
discussion.
In short, Rob can post his essay another two or three hundred times and it still
isn't going to show that labour demand schedules can slope up.
--
Chris Auld (403)220-4098
Economics, University of Calgary <mailto:au...@acs.ucalgary.ca>
Calgary, Alberta, Canada <URL:http://jerry.ss.ucalgary.ca/>
SUSUPPLY
[snip]
>In short, Rob can post his essay another two or three hundred times and it
>still
>isn't going to show that labour demand schedules can slope up.
>
But at least he'll feel good about himself for doing it.
Patrick
Robert Vienneau
Thank you for your comments. You may think they clarify. I wonder if
you notice that you have failed to address my point in my long post
presenting my example.
To address that point, you should outline how to construct
downward-sloping long-run labor demand curves. Or, at least,
illustrate how to construct such curves in my example. Or, if
you like, restrict yourself to conditional labor demand curves,
in which the level of consumer demand is given. I think firms
should be in equilibrium for every point on such curves.
The above would address my central point. But I'll offer some comments
and clarifications on your post.
au...@acs.ucalgary.ca (Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >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?
> As has been pointed out to Rob many times before, he continually misuses
> basic terminology.
This charge, at least for this thread, sees to reflect poor reading
skills on Chris' part. I did use the phrase "labor demand curves" in
my post initiating this thread. My point there, though, was to examine
whether or not that terminology was used in the context of the sort
of analysis that interests me. I found that some economists do
summarize their findings with this terminology. I also found that
some are cautious in doing this. J. E. Woods first described
the analysis and his detailed results, before mentioning
upwarding-sloping input demand curves. Others argue there is no
good reason to expect applicable monotonic relations between
inputs and input prices. This way of describing the argument does
not use the disputed phrase "labor demand" at all. My later posts
on this thread did not mention labor demand curves, expect in
two *questions*, one of which Chris quotes above. These posts use
other technical terms in ways that are not disputed. Chris may
think he is responsible for my caution about the disputed
terminology, given prior interchanges.
If Chris is convinced of his opinion, he might note that the
literature I described gives him an opportunity for a paper.
He could present one clarifying the issues, as he understands
them.
> It is easy to miss the point given Rob's, let us say,
> penchant for longwindedness, but his argument amounts to the following:
>
> The markets for labour and capital are related -- a change in one market
> will change conditions in the other, and these effects will then feedback.
> Labour demand curves are partial equilibrium concepts, that is, they consider
> changes in one market holding all else equal. Since this feedback mechanism
> exists, the 'all else equal' assumption may lead to misleading conclusions.
> In particular, an increase in the wage rate imposed outside the system _may_
> have the counterintuitive effect of increasing labour demanded. It is
> worth noting that this reasoning, contrary to Rob's continual snide
> suggestions to the contrary, is well known to professional economists.
My "longwindedness: has the advantages of (1) allowing the reader to
follow the argument, even if he or she does not have much background,
(2) demonstrating that some professional economists, including some
of very high stature, take these arguments seriously, and (3) avoiding
the vagueness often present in short summaries. Chris' summary above
seems an attempt to be fair (except for the dig in the last sentence).
But consider how vague "feedback mechanism" is. Can one distinguish
my argument from a full neoclassical general equilibrium argument
on the basis of Chris' summary? Also, note that the phrase "markets
for labour and capital" assumes what is in dispute.
> The problem is twofold. First, the empirical relevance of the effect with
> respect to minimum wages is at best highly questionable: small changes in
> the compensation of the lowest paid two percent of labour the force are
> unlikely to change the interest rate enough to produce a perverse effect in
> labour market outcomes. So posting (and posting, and posting, and
posting...)
> the same story whenever the subject comes up is simply a waste of time -- if
> minimum wages do increase or fail to decrease observed employment levels,
> the mechanism generating that result is not the one Rob is so enamored
> with.
Many seem to base their beliefs about the effects of minimum wages
on a logical consequence from a theory thought to be a first order
description of the labor market. My claim is that this theory is
invalid or inapplicable. Despite Chris' claim, this perspective does
not seem to be widely known.
The wages of many workers in the primary sector seem tied to the
minimum wage. There seem to be norms relating the wages of many
workers paid more than the minimum wage to the minimum wage. Thus,
despite Chris' attempt to minimize its effects, a raise in the
minimum wage will have broader effects than on just the "lowest
paid two percent" of the labour force. (I'm trusting Chris'
numbers.)
I'm quite aware that there's lots of other theory relevant to
the study of wages and employment - signalling effects, overlapping
contract periods, Keynesian effective demand considerations, etc.
The Heinrich Bortis quote I gave presents some interesting ideas
on the relations between different theories.
> Second, Rob continually misuses basic economic terminology.
See above.
> He has not
> shown labour demand curves slope up -- in theory, these objects *must*
> slope down. The object he shows may slope up simply isn't a labour demand
> curve. Mathematically, and assuming some standard regularity conditions
> (Rob usually assumes non-differentiability of many of his functions for
> some reason I've never quite been able to understand), we have:
>
> r rate of return on capital
> w wage rate
>
> L = L(w, r) the firm's demand for labour function
>
> 0 = f(w, r) a general way of stating the equilibrium
> relationships between the labour and capital
> markets, sometimes the "factor price frontier."
>
> [ Note here: by *definition*, the firm's labour demand schedule is the
> relationship between L and w holding all else constant: it's slope at
> any point is the partial derivative of L with respect to w. ]
I'm glad to see that Chris finally implicitly acknowledges the
correctness of my example, aside from the question of appropriate
terminology. If he understands the "factor price frontier," he
should also be willing to cheerfully acknowledge that, in
equilibrium, r is generally not equal to the marginal product of
capital. This inequality holds, in general, because of non-zero
price Wicksell effects.
I think it more accurate to say I make no assumptions on
differentiability of certain functions and that I often present
examples in which certain functions are not differentiable. (It is
interesting that those economists responding to my posts have often
mistakenly characterized the technology in my examples as "Leontief
production functions.") Making no assumptions on differentiability
is the general case. I do often discuss the implications of the
special case of differentiability. I'm not sure if differentiability
is assumed more often for mathematical tractability than empirical
relevance.
Perhaps I do not assume differentiability because of the traditions
in which I'm interested. I did learn about linear programming as
an undergraduate math major, and matrices as a high school student.
On the other hand, perhaps economists often assume differentiability
also because of tradition.
> That last relationship can be rewritten (under some more assumptions, which
> Rob implicitly assumes to hold):
>
> r = r(w).
>
> Collapsing the equilibrium condition into the firm's labour demand function,
>
> L = L(w, r(w)).
>
> Essentially, Rob shows that it can be the case that
>
> dL \partial L \partial L \partial r
> -- = ---------- + ---------- ---------- > 0.
> dw \partial w \partial r \partial w
>
> He then claims he's shown that labour demand curves can slope up.
Once again, that claim doesn't seem to be in the post to which Chris
is responding.
> He hasn't:
> the first term on the right hand side of the equation above is, by
definition,
> the slope of the firm's labour demand schedule. This term is negative, even
> in Rob's model.
Chris has not shown this. He hasn't shown how to construct his
function L(w, r) for my example.
> The *total* derivative with respect to the wage rate does not
> represent the firm's labour demand schedule by definition. This is not
> a quibble
> over semantics, as Rob claimed earlier in the week: the term "labour demand
> schedule" is well-defined and relates to a specific mathematical object.
But this mathematical object does not seem have any applicability
under reasonably general conditions.
> Rob
> might as well claim that pi equals 6, as long as one defines pi as twice
> three.
> He'd be quite right, but hindering rather than furthering understanding and
> discussion.
>
> In short, Rob can post his essay another two or three hundred times and it
> still
> isn't going to show that labour demand schedules can slope up.
I might stop posting it, if the argument was adequately addressed and
if I thought economists understood the logical implications of the
choice of a cost-minimizing technique under competitive long-period
assumptions.
Robert Vienneau
> > 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?
> Diminsihing marginal product of labor. P = p*X(k,l) - w*l(p,w,r) - r*k
>
> FOC
> [l] dx/dl*P - w = 0
>
> THis implies dx/dl = w/p The marginal product of labor equals the real wage
> rate.
I do not and have not been arguing with this equality. More generally,
under competitive conditions, the real wage is bounded by the value of
the marginal product of labor, where that marginal product is evaluated
by right-hand and left-hand partial derivatives.
> assumptions neccesary
>
> dx/dl > 0
>
> Xll < 0
>
> As labor rises ouput rises at a decreasing rate. That means with more
> labor the marginal product of labor (dx/dl) decreases. In order for labor to
> increase the wage must fall.
>
> This is inherent in labor deamand curves. Whether you use Samuelson's
> comparitive statics methods or Ronald Jones' linear programing mehtods it
> still holds.
>
> The labor demand curve slopes downward becuase MPL decreases as labor
> increases and factors are paid (in real terms) their marginal products.
It seems Mr. Weatherby also requires the quantity of some input other
than labor to be fixed. Otherwise, the firm will expand production by
expanding the use of all factors in equal proportions. Capital goods
cannot be such inputs, at least in the long period context of this
thread. So we are talking about natural resources of various types.
"The really serious difficulties make their appearance when it
is considered to what extent the supply curves based on the laws
of returns satisfy the conditions necessary to enable them to be
employed in the study of the equilibrium value of single
commodities produced under competitive conditions. This point of
view assumes that the conditions of production and the demand for
a commodity can be considered, in respect to small variations, as
being practically independent, both in regard to each other and
in relation to the supply and demand of all other commodities. It
is well known that such an assumption would not be illegimate
merely because the independence may not be absolutely perfect, as,
in fact, it never can be; and a slight degree of interdependence
may be overlooked without disadvantage if it applies to quantities
of the second order of smalls, as would be the case if the effect
(for example, an increase of cost) of a variation in the industry
which we propose to isolate were to react partially on the price
of the products of industries, and this latter effect were to
influence the demand for the product of the first industry. But,
of course, it is a very different matter, and the assumption
becomes illegimate, when a variation in the quantity produced
by the industry under consideration sets up a force which acts
directly, not merely upon its own costs, but also upon the
costs of other industries; in such a case the conditions of the
'particular equilibrium' which it was intended to isolate are
upset, and it is no longer possible, without contradiction, to
neglect collateral effects.
It unfortunately happens that it is precisely into this latter
category that the applications of the laws of returns fall, in
the great majority of cases. As regards diminishing returns, in
fact, if in the production of a particular commodity a considerable
part of a factor is employed, the total amount of which is fixed
or can be increased only at a more than proportional cost, a
small increase in the production of the commodity will
necessitate a more intense utilisation of that factor, and this
will affect in the same manner the cost of the commodity in
question and the cost of other commodities into the production of
which that factor enters; and since commodities into the
production of which a common special factor enters are frequently,
to a certain extent, substitutes for one another (for example,
various kinds of agricultural produce), the modification in their
price will not be without appreciable effects upon demand in the
industry concerned. If we next take an industry which employs
only a small part of the 'constant factor' (which appears more
appropriate for the study of the particualr equilibrium of a
single industry), we find that a (small) increase in its
production is generally met much more by drawing 'marginal doses'
of the constant factor from other industries than by intensifying
its own utilisation of it; thus the increase of cost will be
practibly negligible, and anyhow it will still operate in a like
degree upon all the industries of the group. Excluding these
cases, and excluding - if we take a point of view embracing long
periods - the numerous cases in which the quantity of a means of
production may be regarded as being only temporarily fixed in
respect to an unexpected demand, very little remains: the imposing
structure of diminishing returns is available only for the study
of the minute class of commodities in the production of which the
whole of a factor of production is employed. Here, of course, by
'a commodity' is to be understood an article in regard to which
it is possible to construct, or at least to conceive, a demand
schedule which is tolerably homogeneous and independent of the
conditions of supply, and not, as frequently implied, a collection
of diverse articles, such as agricultural products or ironware.
It is not by mere chance that, notwithstanding the profoundly
diverse nature of the two law of returns, the same difficulties
also arise, in almost identical form, in connection with increasing
returns. Here again we find that in reality the economies of
production on a large scale are not suitable for the requirements
of the supply curve: their field of action is either wider or more
restricted than would be necessary. On the one hand, reductions
in cost which are due to 'those *external* economies which result
from the general progress of industrial environment" to which
Marshall refers (_Principles_, V. xi. 1) must, of course, be
ignored, as they are clearly incompatible with the conditions of
the particular equilibrium of a commodity. On the other hand,
reductions in cost connected with an increase in a firm's scale of
production, arising from from internal economies or from the
possibility of distributing the overhead charges over a larger
number of product units, must be put aside as being incompatible
with competitive conditions. The only economies which could be
taken into consideration would be such as occupy an intermediate
position between these two extremes; but it is just in the middle
that nothing, or almost nothing, is to be found. Those economies
which are external from the point of view of the individual firm,
but internal as regards the industry in its aggregate, constitute
precisely the class which is most seldom to be met with. As Marshall
has said in the work in which he has intended to approach most
closely the actual conditions of industry, 'the economies of
production on a large scale can seldom be allocated exactly to any
one industry: they are in large measure attached to groups, often
large groups, of correlated industries.' In any case, in so far as
external economies of the kind in question exist, they are not
likely to be called forth by *small* increases in production. Thus
it appears that supply curves showing decreasing costs are not to
be found more frequently than their opposite.
Reduced within such restricted limits, the supply schedule with
variable costs cannot claim to be a general conception applicable
to normal industries; it can prove a useful instrument only in
regard to such exceptional industries as can reasonably satisfy
its conditions. In normal cases the cost of production of commodities
produced competitively - as we are not entitled to take into
consideration the causes which may make it rise or fall - must
be regarded as constant in respect of small variations in the
quantity produced..."
-- Piero Sraffa, "The Laws of Return under Competitive Conditions,"
_Economic Journal_, December 1926.
> The only way to get an upward sloping supply curve is to have marginal
> product of labor increasing. This is stupid to assume. If it were true you
> could grow enough food to feed the whole world in one flower pot by just
> apply more labor. Obviously this can't happen.
Interestingly enough, the technology that I have been describing
does not exhibit increasing marginal returns to any input.
> Second the assumption that outputs can be one hundred percent recycled
> into inputs again is absdurd. One of your post uses this assumption to get
> its conclusion.
Leontief input-output matrices like I described are widely used in
empirical work.
I claimed that my argument did not depend on this assumption:
[ > > 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. ]
Objecting to the realization of an abstraction in a particular example
is not the same as demonstrating that that abstraction is necessary to
the interesting properties of the example. I did note that Samuelson
thinks the assumption Mr. Weatherby objects to is not necessary for
my conclusion.
Christopher Auld
>Thank you for your comments. You may think they clarify. I wonder if
>you notice that you have failed to address my point in my long post
>presenting my example.
My point is that nowhere does Rob show that labour demand schedules can
slope up. Rob might want to casually glance at the subject he assigned
to this thread before claiming, as he does several times below, that he
does not claim that he is demonstrating the possible existence of upward
sloping labour demand curves. If this is all simply semantics, Rob,
why not just use the correct terminology? Demonstrably, you are not.
>To address that point, you should outline how to construct
>downward-sloping long-run labor demand curves.
Sure. The slope of a "long-run" labour demand curve is
\partial L
-----------
\partial w
where L() is the solution to the firm's profit maximization
problem over all inputs. It is _never_ the total derivative of
the firm's labour demand function with respect to changes in
the prices of multiple inputs.
> Or, at least,
>illustrate how to construct such curves in my example. Or, if
>you like, restrict yourself to conditional labor demand curves,
>in which the level of consumer demand is given.
No, a conditional labour demand curve takes the firm's output, not
the "level of consumer demand," as given. Since Rob's story conditions
on output, he isn't dealing with labour demand curves at all. This too
has been pointed out to Rob in the past, but he doesn't seem to be
willing to get basic terminology correct (come on, Rob, even you must
admit the irony in posting to defend your claim to correct terminology
and then blowing the definition of a term that comes up in freshman
economics).
>> As has been pointed out to Rob many times before, he continually misuses
>> basic terminology.
>
>This charge, at least for this thread, sees to reflect poor reading
>skills on Chris' part. I did use the phrase "labor demand curves" in
>my post initiating this thread. My point there, though, was to examine
>whether or not that terminology was used in the context of the sort
>of analysis that interests me.
I don't see the point of any of this. Rob, your story doesn't involve
the existence of upward sloping demand curves. Yes or no?
>If Chris is convinced of his opinion, he might note that the
>literature I described gives him an opportunity for a paper.
>He could present one clarifying the issues, as he understands
>them.
I thank Rob for his research advice. However, I won't take it because
(1) these are dead issues relating to an ancient, by academic standards,
literature, (2) I haven't said anything that any professional economist
isn't already well aware of and (3) the current standard for dealing
with dynamic economies, which is what is at interest here, involves far
more potent tools and leads to much richer and more interesting
analysis. If Rob would like some leads on becoming familiar with
such models, he need only ask.
>But consider how vague "feedback mechanism" is. Can one distinguish
>my argument from a full neoclassical general equilibrium argument
>on the basis of Chris' summary?
If one read even my summary and knew what "full neoclassical general
equilibrium" means, sure. For starters, there isn't enough structure
here to characterize full GE.
>Many seem to base their beliefs about the effects of minimum wages
>on a logical consequence from a theory thought to be a first order
>description of the labor market. My claim is that this theory is
>invalid or inapplicable. Despite Chris' claim, this perspective does
>not seem to be widely known.
Well, I maintain any and every economist is well aware that partial
equilibrium arguments can sometimes be misleading. Since that is
really all that is at issue here, I don't see any reason to grant
Rob's claim.
>The wages of many workers in the primary sector seem tied to the
>minimum wage. There seem to be norms relating the wages of many
>workers paid more than the minimum wage to the minimum wage. Thus,
>despite Chris' attempt to minimize its effects, a raise in the
>minimum wage will have broader effects than on just the "lowest
>paid two percent" of the labour force. (I'm trusting Chris'
>numbers.)
Well, I don't believe it, I've never seen anyone suggest it the
literature, and I'm very confident that other labour econometricians
would share my response. I'm afraid the burden of proof is on you,
Rob.
>I'm glad to see that Chris finally implicitly acknowledges the
>correctness of my example, aside from the question of appropriate
>terminology.
When didn't I? I have occasionally in the past pointed out
technical errors in Rob's essays, but the errors never seem to
be acknowledged. To wit:
> If he understands the "factor price frontier," he
>should also be willing to cheerfully acknowledge that, in
>equilibrium, r is generally not equal to the marginal product of
>capital.
If "capital" is an homogeneous physical good, I beg to differ.
Do you recall, Rob, the lengthy essay you kept reposting to demonstrate
the assertion above that, when solved correctly, actually showed the
equality or the value of the marginal product of capital and the sole
capital good in your model? Of course, there are many reasons why
the interest rate and the value of the marginal product of capital
may differ (if indeed the latter concept is well-defined in the context
under question), many of them explored by mainstream economists in the
past decade.
>I think it more accurate to say I make no assumptions on
>differentiability of certain functions and that I often present
Assuming lack of differentiability is an assumption.
>examples in which certain functions are not differentiable. (It is
>interesting that those economists responding to my posts have often
>mistakenly characterized the technology in my examples as "Leontief
>production functions.")
Here, you have a choice between two Leontief production functions. In
other essays you've posted, there exists only one Leontief production
function.
>> the slope of the firm's labour demand schedule. This term is negative, even
>> in Rob's model.
>Chris has not shown this. He hasn't shown how to construct his
>function L(w, r) for my example.
True, because the intractable assumptions regarding technology imply this
object is an ungainly step function. However, what I wrote above can
easily and generally be shown to be true through a simple axiomatic argument.
>> over semantics, as Rob claimed earlier in the week: the term "labour demand
>> schedule" is well-defined and relates to a specific mathematical object.
>But this mathematical object does not seem have any applicability
>under reasonably general conditions.
Of course it does -- for instance, in the case where the exogenous wage
change only affects a tiny fraction of the labour force (or, Rob, consider
how your story has to change in a small open economy). Here, as in a very
large number of applications, the partial equilibrium story is a good
approximation, and any feedbacks present are likely to be so complex and
widely distributed that their effects are likely to reasonably be captured
the ubiquitous Gaussian disturbance term. Even if none of that were true,
the labour demand schedule could still be recovered in the presence of an
endogenous shock from the capital market simply by controlling for the
interest rate in the econometric specification.
>I might stop posting it, if the argument was adequately addressed and
>if I thought economists understood the logical implications of the
>choice of a cost-minimizing technique under competitive long-period
>assumptions.
Perhaps, Rob, you should take your own advice and write up what you think
the poor ol' economics profession needs to understand and submit your
missive to a peer-reviewed journal. I think the newsgroups are getting
pretty tired of it.
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >Thank you for your comments. You may think they clarify. I wonder if
> >you notice that you have failed to address my point in my long post
> >presenting my example.
> My point is that nowhere does Rob show that labour demand schedules can
> slope up. Rob might want to casually glance at the subject he assigned
> to this thread before claiming, as he does several times below, that he
> does not claim that he is demonstrating the possible existence of upward
> sloping labour demand curves. If this is all simply semantics, Rob,
> why not just use the correct terminology? Demonstrably, you are not.
From my post originating this thread:
[ > > I then bring some literature to your ]
[ > > attention where this topic is discussed. The question addressed here ]
[ > > is whether it is appropriate or the pratice of economists to ]
[ > > describe a certain effect as an upward-sloping labor demand ]
[ > > curve. ]
Chris' insistence on not addressing the text to which he is responding
is his problem. Notice that Chris doesn't even attempt to provide any
evidence that I claimed to demonstrate the possible existence of
upward-sloping labor demand curves.
The title of this thread and my choice of newsgroups was designed to
achieve a certain audience.
> >To address that point, you should outline how to construct
> >downward-sloping long-run labor demand curves.
> Sure.
Despite this response, Chris does not address the point.
> The slope of a "long-run" labour demand curve is
>
> \partial L
> -----------
> \partial w
>
> where L() is the solution to the firm's profit maximization
> problem over all inputs. It is _never_ the total derivative of
> the firm's labour demand function with respect to changes in
> the prices of multiple inputs.
Chris' phrasing is poor. He means to say, "It is _never_ the
total derivative of the firm's labour demand function with
respect to the wage." His point is that there is a difference
between a partial derivative and a total derivative found by
the chain rule.
What is the firm's profit maximization problem in my example?
Chris basically admits he doesn't address my point towards the
end of his post:
--- Out of order -----
> >> the slope of the firm's labour demand schedule. This term is
> >> negative, even
> >> in Rob's model.
> >Chris has not shown this. He hasn't shown how to construct his
> >function L(w, r) for my example.
> True, because the intractable assumptions regarding technology imply this
> object is an ungainly step function. However, what I wrote above can
> easily and generally be shown to be true through a simple axiomatic argument.
----------------------
I'd be happy with a (non-trivial) monotonic step function. A trivial
step function would be
w = constant, 0 <= L <= infinity
But Chris doesn't construct any such function.
> >> As has been pointed out to Rob many times before, he continually misuses
> >> basic terminology.
> >This charge, at least for this thread, sees to reflect poor reading
> >skills on Chris' part. I did use the phrase "labor demand curves" in
> >my post initiating this thread. My point there, though, was to examine
> >whether or not that terminology was used in the context of the sort
> >of analysis that interests me.
> I don't see the point of any of this.
The point is that Chris is arguing strawmen. It's interesting that
he clipped the remainder of my paragraph above.
> Rob, your story doesn't involve
> the existence of upward sloping demand curves. Yes or no?
Once again, from my original post on this thread:
[ > > Some economists are willing to ]
[ > > occassionally describe the Cambridge argument as showing the ]
[ > > logical possibility of upward-sloping input demand curves. ]
In the opinion of some economists (Schefold 1990, Woods 1990),
describing the effect I have been describing as an upward-sloping
labor demand curve is legimate.
I'm quite happy as summarizing my argument like so:
There is no coherent long run neoclassical theory of value and
distribution. Wages and other "factor" prices are not
determined or explained in long-run theory by equilibria
of supply and demand.
Other economists (Bortis 1997, Galbraith 1998) also summarize the
argument along these lines.
> >If Chris is convinced of his opinion, he might note that the
> >literature I described gives him an opportunity for a paper.
> >He could present one clarifying the issues, as he understands
> >them.
> I thank Rob for his research advice. However, I won't take it because
> (1) these are dead issues relating to an ancient, by academic standards,
> literature, (2) I haven't said anything that any professional economist
> isn't already well aware of and (3) the current standard for dealing
> with dynamic economies, which is what is at interest here, involves far
> more potent tools and leads to much richer and more interesting
> analysis. If Rob would like some leads on becoming familiar with
> such models, he need only ask.
(1) The cites in my post originating this thread: Stirati 1994,
Schefold 1990, Woods 1990, and Steedman 1985. Let me add:
P. Garegnani, "Quantity of Capital," _The New Palgrave: Capital
Theory_, 1990.
I know nowhere where the claims in these references have been
refuted.
(2) Chris' comments tend to contain technical errors. In this post
he mischaracterizes the production functions in my example and
fails to understand the "factor price frontier" and price Wicksell
effects.
(3) Seems to be an irrelevant distraction. Dynamic models such
as temporary and intertemporal equilibrium are short run models.
Besides, they have been critized by Garegnani and Schefold. The
Bortis 1997 quote I provided implicitly commented upon such models.
My example can easily be generalized to a multicommodity version
of the Harrod-Domar dynamic model. Pasinetti's structural
economic dynamics is an extension of the approach illustrated by
my posts on this thread. My local public library has an "ancient"
book on dynamic programming, by, I think, Bellman, that I may
read some day.
> >But consider how vague "feedback mechanism" is. Can one distinguish
> >my argument from a full neoclassical general equilibrium argument
> >on the basis of Chris' summary?
> If one read even my summary and knew what "full neoclassical general
> equilibrium" means, sure. For starters, there isn't enough structure
> here to characterize full GE.
Uh, Chris' comment does not seem to be supported by his summary. His
informal comments don't provide enough structure to characterize any
model, let alone to ensure the reader doesn't think he is talking
about a full GE argument.
> >Many seem to base their beliefs about the effects of minimum wages
> >on a logical consequence from a theory thought to be a first order
> >description of the labor market. My claim is that this theory is
> >invalid or inapplicable. Despite Chris' claim, this perspective does
> >not seem to be widely known.
> Well, I maintain any and every economist is well aware that partial
> equilibrium arguments can sometimes be misleading. Since that is
> really all that is at issue here, I don't see any reason to grant
> Rob's claim.
I tend to be interested in the structure, content, and analytical
tools used in an argument as well. Chris continually demonstrates
that he does not understand the perspective of my arguments.
> >The wages of many workers in the primary sector seem tied to the
> >minimum wage. There seem to be norms relating the wages of many
> >workers paid more than the minimum wage to the minimum wage. Thus,
> >despite Chris' attempt to minimize its effects, a raise in the
> >minimum wage will have broader effects than on just the "lowest
> >paid two percent" of the labour force. (I'm trusting Chris'
> >numbers.)
> Well, I don't believe it, I've never seen anyone suggest it the
> literature, and I'm very confident that other labour econometricians
> would share my response. I'm afraid the burden of proof is on you,
> Rob.
Chris, do you know what the "dual labor markets" theory is? Have
you seen any literature discussing the labor market in terms of
norms?
> >I'm glad to see that Chris finally implicitly acknowledges the
> >correctness of my example, aside from the question of appropriate
> >terminology.
> When didn't I? I have occasionally in the past pointed out
> technical errors in Rob's essays, but the errors never seem to
> be acknowledged. To wit:
> > If he understands the "factor price frontier," he
> >should also be willing to cheerfully acknowledge that, in
> >equilibrium, r is generally not equal to the marginal product of
> >capital. [ This inequality holds, in general, because of non-zero
[> > price Wicksell effects. ]
(deleted material restored.)
> If "capital" is an homogeneous physical good, I beg to differ.
Well, Chris is wrong. If "capital" is a homogeneous physical good
different from a homogeneous consumption good, there is still
the problem of determining how much savings one unit of the
capital good represents.
> Do you recall, Rob, the lengthy essay you kept reposting to demonstrate
> the assertion above that, when solved correctly, actually showed the
> equality or the value of the marginal product of capital and the sole
> capital good in your model?
No, I do not recall that. Chris still does not understand his
equivocation.
> Of course, there are many reasons why
> the interest rate and the value of the marginal product of capital
> may differ (if indeed the latter concept is well-defined in the context
> under question), many of them explored by mainstream economists in the
> past decade.
Relevance?
> >I think it more accurate to say I make no assumptions on
> >differentiability of certain functions and that I often present
> Assuming lack of differentiability is an assumption.
The representation of a production function for producing a given
commodity by a set of ordered tuples of coefficients of production
does not require an assumption of a lack of differentiability.
The representation of a technique by a Leontief input-output matrix
does not require an assumption of a lack of differentiability.
The determination of the cost-minimzing technique by constructing
a "factor price frontier" does not require a lack of
differentiability.
All of these analytical tools apply whether a given technology
can be described by differentiable production functions or not.
My statement is correct.
> >examples in which certain functions are not differentiable. (It is
> >interesting that those economists responding to my posts have often
> >mistakenly characterized the technology in my examples as "Leontief
> >production functions.")
> Here, you have a choice between two Leontief production functions. In
> other essays you've posted, there exists only one Leontief production
> function.
The technology in the steel sector in my example is not rigorously
characterized as "a choice between two Leontief production functions"
(although I would not object to that rough phrasing if I thought Chris
understood my favorite methods of describing technology). A production
function relates inputs to outputs. The relationship between
inputs and outputs in the steel sector is not of the form of
a Leontief production function.
The post which demonstrates my point about price Wicksell effects
describes only one point on the production functions for each
sector. It does not provide enough information to draw any conclusion
on the form of the production functions (other than constant returns
to scale). Hence, it does not present only one Leontief production
function (per sector?).
> >> over semantics, as Rob claimed earlier in the week: the term "labour
demand
> >> schedule" is well-defined and relates to a specific mathematical object.
> >But this mathematical object does not seem have any applicability
> >under reasonably general conditions.
> Of course it does -- for instance, in the case where the exogenous wage
> change only affects a tiny fraction of the labour force (or, Rob, consider
> how your story has to change in a small open economy). Here, as in a very
> large number of applications, the partial equilibrium story is a good
> approximation, and any feedbacks present are likely to be so complex and
> widely distributed that their effects are likely to reasonably be captured
> the ubiquitous Gaussian disturbance term.
Interesting claims. I suggest Chris consider the Sraffa (1926) quote
I provided. He may still hold to the above afterwards.
> Even if none of that were true,
> the labour demand schedule could still be recovered in the presence of an
> endogenous shock from the capital market simply by controlling for the
> interest rate in the econometric specification.
I don't know enough to evaluate this claim, other than to note that
Chris hasn't yet explained how to construct this labor demand schedule
in my context.
> >I might stop posting it, if the argument was adequately addressed and
> >if I thought economists understood the logical implications of the
> >choice of a cost-minimizing technique under competitive long-period
> >assumptions.
> Perhaps, Rob, you should take your own advice and write up what you think
> the poor ol' economics profession needs to understand and submit your
> missive to a peer-reviewed journal. I think the newsgroups are getting
> pretty tired of it.
My posts lack the originality required for peer-reviewed journals.
The nice thing about Usenet is that an argument cannot be suppressed
just out of displeasure.
Christopher Auld
[ Follow-ups to sci.econ ]
Robert Vienneau <rv...@see.sig.com> wrote:
>au...@acs.ucalgary.ca (Christopher Auld) wrote:
>Chris' insistence on not addressing the text to which he is responding
>is his problem. Notice that Chris doesn't even attempt to provide any
>evidence that I claimed to demonstrate the possible existence of
>upward-sloping labor demand curves.
>
>The title of this thread and my choice of newsgroups was designed to
>achieve a certain audience.
The second quoted paragraph adequately refutes the first. Rob, if you
don't want to claim you're showing the existence of upward-sloping labour
demand curves, don't use that terminology. Quite simple, really.
>> >To address that point, you should outline how to construct
>> >downward-sloping long-run labor demand curves.
>
>> Sure.
>
>Despite this response, Chris does not address the point.
What do you think the text below is, Rob? Three posts in and I once
again remember why trying to discuss anything with Rob rapidly becomes
excessively frustrating. We are sure to see baseless accusations of
technical incompetence, evasion of insurmountable criticism (oops,
we've already seen that -- Rob clipped the text demonstrating he
doesn't know the definition of "conditional labour demand curve," a
concept central to his analysis), and a veritable landslide of snide
little digs in the text to come.
>> The slope of a "long-run" labour demand curve is
>>
>> \partial L
>> -----------
>> \partial w
>>
>> where L() is the solution to the firm's profit maximization
>> problem over all inputs. It is _never_ the total derivative of
>> the firm's labour demand function with respect to changes in
>> the prices of multiple inputs.
>What is the firm's profit maximization problem in my example?
It isn't there, which is one of the reasons Rob's story doesn't provide
enough structure to characterize general equilibrium. It is a cost-
minimization problem, which generates _conditional_ input demand schedules
as solutions to the firm's program. However, Rob did not ask me how to
construct a long-run conditional labour demand schedule, he asked how
to construct a long-run labour demand schedule. That is the question I
answered. That his little model cannot generate this object is
irrelevant.
>> Rob, your story doesn't involve
>> the existence of upward sloping demand curves. Yes or no?
>
>Once again, from my original post on this thread:
>
>[ > > Some economists are willing to ]
>[ > > occassionally describe the Cambridge argument as showing the ]
>[ > > logical possibility of upward-sloping input demand curves. ]
>
>In the opinion of some economists (Schefold 1990, Woods 1990),
>describing the effect I have been describing as an upward-sloping
>labor demand curve is legimate.
None of the text Rob has quoted contains such an assertion. If these
authors do make this claim, they too are wrong, by definition.
>> I thank Rob for his research advice. However, I won't take it because
>> (1) these are dead issues relating to an ancient, by academic standards,
>> literature, (2) I haven't said anything that any professional economist
>> isn't already well aware of and (3) the current standard for dealing
>> with dynamic economies, which is what is at interest here, involves far
>> more potent tools and leads to much richer and more interesting
>> analysis. If Rob would like some leads on becoming familiar with
>> such models, he need only ask.
>(1) The cites in my post originating this thread: Stirati 1994,
>Schefold 1990, Woods 1990, and Steedman 1985. Let me add:
>
> P. Garegnani, "Quantity of Capital," _The New Palgrave: Capital
> Theory_, 1990.
>
>I know nowhere where the claims in these references have been
>refuted.
I never said these references have been "refuted," I said the entire
issue is no longer of interest to the discipline. That there exists
a fringe literature which still treats these issues using outdated
tools and attacking archaic models hardly weakens my point. If Rob
can cite papers examining these issues published in, say, top *fifty*
journals published since, oh, 1979, I will amend "dead" to "of little
current interest."
>(2) Chris' comments tend to contain technical errors. In this post
>he mischaracterizes the production functions in my example and
>fails to understand the "factor price frontier" and price Wicksell
>effects.
I am having trouble forming a response to this that isn't deeply
sarcastic. Rob, I didn't "mischaracterize" anything nor have you
shown I "fail to understand" anything about these rather simplistic
arguments. Moreover, the technical level in this literature (because
it stems from arguments that occurred thirty to forty years ago) is
very low -- this is hardly the cutting edge of economic theory.
>(3) Seems to be an irrelevant distraction. Dynamic models such
>as temporary and intertemporal equilibrium are short run models.
>Besides, they have been critized by Garegnani and Schefold.
Oh my, "dynamic models" have been criticized by Garegnani and
Schefold? Well, that puts an end to that. (For what it's worth,
the vast majority of contemporary economic modeling is done in
an explicitly dynamic framework. I don't think Rob is vaguely
familiar with any of this literature.)
>my posts on this thread. My local public library has an "ancient"
>book on dynamic programming, by, I think, Bellman, that I may
>read some day.
That would be a good idea. Alpha Chiang has an accessible introduction
to dynamic problems in continuous time you might like to start with.
More recent introductions to dynamic programming can be found in
Sargent's _Dynamic Macroeconomic Theory_ or Stockey and Lucas _Recursive
Methods in Economic Dynamics_. It is impossible to understand the
content of modern economic thought without being familiar with these
tools.
Leaving in a few sweeping and unsubstantiated accusations of ignorance:
>Uh, Chris' comment does not seem to be supported by his summary. His
>informal comments don't provide enough structure to characterize any
>model, let alone to ensure the reader doesn't think he is talking
>about a full GE argument.
>I tend to be interested in the structure, content, and analytical
>tools used in an argument as well. Chris continually demonstrates
>that he does not understand the perspective of my arguments.
>> Well, I don't believe it, I've never seen anyone suggest it the
>> literature, and I'm very confident that other labour econometricians
>> would share my response. I'm afraid the burden of proof is on you,
>> Rob.
>Chris, do you know what the "dual labor markets" theory is? Have
>you seen any literature discussing the labor market in terms of
>norms?
One can only see this as an attempt to divert the discussion. Rob,
do you have any evidence whatsoever that endogenous changes in the
interest rate more than offset own-price induced changes in labour
demand when the minimum wage is increased? Did you grasp my (deleted)
point that it is easy to control for this effect statistically?
>> Do you recall, Rob, the lengthy essay you kept reposting to demonstrate
>> the assertion above that, when solved correctly, actually showed the
>> equality or the value of the marginal product of capital and the sole
>> capital good in your model?
>No, I do not recall that. Chris still does not understand his
>equivocation.
Yet another sweeping and unsubstantiated accusation. Anyone interested
is welcome to seek out my post to sci.econ of June 6, 1996. Rob never
did reply to that post.
>> Of course, there are many reasons why
>> the interest rate and the value of the marginal product of capital
>> may differ (if indeed the latter concept is well-defined in the context
>> under question), many of them explored by mainstream economists in the
>> past decade.
>Relevance?
Rob continually talks as if the condition VMP(K) = r is some sacred
equation which forms a cornerstone of mainstream economics. It isn't,
although it does hold in some models and is sometimes used as a
simplifying assumption. When he posts arguments that this assumption
is false and then proceeds to claim that sounds the death bell for
neoclassical economics, he simply demonstrates he is totally unfamiliar
with capital theory post, say, 1985.
>> >I think it more accurate to say I make no assumptions on
>> >differentiability of certain functions and that I often present
>
>> Assuming lack of differentiability is an assumption.
>
>The representation of a production function for producing a given
Yadda yadda. Posting a model in which there are two fixed-coefficient
production processes "known" is an assumption about differentiability.
That is true whether or not the result holds under more general
assumptions.
>The technology in the steel sector in my example is not rigorously
>characterized as "a choice between two Leontief production functions"
=====
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.
=====
Both "process alpha" and "process beta" describe Leontief production
functions. The firm can choose process alpha or process beta. I would
like Rob to explain why my statement is not entirely accurate.
In passing, I'll chide Rob once again for his ridiculous and obfuscating
numerical examples. Rob, the point of numerical examples is to make
things transparent to the reader: typically, one would assert something
holds in general algebraically and then use a simple numerical example
(with either realistic or easy to work with numbers) to clarify the
argument. Rob, for some reason, constructs examples using numbers like
those above -- this is one reason the longwindedness Rob favours is so
grating. What human being is going to work through his examples when
he chooses to report arbitrary numbers to seven decimal places as part
of a general theoretical argument?
>(although I would not object to that rough phrasing if I thought Chris
>understood my favorite methods of describing technology).
Yeah, Rob, maybe one day I'll understand the concept "production function."
>A production
>function relates inputs to outputs. The relationship between
>inputs and outputs in the steel sector is not of the form of
>a Leontief production function.
Conditional on choice of technique it is.
>The post which demonstrates my point about price Wicksell effects
>describes only one point on the production functions for each
>sector.
I'm not sure which post Rob is referring to here. In the example
actually under discussion, the entire production function is
completely described by the quoted text above ("per ton steel
produced" implies constant returns to scale).
>> Even if none of that were true,
>> the labour demand schedule could still be recovered in the presence of an
>> endogenous shock from the capital market simply by controlling for the
>> interest rate in the econometric specification.
>I don't know enough to evaluate this claim, other than to note that
>Chris hasn't yet explained how to construct this labor demand schedule
>in my context.
Again, that is because it is impossible to construct that schedule in
Rob's context -- he hasn't provided the information necessary. Perhaps
if he reflects on the difference between "labour demand schedule" and
"conditional labour demand schedule" which I've attempted to hammer
home he'll realize that. In any case, my point stands: it is
(conceptually) trivial to hold the interest rate constant statistically.
Since the upward-sloping, umm, let's call it a "wage-labour locus" in
Rob's example obtains because the interest rate varies endogenously with
the wage rate, holding the interest rate constant through the
econometric specification removes this effect.
>The nice thing about Usenet is that an argument cannot be suppressed
>just out of displeasure.
Quite true. As a matter of historical record, Rob is quite free to
repost his essay another couple of hundred times. No one will stop
him, although others may occasionally note its errors and lack of
relevance to modern economic thought.
SUSUPPLY
>>Chris' insistence on not addressing the text to which he is responding
>>is his problem. Notice that Chris doesn't even attempt to provide any
>>evidence that I claimed to demonstrate the possible existence of
>>upward-sloping labor demand curves.
>>
>>The title of this thread and my choice of newsgroups was designed to
>>achieve a certain audience.
>
>The second quoted paragraph adequately refutes the first. Rob, if you
>don't want to claim you're showing the existence of upward-sloping labour
>demand curves, don't use that terminology. Quite simple, really.
Actually Robert has shown remarkable (for him) forbearance with this one
lately. You must bring out the worst in him, Chris.
[snip]
>Three posts in and I once
>again remember why trying to discuss anything with Rob rapidly becomes
>excessively frustrating. We are sure to see baseless accusations of
>technical incompetence, evasion of insurmountable criticism (oops,
>we've already seen that -- Rob clipped the text demonstrating he
>doesn't know the definition of "conditional labour demand curve," a
>concept central to his analysis), and a veritable landslide of snide
>little digs in the text to come.
Without a doubt. I think he warehouses them along with the rest of his stock
posts. In fact here are some more:
>>(2) Chris' comments tend to contain technical errors.
>Chris continually demonstrates
>>that he does not understand the perspective of my arguments.
>>Chris, do you know what the "dual labor markets" theory is?
>Chris still does not understand his
>>equivocation.
>I would not object to that rough phrasing if I thought Chris
>>understood my favorite methods of describing technology).
>>The nice thing about Usenet is that an argument cannot be suppressed
>>just out of displeasure.
Funny, Robert never says that about my posts.
Anyway, thanks for doing all that heavy lifting [which I've snipped], Chris.
It's always fun to see Robert in full flight.
Patrick
Steve
> I wanted to point out some literature that uses that terminology. I wanted
> to do this in a way that brought this literature to the attention of
> readers that had seen some of my previous discussions on this
> topic. That seems an adequate reason for the title.
Which is exactly what trolls do on usenet. Very bad form Bobby. And please
put away that naked picture of Joan Robinson she must be getting very tired
of onanisms by now usenet certainly is. No one wants to talk to you Bobby
because you are boring.
Robert Vienneau
thinks his debating tactics are fair. I'll point out below some
curious editing and misreadings.
On the other hand, I find his reactions to mine curious. If I say
Chris is mistaken about X or seems not to understand Y, I don't
think I am making a "snide little dig." Nor am I challenging him
to list those areas of economics that he does understand.
Furthermore, if I suggest an improvement of phrasing for some
of his statements, I think I am disagreeing in a nuanced and
courteous fashion. His reactions seem not to conform to such
standards of politeness.
I'm not sure how to point out that he is not providing an argument
relevant to my posts in a polite fashion. However, I think any
fair-minded reader of this interchange can see that the heat is
all on his side. There is some history here, and I have been
trying to evolve my Usenet style to be more polite.
au...@acs.ucalgary.ca (Christopher Auld) wrote:
> Robert Vienneau <rv...@see.sig.com> wrote:
> >au...@acs.ucalgary.ca (Christopher Auld) wrote:
> >Chris' insistence on not addressing the text to which he is responding
> >is his problem. Notice that Chris doesn't even attempt to provide any
> >evidence that I claimed to demonstrate the possible existence of
> >upward-sloping labor demand curves.
> >The title of this thread and my choice of newsgroups was designed to
> >achieve a certain audience.
> The second quoted paragraph adequately refutes the first. Rob, if you
> don't want to claim you're showing the existence of upward-sloping labour
> demand curves, don't use that terminology. Quite simple, really.
I wanted to point out some literature that uses that terminology. I wanted
to do this in a way that brought this literature to the attention of
readers that had seen some of my previous discussions on this
topic. That seems an adequate reason for the title.
One respondent to this thread was apparently not aware of the effect
being discussed in the literature I was reviewing. So I illustrated
that effect with a numerical example. I also explained some of
the analytical techniques I use. I deliberately do not claim to
be proving the logical possibility of upward-sloping labor
demand curves in these later posts. I even acknowledged Chris'
previous efforts to explain why he thought that terminology
was inappropriate in this context - implicitly, in my first post
on this thread, explicitly, after he joined this discussion.
> >> >To address that point, you should outline how to construct
> >> >downward-sloping long-run labor demand curves.
> >
> >> Sure.
> >
> >Despite this response, Chris does not address the point.
>
> What do you think the text below is, Rob?
Saying that L( w, r ) is a labor demand function is not an outline
of how to construct the curve. Chris did say the derivation of this
curve comes from a profit-maximizing firm. But in my first post,
I mentioned "equilibrium of the firm" and stated my opinion that
this means that, in a long-run context, the firm should be on the
"factor price frontier". This implies, for a circulating capital
model, that the inverse of the labor demand "function" is
w = constant, 0 <= L <= infinity
That function was in my previous post. Chris deleted that part.
> Three posts in and I once
> again remember why trying to discuss anything with Rob rapidly becomes
> excessively frustrating. We are sure to see baseless accusations of
> technical incompetence, evasion of insurmountable criticism (oops,
> we've already seen that -- Rob clipped the text demonstrating he
> doesn't know the definition of "conditional labour demand curve," a
> concept central to his analysis), and a veritable landslide of snide
> little digs in the text to come.
We have not seen "baseless accusations of technical incompetence." I
merely pointed out where Chris was mistaken in places where he was
mistaken.
I quite agree I should have said "output". Perhaps I should have
acknowledged this, but Chris' style of presenting criticisms
certainly does not encourage such acknowledgement.
I've already addressed his complaint about my style.
> >> The slope of a "long-run" labour demand curve is
> >>
> >> \partial L
> >> -----------
> >> \partial w
> >>
> >> where L() is the solution to the firm's profit maximization
> >> problem over all inputs. It is _never_ the total derivative of
> >> the firm's labour demand function with respect to changes in
> >> the prices of multiple inputs.
> >What is the firm's profit maximization problem in my example?
> It isn't there, which is one of the reasons Rob's story doesn't provide
> enough structure to characterize general equilibrium.
But I gave a labor-demand relation in the post to which Chris was
responding. Furthermore, my informal comments in my long post
containing my numerical example hint why this relation obtains.
> It is a cost-
> minimization problem, which generates _conditional_ input demand schedules
> as solutions to the firm's program. However, Rob did not ask me how to
> construct a long-run conditional labour demand schedule, he asked how
> to construct a long-run labour demand schedule. That is the question I
> answered. That his little model cannot generate this object is
> irrelevant.
Chris is always free to specify what additional structure he thinks
he needs. My example can generate "this object," and I have
generated it.
Furthermore, I anticipated this objection several posts ago:
"To address that point, you should outline how to construct
downward-sloping long-run labor demand curves. Or, at least,
illustrate how to construct such curves in my example. Or, if
you like, restrict yourself to conditional labor demand curves,
in which the level of [output] is given. I think firms
should be in equilibrium for every point on such curves."
I have corrected poor phrasing, at least, in this paragraph. This is
at Chris' insistence. Since he provided this clarification, he should
have noted I was asking him to outline how to construct conditional
labor demand curves, if he did not think a labor demand curve could
be constructed for my example. Furthermore, my last sentence above
hints how I think a long-run labor demand curve should be obtained.
[ Some stuff clipped here.]
> >In the opinion of some economists (Schefold 1990, Woods 1990),
> >describing the effect I have been describing as an upward-sloping
> >labor demand curve is legimate.
> None of the text Rob has quoted contains such an assertion.
"The discovery that factor demand curves may be positively
sloped in the relevant range, not negatively..."
-- Schefold, 1990
"The relation between l(2) and w(2) is a microeconomic demand
curve for labour, that of the second industry. The relation between
v(2) and w(2) can be interpreted as a macroeconomic demand curve
for labour, which would occur if there were a net output
of only the second commodity...in Figure 6.17b, ...the sectoral
demand curve is upward-sloping...I have shown in Figure 6.17c
that the aggregate demand curve is not downward-sloping in
the presence of reswitching: indeed, like the sectoral
demand curve, it is not even monotonic. Reswitching is
sufficient, not necessary, for the aggregate demand curve
for labour not to be downward-sloping..."
--Woods, 1990
The example in Figure 6.17c has a step function approximation to
labor demand curve that is upward-sloping in places.
> If these
> authors do make this claim, they too are wrong, by definition.
Knowing Chris' opinion, I suggested:
If Chris is convinced of his opinion, he might note that the
literature I described gives him an opportunity for a paper.
He could present one clarifying the issues, as he understands
them.
Which is what Chris was responding to below.
> >> I thank Rob for his research advice. However, I won't take it because
> >> (1) these are dead issues relating to an ancient, by academic standards,
> >> literature, (2) I haven't said anything that any professional economist
> >> isn't already well aware of and (3) the current standard for dealing
> >> with dynamic economies, which is what is at interest here, involves far
> >> more potent tools and leads to much richer and more interesting
> >> analysis. If Rob would like some leads on becoming familiar with
> >> such models, he need only ask.
> >(1) The cites in my post originating this thread: Stirati 1994,
> >Schefold 1990, Woods 1990, and Steedman 1985. Let me add:
> >
> > P. Garegnani, "Quantity of Capital," _The New Palgrave: Capital
> > Theory_, 1990.
> >
> >I know nowhere where the claims in these references have been
> >refuted.
> I never said these references have been "refuted," I said the entire
> issue is no longer of interest to the discipline.
Chris states that Schefold and Woods are "wrong."
Saying an issue is not of interest doesn't support any claims about
something being wrong.
> That there exists
> a fringe literature which still treats these issues using outdated
> tools and attacking archaic models hardly weakens my point.
Labeling a literature "fringe" is not a rational argument. Labeling
tools "outdated" is not an argument demonstrating that they yield
incorrect conclusions. Labeling models "archaic" is not an argument.
If Chris' point is that Schefold and Woods are "wrong," he is not
supporting it with the sentence above.
> If Rob
> can cite papers examining these issues published in, say, top *fifty*
> journals published since, oh, 1979, I will amend "dead" to "of little
> current interest."
The challenge is uninteresting to me, especially given how Chris says
he will respond.
> >(2) Chris' comments tend to contain technical errors. In this post
> >he mischaracterizes the production functions in my example and
> >fails to understand the "factor price frontier" and price Wicksell
> >effects.
> I am having trouble forming a response to this that isn't deeply
> sarcastic. Rob, I didn't "mischaracterize" anything nor have you
> shown I "fail to understand" anything about these rather simplistic
> arguments.
Anybody reading this thread that understands "factor price frontiers,"
activity analysis, and price Wicksell effects can draw their own
conclusion.
> Moreover, the technical level in this literature (because
> it stems from arguments that occurred thirty to forty years ago) is
> very low -- this is hardly the cutting edge of economic theory.
The above statement is of no cognitive interest in judging the
correctness of the conclusions of any economic argument.
> >(3) Seems to be an irrelevant distraction. Dynamic models such
> >as temporary and intertemporal equilibrium are short run models.
> >Besides, they have been critized by Garegnani and Schefold.
> Oh my, "dynamic models" have been criticized by Garegnani and
> Schefold? Well, that puts an end to that. (For what it's worth,
> the vast majority of contemporary economic modeling is done in
> an explicitly dynamic framework. I don't think Rob is vaguely
> familiar with any of this literature.)
But these "dynamic models" seem to be of no interest to this thread.
Furthermore, my point was that the literature Chris is abusing me
for being familiar with addresses certain dynamic models. Whether
or "not the vast majority of contemporary economic modeling is done in
an explicitly dynamic framework" or I am "vaguely familiar with any
of this literature" seems to address no relevant point.
Notice Chris deleted the following, where I explicitly discuss dynamic
models that relate to my example:
[ >> The ]
[ >> Bortis 1997 quote I provided implicitly commented upon such models. ]
[ >> My example can easily be generalized to a multicommodity version ]
[ >> of the Harrod-Domar dynamic model. Pasinetti's structural ]
[ >> economic dynamics is an extension of the approach illustrated by ]
[ >> my posts on this thread. ]
[ deleted ]
> Leaving in a few sweeping and unsubstantiated accusations of ignorance:
> >Uh, Chris' comment does not seem to be supported by his summary. His
> >informal comments don't provide enough structure to characterize any
> >model, let alone to ensure the reader doesn't think he is talking
> >about a full GE argument.
> >I tend to be interested in the structure, content, and analytical
> >tools used in an argument as well. Chris continually demonstrates
> >that he does not understand the perspective of my arguments.
These entire threads substantiate this "accusation", whether it is
sweeping or not. Furthermore, compare Chris' statement about what
I'm not even vaguely familiar with with mine. How can he think he's
in any position to object to my statement?
[>>>>The wages of many workers in the primary sector seem tied to the ]
[>>>>minimum wage. There seem to be norms relating the wages of many ]
[>>>>workers paid more than the minimum wage to the minimum wage. Thus, ]
[>>>>despite Chris' attempt to minimize its effects, a raise in the ]
[>>>>minimum wage will have broader effects than on just the "lowest ]
[>>>>paid two percent" of the labour force. (I'm trusting Chris' ]
[>>>>numbers.) ]
> >> Well, I don't believe it, I've never seen anyone suggest it the
> >> literature, and I'm very confident that other labour econometricians
> >> would share my response. I'm afraid the burden of proof is on you,
> >> Rob.
> >Chris, do you know what the "dual labor markets" theory is? Have
> >you seen any literature discussing the labor market in terms of
> >norms?
> One can only see this as an attempt to divert the discussion. Rob,
> do you have any evidence whatsoever that endogenous changes in the
> interest rate more than offset own-price induced changes in labour
> demand when the minimum wage is increased? Did you grasp my (deleted)
> point that it is easy to control for this effect statistically?
I have always said that the effect illustrated in my example was meant
to make a logical point. I objected to Chris' use of statistics to
minimize the effects of a change in the level of the minimum wage. That's
the context of this "attempt to divert the discussion."
[ >>> If he understands the "factor price frontier," he ]
[ >>>should also be willing to cheerfully acknowledge that, in ]
[ >>>equilibrium, r is generally not equal to the marginal product of ]
[ >>>capital. ]
[ >> ]
[ >> If "capital" is an homogeneous physical good, I beg to differ. ]
[ >> Well, Chris is wrong. If "capital" is a homogeneous physical good ]
[ >> different from a homogeneous consumption good, there is still ]
[ >> the problem of determining how much savings one unit of the ]
[ >> capital good represents. ]
> >> Do you recall, Rob, the lengthy essay you kept reposting to demonstrate
> >> the assertion above that, when solved correctly, actually showed the
> >> equality or the value of the marginal product of capital and the sole
> >> capital good in your model?
> >No, I do not recall that. Chris still does not understand his
> >equivocation.
> Yet another sweeping and unsubstantiated accusation. Anyone interested
> is welcome to seek out my post to sci.econ of June 6, 1996. Rob never
> did reply to that post.
The substantiation is in the deleted paragraph. I've now tried several
times to explain to Chris why the equality of the price of a capital
good and the discounted value of the marginal product of that capital
good, or the equality of the rental price of a capital good to the
discounted value of the marginal product of its services, is consistent
with the existence of non-zero price Wicksell effects. It is the
existence of those effects which generally lead to the inequality
of the interest rate and the marginal product of capital, as that
equality is understood in aggregate models.
Note that Chris mistated the equality that I was arguing against in his
comments above.
> >> Of course, there are many reasons why
> >> the interest rate and the value of the marginal product of capital
> >> may differ (if indeed the latter concept is well-defined in the context
> >> under question), many of them explored by mainstream economists in the
> >> past decade.
> >Relevance?
> Rob continually talks as if the condition VMP(K) = r is some sacred
> equation which forms a cornerstone of mainstream economics. It isn't,
> although it does hold in some models and is sometimes used as a
> simplifying assumption. When he posts arguments that this assumption
> is false and then proceeds to claim that sounds the death bell for
> neoclassical economics, he simply demonstrates he is totally unfamiliar
> with capital theory post, say, 1985.
I think the above is a misrepresentation of my statements, even aside
from Chris' continued misrepresentation of the equality I dispute. I'm
of the opinion that there is no well-founded long run neoclassical
theory of value and distribution. I am of this opinion because
there is no good reason for assuming the well-behaved *microeconomic*
relations that I think are necessary to say one has a neoclassical
theory of value. The price Wicksell effects that lead to the
failure of the equality fo the marginal product of capital and the
interest rate in aggregate models is only one component of that critique.
I find the following good introductions to capital theory:
Syed Ahmad, _Capital in Economic Theory: Neo-classical,
Cambridge, and Chaos_, 1991.
John Eatwell, Murray Milgate, and Peter Newman (editors),
_The New Palgrave: Capital Theory_, 1990
Why is Chris making "sweeping and unsubstantiated accusations of
ignorance?"
> >> >I think it more accurate to say I make no assumptions on
> >> >differentiability of certain functions and that I often present
[>>> >examples in which certain functions are not differentiable. ]
(The restored portion was edited out by Chris in the post to
which he responded with the following sentence.)
> >> Assuming lack of differentiability is an assumption.
> >The representation of a production function for producing a given
[>> commodity by a set of ordered tuples of coefficients of production ]
[>> does not require an assumption of a lack of differentiability. ]
[>> The representation of a technique by a Leontief input-output matrix ]
[>> does not require an assumption of a lack of differentiability. ]
[>> The determination of the cost-minimzing technique by constructing ]
[>> a "factor price frontier" does not require a lack of ]
[>> differentiability. ]
[>> ]
[>> All of these analytical tools apply whether a given technology ]
[>> can be described by differentiable production functions or not. ]
[>> ]
[>> My statement is correct. ]
> Yadda yadda.
Notice how Chris responds to a substantial argument.
> Posting a model in which there are two fixed-coefficient
> production processes "known" is an assumption about differentiability.
> That is true whether or not the result holds under more general
> assumptions.
Notice my statement distinguished between my numerical example, in
which the production function is not always differentiable, and
more general models illustrated by my example. Chris edited my
statement to remove that distinction, and then argues about the
example.
> >The technology in the steel sector in my example is not rigorously
> >characterized as "a choice between two Leontief production functions"
> =====
> 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.
> =====
> Both "process alpha" and "process beta" describe Leontief production
> functions. The firm can choose process alpha or process beta. I would
> like Rob to explain why my statement is not entirely accurate.
Sure. A Leontief production function is of the form:
Q = min ( L/a0, X1/a1, ..., Xn/an )
Alternatively, one can define a Leontief production function as the
solution of the following Linear Program:
Max Q
such that
a0 Q <= L
a1 Q <= X1
.
.
.
an Q <= Xn
where Q >= 0
Now consider my example. Let L, X1, and X2 be the labor, steel, and
corn used by the steel sector as inputs. The production function in
the steel sector in my example is the solution of the following Linear Program:
Max Q = Q1 + Q2
such that
0.19321 Q1 - L1 <= 0
0.033594 Q2 - L2 <= 0
L1 + L2 <= L
0.35 Q1 - X11 <= 0
0.13329 Q2 - X12 <= 0
X11 + X12 <= X1
0.0095553 Q1 - X21 <= 0
0.15590 Q2 - X22 <= 0
X21 + X22 <= X2
where Q1 >= 0, Q2 >= 0, L1 >= 0, L2 >= 0, X11 >= 0
X12 >= 0, X21 >= 0, X22 >= 0
Q1 is the tons steel produced by the alpha process, and Q2 is the
tons steel produced by the beta process. Notice that L, X1, and X2
are parameters, not decision variables found by solving this LP.
Thus, one can express the solution value of the objective function
as a function of these parameters:
Q = f( L, X1, X2 )
Since this second LP is not of the same form as the first, the
production function f( L, X1, X2 ) is not Leontief.
> In passing, I'll chide Rob once again for his ridiculous and obfuscating
> numerical examples. Rob, the point of numerical examples is to make
> things transparent to the reader: typically, one would assert something
> holds in general algebraically and then use a simple numerical example
> (with either realistic or easy to work with numbers) to clarify the
> argument. Rob, for some reason, constructs examples using numbers like
> those above -- this is one reason the longwindedness Rob favours is so
> grating. What human being is going to work through his examples when
> he chooses to report arbitrary numbers to seven decimal places as part
> of a general theoretical argument?
I presented my example by working it through it myself. A more complete
analysis than I present in my example would find switch points at
r = 75% and r = 125%. I chose the numbers to yield simple results.
> >(although I would not object to that rough phrasing if I thought Chris
> >understood my favorite methods of describing technology).
> Yeah, Rob, maybe one day I'll understand the concept "production function."
Whatever.
> >A production
> >function relates inputs to outputs. The relationship between
> >inputs and outputs in the steel sector is not of the form of
> >a Leontief production function.
> Conditional on choice of technique it is.
This is amusing. Chris wants me to distinguish between labor demand
curves and conditional labor demand curves. Now here he wants to
introduce a new concept, never before found in economics to my
knowledge: a conditional production function.
Anyways, I've shown above that the steel sector does not have a
Leontief production function. I hope Chris understands the difference
between a process and a technique in my posts. Also, notice that
for some L, X1, and X2, the solution of the second LP above has
both Q1 and Q2 strictly positive.
> >The post which demonstrates my point about price Wicksell effects
> >describes only one point on the production functions for each
> >sector.
>
> I'm not sure which post Rob is referring to here.
The one which Chris previously referred to as "the lengthy essay you
kept reposting to demonstrate the assertion above that, when solved
correctly, actually showed the equality or the value of the marginal
product of capital and the sole capital good in your model." The one
I have repeatedly used to discuss price Wicksell effects. The
primary one that I presume Chris had in mind when he wrote "In
other essays you've posted, there exists only one Leontief production
function." If Chris is not sure what he was referring to in elicitating
my response, that's his problem.
> In the example
> actually under discussion, the entire production function is
> completely described by the quoted text above ("per ton steel
> produced" implies constant returns to scale).
Sure. But a good reader would think I had the post Chris presumably
had in mind in his previous statement.
> >> Even if none of that were true,
> >> the labour demand schedule could still be recovered in the presence of an
> >> endogenous shock from the capital market simply by controlling for the
> >> interest rate in the econometric specification.
> >I don't know enough to evaluate this claim, other than to note that
> >Chris hasn't yet explained how to construct this labor demand schedule
> >in my context.
> Again, that is because it is impossible to construct that schedule in
> Rob's context -- he hasn't provided the information necessary. Perhaps
> if he reflects on the difference between "labour demand schedule" and
> "conditional labour demand schedule" which I've attempted to hammer
> home he'll realize that.
But I have constructed that schedule in my context. Besides, if it's
so difficult to construct, how did he know "this object is an ungainly
step function."
> In any case, my point stands: it is
> (conceptually) trivial to hold the interest rate constant statistically.
> Since the upward-sloping, umm, let's call it a "wage-labour locus" in
> Rob's example obtains because the interest rate varies endogenously with
> the wage rate, holding the interest rate constant through the
> econometric specification removes this effect.
I like that Chris seems to find it awkward to refer to it without
using the phrase "labor demand function." I don't understand Chris'
statement, but I wonder how he manages to distinguish long-run and
short-run effects in his econometrics.
> >The nice thing about Usenet is that an argument cannot be suppressed
> >just out of displeasure.
> Quite true. As a matter of historical record, Rob is quite free to
> repost his essay another couple of hundred times. No one will stop
> him, although others may occasionally note its errors and lack of
> relevance to modern economic thought.
I haven't seen anybody note any errors in that essay. It doesn't
surprise me that within a couple of posts after agreeing that my
numerical example is correct, Chris is now insinuating that it
is mistaken.
Anybody reading this thread might guess other reasons for Chris'
"frustation" than those he mentioned. He might as well declare
victory and quit.
SUSUPPLY
>These discussions with Chris always leave me wondering if he really
>thinks his debating tactics are fair.
and
>If I say
>Chris is mistaken about X or seems not to understand Y, I don't
>think I am making a "snide little dig."
>Furthermore, if I suggest an improvement of phrasing for some
>of his statements, I think I am disagreeing in a nuanced and
>courteous fashion. His reactions seem not to conform to such
>standards of politeness.
and
> I think any
>fair-minded reader of this interchange can see that the heat is
>all on his side.
>There is some history here, and I have been
>trying to evolve my Usenet style to be more polite.
Poor mistreated Robert.
Casey Stengel was sitting in the stands watching his inept NY Mets practice one
day, while the General Manager was regaling some visitors with stories about
one of the youngsters out on the field. To the effect that he was an
exceptionally fine person, went to Church regularly, wrote to his mother twice
a week etc. etc.
Finally Stengel could take no more, he stood up, turned to the GM, and said:
"Why don't you spend your time finding me a juvenile delinquent who can hit
.300!
The point for you, Robert, is that if instead you would, "... have been trying
to evolve [your] Usenet style to be more" honest and COHERENT.
We wouldn't have to be listening to your sniveling.
An example:
>We have not seen "baseless accusations of technical incompetence." I
>merely pointed out where Chris was mistaken in places where he was
>mistaken.
Occurs in the same post as your previous:
>> >(2) Chris' comments tend to contain technical errors.
Just to point out one.
>Anybody reading this thread might guess other reasons for Chris'
>"frustation" than those he mentioned. He might as well declare
>victory and quit.
Rich. Coming from the sci.econ champion of gutless withdrawals.
Patrick
Christopher Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>These discussions with Chris always leave me wondering if he really
>thinks his debating tactics are fair. I'll point out below some
>curious editing and misreadings.
In Rob's opinion, is the unstated caveat. I am always happy to let
readers decide for themselves if my editing is "fair." I have, for
instance, edited liberally here.
>On the other hand, I find his reactions to mine curious. If I say
>Chris is mistaken about X or seems not to understand Y, I don't
>think I am making a "snide little dig." Nor am I challenging him
>to list those areas of economics that he does understand.
>Furthermore, if I suggest an improvement of phrasing for some
>of his statements, I think I am disagreeing in a nuanced and
>courteous fashion. His reactions seem not to conform to such
>standards of politeness.
I wonder if Rob really thinks relentless accusations of
misunderstanding, ignorance, and technical error really constitute
"nuanced and courteous" discussion.
>> >Chris' insistence on not addressing the text to which he is responding
>> >is his problem. Notice that Chris doesn't even attempt to provide any
>> >evidence that I claimed to demonstrate the possible existence of
>> >upward-sloping labor demand curves.
>
>> >The title of this thread and my choice of newsgroups was designed to
>> >achieve a certain audience.
>
>> The second quoted paragraph adequately refutes the first. Rob, if you
>> don't want to claim you're showing the existence of upward-sloping labour
>> demand curves, don't use that terminology. Quite simple, really.
>
>I wanted to point out some literature that uses that terminology. I wanted
>to do this in a way that brought this literature to the attention of
>readers that had seen some of my previous discussions on this
>topic. That seems an adequate reason for the title.
I went back and reread one of Rob's oft-posted essays. Rob, please do
explain 1) the title of this thread, 2) comments like
>What, then, is the rational basis for assuming downward-sloping
>labor demand curves?
and 3) the continual accusation that economists teach "exploded dogma"
when they convey the idea that input demand scedules slope down, if
you weren't trying to argue that labour demand curves can slope up.
I see no reason to be polite here: Rob knows damn well he's abusing
terminology (I explained it to him before), and now he's trying to
weasel out of his disingenuousness.
>Saying that L( w, r ) is a labor demand function is not an outline
>of how to construct the curve. Chris did say the derivation of this
>curve comes from a profit-maximizing firm. But in my first post,
>I mentioned "equilibrium of the firm" and stated my opinion that
>this means that, in a long-run context, the firm should be on the
>"factor price frontier".
Rob has a lot of nerve accusing others of technical incompetence.
Here, he's confusing a firm's problem with market equilibria. A
firm's labour demand schedule is derived without any assumptions
regarding how prices are determined -- if the firm is on its
demand function, then it is in "equlibrium" even if the market
is not. In Rob's context, one can derive a "long run" input
demand schedule for the firm without any knowledge of the "factor
price frontier," and requiring that the economy be on that frontier
in the firm's problem implies that whatever solution falls out is
no longer an input demand function.
>We have not seen "baseless accusations of technical incompetence." I
>merely pointed out where Chris was mistaken in places where he was
>mistaken.
I suppose Rob forgot about:
>> >(2) Chris' comments tend to contain technical errors. In this post
>> >What is the firm's profit maximization problem in my example?
>
>> It isn't there, which is one of the reasons Rob's story doesn't provide
>> enough structure to characterize general equilibrium.
>
>But I gave a labor-demand relation in the post to which Chris was
>responding.
No, Rob, you gave a *conditional* labour demand schedule. Are you ever
going to grasp the distinction? ...
>Chris is always free to specify what additional structure he thinks
>he needs. My example can generate "this object," and I have
>generated it.
I guess not. Rob, please look it up in the discussion of the theory
of the firm in any micro text. In your problem, you need at least
the demand curve the firm faces -- I can't recall, but you have perfect
competition in this model, it's inconsistent with your constant returns
assumption.
> Since he provided this clarification, he should
>have noted I was asking him to outline how to construct conditional
>labor demand curves, if he did not think a labor demand curve could
>be constructed for my example.
Look it up in any micro text, Rob.
>> >In the opinion of some economists (Schefold 1990, Woods 1990),
>> >describing the effect I have been describing as an upward-sloping
>> >labor demand curve is legimate.
>
>> None of the text Rob has quoted contains such an assertion.
[ quotes from: ]
> -- Schefold, 1990
>
> --Woods, 1990
I don't believe Rob has quoted that text before. If he did, I stand
corrected. In any case, both these authors are abusing terminology,
and I would hope that somewhere in the text they acknowledge this.
If they do, then Rob is deliberately misrepresenting these pieces.
If they don't, these authors deserve to be chided, not unlike Rob,
for misusing basic terminology.
[ Much bickering deleted. I am not, in particular, going to discuss
dynamic economic modelling with Rob when he himself admits he isn't
familiar with the literature, ie, the vast majority of economic
theory developed in the past three decades. ]
>> One can only see this as an attempt to divert the discussion. Rob,
>> do you have any evidence whatsoever that endogenous changes in the
>> interest rate more than offset own-price induced changes in labour
>> demand when the minimum wage is increased? Did you grasp my (deleted)
>> point that it is easy to control for this effect statistically?
>I have always said that the effect illustrated in my example was meant
>to make a logical point.
Much like Rob's refusal to actually either defend or dismiss the idea
that labour demand curves can slope up, Rob doesn't seem to want to
either defend or dismiss the idea that the mechanism he presents is
responsible for counter-intuitive effects of a minimum wage. Contrary
to his sentence above, his lengthy oft-posted essay uses the effects
of a minimum wage to motivate the discussion. Well, Rob, are you going
to take a position or are you not?
> I objected to Chris' use of statistics to
>minimize the effects of a change in the level of the minimum wage. That's
>the context of this "attempt to divert the discussion."
Fine, then are you willing to defend the notion that endogenous changes
in the interest rate more than offset own-price induced changes in labour
demand when the minimum wage is increased? If not, will you stop reposting
this essay every time the subject of minimum wages comes up in a thread?
Well, first,
Q = f( L, X1, X2)
is, in fact, a special case of
Q = min ( L/a0, X1/a1, ..., Xn/an )
so Rob's pointlessly elaborate "proof" doesn't cut it. But it is
also intending to prove wrong an assertion I never made -- I said
the technology here can be described as "a choice between two
Leontief production functions," *not* "a Leontief production
function."
>> Rob's context -- he hasn't provided the information necessary. Perhaps
>> if he reflects on the difference between "labour demand schedule" and
>> "conditional labour demand schedule" which I've attempted to hammer
>> home he'll realize that.
>But I have constructed that schedule in my context. Besides, if it's
>so difficult to construct, how did he know "this object is an ungainly
>step function."
1) There is no labour demand schedule in Rob's example, there is a
conditional labour demand schedule. 2) I know it's an step function
because the isoquants, given the technology, are kinked -- there will
be switch points as the price ratio passes the relevant thresholds.
I refuse, however, to pull out a calculator and work through Rob's
unwieldy numerical example to present those thresholds, nor do I see
any point in his insistence that I do so.
>I like that Chris seems to find it awkward to refer to it without
>using the phrase "labor demand function."
And yet I don't use that term because doing so would be incorrect and
misleading. Many models generate relationships which superficially
look like defined theoretical objects but we don't just misapply
jargon right and left to make the text a little shorter -- that would
hinder rather than aid communication.
> I don't understand Chris'
>statement, but I wonder how he manages to distinguish long-run and
>short-run effects in his econometrics.
Neither do I, in this context. That's one reason the explicitly dynamic
models the profession has long since adapted are superior to the ad hoc
"dynamics" in the old models Rob continually mischaracterizes as mainstream
tools.
The econometric point is really quite simple. Ignoring endogeneity and
other potential econometric problems, if we estimate a relationship such
as
labour = constant + b(wage) + (other stuff) + residuals
then the paramter b is the change in labour induced by a change in the
wage rate holding "other stuff" equal. If "other stuff" does not include
prices of other inputs which vary endogenously with the wage rate, then
b picks up all these endogenous second-order effects as well. It is then
the slope that can be positive in Rob's model. If however, "other stuff"
includes the prices of other inputs (such as the interest rate/rental
rate of capital), then b is the impact of a change in the wage rate on
labour demanded holding all those other prices fixed. It is then
purged of changes in the interest rate or other prices induced by changes
in the wage, and theory unambiguously predicts it should be negative.
>> Quite true. As a matter of historical record, Rob is quite free to
>> repost his essay another couple of hundred times. No one will stop
>> him, although others may occasionally note its errors and lack of
>> relevance to modern economic thought.
>I haven't seen anybody note any errors in that essay. It doesn't
>surprise me that within a couple of posts after agreeing that my
>numerical example is correct, Chris is now insinuating that it
>is mistaken.
I am? In what way? Have I not pointed out other assertions I
believe are erroneous?
>Anybody reading this thread might guess other reasons for Chris'
>"frustation" than those he mentioned. He might as well declare
>victory and quit.
Grand idea that. If Rob has nothing interesting to say in response
to this note , I don't see much point in continuing the discussion. I
think it has been very well established that Rob does not show that
labour demand curves can slope up. If he starts reposting his essay
again under the current title, or including the jabs about "exploded
dogma" and the like, I'll make a habit of reposting my initial
rejoinder in this thread.
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >On the other hand, I find his reactions to mine curious. If I say
> >Chris is mistaken about X or seems not to understand Y, I don't
> >think I am making a "snide little dig." Nor am I challenging him
> >to list those areas of economics that he does understand.
> >Furthermore, if I suggest an improvement of phrasing for some
> >of his statements, I think I am disagreeing in a nuanced and
> >courteous fashion. His reactions seem not to conform to such
> >standards of politeness.
> I wonder if Rob really thinks relentless accusations of
> misunderstanding, ignorance, and technical error really constitute
> "nuanced and courteous" discussion.
I think what I wrote above about disagreeing in a "nuanced and
courteous fashion." Perhaps some find my posts more well-thought out
than Chris' posts. If so, one reason might be that I take longer to
reply. I am even sometimes slower in replying to e-mail, if I
reply at all.
Scholarly work is a collective enterprise. No one person can be
expected to have mastered all fields, techniques, etc. However,
communities of scholars should be willing to talk to one another,
especially when exploring related subject matter.
[ Some stuff where Chris asks questions already answered. ]
> >Saying that L( w, r ) is a labor demand function is not an outline
> >of how to construct the curve. Chris did say the derivation of this
> >curve comes from a profit-maximizing firm. But in my first post,
> >I mentioned "equilibrium of the firm" and stated my opinion that
> >this means that, in a long-run context, the firm should be on the
> >"factor price frontier".
> Rob has a lot of nerve accusing others of technical incompetence.
The word "incompetence" rarely appears in my posts, if ever. It
hasn't appeared in any of my posts in this thread.
> Here, he's confusing a firm's problem with market equilibria. A
> firm's labour demand schedule is derived without any assumptions
> regarding how prices are determined -- if the firm is on its
> demand function, then it is in "equlibrium" even if the market
> is not. In Rob's context, one can derive a "long run" input
> demand schedule for the firm without any knowledge of the "factor
> price frontier," and requiring that the economy be on that frontier
> in the firm's problem implies that whatever solution falls out is
> no longer an input demand function.
The number of firms and their capacities is not fixed in long
run analysis. A neoclassical firm may operate at a loss in short
run analysis. This will obtain if returns do not cover the sum of
variable and fixed costs, but marginal variable costs do not exceed
marginal revenues. Likewise, a neoclassical firm may receive profits
in the short run if it operates in an industry where capacity is low,
perhaps because demand was incorrectly anticipated.
The number of firms will expand if there are any pure economic
profits available. Thus, firms cannot obtain pure economic
profits in consistent competitive long-run models. Likewise,
firms will not operate at levels in which costs exceed revenues
in competitive long-run models. If the economy is off the
"factor price frontier," one of these possibilities applies. Note
that the "factor price frontier" is used to model *production*,
but neither consumer behavior nor household decisions about
supplies of non-produced inputs. It would seem that a firm is
not in long-run equilibrium if it is making decisions inconsistent
with the economy being on the "factor price frontier."
Note when using the "factor price frontier" to analyze the
competitive profit-maximizing choice of technique, one assumes
firms take prices as given. They do not account for the
association between a lower wage, a higher interest rate, and
different levels of prices. In other words, I am not making
the mistake of treating the demand for an individual competitive
firm's output as the same relation as the market demand relation.
Given this requirement that the firm be on the "factor price
frontier", the following solution seems to fall out, pace
Chris, as a labor demand "function":
w = constant, 0 <= L <= infinity
(The firms vary other inputs with labor along this relation,
thereby keeping relative quantities unchanged.)
This is the third time I've given the above relation.
[ Silliness and misreadings deleted. ]
> In your problem, you need at least
> the demand curve the firm faces -- I can't recall, but you have perfect
> competition in this model, it's inconsistent with your constant returns
> assumption.
I don't think that's quite right. Perfect competition is inconsistent
with increasing returns to scale that are internal to the firm.
Constant returns to scale are widely assumed, along with diminishing
marginal returns to individual inputs. The number and size of firms
are indeterminate under these assumptions. I don't think that's
exactly the same as being inconsistent with constant returns to
scale.
> > Since he provided this clarification, he should
> >have noted I was asking him to outline how to construct conditional
> >labor demand curves, if he did not think a labor demand curve could
> >be constructed for my example.
> Look it up in any micro text, Rob.
That's a non-answer. Notice that Chris doesn't even specify a
specific micro text. Providing valid arguments requires some
work.
[ snip ]
> [ quotes from: ]
>
> > -- Schefold, 1990
> >
> > --Woods, 1990
>
> I don't believe Rob has quoted that text before...
And so on. Chris' beliefs are false, as anybody can see from
DejaNews. Furthermore, I already commented on these quotes.
[ Chris drops the topic of "dynamics" with a random insult, after
having failed to even attempt any demonstration of relevance to
this thread. ]
> >> One can only see this as an attempt to divert the discussion. Rob,
> >> do you have any evidence whatsoever that endogenous changes in the
> >> interest rate more than offset own-price induced changes in labour
> >> demand when the minimum wage is increased? Did you grasp my (deleted)
> >> point that it is easy to control for this effect statistically?
> >I have always said that the effect illustrated in my example was meant
> >to make a logical point.
> Much like Rob's refusal to actually either defend or dismiss the idea
> that labour demand curves can slope up, Rob doesn't seem to want to
> either defend or dismiss the idea that the mechanism he presents is
> responsible for counter-intuitive effects of a minimum wage. Contrary
> to his sentence above, his lengthy oft-posted essay uses the effects
> of a minimum wage to motivate the discussion. Well, Rob, are you going
> to take a position or are you not?
I know of no reason whatsoever for believing that technology does
not have the properties that produce the effect illustrated in my
example. Furthermore, economists do not even know how to specify
suitable restrictions on technology that rule out this effect. I
think economic theory, if it is to be developed with the kinds
of abtract specifications of technology typical of neoclassical
theory over the last century, should be developed with specifications
that do not rule out this effect.
Notice that these beliefs of mine are independent of any position
on whether comparisons of long run positions or "dynamic" sequences
of temporary equilibria are more appropriate methods of analysis.
Neoclassical economists such as Christopher Bliss, Frank Hahn, and
Paul Samuelson seem to argue both that these "dynamic" methods are
more appropriate and that general neoclassical theory should
accept technology in which the effect in my numerical example can
arise. Of course, the effect is manifested in a different way
in "dynamic" models. It seems to show up there as certain paths
in which both wages and employment increase. Such paths might not
be stable, but such models are well-known to possibly exhibit
multiple equilibria, instability, and other interesting dynamics.
I also doubt that the sophisticated mathematics of such models
are necessarily accompanied by enough insight into economics
to justify the expenditure of intellectual effort put into
them. I am less sure of this judgement than I am about my
understanding of long run models of production.
Suppose one thinks that a comparison of long run positions is a
valid method of analysis. Perhaps one believes this because one
also believes that market economies exhibit a tendency to
approach long run equilibria. I know of no reason whatsoever to
think that the effect illustrated by my example is unlikely
to arise in (large) multiple-commodity economies.
Are long run models empirically applicable? Leontief's input-output
matrices are widely applied empirically. This is a long run model
of production, given technique. I do not know how to empirically
explore the issues at play here in the analysis of the long run
choice of technique. I think it naive to directly use observed
wages and interest rates to construct a "factor price frontier."
Some economists have used Leontief matrices observed at different
points of time to construct a "factor price curve" for each
matrix. This is different than comparing two curves for different
techniques known at the same point of time.
This is not to say that long run analysis can have no implications on
empirical observations at any structural level. Bortis (1997) has
some interesting, though incomplete, thoughts on this topic. I
think this is still a research question. It is partly a matter of
economic theory, not merely a question of how to develop elaborate
statistics.
> > I objected to Chris' use of statistics to
> >minimize the effects of a change in the level of the minimum wage. That's
> >the context of this "attempt to divert the discussion."
> Fine, then are you willing to defend the notion that endogenous changes
> in the interest rate more than offset own-price induced changes in labour
> demand when the minimum wage is increased? If not, will you stop reposting
> this essay every time the subject of minimum wages comes up in a thread?
It's interesting that economists often ask how their story could be
wrong in such threads. Keynes' chapter 19 analysis might have more
direct applicability. But some economists mistakenly dismiss Keynes
as being concerned solely with short-run problems caused by sticky
or rigid money wages or prices. These economists also think that if
prices and wages were flexible, markets would always clear. The
dynamic stories they tell seem to rely on some long run decreasing
relation between wages and the employment offered by firms.
My example clearly shows such stories are unfounded. This logical point
is relevant to the subject of wages and to labor economics.
> >> Both "process alpha" and "process beta" describe Leontief production
> >> functions. The firm can choose process alpha or process beta. I would
> >> like Rob to explain why my statement is not entirely accurate.
> >
> >Sure. A Leontief production function is of the form:
> >
> > Q = min ( L/a0, X1/a1, ..., Xn/an )
[ snip ]
> >Now consider my example. Let L, X1, and X2 be the labor, steel, and
> >corn used by the steel sector as inputs. The production function in
> >the steel sector in my example is the solution of the following Linear
> >Program:
> >
> > Max Q = Q1 + Q2
> > such that
> > 0.19321 Q1 - L1 <= 0
> > 0.033594 Q2 - L2 <= 0
> > L1 + L2 <= L
> > 0.35 Q1 - X11 <= 0
> > 0.13329 Q2 - X12 <= 0
> > X11 + X12 <= X1
> > 0.0095553 Q1 - X21 <= 0
> > 0.15590 Q2 - X22 <= 0
> > X21 + X22 <= X2
> >
> >
> > where Q1 >= 0, Q2 >= 0, L1 >= 0, L2 >= 0, X11 >= 0
> > X12 >= 0, X21 >= 0, X22 >= 0
[ snip ]
> >Thus, one can express the solution value of the objective function
> >as a function of these parameters:
> > Q = f( L, X1, X2 )
> >Since this second LP is not of the same form as the first, the
> >production function f( L, X1, X2 ) is not Leontief.
> Well, first,
>
> Q = f( L, X1, X2)
>
> is, in fact, a special case of
>
> Q = min ( L/a0, X1/a1, ..., Xn/an )
>
> so Rob's pointlessly elaborate "proof" doesn't cut it.
No. The form of f( L, X1, X2 ) is not merely a function of three
variables. I defined f() to be the solution to the LP above, and
its form is restricted by this definition. Although I haven't
been bloody-minded enough to solve this LP, it seems obvious to
me that the solution will not be a special case of the minimum
function given above.
And I consider my proof more trivial, than "elaborate."
> But it is
> also intending to prove wrong an assertion I never made -- I said
> the technology here can be described as "a choice between two
> Leontief production functions," *not* "a Leontief production
> function."
The discussion went as follows:
RV: (It is interesting that those economists responding to my posts
have often mistakenly characterized the technology in my examples
as "Leontief production functions.")
CA: [1] Here, you have a choice between two Leontief production
functions. [2] In other essays you've posted, there exists only
one Leontief production function.
I assumed that Chris, in his second statement, had mainly my long
essay on price Wicksell effects in mind. Rather than admit that
he mischaracterizes the assumptions on technology in that post,
he now seems to feel that he doesn't know what he had in mind.
His position on his first statement now seems to be that it was
a non sequitur. But let's consider whether it is true.
If the alpha (or beta) process in my example were the only
process known for producing steel, then the technology in the
steel sector would be accurately characterized as being described
by a Leontief production function. But the term "production
function" cannot be rigorous used to describe these processes
when both are known. The production function is a solution to
an optimization problem. Part of data for this problem cannot
be described as a production function.
Chris' abuse of terminology does no harm as long as it does not
mislead. In particular, Leontief production functions have
fixed coefficients. But those who have described the technology
in my example as exhibiting fixed coefficients are simply
wrong. (I don't recall Chris exhibiting this confusion.)
It's also ironic that Chris is defending *this* abuse of
terminology.
> >> Rob's context -- he hasn't provided the information necessary. Perhaps
> >> if he reflects on the difference between "labour demand schedule" and
> >> "conditional labour demand schedule" which I've attempted to hammer
> >> home he'll realize that.
> >But I have constructed that schedule in my context. Besides, if it's
> >so difficult to construct, how did he know "this object is an ungainly
> >step function."
> 1) There is no labour demand schedule in Rob's example,
See above. This is my *third* post in this thread in which I
presented an object that Chris should be willing to characterize
as a long-run labor demand schedule.
> there is a conditional labour demand schedule.
Not by Chris' definition. The interest rate is different at
different points along the curve constructed in my long essay
presenting my example.
> 2) I know it's an step function
> because the isoquants, given the technology, are kinked -- there will
> be switch points as the price ratio passes the relevant thresholds.
> I refuse, however, to pull out a calculator and work through Rob's
> unwieldy numerical example to present those thresholds, nor do I see
> any point in his insistence that I do so.
I'm not sure know what Chris means by switch points in this context.
The term "switch point" has a well-defined meaning in the construction
of "factor price frontiers."
Well, there's one more refusal of Chris' to consider my argument.
He could always substitute letters for numbers in my example. I
deliberately minimize the level of mathematics needed to check
my example. One hardly needs algebra to read my essay.
[ snip ]
> > I don't understand Chris'
> >statement, but I wonder how he manages to distinguish long-run and
> >short-run effects in his econometrics.
>
> Neither do I, in this context. That's one reason the explicitly dynamic
> models the profession has long since adapted are superior to the ad hoc
> "dynamics" in the old models Rob continually mischaracterizes as mainstream
> tools.
Whether a tool is "mainstream" is irrelevant to whether it yields
correct results. Activity analysis and mathematical programming are
standard. Paul Samuelson seems proud of his independent rediscovery
of "factor price frontiers." The use of "factor price frontiers" to
analyze the choice of technique in long run circulating capital models
is standard. (Price and real) Wicksell effects are well-accepted.
The fact that non-zero price Wicksell effects generally lead to an
inequality between the marginal product of social capital and the
equilibrium interest rate is standard. The logical possibility of
both reswitching and capital-reversing was accepted in both Cambridges.
I also think that substitution is the historical and logical basis
for well-behaved relations between quantities and prices in neoclassical
economics. The logic of prices as scarcity indices has been shown to
be unfounded in long run theories of production. I don't know of any
convincing refutation of these claims.
[ Chris gives a good explanation of how he thinks multivariate
linear regression applies here. ]
I've commented on empirical applicability above, doubtless in a
way that Chris will find unsatisfactory.
> It is then
> purged of changes in the interest rate or other prices induced by changes
> in the wage, and theory unambiguously predicts it should be negative.
That's assertion, not argument.
> >> [...] Rob is quite free to repost his essay
> >> [...] others may occasionally note its errors.
> >I haven't seen anybody note any errors in that essay. It doesn't
> >surprise me that within a couple of posts after agreeing that my
> >numerical example is correct, Chris is now insinuating that it
> >is mistaken.
> I am? In what way? Have I not pointed out other assertions I
> believe are erroneous?
The third question above in that paragraph is irrelevant, unless
he is referring to *assertions* in *that* essay. I know of no
such assertions that he has described as false.
> > [...] He might as well declare victory and quit.
> Grand idea that. [...] If he starts reposting his essay
> again under the current title, or including the jabs about "exploded
> dogma" and the like, I'll make a habit of reposting my initial
> rejoinder in this thread.
Chris might want to edit it so that he is not so easily charged
with misreading. He also might want to derive labor demand and
conditional labor demand curves in the context of my example
(e.g. using letters to replace the numbers in my example).
Maybe we can both use 'bots and need not read this newsgroup
at all.
Christopher Auld
>[ Some stuff where Chris asks questions already answered. ]
Rob is referring here to the text in which I asked whether he actually
thinks he's showing that labour demand curves can slope up. He has not
"already answered" this questoin. He simply refuses, one supposes,
to answer or defend his oft-repeated allegations that the profession
teaches "exploded dogma" when asserting these schedules slope down. Rob,
for the fourth time, do you think labour demand curves can slope up? If
so, please show how your example demonstrates this result. If not, are
you willing to retract your insulting rhetoric?
Note the above is supposed to be the point of this entire thread. All
the text below is basically irrelevant, with the exception of the
question whether Rob thinks that endogenous changes in the interest
rate are responsible for non-negative employment effects of minimum
wage increases. Rob also adamantly refuses to actually answer that
question.
BTW, I tried to leave all of Rob's text intact, lest I am accused
again of "unfair editing," but my reader will not accept a post with
more included than new text, and I confess to a terser style than
Rob's.
>> Here, he's confusing a firm's problem with market equilibria. A
>> firm's labour demand schedule is derived without any assumptions
>> regarding how prices are determined -- if the firm is on its
>> demand function, then it is in "equlibrium" even if the market
>> is not. In Rob's context, one can derive a "long run" input
>> demand schedule for the firm without any knowledge of the "factor
>> price frontier," and requiring that the economy be on that frontier
>> in the firm's problem implies that whatever solution falls out is
>> no longer an input demand function.
>
>The number of firms and their capacities is not fixed in long
>run analysis.
[...]
>in competitive long-run models. If the economy is off the
>"factor price frontier," one of these possibilities applies.
You are still missing the point, Rob. The firm's labour demand
schedule is gives labour demanded as a function of the price of
output and the vector of input prices. Given the firm's
technology, it is possible to compute factor demand schedules.
The critical point is that one need know nothing whatsoever
about aggregate market conditions (beyond price taking behaviour)
to compute factor demand schedules. If "long run" in this
context means all factors are variable and the firm can choose
to shut down, then a "long run" labour demand schedule can be
computed off the firm's problem with a non-negative profits
constraint. Note that the *firm* can still be on its factor
demand schedule even if the *economy* is out of equilibrium.
Imposing the condition that the *economy* be in equilibrium
on the *firm's* problem implies that whatever falls out is
no longer a labour demand schedule. In this context, and using
my notation, the *firm's* labour demand schedule is a function
L = L( w, r, p).
Rob imposes a condition which can be written w=w(r) and
normalizes the price of output to unity, so his "labour/wage
locus can be written:
L = L(w).
The second equation is consistent with the first but it *isn't
a labour demand schedule*. We do not need the condition that
the *economy* be in equilibrium to work out *a* firm's choices
under varying factor price vectors.
>Given this requirement that the firm be on the "factor price
>frontier", the following solution seems to fall out, pace
>Chris, as a labor demand "function":
>
> w = constant, 0 <= L <= infinity
>
>(The firms vary other inputs with labor along this relation,
>thereby keeping relative quantities unchanged.)
>
>This is the third time I've given the above relation.
This does not follow from the economy being on the "factor
price frontier," it follows from the assumptions of perfect
competition and constant returns to scale. That is, it
would if Rob had written:
L = 0 w < w*
0 <= L <= \infty w = w*
L -> \infty w > w*
I asked Rob to clarify the structure of the output market in
his model before. If he'd done so, it would have been immediate
that the labour demand scedule takes this form. Note, again,
it has nothing to do with the "factor price frontier."
>[ Silliness and misreadings deleted. ]
There's Rob being "courteous and nuanced" again. One begins to
wonder if he even realizes how grating his style can be.
>> In your problem, you need at least
>> the demand curve the firm faces -- I can't recall, but you have perfect
>> competition in this model, it's inconsistent with your constant returns
>> assumption.
>
>I don't think that's quite right. Perfect competition is inconsistent
>with increasing returns to scale that are internal to the firm.
>
>Constant returns to scale are widely assumed, along with diminishing
>marginal returns to individual inputs. The number and size of firms
>are indeterminate under these assumptions. I don't think that's
>exactly the same as being inconsistent with constant returns to
>scale.
True, I should have said "leads to a pointless model" rather than
"inconsistent."
>> > Since he provided this clarification, he should
>> >have noted I was asking him to outline how to construct conditional
>> >labor demand curves, if he did not think a labor demand curve could
>> >be constructed for my example.
>
>> Look it up in any micro text, Rob.
>
>That's a non-answer. Notice that Chris doesn't even specify a
>specific micro text. Providing valid arguments requires some
>work.
For the third time, why does Rob insist I compute this function in
this example? The solutions are of the form L(w,r,q) and fall out
of the firm's cost-minimation problem. They are not step functions
due to the non-differtiable technology Rob assumes. The steps are
at points that must be computed off Rob's ridiculous seven-decimal
place numerical exposition. I'm not even making an "argument"
here, I'm pointing out the definiion of "conditional labour demand
curve" is not exactly obscure and can be found in any micro text.
>> [ quotes from: ]
>>
>> > -- Schefold, 1990
>> >
>> > --Woods, 1990
>>
>> I don't believe Rob has quoted that text before...
>
>And so on. Chris' beliefs are false, as anybody can see from
>DejaNews. Furthermore, I already commented on these quotes.
Ah, courteous and nuanced yet again. Rob's wonderful editing
here snips "but if he has, I stand corrected."
>[ Chris drops the topic of "dynamics" with a random insult, after
> having failed to even attempt any demonstration of relevance to
> this thread. ]
I didn't "drop the topic," I said, again, that the mainstream has
long since switched to explicitly dynamic models which makes the
sort of models Rob seeks to topple with his thirty year old
counterexamples simply archaic. Rob, why don't you read some of
the work that mainstream economists have done on capital theory
and modelling economies through time?
>> Much like Rob's refusal to actually either defend or dismiss the idea
>> that labour demand curves can slope up, Rob doesn't seem to want to
>> either defend or dismiss the idea that the mechanism he presents is
>> responsible for counter-intuitive effects of a minimum wage. Contrary
>> to his sentence above, his lengthy oft-posted essay uses the effects
>> of a minimum wage to motivate the discussion. Well, Rob, are you going
>> to take a position or are you not?
Now, five lengthy paragraphs of dancing around the point:
>I know of no reason whatsoever for believing that technology does
>not have the properties that produce the effect illustrated in my
>example. Furthermore, economists do not even know how to specify
>suitable restrictions on technology that rule out this effect. I
>think economic theory, if it is to be developed with the kinds
[ Snipped against will. ]
>think this is still a research question. It is partly a matter of
>economic theory, not merely a question of how to develop elaborate
>statistics.
Rob:
1. Do you think you've shown that, in theory, labour demand schedules
can slope up?
2. Do you think that the effect you've outlined is responsible for the
any counterintuitive effects of minimum wages?
Actually addressing these questions would be appreciated.
>> Fine, then are you willing to defend the notion that endogenous changes
>> in the interest rate more than offset own-price induced changes in labour
>> demand when the minimum wage is increased? If not, will you stop reposting
>> this essay every time the subject of minimum wages comes up in a thread?
>
>It's interesting that economists often ask how their story could be
>wrong in such threads. Keynes' chapter 19 analysis might have more
>direct applicability. But some economists mistakenly dismiss Keynes
>as being concerned solely with short-run problems caused by sticky
>or rigid money wages or prices. These economists also think that if
>prices and wages were flexible, markets would always clear. The
>dynamic stories they tell seem to rely on some long run decreasing
>relation between wages and the employment offered by firms.
>
>My example clearly shows such stories are unfounded. This logical point
>is relevant to the subject of wages and to labor economics.
It appears Rob doesn't want to answer any question today, alas. Rob,
" are you willing to defend the notion that endogenous changes
in the interest rate more than offset own-price induced changes in labour
demand when the minimum wage is increased? "
Yes or no? Do you think you could respond directly?
>> >Thus, one can express the solution value of the objective function
>> >as a function of these parameters:
>
>> > Q = f( L, X1, X2 )
>
>> >Since this second LP is not of the same form as the first, the
>> >production function f( L, X1, X2 ) is not Leontief.
>
>> Well, first,
>>
>> Q = f( L, X1, X2)
>>
>> is, in fact, a special case of
>>
>> Q = min ( L/a0, X1/a1, ..., Xn/an )
>>
>> so Rob's pointlessly elaborate "proof" doesn't cut it.
>
>No. The form of f( L, X1, X2 ) is not merely a function of three
>variables. I defined f() to be the solution to the LP above, and
>its form is restricted by this definition. Although I haven't
>been bloody-minded enough to solve this LP, it seems obvious to
>me that the solution will not be a special case of the minimum
>function given above.
Yes, I agree, but you didn't show that, Rob. Your "proof" is no
such thing.
> RV: (It is interesting that those economists responding to my posts
> have often mistakenly characterized the technology in my examples
> as "Leontief production functions.")
>
> CA: [1] Here, you have a choice between two Leontief production
> functions. [2] In other essays you've posted, there exists only
> one Leontief production function.
>
>I assumed that Chris, in his second statement, had mainly my long
>essay on price Wicksell effects in mind. Rather than admit that
>he mischaracterizes the assumptions on technology in that post,
>he now seems to feel that he doesn't know what he had in mind.
Rob, have you ever posted an essay with a Leontief production function?
If you answer "no," I am going to subject myself to diffing through
my files and dredging up such an example. If "yes," you will please
explain what you're arguing about.
>His position on his first statement now seems to be that it was
>a non sequitur. But let's consider whether it is true.
I admit I should have said "choice between two techniques which,
alone, would form Leontief production functions" and apologize for
my very slight and obvious abuse of terminology.
>> 2) I know it's an step function
>> because the isoquants, given the technology, are kinked -- there will
>> be switch points as the price ratio passes the relevant thresholds.
>> I refuse, however, to pull out a calculator and work through Rob's
>> unwieldy numerical example to present those thresholds, nor do I see
>> any point in his insistence that I do so.
>
>I'm not sure know what Chris means by switch points in this context.
>The term "switch point" has a well-defined meaning in the construction
>of "factor price frontiers."
Which isn't how I'm using it. I mean simply that the firm will switch
from one technique to the other.
>Well, there's one more refusal of Chris' to consider my argument.
>He could always substitute letters for numbers in my example. I
>deliberately minimize the level of mathematics needed to check
>my example. One hardly needs algebra to read my essay.
For the fourth time, Rob, I am *not* going to get my calculator
out to compute this function for your model. For the fourth time,
I don't see the point in wasting my time doing that, and Rob refuses
to say what purpose it would serve.
>> Neither do I, in this context. That's one reason the explicitly dynamic
>> models the profession has long since adapted are superior to the ad hoc
>> "dynamics" in the old models Rob continually mischaracterizes as mainstream
>> tools.
>
>Whether a tool is "mainstream" is irrelevant to whether it yields
>correct results. Activity analysis and mathematical programming are
>standard. Paul Samuelson seems proud of his independent rediscovery
>of "factor price frontiers." The use of "factor price frontiers" to
>analyze the choice of technique in long run circulating capital models
>is standard. (Price and real) Wicksell effects are well-accepted.
>The fact that non-zero price Wicksell effects generally lead to an
>inequality between the marginal product of social capital and the
>equilibrium interest rate is standard. The logical possibility of
>both reswitching and capital-reversing was accepted in both Cambridges.
>
>I also think that substitution is the historical and logical basis
>for well-behaved relations between quantities and prices in neoclassical
>economics. The logic of prices as scarcity indices has been shown to
>be unfounded in long run theories of production. I don't know of any
>convincing refutation of these claims.
And, as is becoming the staus quo, I don't see how any of this verbiage
addresses what I said.
>> It is then
>> purged of changes in the interest rate or other prices induced by changes
>> in the wage, and theory unambiguously predicts it should be negative.
>That's assertion, not argument.
Which, the interpretation of coefficients in a regression context, or
the idea that properly defined labour demand curves slope down?
>Maybe we can both use 'bots and need not read this newsgroup
>at all.
Unlike Rob, I have never reposted exactly the same material to any
newsgroup, with the exception of very, very occasionally ceding to
requests for reposts. I envourage Rob to adopt the same philosophy.
He'd be much more interesting to talk to if he would only get a
new subject in economics to be a rebel about. How about posting
why real business cycles are bad rather than why incorrectly
defined labour demand curves slope up, Rob?
SUSUPPLY
>I think what I wrote above about disagreeing in a "nuanced and
>courteous fashion." Perhaps some find my posts more well-thought out
>than Chris' posts.
[When hell freezes over.]
>If so, one reason might be that I take longer to
>reply. I am even sometimes slower in replying to e-mail, if I
>reply at all.
With all this time devoted to replying I would have thought you might've found
it possible to write coherent sentences, instead of:
>I think what I wrote above about disagreeing in a "nuanced and
>courteous fashion."
Or is it, I think therefore I am courteous and nuanced? So, this:
>[ Silliness and misreadings deleted. ]
automatically quallifies?
[snip]
>> Look it up in any micro text, Rob.
>
>That's a non-answer. Notice that Chris doesn't even specify a
>specific micro text.
Say! You are a sharp cookie, Robert. He said "any".
>[ Chris drops the topic of "dynamics" with a random insult, after
> having failed to even attempt any demonstration of relevance to
> this thread. ]
After you admitted you didn't know anything about it. Why should he waste his
time, given that?
[snip]
>> Much like Rob's refusal to actually either defend or dismiss the idea
>> that labour demand curves can slope up, Rob doesn't seem to want to
>> either defend or dismiss the idea that the mechanism he presents is
>> responsible for counter-intuitive effects of a minimum wage. Contrary
>> to his sentence above, his lengthy oft-posted essay uses the effects
>> of a minimum wage to motivate the discussion. Well, Rob, are you going
>> to take a position or are you not?
As they say in the Hertz commercial, "Well, not exactly.". Robert must
be...Robert:
>I know of no reason whatsoever for believing that technology does
>not have the properties that produce the effect illustrated in my
>example. Furthermore, economists do not even know how to specify
>suitable restrictions on technology that rule out this effect. I
>think economic theory, if it is to be developed with the kinds
>of abtract specifications of technology typical of neoclassical
>theory over the last century, should be developed with specifications
>that do not rule out this effect.
[snip of the rest (some 5 paragraphs) of the ballroom dancing].
>It's interesting that economists often ask how their story could be
>wrong in such threads.
Just about as often as Vienneau posts. Since he refuses to answer
straightforward questions.
[snip some more dancing]
>My example clearly shows such stories are unfounded. This logical point
>is relevant to the subject of wages and to labor economics.
Which can mean anything. And probably will if this discussion goes on much
longer.
Patrick
marcel simkens
final goal of proving that the sloping is, or can be, upward ?
Are graphs of great use for economics ? In The General Theory, Keynes has
used only 1 graph with the footnote that it was suggested by Mr... Harrod.
John J Weatherby
You actually read Keynes wow. I haven't know to many people who could get
through. It is easier to read Hicks and let him explain it to you.
marcel simkens
John J Weatherby wrote in message
<7ehdg1$13eq$1...@newssvr01-int.news.prodigy.com>...
> Graphs aren't necessary but they can help to show a situtation eaiser.
>You actually read Keynes wow. I haven't know to many people who could get
>through. It is easier to read Hicks and let him explain it to you.
My question was :
Why is the Sloping of the Labor Demand Curve so important and what is the
final goal of proving that the sloping is, or can be, upward ?
Robert is social minded and I guess that his final goal is to prove that
unemployment can decrease by increasing the real wage. This is an
assumption and only Robert can answer my question.
I have problems with graphs if the equation is not exactly known and if they
are made by assumptions. Economic situations are very complicated and
depending on so many variables that a simple graph can be confusing.
Robert Vienneau
> Why is the Sloping of the Labor Demand Curve so important and what is the
> final goal of proving that the sloping is, or can be, upward ?
"Thus the reswitching anomaly, along with its theoretical developments
and implications, has been placed in abeyance. And so it must be, for
if this criticism were taken as being no less applicable to the real
world than the theoretical, then it follows, as already noted, that
orthodox economics is unable to make any reliable statements concerning
the relationship of production to the various input markets. That is,
the neoclassical vision of a market-coordinated production system, along
with derivative growth and distribution theories, are all invalidated.
As a consequence, the nature of the entire traditional circular flow
conception is called into question...
...It is one thing to say that this conception of indirect economic
management does not satisfactorily achieve its goals because of the
existence of such real-world problems as bottlenecks, power, premature
inflation, inflationary expectations, random shocks, ratchet and
spillover effects, and the like. In such situations, an economically
coherent and consistent market-based system of production and
distribution is still assumed to exist, though it is overlaid with
political, institutional, and psychological factors that affect
economic adjustments and performance. The basic strategy, in this case,
would be to maintain the general neoclassical-synthetic emphasis on
fiscal and monetary management (with perhaps somewhat greater stress on
the monetary tool, if the monetarists were to have their way), and
supplement these tools with finely targeted direct and specific devices -
for example, stricter antitrust enforcement, more sharply focused
incentive (and disincentive) taxes, expanded job training and subsidization
programs - so as to allow and encourage the effective functioning of
centerpiece fiscal and monetary devices.
It is quite another thing to argue that key markets in the system,
particularly those in the resource or input sector, do not possess the
fundamental economic characteristics necessary to the orderly systematic
functioning that is postulated by mainstream theory..."
-- Richard X. Chase, "Production Theory," in _A Guide to Post-Keynesian
Economics_, (edited by Alfred S. Eichner), M. E. Sharpe, 1978, p. 79-80
Robert Vienneau
> Graphs aren't necessary but they can help to show a situtation eaiser.
> You actually read Keynes wow. I haven't know to many people who could get
> through. It is easier to read Hicks and let him explain it to you.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Laughing Out Loud.
dav...@my-dejanews.com
"marcel simkens" <marcel....@village.uunet.be> wrote:
> Why is the Sloping of the Labor Demand Curve so important and what is the
> final goal of proving that the sloping is, or can be, upward ?
The slope of the labor demand curve is important because it can be used to
separate those who understand what a demand curve is from those who don't.
Of course, it is easy to mimic those who do understand: just state as a
matter of definition a factor demand curve must always slope downward.
> Robert is social minded and I guess that his final goal is to prove that
> unemployment can decrease by increasing the real wage. This is an
> assumption and only Robert can answer my question.
Robert wants to show that equilibria in some models can generate a positive
correlation between wages and labor demand. However, the set of equilibria
in a model do not trace out a demand curve; rather, they are a set of
intersections of between supply and demand. If these both shift in the
right way, and one assumes supply doesn't shift, one would estimate an
upward sloping demand curve, but this isn't sensible.
There's a whole literature on hedonics that analyzes the set of observed
equilibria and draws inferences from that. Robert's analysis is similar
to that, though he isn't asking the same questions as the hedonics
literature. Hedonics doesn't estimate a demand curve (except in particular
cases), and Robert hasn't calculated one either.
> I have problems with graphs if the equation is not exactly known and if they
> are made by assumptions. Economic situations are very complicated and
> depending on so many variables that a simple graph can be confusing.
I'm not sure what your point is here. Do you mean that simple models can
provide misleading conclusions?
Robert's post illustrates an interesting point that I (no labor economist
or general equilibrium expert) had never considered before, but I wonder how
general these results would turn out to be in rich GE models. I know that
in Robert's quotation of Steedman, Steedman claims that GE is not needed
to prove his point. If he's going to criticize partial equilibrium analysis,
though, the obvious alternative is GE.
--Dave
dav...@my-dejanews.com
-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
Christopher Auld
>> Why is the Sloping of the Labor Demand Curve so important and what is the
>> final goal of proving that the sloping is, or can be, upward ?
> "Thus the reswitching anomaly, along with its theoretical developments
> and implications, has been placed in abeyance. And so it must be, for
[...]
1. Rob has yet to provide a model, an informal argument, or anything resembling
empirical evidence which shows that labour demand curves can slope up in
theory or in practice. Reswitching does *not* imply upward-sloping factor
demands. This answer, in response to Mr. Simkens' question is, at best
disingenuous.
2. The text Rob quotes is rubbish. Reswitching does not imply that
> the relationship of production to the various input markets. That is,
> the neoclassical vision of a market-coordinated production system, along
> with derivative growth and distribution theories, are all invalidated.
In particular, A-D GE -- the simplest formal exposition of an idealized
economy in which Smith's vision "of a market-coordinated production system"
can be shown to work -- is entirely untouched by the entire issue.
Reswitching poses a serious problem for capital aggregation and measurement,
and that's about it.
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >au...@acs.ucalgary.ca (Christopher Auld) wrote:
>
> >[ Some stuff where Chris asks questions already answered. ]
> Rob is referring here to the text in which I asked whether he actually
> thinks he's showing that labour demand curves can slope up.
Here Chris misrepresents his own posts. He has asked and I have
answered why I named this thread as above. I also explained why
I reposted my essay containing my numerical example.
> [ snip ] If not, are you willing to retract your insulting rhetoric?
I think students should learn about the controversies from which I
draw the effect illustrated in my example. I think the questions
with which I conclude my essay explaining my numerical example are
good questions. Would Chris object if I had written "irrelevant
dogma," instead of "exploded dogma"?
[snip]
> BTW, I tried to leave all of Rob's text intact, lest I am accused
> again of "unfair editing," but my reader will not accept a post with
> more included than new text, and I confess to a terser style than
> Rob's.
I agree I don't often have that problem with my newsreader. I think
Chris misrepresents past posts whether he leaves text in or deletes
it, whether he or I wrote it. I suggest that he might be less open
to the charge of "unfair editing" if he would respond slower.
[ Chris repeats his point about partial and total derivatives.
See, there's places where he could be more terse. ]
> Rob imposes a condition which can be written w=w(r) and
> normalizes the price of output to unity
[ snip ]
> >Given this requirement that the firm be on the "factor price
> >frontier", the following solution seems to fall out, pace
> >Chris, as a labor demand "function":
> > w = constant, 0 <= L <= infinity
> >
> >(The firms vary other inputs with labor along this relation,
> >thereby keeping relative quantities unchanged.)
> >This is the third time I've given the above relation.
> This does not follow from the economy being on the "factor
> price frontier," it follows from the assumptions of perfect
> competition and constant returns to scale. That is, it
> would if Rob had written:
>
> L = 0 w < w*
>
> 0 <= L <= \infty w = w*
>
> L -> \infty w > w*
I had earlier correctly described my function above as "the
inverse of the labor demand 'function.'" So I accept Chris'
correction of my sloppiness in the later post to which he is
responding.
w* is found as w* = w( r ). The above "function" does follow
from something being on the factor price frontier, for
example, a vertically integrated firm.
> ...it would have been immediate
> that the labour demand scedule takes this form. Note, again,
> it has nothing to do with the "factor price frontier."
I find that Chris has finally accepted what the labor demand
"function," as he defined it, looks like in my example. It does
seem to have something to do with the "factor price frontier."
> >[ Silliness and misreadings deleted. ]
> There's Rob being "courteous and nuanced" again. One begins to
> wonder if he even realizes how grating his style can be.
And how does Chris thinks "Look it up in any micro text" comes
across? I think my style comes across as full of romantic
overstatements, even though it's sometimes difficult to find
those overstatements when my posts are examined in detail.
"Misreadings" is courteous. If Chris reviews the deleted text, he
will see that he continually misunderstands my references
to the function above, which he now accepts as the inverse of a
labor demand "function," to be references to the locus in my
example. I don't know why Chris doesn't think "silliness" is not
a polite way to describe the personal comments in that part, on
either side. Chris has led too sheltered a life if he cannot
imagine a more impolite way of characterizing the deleted text.
[ Some stuff where I somewhat disagreed with Chris in a manner
that he seems to have found courteous, and Chris agreed with
my correction, albeit not as graciously as could be imagined. ]
[ snip ]
> >> Look it up in any micro text, Rob.
> >That's a non-answer. Notice that Chris doesn't even specify a
> >specific micro text. Providing valid arguments requires some
> >work.
> For the third time, why does Rob insist I compute this function in
> this example?
Chris could try to present an argument in any valid manner he thinks
will convince.
> [ snip ] I'm not even making an "argument"
> here, I'm pointing out the definiion of "conditional labour demand
> curve" is not exactly obscure and can be found in any micro text.
Whether this definition is obscure is irrelevant.
It's not in:
Jack Hirshleifer, _Price Theory and Applications_, 2nd edition, 1980.
R. R. Russell and M. Wilkinson, _Microeconomics: A Synthesis of Modern
and Neoclassical Theory_, 1979.
Hirshleifer derives long run "factor demand curves" with the usual
irrelevant and outdated dogmas. R & W don't even talk about such curves;
they have demands for "inputs." This is better wording.
Conditional labor demand curves are derived in
H. R. Varian, _Microeconomic Analysis_, 2nd Edition, 1984.
It's part of a presentation of Marshallian theory of the firm, a theory
I think of questionable worth. I think this for reasons known since the
1920s.
> >> [ quotes from: ]
> >> > -- Schefold, 1990
> >> > --Woods, 1990
> >>
> >> I don't believe Rob has quoted that text before. [ If he did, I stand ]
[ >>> corrected. In any case, both these authors are abusing terminology, ]
[ >>> and I would hope that somewhere in the text they acknowledge this. ]
[ >>> If they do, then Rob is deliberately misrepresenting these pieces. ]
[ >>> If they don't, these authors deserve to be chided, not unlike Rob, ]
[ >>> for misusing basic terminology. ]
> >And so on. Chris' beliefs are false, as anybody can see from
> >DejaNews. Furthermore, I already commented on these quotes.
> Ah, courteous and nuanced yet again. Rob's wonderful editing
> here snips "but if he has, I stand corrected."
My apologies if Chris takes offense, although I don't understand
why he should. I left in, "I don't believe. I don't know why Chris
couldn't have checked to see that I had provided these quotes
before.
The stuff I left out makes Chris look silly to anybody that reviews
my first post on this topic and my later comments on the literature
that I was reviewing. This literature review was the point of my
initiation of this thread.
[ Reiteration of points I have already addressed. ]
> >> Much like Rob's refusal to actually either defend or dismiss the idea
> >> that labour demand curves can slope up, Rob doesn't seem to want to
> >> either defend or dismiss the idea that the mechanism he presents is
> >> responsible for counter-intuitive effects of a minimum wage. Contrary
> >> to his sentence above, his lengthy oft-posted essay uses the effects
> >> of a minimum wage to motivate the discussion. Well, Rob, are you going
> >> to take a position or are you not?
>
> Now, five lengthy paragraphs of dancing around the point:
>
> >I know of no reason whatsoever for believing that technology does
> >not have the properties that produce the effect illustrated in my
> >example. Furthermore, economists do not even know how to specify
> >suitable restrictions on technology that rule out this effect. I
> >think economic theory, if it is to be developed with the kinds
>
> [ Snipped against will. ]
>
> >think this is still a research question. It is partly a matter of
> >economic theory, not merely a question of how to develop elaborate
> >statistics.
> 1. Do you think you've shown that, in theory, labour demand schedules
> can slope up?
I think I shown that the relevant long run locus of the quantity of
labor that firms want to employ at any given wage can slope up.
> 2. Do you think that the effect you've outlined is responsible for the
> any counterintuitive effects of minimum wages?
I think that if one thinks that long run analysis were appropriate for
analysing wages, there is no reason to expect minimum wages to create
lower employment than would otherwise be the case.
I don't think wages are determined by the supply of and demand for labor.
I think the relevance of long run theory for empirical results is
a question for contemporary research.
> Actually addressing these questions would be appreciated.
[ snip ]
> It appears Rob doesn't want to answer any question today, alas. Rob,
> " are you willing to defend the notion that endogenous changes
> in the interest rate more than offset own-price induced changes in labour
> demand when the minimum wage is increased? "
> Yes or no? Do you think you could respond directly?
I think that if one thinks that long run analysis were appropriate for
analysing wages, there is no reason to expect minimum wages to create
lower employment than would otherwise be the case.
I think economists should understand a valid long run theory of production.
I created my numerical example by drawing on such a theory.
> >> >Thus, one can express the solution value of the objective function
> >> >as a function of these parameters:
> >
> >> > Q = f( L, X1, X2 )
> >
> >> >Since this second LP is not of the same form as the first, the
> >> >production function f( L, X1, X2 ) is not Leontief.
> >
> >> Well, first,
> >>
> >> Q = f( L, X1, X2)
> >>
> >> is, in fact, a special case of
> >>
> >> Q = min ( L/a0, X1/a1, ..., Xn/an )
> >>
> >> so Rob's pointlessly elaborate "proof" doesn't cut it.
> >
> >No. The form of f( L, X1, X2 ) is not merely a function of three
> >variables. I defined f() to be the solution to the LP above, and
> >its form is restricted by this definition. Although I haven't
> >been bloody-minded enough to solve this LP, it seems obvious to
> >me that the solution will not be a special case of the minimum
> >function given above.
> Yes, I agree, but you didn't show that, Rob. Your "proof" is no
^^^^^^^
> such thing.
My proof was offered in response to Chris' request for me "to explain
why [ his ] statement is not entirely accurate." And I did not
characterize my mathematics as a "proof" until Chris already had.
My explanation is not a formal proof, as such objects are characterized
in formal logic. It might be characterized as a "proof outline." Such
objects are what are normally presented as "proofs" in most math
textbooks. Even the proofs offered about properties of formal proofs
are often only proof outlines.
> > RV: (It is interesting that those economists responding to my posts
> > have often mistakenly characterized the technology in my examples
> > as "Leontief production functions.")
> > CA: [1] Here, you have a choice between two Leontief production
> > functions. [2] In other essays you've posted, there exists only
> > one Leontief production function.
> >I assumed that Chris, in his second statement, had mainly my long
> >essay on price Wicksell effects in mind. Rather than admit that
> >he mischaracterizes the assumptions on technology in that post,
> >he now seems to feel that he doesn't know what he had in mind.
> Rob, have you ever posted an essay with a Leontief production function?
> If you answer "no," I am going to subject myself to diffing through
> my files and dredging up such an example. If "yes," you will please
> explain what you're arguing about.
I'm tempted to answer "no" just to see what posts Chris has saved. I
have used Leontief production functions in some posts. I have also
presented posts in which some have read me as using Leontief production
functions. In some of those latter posts, I thought I had only
specified one point on each production function, and had left the
form of the production function mostly unspecified. (I often
assume constant returns to scale.) Sensitive to this misreading,
I have evolved the wording in some of my essays to explicitly
state that I am assuming neither Leontief production functions,
nor other restrictions on the form, other than constant returns to
scale.
In particular, versions of my essay on price Wicksell effects that
I have posted over, say, the last year do not use Leontief
production functions. Nevertheless, "economists responding to
[that] post have often mistakenly characterized the technology...
as 'Leontief production functions.'" Furthermore, some have
mistakenly "described the technology in my example [in this
thread] as exhibiting fixed coefficients." (It's interesting
that this further elaboration of what I am arguing about
was snipped by Chris while making his already answered
request.)
Chris' position on both statements in his reply now seems to be
that they were both complete non sequiturs.
> >His position on his first statement now seems to be that it was
> >a non sequitur. But let's consider whether it is true.
> I admit I should have said "choice between two techniques which,
> alone, would form Leontief production functions" and apologize for
> my very slight and obvious abuse of terminology.
Fantastic. And I have characterized Chris' abuse as "rough" and
said it "does no harm."
> >> 2) I know it's an step function
> >> because the isoquants, given the technology, are kinked -- there will
> >> be switch points as the price ratio passes the relevant thresholds.
> >> I refuse, however, to pull out a calculator and work through Rob's
> >> unwieldy numerical example to present those thresholds, nor do I see
> >> any point in his insistence that I do so.
> >
> >I'm not sure know what Chris means by switch points in this context.
> >The term "switch point" has a well-defined meaning in the construction
> >of "factor price frontiers."
> Which isn't how I'm using it. I mean simply that the firm will switch
> from one technique to the other.
Again with the irony.
> >Well, there's one more refusal of Chris' to consider my argument.
> >He could always substitute letters for numbers in my example. I
> >deliberately minimize the level of mathematics needed to check
> >my example. One hardly needs algebra to read my essay.
> For the fourth time, Rob, I am *not* going to get my calculator
> out to compute this function for your model. For the fourth time,
> I don't see the point in wasting my time doing that, and Rob refuses
> to say what purpose it would serve.
Again with the misreading.
My numerical example proves that it is logically possible that, in a
comparison of long run positions, a higher wage may be associated with
a decision by firms to adopt a more labor-intensive technique. It
would seem the substitution patterns needed for downward-sloping labor
demand curves, whether conditional or not, to be relevant are not
necessary implications of neoclassical theory.
Some people have difficulty with math. My argument is presented such
that one doesn't even need algebra to follow it. It is sufficient to
be willing to follow arithmetic. I'm not sure how helpful this is to
those who dislike mathematics; often any use of an equals sign in
a text is enough to give such people difficulty.
> >> Neither do I, in this context. That's one reason the explicitly dynamic
> >> models the profession has long since adapted are superior to the ad hoc
> >> "dynamics" in the old models Rob continually mischaracterizes as mainstream
> >> tools.
> >Whether a tool is "mainstream" is irrelevant to whether it yields
> >correct results. Activity analysis and mathematical programming are
> >standard. Paul Samuelson seems proud of his independent rediscovery
> >of "factor price frontiers." The use of "factor price frontiers" to
> >analyze the choice of technique in long run circulating capital models
> >is standard. (Price and real) Wicksell effects are well-accepted.
> >The fact that non-zero price Wicksell effects generally lead to an
> >inequality between the marginal product of social capital and the
> >equilibrium interest rate is standard. The logical possibility of
> >both reswitching and capital-reversing was accepted in both Cambridges.
> >I also think that substitution is the historical and logical basis
> >for well-behaved relations between quantities and prices in neoclassical
> >economics. The logic of prices as scarcity indices has been shown to
> >be unfounded in long run theories of production. I don't know of any
> >convincing refutation of these claims.
> And, as is becoming the staus quo, I don't see how any of this verbiage
> addresses what I said.
I find Chris' grammar there sufficiently non-standard or complex that I
don't know what he is trying to say. He's probably trying to say
something irrelevant. My point is that my tools are widely accepted as
correct, and they yield correct and accepted conclusions.
Whether they are "mainstream" or whether the majority of economists
Chris is willing to communicate with understand them is irrelevant
to any valid argument.
[ snip ]
> >Maybe we can both use 'bots and need not read this newsgroup
> >at all.
> Unlike Rob, I have never reposted exactly the same material to any
> newsgroup, with the exception of very, very occasionally ceding to
> requests for reposts. I envourage Rob to adopt the same philosophy.
> He'd be much more interesting to talk to if he would only get a
> new subject in economics to be a rebel about. How about posting
> why real business cycles are bad rather than why incorrectly
> defined labour demand curves slope up, Rob?
I have reposted exactly the same material sometimes. There are always
new students of economics that need to be informed how misleading is
the stuff they are being taught.
I have also sometimes evolved my wording to respond to criticism of
some of essays. Notice that Chris mentioned diffing his files, not
greping. Apparently, he knows I have made improvements sometimes.
Christopher Auld
Quoting out of order:
>> 1. Do you think you've shown that, in theory, labour demand schedules
>> can slope up?
>I think I shown that the relevant long run locus of the quantity of
>labor that firms want to employ at any given wage can slope up.
The main point of the discussion is conceded (although, alas, see below
for a bizarre recantation). I trust Rob will not post his essay under
the title above again. I trust he will quit repeatedly asserting that
there is no logical reason to assert labour demand curves slope down.
And:
>I think students should learn about the controversies from which I
>draw the effect illustrated in my example. I think the questions
>with which I conclude my essay explaining my numerical example are
>good questions. Would Chris object if I had written "irrelevant
>dogma," instead of "exploded dogma"?
I trust Rob will no longer accuse the profession of teaching "exploded
dogma" when we teach that factor demands have non-positive slopes.
Responding to the comments above; yes, Rob, I would object to both
"irrelevant" and "dogma" as characterizations of the idea that labour
demand curves slope down. To illustrate, it is much easier to understand
*your* model if one knows what a conditional labour demand schedule
is, and I have already pointed out that the usual econometric tools
can differentiate between the total and partial derivatives of labour
demand with respect to the wage rate. Factor demand curves are a
basic and important tool in both theory and empirical applications,
as is partial equilibrium analysis in general. It is not "dogma"
and it is not "irrelevant," indeed, it is simply the imposition of
"all else equal" in furtherance of understanding how a system works,
a tactic common to all of scientific inquiry.
As for what Rob think student should learn about, well, I don't know
why he thinks he's qualified to form a sound opinion on the topic.
>Conditional labor demand curves are derived in
>
> H. R. Varian, _Microeconomic Analysis_, 2nd Edition, 1984.
>
>It's part of a presentation of Marshallian theory of the firm, a theory
>I think of questionable worth. I think this for reasons known since the
>1920s.
The reason you didn't find it in the other texts, Rob, is that it's of
more use in more advanced contexts, so intermediate texts may or may not
include it. Varian, Mas-Colell et al, Jehle, and other advanced micro
texts will all include the concept. Perhaps I should have specified
"any advanced micro text," but then Rob likes to tell us he prefers to
learn economics by reading work intended for experts, so I assumed he
would not turn to references aimed at novices.
>The stuff I left out makes Chris look silly to anybody that reviews
>my first post on this topic and my later comments on the literature
>that I was reviewing. This literature review was the point of my
>initiation of this thread.
I look "silly" (curious, nuanced, and "romantic" phrasing to be sure)
because I can't recall the entire text of one of Rob's lengthy essays?
Silly me. I do recall the "literature review" including lots of material
not directly relevant to "the point" and at least one author referring
to "labour demand curves" in that manner -- quoted -- indicating the
nonstandard use of terminology. I also recall pointing out that it
cannot be inferred from Rob's quoted text whether the authors who
explicitly misuse the term elsewhere note their abuse of terminology.
>I don't think wages are determined by the supply of and demand for labor.
One of the frustrating aspects of trying to discuss economics with Rob
is his inability to understand models as tools. My areas of expertise
are health and labour economics; I am familiar with many, many models
in both fields in which wages are not determined in a simple supply
and demand framework. Yet I might also use supply and demand to predict
gross quantity flows and price movements in response to large exogenous
shocks, and I might write down an econometric specification in which
the structural equations in a model of wages correspond to supply and
demand relationships. In short, Rob's statement is either false or
true but meaningless, depending on one's epistemological mood.
>I think economists should understand a valid long run theory of production.
>I created my numerical example by drawing on such a theory.
As I've said, Rob, I think you should learn more economics before
lecturing the profession on what it should and shouldn't do. Perhaps
you might reflect on how absurd this sort of statement is when you admit
you aren't familiar with the dynamic models which have dominated the
literature for the past three decades.
>> >No. The form of f( L, X1, X2 ) is not merely a function of three
>> >variables. I defined f() to be the solution to the LP above, and
>> >its form is restricted by this definition. Although I haven't
>> >been bloody-minded enough to solve this LP, it seems obvious to
>> >me that the solution will not be a special case of the minimum
>> >function given above.
>
>> Yes, I agree, but you didn't show that, Rob. Your "proof" is no
> ^^^^^^^
>> such thing.
>My proof was offered in response to Chris' request for me "to explain
>why [ his ] statement is not entirely accurate." And I did not
>characterize my mathematics as a "proof" until Chris already had.
>My explanation is not a formal proof, as such objects are characterized
>in formal logic. It might be characterized as a "proof outline." Such
>objects are what are normally presented as "proofs" in most math
>textbooks. Even the proofs offered about properties of formal proofs
>are often only proof outlines.
What is "agree" underlined for? I am agreeing that Rob's two technique
function is not Leontief, and I never said it was. The disagreement
here is over whether Rob proved this or not.
Rob, your "explanation" is not an "explanation" any more than it is a
proof. Nor is it a "proof outline," although it might form the first
part of a rather inelegant proof. To reiterate, Rob stated that
(in slightly simplified form):
- A Leontief prod'n f'n is of the form Q = min{ aL, bK }
- The solution to an LP problem characterizing his technology is a
function f( L, K ).
- f(L, K) is not of the form min{aL, bK}, therefore, the
technology is not Leontief.
But, of course, he did not show or argue that f() is not of the form
min(), so his argument is neither "proof" nor even "explanation."
Consider this "proof" :
- A Cobb-Douglas demand function is of the form X = Y / 2Px.
- The solution to a utility maximization program A is of the form
X(P,Y).
- Since X(P,Y) is not of the form Y/2Px, A is not Cobb-Douglas.
But A could be a Cobb-Douglas utility function, so this "explanation"
doesn't hold water. This is an interesting test case: as a matter of
sheer mathematics, Rob is wrong. Can he admit it? (In the past, he
has simply stopped responding when confronted with cold, hard
mathematical proof of error.)
Anyone wanting to start a pool should email me.
>> >I'm not sure know what Chris means by switch points in this context.
>> >The term "switch point" has a well-defined meaning in the construction
>> >of "factor price frontiers."
>
>> Which isn't how I'm using it. I mean simply that the firm will switch
>> from one technique to the other.
>
>Again with the irony.
Huh? Rob, do you think a sentence such as, "the firm will switch from
process A to process B when the wage to interest ratio passes above
2.3" is inherently an abuse of terminology?
Perhaps we will next argue about the definition of "is."
>> For the fourth time, Rob, I am *not* going to get my calculator
>> out to compute this function for your model. For the fourth time,
>> I don't see the point in wasting my time doing that, and Rob refuses
>> to say what purpose it would serve.
>
>Again with the misreading.
>
>My numerical example proves that it is logically possible that, in a
>comparison of long run positions, a higher wage may be associated with
>a decision by firms to adopt a more labor-intensive technique. It
>would seem the substitution patterns needed for downward-sloping labor
>demand curves, whether conditional or not, to be relevant are not
>necessary implications of neoclassical theory.
< slams head into desk >
OK, Rob, you state above that you don't think you're showing that
labour demand curves slope up, and now you relapse. What part of
"that locus is not a labour demand curve" is so very difficult
for to understand? How many times do people have to explain this
to you? Are you being deliberately dishonest, or is this some
form of bizarre neurosis you're unfortunately afflicted with?
Rob also won't directly answer the question, 'do you think that
counterintuitive empirical results stemming from minimum wage
changes are a result of the mechanism you describe.' Rob, I'm
simply going to tell you that no econometrician on the planet
would agree with that notion. Look,
dL \partial L \partial r \partial L
-- > 0 <==> abs ---------- < ---------- ---------- .
dW \partial W \partial W \partial r
Is this likely to hold? We need for the cross-price elasticity of
labour demand with respect to the interest rate to be large relative
to the own-price elasticity, which is generally not the case, and
we also need the interest rate to be highly responsive to changes
in the minimum wage. As I already pointed out, about 2% of the
U.S. labour force is at the minimum wage -- even with "ratcheting"
and similar effects small changes in the minimum wage are simply
not going to push the interest rate around much, particularly when
we consider that U.S. rates are at least partially determined in
world markets. It is simply totally implausible that this effect
explains Card and Krueger type anomolies.
>Some people have difficulty with math. My argument is presented such
>that one doesn't even need algebra to follow it.
Rob -- in all honesty, not meant as a jab -- your style is much, much
harder to follow than either a *simple* numerical example or an
algebraic exposition. Why would think someone who couldn't handle
junior high school math could or would follow a numerical example
with unrealistic numbers reported to seven decimal places? And
whose exposition of the basic idea do you think is more readily
accessible to economically literate readers, mine or yours?
>I have reposted exactly the same material sometimes. There are always
>new students of economics that need to be informed how misleading is
>the stuff they are being taught.
Rob -- seriously -- do you understand that when you say things like
this, you are insulting all the academic economists who happen to
read the post? It doesn't help that your argument here is based
solely on coming up with a new definition of basic terms, asserting
the definitions are one and the same, and showing that under the
new definition the standard result doesn't hold. How did I put it
before? (I wouldn't want to misquote myself again or Rob will think
I'm very silly.) Perhaps, "Rob might as well claim that pi equals
six, so long as one defines pi as twice three. He would be correct
but impeding rather than furthering communication and understanding."
I'd ask Rob to stay away from my students, but, being far more clever
than I am, they seem to do a good job of steering clear of Rob
themselves.
So, Rob, going to take me up on my challenge to come up with a new
topic to be a maverick about, or are you just going to wait a few
weeks and then start spamming the same essays yet again?
Shawn A. Wilson
Christopher Auld <au...@acs.ucalgary.ca> wrote in message
news:7emcj3$8...@ds2.acs.ucalgary.ca...
> I'd ask Rob to stay away from my students, but, being far more clever
> than I am, they seem to do a good job of steering clear of Rob
> themselves.
Yeah, Robert is the kind of person you need to steer away from. Nice job
fighting the good fight though, I think you did a better job than I did when
I fought that fight. For future reference C Post and kenfran should also be
steered away from, if you hope to convince them of anything but their own
infallibility that is. Though C Post was kinda fun.
SUSUPPLY
(while still alive!) for his good deeds, writes:
>Rob is wrong. Can he admit it? (In the past, he
>has simply stopped responding when confronted with cold, hard
>mathematical proof of error.)
>
>Anyone wanting to start a pool should email me.
Put me down for $10 on "when hell freezes over".
>How many times do people have to explain this
>to you? Are you being deliberately dishonest, or is this some
>form of bizarre neurosis you're unfortunately afflicted with?
I think you're on the right track here, Chris.
>Rob -- in all honesty, not meant as a jab -- your style is much, much
>harder to follow than either a *simple* numerical example or an
>algebraic exposition. Why would think someone who couldn't handle
>junior high school math could or would follow a numerical example
>with unrealistic numbers reported to seven decimal places?
Because he said it to show-off.
And
>whose exposition of the basic idea do you think is more readily
>accessible to economically literate readers, mine or yours?
I see a mega-reply to that being formulated as we speak.
>I'd ask Rob to stay away from my students, but, being far more clever
>than I am, they seem to do a good job of steering clear of Rob
>themselves.
It's the students of psychology who should be reading Robert.
Patrick
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >"marcel simkens" <marcel....@village.uunet.be> wrote:
> >> Why is the Sloping of the Labor Demand Curve so important and what is the
> >> final goal of proving that the sloping is, or can be, upward ?
> > "Thus the reswitching anomaly, along with its theoretical developments
> > and implications, has been placed in abeyance. And so it must be, for
> 1. Rob has yet to provide a model, an informal argument, or anything
> resembling
> empirical evidence which shows that labour demand curves can slope up in
> theory or in practice. Reswitching does *not* imply upward-sloping factor
> demands. This answer, in response to Mr. Simkens' question is, at best
> disingenuous.
I took Mr. Simkens to be asking about what is the point of this
discussion. I answered that. Reswitching *does* imply that the
relevant long-run locus showing how much labor firms want to
employ per unit output at any given wage can slope up. (The
relevant prices and interest rates are endogeneously determined,
given the wage, in long run positions.)
> 2. The text Rob quotes is rubbish. Reswitching does not imply that
> > the relationship of production to the various input markets. That is,
> > the neoclassical vision of a market-coordinated production system, along
> > with derivative growth and distribution theories, are all invalidated.
I took the "reswitching anomaly" in the passage I quoted from
Richard X. Chase to be acting as a synecdoche - a rhetorical figure
in which a part is substituted for the whole. The whole, in this case,
is a decades-long controversy in economic theory.
> In particular, A-D GE -- the simplest formal exposition of an idealized
> economy in which Smith's vision "of a market-coordinated production
> system"
> can be shown to work -- is entirely untouched by the entire issue.
> Reswitching poses a serious problem for capital aggregation and
> measurement,
> and that's about it.
Chris' position is often argued for in some dated literature. In my
opinion, it is mistaken, and not merely in the historically dubious
connection between the Arrow-Debreu General Equilibrium model and
Adam Smith. Keeping in mind that there is a close relationship between
correctly anticipated sequences of temporary equilibrium and
intertemporal equilibria, I have already explained why it is mistaken:
I know of no reason whatsoever for believing that technology does
not have the properties that produce the effect illustrated in my
example. Furthermore, economists do not even know how to specify
suitable restrictions on technology that rule out this effect. I
think economic theory, if it is to be developed with the kinds
of abtract specifications of technology typical of neoclassical
theory over the last century, should be developed with specifications
that do not rule out this effect.
Notice that these beliefs of mine are independent of any position
on whether comparisons of long run positions or "dynamic" sequences
of temporary equilibria are more appropriate methods of analysis.
Neoclassical economists such as Christopher Bliss, Frank Hahn, and
Paul Samuelson seem to argue both that these "dynamic" methods are
more appropriate and that general neoclassical theory should
accept technology in which the effect in my numerical example can
arise. Of course, the effect is manifested in a different way
in "dynamic" models. It seems to show up there as certain paths
in which both wages and employment increase. Such paths might not
be stable, but such models are well-known to possibly exhibit
multiple equilibria, instability, and other interesting dynamics.
Also, notice that the passages I have quoted from Bertram Schefold
are attacking the position that Chris quotes(?). Schefold further
elaborates why the Arrow-Debreu General Equilibrium model is
no defense against the Cambridge Capital Controversy in a paper
he has made available over the Web:
Bertram Schefold, "Paradoxes of Capital and Counterintuitive
Changes of Distribution in an Intertemporal Equilibrium Model,"
<http://www.wiwi.uni-frankfurt.de/professoren/schefold/bsdocs.html>,
July 1996.
Garegnani also explains a similar position:
P. Garegnani, "Quantity of Capital," _The New Palgrave: Capital
Theory_, 1990.
I happen to know that Burmeister was in the audience for a conference
in Italy a number of years ago in which Garegnani explained his views.
I don't know that Burmeister has ever responded to this view.
Robert Vienneau
> > Robert is social minded and I guess that his final goal is to prove that
> > unemployment can decrease by increasing the real wage. This is an
> > assumption and only Robert can answer my question.
> Robert wants to show that equilibria in some models can generate a positive
> correlation between wages and labor demand. However, the set of equilibria
> in a model do not trace out a demand curve; rather, they are a set of
> intersections of between supply and demand. If these both shift in the
> right way, and one assumes supply doesn't shift, one would estimate an
> upward sloping demand curve, but this isn't sensible.
Dave,
I hope you appreciate that I have not considered supply of labor or a
utility-maximizing tradeoff between commodities and leisure yet. The
locus between wages and employment in my example is based on a long
run model of production. I am examining the choice of the
cost-minimizing technique at different wages.
> There's a whole literature on hedonics that analyzes the set of observed
> equilibria and draws inferences from that. Robert's analysis is similar
> to that, though he isn't asking the same questions as the hedonics
> literature. Hedonics doesn't estimate a demand curve (except in particular
> cases), and Robert hasn't calculated one either.
I do not know the literature on hedonics. The name suggests it may
have something to do with utility and consumption. If so, I agree
it isn't the same as my analysis. I cannot comment on similarities.
It seems to me some important questions in considering long run
input demand curves are (1) Can one coherently consider different
values of one price, while keeping all other prices constant? and
(2) Would a profit-maximizing firm be in a long run equilibrium at
different values of an input price, if all other prices are kept
constant? One should keep in mind that the interest rate is not a
price.
If the answers to these questions are no, then the long run labor demand
curve would seem to be the horizontal line I have drawn in wage-
employment space. This line doesn't seem to be an useful tool of
analysis. If one considers long run positions consistent with
different wages, the location of the line would be different.
> > I have problems with graphs if the equation is not exactly known and if they
> > are made by assumptions. Economic situations are very complicated and
> > depending on so many variables that a simple graph can be confusing.
> I'm not sure what your point is here. Do you mean that simple models can
> provide misleading conclusions?
> Robert's post illustrates an interesting point that I (no labor economist
> or general equilibrium expert) had never considered before, but I wonder how
> general these results would turn out to be in rich GE models.
I think the effect is more likely to be possible, given more goods.
You might have been too bored to read to the end, but my post
presenting my numerical example also included a quote from Samuelson
stating that there was nothing perverse about this effect.
> I know that
> in Robert's quotation of Steedman, Steedman claims that GE is not needed
> to prove his point. If he's going to criticize partial equilibrium analysis,
> though, the obvious alternative is GE.
Arrow-Debreu intertemporal equilibria do not depict long run positions.
Initial endowments, including quantities of previously produced means
of production, are taken as given in the Arrow-Debreu model. These
given quantities may reflect mistaken past expectations about the
present. Yet present expectations about the future are assumed to
be correct. This confusing mixture of short run and long run
considerations suggests that the Arrow-Debreu model is incoherent,
even if there are no mathematical errors in Debreu (1959).
Perhaps a little history might help clarify Steedman's position. His
examples are based on a long run model of production, namely that
presented in:
Piero Sraffa, _Production of Commodities by Means of Commodities:
Prelude To A Critique of Economic Theory_, CUP, 1960.
This model is open to various interpretations. Although I don't
think this is the best interpretation, a neoclassical economist
might see it as half a General Equilibrium model. Sraffa's
purpose, however, seems to have included a reinterpretation of
Classical economics. "This standpoint," which "has been submerged
and forgotten since the advent of the 'marginal' method,"
does not explain Smith's "natural prices" or Marx' "prices of
production" as determined by Supply and Demand. However, by
just presenting the production model, one can show one
way markets interact, without taking a stand on these questions
of historical interpretation.
Let me outline how to close my example to make it a complete long run
neoclassical model of General Equilibrium, in some sense. (This model
is neoclassical in that it considers equilibria found by summing
over optimizing atomic agents. It doesn't, though, necessarily
exhibit the substitution relationships I think necessary to
interpret prices as scarcity indices and to justify the neoclassical
theory of value.) Supplement my example with intertemporal
utility-maximization. The formulation I prefer is an overlapping
generations framework. Assume a single (representative) agent is born
each year. Each agent lives for two years and then dies. The agent
works the first year and is retired the second year. The agent is
paid a wage, w, at the end of the first year. Out of this income,
the agent chooses to consume c0 units of corn immediately and
save ( w - c0 ) numeraire units - recall corn is the numeraire. At
the end of the second year, the agent has c1 = ( w - c0 )*(1 + r)
numeraire units which are immediately spent on corn consumption. After
this final bout of consumption, the agent dies. Assume all agents
have a Cobb-Douglas utility function:
U( c0, c1 ) = ( c0^gamma ) * ( c1^*( 1 - gamma ) )
With the data on technology in my example, I have now presented a
complete specification of a neoclassical model. One can
determine equilibrium prices and perform a comparative statics
exercise by exploring how equilibria differ with different values
of gamma, given technology.
The equilibria in this completion of the model consist of stationary
states, since technological change is not assumed and the labor
force is taken as neither increasing nor decreasing. Quantities of
steel and corn used as inputs are assumed to be adjusted at the
begining of time - that is, they are determined endogeneously.
Thus, the above exercise is one of long-run comparative statics.
SUSUPPLY
> One should keep in mind that the interest rate is not a
>price.
One should keep in mind who is writing such baloney. Interest rates are the
prices of renting money.
Patrick
Christopher Auld
>au...@acs.ucalgary.ca (Christopher Auld) wrote:
>> >"marcel simkens" <marcel....@village.uunet.be> wrote:
>> >> Why is the Sloping of the Labor Demand Curve so important and what is the
>> >> final goal of proving that the sloping is, or can be, upward ?
>I took Mr. Simkens to be asking about what is the point of this
>discussion. I answered that. Reswitching *does* imply that the
>relevant long-run locus showing how much labor firms want to
That locus is NOT A LABOUR DEMAND CURVE.
-------------------------
Do you understand, Rob? What does one have to do to get this across
to you?
>I took the "reswitching anomaly" in the passage I quoted from
>Richard X. Chase to be acting as a synecdoche - a rhetorical figure
>in which a part is substituted for the whole. The whole, in this case,
>is a decades-long controversy in economic theory.
And decades-outdated controversy in economic theory.
>> Reswitching poses a serious problem for capital aggregation and
>> measurement,
>> and that's about it.
>Chris' position is often argued for in some dated literature.
"Again with the irony." To wit:
>Adam Smith. Keeping in mind that there is a close relationship between
>correctly anticipated sequences of temporary equilibrium and
>intertemporal equilibria, I have already explained why it is mistaken:
Rob, the sort of pseduo-dynamics you're talking about have been collecting
dust on a shelf since the late 60s. Why don't you make good on your threat
to learn some dynamic programming so you can figure out what the discipline
has been up to since that time?
marcel simkens
Dave wrote
<The slope of the labor demand curve is important because it can be used to
<separate those who understand what a demand curve is from those who don't.
I do understand the demand curve (labor or commodities) in microeconomics
but I have more problems with these curve in macroeconomics.
<Of course, it is easy to mimic those who do understand: just state as a
matter of <definition a factor demand curve must always slope downward.
Is it a matter of definition or a matter of assumption that a factor demand
curve must always slope downward ?
To prove that the sloping demand curve is downward, the economist Robert
Barro in his book Macroeconomics (fifth edition) use the Graph of Production
Function that shows the level of output to the labor input.
On page 61, figure 2.1 shows the graph of the production function to input
of labor, designed with the assumption of diminishing marginal productivity,
which means that each successive unit of work effort generates progressively
smaller, but still positive responses of output.
On page 62, figure 2.2 shows the MPL to the level of work. These curve has
been drawn by means of figure 2.1 ; The positive slope of the curve (that
is, of a straight line that is tangent to the curve) at any point indicates
the additional output that results from extra labor input, which is the
marginal product of labor.
Remark : It is not very important, but the curve in figure 2.2 has not been
drawn by means of the curve in fig 2.1 as described by Barro. The curve in
figure 2.2 is concave and she should be convex and intersect the ordinate.
On page 209: To maximize profit a firm expands employment Ld up to the point
at which the value of the marginal product just equals the wage rate, that
is, until P.MPL = w. If we divide through by the price level, then the
condition that each firm satisfies in every period is:
MPL = w/P
w/P is the real wage.
The models are different for chapter 2 and chapter 6, but this will not
modify the shape of the curves.
<I'm not sure what your point is here. Do you mean that simple models can
provide <misleading conclusions?
A model is always a simplification of a real economical situation and can be
very useful but if these simplification is not corresponding with the real
economy, the model can provide misleading conclusions.
The 3 graphs, the production function, the marginal product of labor
function and the demand for labor function to the input of labor are drawn
with the assumption of a constant level of technology.
250 Years ago, the period of Adam Smith and Thomas Malthus, it was more
obvious to consider a model with such a constant level of technology and
also a growing level of population.
Agriculture was very important and by an increase of the population,
agriculture must also be increased by using less fertile land, so that the
marginal product of labor was decreasing by increasing the labor input.
The situation in 1999 is very different. The economy is dynamic and the
level of technology is increasing at a high rate but the level of the
population is nearly constant for the industrialized countries.
The labor demand curve, corresponding with an economy of 250 years ago, will
not provide misleading conclusions.
The labor demand curve, with the assumption of a constant level of
technology, does not correspond with the economy of 1999 that has a high
level of technology increasing at a high rate. In this case, the labor
demand curve will be misleading if she is always downward sloping by
definition. Is these definition correct ?
Without the use of a graph it can be proved that an increase of the real
wage can be necessary to become an increase in the real output. This is not
in accordance with the downward sloping labor demand graph.
dav...@my-dejanews.com
> I do understand the demand curve (labor or commodities) in microeconomics
> but I have more problems with these curve in macroeconomics.
Which curve(s) trouble you? The aggregate demand curve? The demand curve
for all the labor in an economy?
> Is it a matter of definition or a matter of assumption that a factor demand
> curve must always slope downward ?
It necessarily follows from the profit maximization hypothesis. I don't
think it requires any additional assumptions. (It may stem simply from
cost minimization, which is implied by profit maximization. I don't recall
offhand.)
> To prove that the sloping demand curve is downward, the economist Robert
> Barro in his book Macroeconomics (fifth edition) use the Graph of Production
> Function that shows the level of output to the labor input.
You are talking about the aggregate demand curve or the labor demand curve?
> A model is always a simplification of a real economical situation and can be
> very useful but if these simplification is not corresponding with the real
> economy, the model can provide misleading conclusions.
> The labor demand curve, corresponding with an economy of 250 years ago, will
> not provide misleading conclusions.
> The labor demand curve, with the assumption of a constant level of
> technology, does not correspond with the economy of 1999 that has a high
> level of technology increasing at a high rate. In this case, the labor
> demand curve will be misleading if she is always downward sloping by
> definition. Is these definition correct ?
(1) The demand curve for labor will shift in response to changes in anything
exogenous such as technology and population. (Though in the long run they
obviously aren't exogenous, the model can be adapted to include them as
endogenous factors.)
> Without the use of a graph it can be proved that an increase of the real
> wage can be necessary to become an increase in the real output. This is not
> in accordance with the downward sloping labor demand graph.
The first sentence is what Robert's post was designed to show (if you replace
output with labor, or if labor bears a fixed relationship to output). The
second sentence is incorrect. The title of the thread is unfortunate because
it might lead one to think that the result is inconsistent with a downward
sloping labor demand graph.
Put succinctly, the labor demand curve shows the relationship of the
quantity of labor demanded and the wage rate. If anything else changes, e.g.
the interest rate, that isn't on the graph, the demand curve itself is going
to shift. This may mean that in equilibrium the real wage and quantity
demanded of labor) are positively correlated; it does not mean that, holding
all other factors fixed, when the real wage rises the quantity demanded of
labor also rises.
A locus of equilibria does not trace out the demand curve, or the supply
curve, unless one curve is shifting while the other is not moving. Rob would
have you believe this is news. I've never thought about it before in the
context of labor economics, but it should be obvious to anyone who's ever
tried to (correctly) estimate a demand or supply function.
--Dave
dav...@my-dejanews.com
-----------== Posted via Deja News, The Discussion Network ==----------
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Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >au...@acs.ucalgary.ca (Christopher Auld) wrote:
> Quoting out of order:
> >> 1. Do you think you've shown that, in theory, labour demand schedules
> >> can slope up?
> >I think I shown that the relevant long run locus of the quantity of
> >labor that firms want to employ at any given wage can slope up.
> The main point of the discussion is conceded (although, alas, see below
> for a bizarre recantation). I trust Rob will not post his essay under
> the title above again. I trust he will quit repeatedly asserting that
> there is no logical reason to assert labour demand curves slope down.
There is no logical reason to asset that cost minimizing firms
will necessarily adopt less labor-intensive techniques at higher
wages, given technology. The relevant long run locus of the quantity
of labor that firms want to employ at any given wage can slope up.
> And:
> >I think students should learn about the controversies from which I
> >draw the effect illustrated in my example. I think the questions
> >with which I conclude my essay explaining my numerical example are
> >good questions. Would Chris object if I had written "irrelevant
> >dogma," instead of "exploded dogma"?
> I trust Rob will no longer accuse the profession of teaching "exploded
> dogma" when we teach that factor demands have non-positive slopes.
> Responding to the comments above; yes, Rob, I would object to both
> "irrelevant" and "dogma" as characterizations of the idea that labour
> demand curves slope down.
I don't care. I see no reason to avoid the use of "irrelevant dogma"
in characterizing mainstream teaching. I will change the final
paragraph as follows:
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 irrelevant dogma?
There's nothing about the slope of labor demand curves there.
> To illustrate, it is much easier to understand
> *your* model if one knows what a conditional labour demand schedule
> is, and I have already pointed out that the usual econometric tools
> can differentiate between the total and partial derivatives of labour
> demand with respect to the wage rate. Factor demand curves are a
> basic and important tool in both theory and empirical applications,
> as is partial equilibrium analysis in general. It is not "dogma"
> and it is not "irrelevant," indeed, it is simply the imposition of
> "all else equal" in furtherance of understanding how a system works,
> a tactic common to all of scientific inquiry.
> As for what Rob think student should learn about, well, I don't know
> why he thinks he's qualified to form a sound opinion on the topic.
Whatever.
It's bizarre that the existence of a raging decades-long controversy
in the professional literature is barely acknowledged in textbooks.
Many textbooks, including advanced textbooks, do not even go so
far as to acknowledge the existence of this controversy.
[ Some stuff where Chris avoids acknowleding he doesn't mean "any"
when he writes "any micro text. ]
> >The stuff I left out makes Chris look silly to anybody that reviews
> >my first post on this topic and my later comments on the literature
> >that I was reviewing. This literature review was the point of my
> >initiation of this thread.
> I look "silly" (curious, nuanced, and "romantic" phrasing to be sure)
> because I can't recall the entire text of one of Rob's lengthy essays?
> Silly me. I do recall the "literature review" including lots of material
> not directly relevant to "the point" and at least one author referring
> to "labour demand curves" in that manner -- quoted -- indicating the
> nonstandard use of terminology. I also recall pointing out that it
> cannot be inferred from Rob's quoted text whether the authors who
> explicitly misuse the term elsewhere note their abuse of terminology.
Schefold and Woods use the disputed phrasing in *summaries* of their
arguments. I pointed out that Woods steps his reader through the
details of his examples and explains the interesting behavior
before ever speaking of demand curves.
> >I don't think wages are determined by the supply of and demand for labor.
> One of the frustrating aspects of trying to discuss economics with Rob
> is his inability to understand models as tools. [ and so on with the
> the irrelevancies. ]
Whatever. I don't think the earth is the center of the universe either.
It's look that way, though, if one spends a clear summer night in a
field away from city lights. Who is more likely to accept Alan Sokal's
invitation to step out of his 21st floor apartment window, Chris or
me?
> >I think economists should understand a valid long run theory of production.
> >I created my numerical example by drawing on such a theory.
> As I've said, Rob, I think you should learn more economics before
> lecturing the profession on what it should and shouldn't do. Perhaps
> you might reflect on how absurd this sort of statement is when you admit
> you aren't familiar with the dynamic models which have dominated the
> literature for the past three decades.
It's a funny dynamics in which the location of limit points is of
no concern.
Chris is being silly. I never admitted any such thing. For Chris'
information:
o I have written software to implement
- Algorithms for estimating parameters of state space models
- Kalman filters
- Algorithms for synthesizing Vector AutoRegressive models
- Algorithms for estimating parameters of VAR models
- Filters of various sorts, etc.
o To a certain extent, I learned in my undergraduate study about
phase spaces in the context of dynamical systems specified by
systems of Ordinary Differential Equation
o I have read a book on the Lorenz equation and briefly examined
other books on dynamical systems
o I have read certain works on economics discussing mainstream
dynamics, including:
- J. R. Hicks, _Value and Capital_, 2nd Edition, 1939, 1946
- Robert Dorfman, Paul A. Samuelson, and Robert M. Solow,
_Linear Programming and Economic Analysis_, 1958
- Gerard Debreu, _Theory of Value_, 1959
- Edwin Burmeister, _Capital Theory and Dynamics_, 1980
(although I only skimmed the later chapters)
- Robert E. Lucas, Jr., _Models of Business Cycles_, 1987
- Syed Ahmad, _Capital in Economic Theory: Neoclassical,
Cambridge, and Chaos_, 1991
- E. Roy Weintraub, _Stabilizing Dynamics_
o I am currently reading a book on Thomas Sargent which tells
some stories in which his contributions to rational expectations
were attempts to make economic theory more coherent. I have
already read two journal articles used for chapters in this
book.
Nevertheless, I don't feel I have mastered either the mathematics
or the economics in this literature. I do think I understand the
Turnpike theorem, though.
Of course, my qualifications are of no relevance for valid
arguments in this thread.
[ >>>>> Well, first, ]
[ >>>>> ]
[ >>>>> Q = f( L, X1, X2) ]
[ >>>>> ]
[ >>>>> is, in fact, a special case of ]
[ >>>>> ]
[ >>>>> Q = min ( L/a0, X1/a1, ..., Xn/an ) ]
[ >>>>> ]
[ >>>>> so Rob's pointlessly elaborate "proof" doesn't cut it. ]
> >> >No. The form of f( L, X1, X2 ) is not merely a function of three
> >> >variables. I defined f() to be the solution to the LP above, and
> >> >its form is restricted by this definition. Although I haven't
> >> >been bloody-minded enough to solve this LP, it seems obvious to
> >> >me that the solution will not be a special case of the minimum
> >> >function given above.
> >> Yes, I agree, but you didn't show that, Rob. Your "proof" is no
> > ^^^^^^^
> >> such thing.
> >My proof was offered in response to Chris' request for me "to explain
> >why [ his ] statement is not entirely accurate." And I did not
> >characterize my mathematics as a "proof" until Chris already had.
> >My explanation is not a formal proof, as such objects are characterized
> >in formal logic. It might be characterized as a "proof outline." Such
> >objects are what are normally presented as "proofs" in most math
> >textbooks. Even the proofs offered about properties of formal proofs
> >are often only proof outlines.
> What is "agree" underlined for?
When Chris said, "I agree," he was disagreeing with his previous
position.
> I am agreeing that Rob's two [ process ]
> function is not Leontief, and I never said it was. The disagreement
> here is over whether Rob proved this or not.
The disagreement seems to be over whether a step I thought, in
context, to be obvious is indeed obvious. The step is a matter of
solving the LP characterizing my example. In other contexts, Chris
has said he has no interest in steping through these calculations
with awkward decimals.
Chris' judgement is that it is not obvious that the solution to
this LP is not Leontief. This disagreement doesn't seem to be amenable
to formal proof one way or another.
> Rob, your "explanation" is not an "explanation" any more than it is a
> proof. Nor is it a "proof outline," although it might form the first
> part of a rather inelegant proof. To reiterate, Rob stated that
> (in slightly simplified form):
> - A Leontief prod'n f'n is of the form Q = min{ aL, bK }
Even here, Chris writes stuff to which he should know I'm likely
to object. His use of "K" is part of a tradition that suggests
there's some well-defined factor called capital. I used the more
neutral X. Furthermore, I used the more general case of n inputs.
Chris' use of L and K suggests there's no need to consider more
factors, at least if one is abstracting from land.
Furthermore, I used parameters, a0, a1, a2, ..., an, that suggest
the standard notation for the entries in a column (industry) in
Leontief input-output matrices.
Maybe I'm reading too much into notation.
> - The solution to an LP problem characterizing his technology is a
> function f( L, K ).
Chris leaves out a step of some use in my explanation. I gave two LPs.
One yielded a Leontief production function. The one characterizing
my technology doesn't.
> - f(L, K) is not of the form min{aL, bK}, therefore, the
> technology is not Leontief.
> But, of course, he did not show or argue that f() is not of the form
> min(), so his argument is neither "proof" nor even "explanation."
I stated:
"Since this second LP is not of the same form as the first, the
production function f( L, X1, X2 ) is not Leontief."
where f was defined as the solution of the LP characterizing my
technology. I did "not show or argue" a point I thought obvious.
However, the point follows from solving the LP I gave.
I don't know what Chris' problem is here. I had even pointed
out that one process does not dominate the other in my original
description of the processes available to the steel industry in
my long essay.
Chris is going to have difficulty in asserting that he was
referring to the above quoted argument of mine as a
mathematical error, while maintaining I did not argue that
the relevant production function is not Leontief.
> Consider this "proof" :
>
> - A Cobb-Douglas demand function is of the form X = Y / 2Px.
The point here is that the above demand function is not the
general form that can be derived from a Cobb-Douglas utility
function. The constant 2 should be replaced by an algebraic
expression.
Chris' analogy is backwards. I wrote the general form of
a Leontief production function in my context. I suppose one
could generalize it to account for machines that last several
production periods, but that's of no point here.
Given the general form, I argued my specific example was not
of that form.
[ Rest of a non-analogy deleted ]
> This is an interesting test case: as a matter of
> sheer mathematics, Rob is wrong. Can he admit it? (In the past, he
> has simply stopped responding when confronted with cold, hard
> mathematical proof of error.)
I suppose Chris still does not understand why non-zero price
Wicksell effects lead to an inequality between the interest rate
and the marginal value of capital.
Certainly somebody here seems to have difficultly acknowledging
error. But it is not me. I'm not going to acknowledge error until
somebody explains why I am in error in a way that I or anybody
else can understand.
In particular, if Chris wants to argue that there are LPs for
production functions that cannot be reduced to the form of the
general LP I gave for the Leontief production function, but
still yield a solution of the appropriate form, min(), let
him argue it.
[ >>>>> ...there will be switch points ]
[ >>>>> as the price ratio passes the relevant thresholds... ]
>>>>I'm not sure know what Chris means by switch points in this context.
>>>>The term "switch point" has a well-defined meaning in the construction
>>>>of "factor price frontiers."
>>> Which isn't how I'm using it. I mean simply that the firm will switch
>>> from one technique to the other.
>>Again with the irony.
> Huh? Rob, do you think a sentence such as, "the firm will switch from
> process A to process B when the wage to interest ratio passes above
> 2.3" is inherently an abuse of terminology?
> Perhaps we will next argue about the definition of "is."
Chris, of course, is being silly. I think, "The term 'switch point'
has a well-defined meaning in the construction of 'factor price
frontiers.'" Chris is abusing a technical term with a precise
definition relevant for this thread.
Once again, one cannot help wonder about Chris' editing.
> >My numerical example proves that it is logically possible that, in a
> >comparison of long run positions, a higher wage may be associated with
> >a decision by firms to adopt a more labor-intensive technique. It
> >would seem the substitution patterns needed for downward-sloping labor
> >demand curves, whether conditional or not, to be relevant are not
> >necessary implications of neoclassical theory.
> < slams head into desk >
> OK, Rob, you state above that you don't think you're showing that
> labour demand curves slope up, and now you relapse. [ Silliness
> deleted. ]
Nowhere in the quoted text do I say labor demand curves can slope
up. Perhaps Chris might want to review my quotes from Steedman in
my initial post on this thread.
> Rob also won't directly answer the question, 'do you think that
> counterintuitive empirical results stemming from minimum wage
> changes are a result of the mechanism you describe.' Rob, I'm
> simply going to tell you that no econometrician on the planet
> would agree with that notion. Look,
> dL \partial L \partial r \partial L
> -- > 0 <==> abs ---------- < ---------- ---------- .
> dW \partial W \partial W \partial r
In my example, and, in fact, for any circulating capital technology,
del L/del W is undefined. So however interesting Chris' explanation
may be, it needs, at least, further development.
I suggest he might want to clarify the arguments of his labor
demand function in such further development. I presented two
characterizations of the techniques in my technology. The price
of steel might also appropriately appear in the characterization
for which only one wage is appropriate. So perhaps the arguments
of Chris' labor demand function should appear as L( w, ps; r ).
The semicolon is used to emphasize that r is not a price. If
the price of steel and r are not in the appropriate configuration,
it is not clear that a long run labor demand 'function' can be
defined. (Both steel and corn must be equally profitable to
produce in a long run equilibrium of the vertically integrated
firm.)
Or perhaps one should list two prices for corn and steel each -
spot prices for corn and steel purchased at the beginning of
the period, and one year forward prices. In this case, the
arguments of the labor demand function appear as
L( w, ps( 1 ), ps( 2 ), pc( 2 ) ), where I have normalized
on the spot price of corn. One might specify that the firm
is in a long run equilibrium in the sort of models in which
I am interested by imposing some condition on some of the
prices, e.g.
ps( 2 )/pc( 2 ) = ps( 1 )
Changing relative prices would otherwise reflect the influence
of unadjusted quantities of steel and corn. In this formulation,
the non-price r does not appear.
Or one could express the arguments of a labor demand function
as a countable infinity of wages L( w( 1 ), w( 2 ), ... ). If
these are wages in forward markets for labor, one might want to
express a long run condition for the firm to be in long run
equilibrium by imposing constraints relating dated wages,
interest rates, and forward markets.
I am not sure how well thought out any of these formulations
are in terms of labor demand functions. In particular, I do
not see how the structure imposed by requiring the vertically
integrated firm to be in long run equilibrium along a long run
labor demand function, as Chris understands such a function,
is satisfied within any of these formulations. It is apparent to
me, however, that my sometimes upward-sloping locus between the
employment the firms want to employ, given the level of net output,
and the wage falls out of the condition that the vertically
integrated firm be in long run equilibrium.
Perhaps Chris can comment on what he understands a labor
demand curve to be in the context of these expansions on
what prices and commodities are? And what does he understand
the relevant price elasticities to be in determining the
slope of my locus? Does the specification of technology in
which a countable infinity of wages is appropriate in
calculating economic profit suggest that the answer to
to this latter question may be more complicated than Chris'
comments above?
> Is this likely to hold? We need for the cross-price elasticity of
> labour demand with respect to the interest rate to be large relative
> to the own-price elasticity, which is generally not the case, and
> we also need the interest rate to be highly responsive to changes
> in the minimum wage. As I already pointed out, about 2% of the
> U.S. labour force is at the minimum wage -- even with "ratcheting"
> and similar effects small changes in the minimum wage are simply
> not going to push the interest rate around much, particularly when
> we consider that U.S. rates are at least partially determined in
> world markets. It is simply totally implausible that this effect
> explains Card and Krueger type anomolies.
So the reason why minimum wages create unemployment is not the
introductory economics supply and demand story. Rather, it is
the consequence of certain claims about the relative sizes of
effects influencing the locus in my example. So much for Chris'
logical consistency.
"Long-period comparisons would certainly seem to be more
appropriate for the analysis of major policy changes, or
exogeneous 'shocks,' than are partial equilibrium comparisons.
As a purely hypothetical example, reconsider our Example 3,
now taking the economy to be open and to be producing corn
by means of corn, labour, and imported oil. Will a sharp
increase in the exogeneously given (corn) price of oil *entail*
a reduction in the use of oil input per unit of corn output?
We already know that, once the (corn) wage and the choice of
technique have adjusted to restore a long-period position,
the answer is 'No.' Such a reduction does *not follow* from
the assumptions of constant returns and competitive cost
minimisation. One might have other grounds for predicting
such a reduction - and one's prediction might even turn out
to be correct - but one should not carelessly assume that the
partial equilibrium prediction *must* coincide with the
long-period prediction, which is the more valuable one. The
burden of proof, concerning the acceptability of partial
equilibrium based predictions and recommendations, always
lies with those who make them."
-- Ian Steedman
For empirical evidence from the United Kingdom agricultural sector
of an effect related to the one illustrated by my numerical
example, see:
Adam Ozanne, "Do Supply Curves Slope Up? The Empirical
Relevance of the Sraffian Critique of Neoclassical Production
Economics," _The Cambridge Journal of Economics_, V. 20,
pp. 749-762, 1996.
Anybody wanting to address the literature I have previously
summarized should take a look at this article. Its discussion
of why the empirically-relevant locus of commodities produced
for final consumption and prices might have a negative
own-derivative builds on Steedman's paper. From the introduction:
"The notion of Marshallian upward-sloping output supply curves
and downward-sloping input demand curves is based on two
assumptions: first the ceteris paribus assumption that it is
possible for one price to change while all other prices remain
fixed; and second, the assumption that commodities can be
identified as either outputs or inputs."
From the conclusion:
"It has been shown that if the conventional distinction between
outputs and inputs is relaxed to allow for the existence of
produced means of production, the laws of output supply and
input demand break down as a result of the abrogation of the
ceteris paribus assumption. Empirical work on a model of UK
agriculture supports this view: evidence has been found of
perverse aggregate supply response from a feedback effect
induced by the use of feedgrain, an output from the cereal
sector, as produced input in the livestock sectors, together
with the greater responsiveness in the latter.
This result, which arises not so much from the physical presence
of produced inputs in the production process as from direct
relationships between the prices of commodities hitherto
viewed as distinct outputs and inputs, is consistent with the
broader, Sraffian critique of neoclassical economics. Sraffian
economists, however, have tended to concentrate their criticisms
of Marshallian partial analysis on the input rather than the
output side of production processes - in particular, criticism
of neoclassical capital theory. Furthermore, when they have
addressed supply questions, they have been concerned with
individual commodities rather than joint commodity production -
corn used to produce corn rather than corn used to produce
beef and milk as well - or aggregate supply. This paper has
extended the analysis to cover these topics.
Finally, it should be noted that the mechanism generating
perversity outlined here is not inconsistent with econmically
rational behavior. Rather, it arises from the neglect of
produced means of production in conventional production theory
and the need to take account of the existence of produced
inputs when aggregating commodities. Computation of *net
output equivalents*, if practiable, should remove apparent
perversities and re-establish the laws of output supply and
input demand at whatever level of aggregation analysis is
conducted. If, however, such allowance is not made for
produced means of production, there is no justification for
the belief that perversity does not occur. Given that one of
the main criticisms of the Sraffian school is that its
hypotheses have seldom been tested empirically, this is
thought to be a worthwhile finding."
> >Some people have difficulty with math. My argument is presented such
> >that one doesn't even need algebra to follow it.
> Rob -- in all honesty, not meant as a jab -- your style is much, much
> harder to follow than either a *simple* numerical example or an
> algebraic exposition. Why would think someone who couldn't handle
> junior high school math could or would follow a numerical example
> with unrealistic numbers reported to seven decimal places? And
> whose exposition of the basic idea do you think is more readily
> accessible to economically literate readers, mine or yours?
It is certainly a challenge to explain advanced ideas to readers
without advanced backgrounds. I think Chris and I are in agreement
here.
Chris' exposition of the basic idea doesn't explain where the "factor
price frontier" comes from or draw on the tools I find interesting
for the long run theory of production.
I don't expect most readers to actually check my arithmetic. I
expect those who are inclined to assert I am in error to check it.
I expect some readers, amused by these exercises in
non-communication, might be sufficiently motivated to check
my arithmetic.
The main difficulty in following my example, I think, is recognizing
the numbers I plug into my equations come from the text above.
Besides, I did give an algebraic exposition of the basic idea
in this thread already.
Why is my example not simple? A constraint I put on the problem
is one reason I had difficulty creating a simple numerical example.
I wanted this to be a two good example. Both processes for producing
steel use the same set of goods as inputs, although in different
proportions. An example with this constraint demonstrates that a
certain comment of Mark Blaug's reflects a misunderstanding of
certain technical details of the Cambridge Capital Controversy.
I have created a three good numerical example with "round," but
unrealistic, numbers. I'll post an essay presenting this example
along with this response. (I have modified this essay since
last posting by adding several quotation marks and deleting
a passage unrelated to topics being discussed on this thread.)
> >I have reposted exactly the same material sometimes. There are always
> >new students of economics that need to be informed how misleading is
> >the stuff they are being taught.
> Rob -- seriously -- do you understand that when you say things like
> this, you are insulting all the academic economists who happen to
> read the post?
No, I do not understand that.
Robert Vienneau
The Cambridge Capital Controversy was a major theoretical controversy
arising out of the work of Piero Sraffa. By use of an example, this
article summarizes some negative consequences of the CCC for mainstream
theory. It concludes with some conjectures on how the CCC has
influenced contemporary directions of mainstream research.
2.0 Technical Data
I created this reswitching example, but there's plenty of other examples
in the literature. Consider a simple economy in which only one consumption
good, corn, is produced. Corn can be produced with either iron or tin.
Both iron and tin are produced goods; one process exists for producing
each.
All production processes require one year to complete. The inputs are
hired at the beginning of the year and render their services throughout
the year. Outputs become available at the end of the year. The
following "fixed coefficient" functions define the processes for
producing corn:
X1 = min[ Q2, L ] (2-1)
X1 = min[ 4 Q3, (2/3) L ] (2-2)
where
X1 is the bushels of corn produced by the process at the end of
the year
Q2 is the tons of iron purchased at the beginning of the year
Q3 is the tons of tin purchased at the beginning of the year
L is the person-years of labor hired at the beginning of the year
The process for manufacturing iron is defined by the following production
function:
X2 = min[ 6 Q2, 3 L ] (2-3)
Finally, here's the production function for tin:
X3 = min[ 4 Q3, 2 L ] (2-4)
3.0 Quantity Flows in Stationary States
The analysis is based on comparing long run positions. When
all non-labor inputs into production are themselves the output of
production processes, a long run position is characterized by
constant (spot) prices. A firm producing iron, for instance, must pay
the same price for their iron inputs at the beginning of the year as
they sell iron at at the end of the year. These prices arise when all
industries in use grow at the same rate. For concreteness, assume the
rate of growth is zero. In other words, compare stationary states. The
general conclusions of this analysis generalize to other rates of
growth, although numerical values differ.
Two stationary states, or linear combinations of these states, are
possible for any given net output of corn. Table 3-1 shows the quantity
flows per bushel corn for the iron technique.
TABLE 3-1: STATIONARY STATE WITH IRON
INPUTS Corn Process Iron Process
Labor 1 Person years 0.4 Person years
Iron 1 Ton 0.2 Tons
OUTPUTS 1 Bushel 1.2 Tons
Net output per head: (5/7) Bushels
Iron per head: (6/7) Tons
Every year, the output of the iron industry replaces the iron used up in
both industries, thereby allowing the same flows to be repeated year after
year. Both the labor and iron constraints implied by the fixed coefficient
production processes in use are met with equality. Otherwise, labor or
iron would be a free good. Table 3-2 shows the corresponding quantity flows
for the tin technique.
TABLE 3-2: STATIONARY STATE WITH TIN
INPUTS Corn Process Tin Process
Labor 1.5 Person years 0.1667 Hours
Tin 0.25 Tons 0.0833 Tons
OUTPUTS 1 Bushel 0.3333 Tons
Net output per head: 0.6 Bushels
Tin per head: 0.2 Tons
4.0 Prices in the Iron System
Let pc be the price of corn, pi the price of iron, w the wage and r the
interest rate. The interest rate is also known as the rate of profits in
some of the literature. A long run position using the iron technique
is characterized by the following system of price equations:
( pi ) (1 + r) + w = pc (4-1)
[ (1/6) pi ] (1 + r) + (1/3) w = pi (4-2)
These equations show that wages are paid at the end of the year, and that
the rate of profits is the same in both processes in use, that producing
corn and that replacing iron.
Let corn be the numeraire. Then the price equations imply a tradeoff
between the wage and the rate of profits when comparing long run positions:
w/pc = ( 5 - r )/(7 + r) (4-3)
As with all viable pure circulating capital techniques, this trade off
shows a higher wage is associated with a lower rate of profits. The
maximum wage is (5/7) bushels of corn, corresponding to a rate of
profits of 0%. The maximum rate of profits is 500%, corresponding
to a wage of zero. Figure 4-1 shows the wage-rate of profits curve for
the iron technique.
5/7 +
| x
| x
w/pc | x
| x
| x
| x
+--------------------------------+-----
500%
r
FIGURE 4-1: THE IRON WAGE-RATE OF PROFITS CURVE
One can also find the price of iron in any long run position employing
the iron technique. Equation 4-4 is needed to find the value of capital.
pi/pc = [ 1 + (w/pc) ]/6 (4-4)
5.0 Prices in the Tin System
A system of equations also exists to define long run prices for the
tin technique. Let pt be the price of tin. Then Equations 5-1 and 5-2
give the price system:
[ (1/4) pt ] (1 + r) + (3/2) w = pc (5-1)
[ (1/4) pt ] (1 + r) + (1/2) w = pt (5-2)
Equation 5-3 gives the corresponding wage-rate of profits curve for
the tin system:
w/pc = ( 3 - r )/( 5 - r ) (5-3)
As shown in Figure 5-1, the maximum wage is 3/5 bushels corn, and the
maximum rate of profits is 300%.
|
|
3/5 +
w/pc | x
| x
| x
| x
+--------------+----------
300%
r
FIGURE 5-1: THE TIN WAGE-RATE OF PROFITS CURVE
Equation 5-4 shows the price of tin as a function of the wage.
pt/pc = 1 - w (5-4)
6.0 Reswitching
A long run position is not consistent with a suboptimal choice of
technique. Accordingly, the technique chosen at a given rate of profits
is the one that maximizes the corn wage. Likewise, given the corn wage,
the selected technique maximizes the rate of profit. This rule implies that
the wage-rate of profits frontier for long run position, allowing for
the choice of technique, is the envelope curve formed out of the wage-rate
of profits curves for all available techniques (Figure 6-1).
5/7 +
| x
| + (100%, 1/2)
w/pc | x
| + (200%, 1/3)
| x
| x
+-------------------------------+-----
500%
r
FIGURE 6-1: THE WAGE-RATE OF PROFITS FRONTIER
The frontier between 100% and 200% is from the tin technique. The frontier
at the extremes outside this interval is from the iron technique. Reswitching
is the phenomenon in which a technique is chosen at at least two
different ranges of the rate of profits, with other techniques chosen at
intermediate rates of profits. Figure 6-2 shows the technique chosen
for any exogeneously given income distribution.
r 500% 200% 100% 0%
+-- Iron Technique --|-- Tin Technique --|-- Iron Technique --|
w/pc 0 1/3 1/2 5/7
FIGURE 6-2: THE CHOICE OF TECHNIQUE AT DIFFERENT FACTOR PRICES
7.0 Some Implications
This simple example has some surprisingly wideranging and disturbing
implications. These counterintuitive conclusions can arise in much
more complicated models with many techniques, many more commodities,
land-like natural resources, and fixed capital. In fact, these
complications create even more difficulties for traditional Neoclassical
theory. For example, depreciation allowances and the economic life of
machines are not determined by technical data; they must be solved
simultaneously with prices and the choice of technique. A higher
interest rate need not be associated with a choice of technique that
extends the economic life of machines. The ordering of land from
high rent to low rent land is not determined by technical data on
fertility; even with unchanged net output the order of rentability can
differ for different exogeneously given income distributions. Different
types of factors cannot be treated symmetrically in this theory, but
must be handled by models with different structures.
7.1 Marginal Productivity Theory of Distribution
An important negative implication of this analysis concerns the marginal
productivity theory of distribution - there is no such thing. This analysis
could be recast in the form of inequalities and marginal productivity
relationships. Such a recasting would yield no new results. The location
on the envelope curve forming the wage-rate of profits frontier is still
unspecified. The distribution of income must be given from outside the
marginal productivity relationships. Notice that this implication does
not rely on reswitching and holds even with a continuum of continuous
production functions for available processes.
Once either the wage or the rate of profits is known, the preferred
technique, the other distributive variables, and all prices are
determined. Reswitching shows this relationship is not invertible.
Suppose the technique actually in use in a long run position and all
possible techniques are known. That technique may be compatible with
widely separate discrete intervals for the distributive variables and
different price systems. In the example, the choice of the iron
technique is compatible with both high and low wages, but not
intermediate wages. The distribution of income is not determined
by physical data about the technique employed.
This conclusion may not be surprising. The determinates of final demand
have not yet been specified in the model. A traditional response is to
add utility functions relating consumption and the disutility of labor.
Closing the model in this way, though, is questionable. Suppose the wage
or the rate of profits is given. In a pure circulating capital model,
such as the example, the level and composition of final demand has no
influence on prices. In a model with more than one consumption good, long
run prices are uninfluenced by whether consumers want more cloth and
less corn. In models with land, the level of demand for each good will
influence final prices, but may not exhibit well-behaved substitution
relationships. Likewise, different wages or rates of profits can be
associated with equilibria in which labor and capital are not
substituted in a manner consistent with traditional theory. Luckily
alternative theories of distribution exist for closing the model that do
not depend on substitution.
7.2 "Demand" for Labor
The relationship between wages and the demand for labor in the example
illustrates the possibility of behavior incompatible with traditional
theory. The person years of labor required per bushel of corn can be
computed for each available technique. Which technique will be preferred
at each wage has already been determined. Consequently, the person years
of labor per bushel corn can be graphed against the wage, as shown in
Figure 7-1.
|
5/7 +------+
| |
| |
1/2 + +-----+
| |
w/pc | |
| |
1/3 + +-----+
| |
+------+-----+----------
1.4 1.7
Person years per bushel
FIGURE 7-1: THE "DEMAND" FOR LABOR
For wages above 1/3 bushels, this curve looks like a discrete approximation
to the traditional demand curve. But the switch at 1/3 bushels appears
"perverse" from the standpoint of traditional theory. A lower wage is
associated with a less labor-intensive profit-maximizing technique.
7.3 "Demand" for Capital
Another traditional belief in some Neoclassical models is that the demand
and supply are equated in the market for capital. The interest rate is
thought to be the price of capital. This belief can be investigated by
this model as well. Capital is irretrievably a value quantity. So first
the equilibrium price of iron and tin must be determined. Table 7-1
was constructed based on Equations 4-4 and 5-4.
TABLE 7-1: PRICES OF CAPITAL GOODS
Interest
Rate Iron Tin
0% 2/7 Bushels
100% 1/4 1/2 Bushels
200% 2/9 2/3
500% 1/6
Once prices are given, the value of capital can be determined for
each technique. Table 7-2 shows the results, while Figure 7-2 shows the
graph of capital intensity against the interest rate.
TABLE 7-2: VALUE OF CAPITAL PER BUSHEL
Interest Iron Tin
Rate System System
0% 12/35 Bushels
100% 3/10 1/6 Bushels
200% 4/15 2/9
500% 1/5
|
500% +-----------+
| +
| +
200% + +-----+
| +
r | +
100% + +-------------------------+
| +
| +
0% +---+-------+-----+-----+-----+-----+--
0.17 0.20 0.22 0.27 0.30 0.34
Capital per unit output (Bushels)
FIGURE 7-2: THE "DEMAND" FOR "CAPITAL"
Figure 7-2 cannot be reconciled with the traditional view. With rates of
profits between 100% and 200%, the tin technique is preferred. In this region
a higher interest rate is associated with a higher value of the capital used
in producing corn. Furthermore, the switch point at 200%, once again,
is "perverse" from the viewpoint of traditional theory. A higher interest
rate is associated with a switch to a more capital-intensive technique.
Clearly the interest rate is not a "scarcity index" for "capital."
The point of the example is "capital-reversing," not reswitching. Imagine
a third technique is available, and that this technique dominates at rates
of profits below a value slightly above 100%. Then the wage-rate of
profits frontier formed from the envelope curve corresponding to the
three techniques will not exhibit reswitching. Each technique will
appear once and only once. Still, a "perverse" switch will exist at a
rate of profits of 200%.
7.4 Aggregate Production Functions
The Cambridge Capital Controversy developed other insights into capital
theory. Consider Eugen von Bohm-Bawerk's theory. He thought lower
interest rates were associated with a switch towards techniques with
a longer "period of production." The period of production was intended to
be a physical measure of capital intensity. The example shows that no
such measure is available in the general case. Techniques may not be
capable of being ordered uniquely by a capital intensity that varies
monotonically with the interest rate. Around interest rates of 100%,
the iron technique is preferred at lower interest rates. On the other
hand, the tin technique is preferred at lower interest rates around
200%. Bohm-Bawerk's theory is mistaken. At least Knut Wicksell realized
he never got it completely right.
Another approach to capital theory is associated with the concept of
aggregate production functions:
Y = F( K, L ), (7-1)
where Y is net output, K is "capital," and L is total labor. Constant
returns to scale are assumed, so the aggregate production function can
be expressed on a per capita basis:
y = Y/L = F( K/L, 1 ) = f( k ), (7-2)
Other typical assumptions are that more capital per head is associated with
more output per head:
df/dk > 0, (7-3)
and that capital exhibits diminishing marginal returns:
2 2
d f/dk < 0 (7-4)
Figure 7-3 illustrates a conventional aggregate production function.
| x
| x
Output | x
per | x
head | x
(y) | x
| x
| x
+----------------------------------
Capital per head (k)
FIGURE 7-3: A CONVENTIONAL PRODUCTION FUNCTION
Profit is assumed to be maximized, where profit is defined as in
Equation 7-5:
profit = F( K, L ) - r K - w L (7-5)
Ignoring the dependence of the value of capital on the interest rate, the
first order conditions for a maximum are that the wage equal the
marginal product of labor:
w = dF/dL, (7-6)
and that the interest rate equal the marginal product of "capital:"
r = dF/dK = df/dk (7-7)
These conditions are supposed to ensure that the factor payments exhaust
the value of the output:
y = w + r k (7-8)
The reswitching example shows that the assumptions on which this
traditional story are based are without foundation in a multicommodity
world. Table 7-3 shows the value of capital per head at selected interest
rates for the example. One can also calculate output per head at
different interest rates. The resulting production "function" is shown
in Figure 7-4.
TABLE 7-3: VALUE OF CAPITAL PER HEAD
Interest Iron Tin
Rate System System
0% 12/49 Bushels
100% 3/14 1/10 Bushels
200% 4/21 2/15
500% 1/7
| F E B A
0.7 + +------+ x------+
Output | + x
per | + x
head | x +
(y) 0.6 + x------+
| C D
|
+----+------+-----+------+-----+------+---
0.10 0.13 0.14 0.19 0.21 0.25
Capital per head (k)
FIGURE 7-4: THE EXAMPLE PRODUCTION "FUNCTION"
Point A corresponds to the long run position associated with an interest
rate of 0%. Equilibria with interest rates between 0% and 100% lie along
the segment between A and B. There is a switch point at 100%, and the
equilibrium values of output and capital per head are shown by point C.
Equilibria associated with the tin technique lie along the segment
between C and D. Finally, the iron technique is preferred again at
interest rates above 200%, as shown by the segment between E and F.
Figure 7-4 is hardly a step function approximation to a well-behaved
production function. In fact, Figure 7-4 does not show a function at all.
It is almost as if any scribble in y-k space could be a production
function. Thus, the conventional story, in which the wage is the
marginal product of labor and the interest rate is the marginal product
of capital, is invalid.
The failure of the traditional story to hold is particularly conspicuous
if reswitching and capital reversing occur. However, even assuming a
continuum of continuous production functions and the absence of both
phenomena, the traditional story does not hold. The problem is that
capital intensity depends parametrically on the interest rate. A
vicious circle arises if the interest rate is then said to be determined
by the marginal product of capital.
To see this, consider once again the wage-rate of profits frontier for
a single technique, as in Figure 7-5. The dotted line is supposed to be
a concave wage-rate of profits frontier for a single technique, the solid
line is the tangent at Point B. Let the net product be the numeraire.
|\
| \
| \
Ax \
| x \
w | \B
| \
| x\
+-------++---
r
FIGURE 7-5: A WAGE-RATE OF PROFITS FRONTIER
Equation 7-8 expresses the condition that factor payments exhaust the
net product. A simple manipulation of Equation 7-8 yields Equation 7-9:
w = - k r + y (7-9)
Suppose the interest rate is as at Point B in Figure 7-5. Then Equation
7-9 shows the capital intensity at this point is the absolute value of
the slope of a secant connecting the intercept of the frontier with the
wage axis (Point A) and Point B. On the other hand, take total
differentials of Equation 7-8:
dy = dw + r dk + k dr (7-10)
Dividing Equation 7-10 through by dy yields Equation 7-11:
1 = dw/dy + r dk/dy + k dr/dy (7-11)
Now suppose the traditional aggregate Neoclassical story was true and
the interest rate was the marginal product of capital, as expressed by
Equation 7-7. Then, Equation 7-12 must hold:
k = - (dw/dy) / (dr/dy) = - dw/dr (7-12)
But Equation 7-12 shows that the value of capital per head is the absolute
value of the slope of the tangent line at Point B.
In general, capital intensity can hardly be the additive inverse of the
slopes of both the tangent and the secant at point B. Except for
uninteresting special cases, the traditional story requires that the
wage-rate of profits frontier be a straight line for each individual
technique on the envelope curve. A smooth differentiable frontier can be
created as the envelope curve of a continuum of individual frontiers. If
all techniques had straight line frontiers, both Equations 7-9
and 7-12 would hold. Marginal products would explain income
distribution.
What is needed to ensure linear frontiers? The answer is that the
capital intensity be the same in all processes. For the simple two good
example considered here, the ratio of iron and labor inputs in producing
corn would need to be the same as the ratio in producing iron. Similarly,
the ratio of tin and labor inputs in producing corn would need to be the
same as the ratio in producing tin. If the example was so modified, the
result would be a discrete approximation to the traditional story. Those
familiar with Marx have pointed out that this assumption of equal
capital intensity also validates the labor theory of value as a theory of
relative prices. But just as the labor theory of value is insufficiently
general, so marginal productivity theory based on aggregate production
functions relies on too restrictive assumptions to have any hope of
being descriptive of capitalist reality.
Even if all wage-rate of profits frontiers were linear, the traditional
story would still be sensitive to a criticism due to Joan Robinson. The
resulting production function is constructed by comparing equilibria
constructed out of the same available technical knowledge. The economy is
not capable of moving along a production function. If the interest rate
dropped, the array of capital goods in existence would no longer be
appropriate. Iron might be wanted instead of tin. Unless one assumes
capital goods can costlessly change their form, a long disequilbrium
process would result. In no way would this process be captured by a
movement from one adjacent point to another on the production function.
7.5 Interest as A Reward for Waiting
Once Robert Solow began to realize the negative consequences of the
Cambridge criticism for his eponymous growth model, he proposed an
alternative basis for capital theory. He argued that the central concept
of capital theory should not be capital, but the rate of interest as
expressing a rate of return. Interest reflects a payment for deferring
present consumption. By deferring present consumption, one can redirect
the resources set free to produce tools that will result in a greater
stream of consumption in the future. Interest rates measure this supposed
return on investment.
Consider a stationary state in which one consumption good is produced by
a multitude of capital goods and in which a multitude of alternate
techniques are available. Let
C( 0 ) = C( 1 ) = C( 2 ) = ... (7-13)
denote the quantity of the consumption good that is available at the end
of years 0, 1, 2, ... Now consider a slight displacement from this
position. Suppose h less units of the consumption good are produced in
year zero. Instead, the resources released are used to construct capital
goods that, with maintenance, will ensure an additional perpetual
future stream of g units of the consumption good. So the new stream of
the consumption good will be:
C( 0 ) - h, C( 1 ) + g, C( 2 ) + g, C( 3 ) + g, ... (7-14)
Solow defines the rate of return as follows:
r = g / h, (7-15)
and claims that the market rate will converge to this value in long
term equilibrium. (Note that the present values of the infinite stream
of g units of the consumption good and the h units abstained from
consumption are equal at the interest rate given by Equation 7-15.) No
aggregate measure of capital seems to appear in this formulation of
interest rate theory. The interest rate appears to be purely a
technocratic notion independent of all considerations of pricing.
Luigi Pasinetti has argued that this conception founders on reswitching
just as badly as the aggregate production function/Solow growth model. The
above reswitching example can be used to illustrate Pasinetti's argument.
To determine the rate of return, consider a switch from the tin technique to
the iron technique. Each year the tin technique produces a net output
of 3/5 bushels corn per head. In the year in which the switch occurs, the
labor force is no longer hired to work up 1/5 tons of tin per head. Instead,
they combine their labor with 6/7 tons iron per head. As a consequence, the
net output in the future will be 5/7 bushels per head. A perpetual
additional stream of 4/35 bushels per head is the return from "deferring
consumption" in the year in which the switch occurs.
The return on investment can only be found after determining how much corn
is immediately given up by switching from the tin technique to the iron
technique. But this quantity can only be found by valuing iron and tin in
terms of corn. So questions of valuation are necessary to calculate the
return on investment, after all. If there were only one set of prices at
which this switch would occur, no problem would arise for the
technocratic conception of the rate of interest. The return on investment
would then be uniquely determined by the technical data. But this is not
the case.
Recall Table 7-3 expresses the value of capital per head in bushels of corn.
At a switch point of an interest rate of 100%, the iron technique
requires 4/35 bushels of corn per head more than the tin technique. Thus,
in Solow's jargon the additional perpetual net output of 4/35 bushels is
obtained by sacrificing 4/35 bushels per head in the first year.
The rate of return is then:
r = [ (5/7) - (3/5) ]/[ (3/14) - (1/10) ] = 100% (7-16)
Now consider the switch point at an interest rate of 200%. In this case,
the iron technique requires an additional 2/35 bushels of corn per head,
as compared with the tin technique. Solow's rate of return is given by
Equation 7-17:
r = [ (5/7) - (3/5) ]/[ (4/21) - (2/15) ] = 200% (7-17)
The same physical quantity flows are associated with a lower interest rate
in the neighborhood of 100%, and a higher interest rate in the neighborhood
of 200%. Both cases are associated with a switch from the tin technique to
the iron technique. But the calculation of the rate of return is vastly
different in both cases because of the need to value heterogeneous capital
goods in terms of the single consumption good. This shows the "abstention
from consumption" used in calculating the rate of return is not determined
by purely technical data. Luigi Pasinetti argues that the above definition
of the rate of return is a tautology. The rate of interest can always be
expressed as a ratio in which the denominator is called "current abstention
from consumption," and the numerator is called "a perpetual future
increase in consumption." Such an expression casts no light on what
determines the rate of interest.
8.0 Conclusion
The Cambridge Capital Controversy showed that an abundance of traditional
models implicitly relied on special and unstated assumptions. Generally,
these models are mistaken in a multicommodity world. One response of
mainstream theorists was to retreat to disaggregated theory. It is still
open to debate whether Neoclassical long-run equilibrium theories can
survive without a centralized capital market equating investment and
savings or the demand and supply of capital. It is also a subject of
discussion what, if anything, has been abandoned in such models.
Reswitching examples lead one to doubt whether prices in such models can
be interpreted as "scarcity indices."
Unlike the long run, short run equilibrium models exist which exhibit
traditional substitution behavior. But these models are disequilibrium
models from the standpoint of the long run. The given quantities of
produced commodities in existence at the beginning of the period
reflects mistaken past expectations about the current situation. The
disequilibrium nature of short run models raises the issue of their
adequacy for economic theory. Perhaps what is needed are models in which
the modeled agents are conscious of their disequilibrium nature.
Furthermore, how are expectations formed? What happens if agents are
aware of their strategic interdependence? How can agents coordinate
their strategies if multiple equilibria exist? How should stability
issues be handled? These questions have all become topics of current
research, and an abundance of models have been developed to investigate
them. The result seems to be a world in which "anything can happen, and
nothing need happen."
The nature of the questions posed by these developments is also unclear.
Are these questions matters of logic to be answered by mathematical
modeling? Will the answers be universal or vary with the institutional
structure of the societies to which they are applied? How do empirical
considerations enter? One thing is clear though - there exists a
reading of contemporary trends in which the work of Piero Sraffa is
central. As the leader of a school of thought, he can be said to have
redirected the whole tendency of mainstream theory.
----------------------------------------------------------------
...there is a general theoretical agreement (which is ignored
in a scandalous way by most textbooks) about the untenability of
neoclassical theories that take their point of departure from
aggregate capital.
-- Bertram Schefold
Christopher Auld
>7.2 "Demand" for Labor
Rob, are you admitting with the quotes that this object is not actually
a labour demand curve? In which case,
>The relationship between wages and the demand for labor in the example
>illustrates the possibility of behavior incompatible with traditional
>theory.
this statement is bullocks?
>modeling? Will the answers be universal or vary with the institutional
>structure of the societies to which they are applied? How do empirical
>considerations enter? One thing is clear though - there exists a
>reading of contemporary trends in which the work of Piero Sraffa is
>central. As the leader of a school of thought, he can be said to have
>redirected the whole tendency of mainstream theory.
Rob, could you tell us a little about contemporary trends in capital
theory? I've never noticed you say anything to suggest that you are
anything but completely innocent of that field of economic theory.
Christopher Auld
>There is no logical reason to asset that cost minimizing firms
>will necessarily adopt less labor-intensive techniques at higher
>wages, given technology.
But not, "given technology, and all else, equal." This is the point of
the discussion, after all. For the fifth time:
>> >> 1. Do you think you've shown that, in theory, labour demand schedules
>> >> can slope up?
This is where I would ask the judge for permission to treat the witness
as hostile if this were a different venue. Rob, are you ever going to
actually answer this question?
(You could always plead the fifth.)
>I don't care. I see no reason to avoid the use of "irrelevant dogma"
>in characterizing mainstream teaching. I will change the final
"Whatever." I note in passing Rob didn't respond to --
>> To illustrate, it is much easier to understand
>> *your* model if one knows what a conditional labour demand schedule
>> is, and I have already pointed out that the usual econometric tools
>> can differentiate between the total and partial derivatives of labour
>> demand with respect to the wage rate. Factor demand curves are a
>> basic and important tool in both theory and empirical applications,
>> as is partial equilibrium analysis in general. It is not "dogma"
>> and it is not "irrelevant," indeed, it is simply the imposition of
>> "all else equal" in furtherance of understanding how a system works,
>> a tactic common to all of scientific inquiry.
In particular the point that *his* model is much easier to understand
if one knows the tools Rob insists on referring to as "irrelevant" and
"exploded" "dogma."
>Whatever. I don't think the earth is the center of the universe either.
>It's look that way, though, if one spends a clear summer night in a
>field away from city lights. Who is more likely to accept Alan Sokal's
>invitation to step out of his 21st floor apartment window, Chris or
>me?
"Whatever." (Gosh, that is a terrific debating device.)
>> >I think economists should understand a valid long run theory of production.
>> >I created my numerical example by drawing on such a theory.
>> you might reflect on how absurd this sort of statement is when you admit
>> you aren't familiar with the dynamic models which have dominated the
>> literature for the past three decades.
>Chris is being silly. I never admitted any such thing. For Chris'
Rob told us he might dig up a forty year old book by Richard Bellman so
he could learn what dynamic programming is all about. Since dynamic
programming is pretty much essential to reading dynamic economic theory,
his comment is tantamount to my assessment. He certainly never gives
any indication in his essays that he's at all familiar with developments
that have occurred within mainstream though since circa 1970.
> o I have written software to implement
Dynamic statistical models are not the same as dynamic economic theory,
as I should hope Rob knows. This background, though, not unlike
> phase spaces in the context of dynamical systems specified by
> systems of Ordinary Differential Equation
> o I have read a book on the Lorenz equation and briefly examined
> other books on dynamical systems
will help Rob progress quickly if he plunges into the exciting world
of modern economic thought.
> o I have read certain works on economics discussing mainstream
> dynamics, including:
>
> - J. R. Hicks, _Value and Capital_, 2nd Edition, 1939, 1946
>
> - Robert Dorfman, Paul A. Samuelson, and Robert M. Solow,
> _Linear Programming and Economic Analysis_, 1958
>
> - Gerard Debreu, _Theory of Value_, 1959
>
> - Edwin Burmeister, _Capital Theory and Dynamics_, 1980
> (although I only skimmed the later chapters)
>
> - Robert E. Lucas, Jr., _Models of Business Cycles_, 1987
>
> - Syed Ahmad, _Capital in Economic Theory: Neoclassical,
> Cambridge, and Chaos_, 1991
>
> - E. Roy Weintraub, _Stabilizing Dynamics_
Well, most of these clearly predate modern dynamic theory, Rob. Save
Lucas, and I don't see how one can read Lucas or:
> o I am currently reading a book on Thomas Sargent which tells
> some stories in which his contributions to rational expectations
> were attempts to make economic theory more coherent. I have
> already read two journal articles used for chapters in this
> book.
without knowing what dynamic programming is all about. Nonetheless,
it warms my heart to see Rob is doing some reading outside of the
CCC and learning some modern thought.
>Of course, my qualifications are of no relevance for valid
>arguments in this thread.
"He opened the door, your honour." Recall my comment was in response
to
>> >I think economists should understand a valid long run theory of production.
>> >I created my numerical example by drawing on such a theory.
and it is of course relevant what Rob knows about dynamic economic
theory if he's going to presume to lecture the discipline on what
it "should understand" about dynamic processes.
>> >> >No. The form of f( L, X1, X2 ) is not merely a function of three
>> >> >variables. I defined f() to be the solution to the LP above, and
>> >> >its form is restricted by this definition. Although I haven't
>> >> >been bloody-minded enough to solve this LP, it seems obvious to
>> >> >me that the solution will not be a special case of the minimum
>> >> >function given above.
>
>> >> Yes, I agree, but you didn't show that, Rob. Your "proof" is no
>> > ^^^^^^^
>> >> such thing.
>> What is "agree" underlined for?
>
>When Chris said, "I agree," he was disagreeing with his previous
>position.
That's simply not true. Again, Rob deliberately misrepresented my
statement "choice between two Leontief production functions" as
"a Leontief production function." I am "agreeing" that these two
objects differ, and certainly never asserted otherwise (it would
help discussion if Rob could possibly concede that it's fairly
likely I understand concepts introduced in second-year micro).
I disagree that Rob proved that statement.
>> I am agreeing that Rob's two [ process ]
>> function is not Leontief, and I never said it was. The disagreement
>> here is over whether Rob proved this or not.
>
>The disagreement seems to be over whether a step I thought, in
>context, to be obvious is indeed obvious. The step is a matter of
>solving the LP characterizing my example.
This isn't a "step," this is, in fact, the proof itself, which
is nowhere to be found.
>> - A Leontief prod'n f'n is of the form Q = min{ aL, bK }
>
>Even here, Chris writes stuff to which he should know I'm likely
>to object. His use of "K" is part of a tradition that suggests
Who cares? Is this the point here?
>Chris leaves out a step of some use in my explanation. I gave two LPs.
>One yielded a Leontief production function. The one characterizing
>my technology doesn't.
Asserted _without proof_. That's the point.
>> - f(L, K) is not of the form min{aL, bK}, therefore, the
>> technology is not Leontief.
>
>> But, of course, he did not show or argue that f() is not of the form
>> min(), so his argument is neither "proof" nor even "explanation."
>
>I stated:
>
> "Since this second LP is not of the same form as the first, the
> production function f( L, X1, X2 ) is not Leontief."
>
>where f was defined as the solution of the LP characterizing my
>technology. I did "not show or argue" a point I thought obvious.
>However, the point follows from solving the LP I gave.
Which would be the proof. Therefore, you have not proved what
you set out to prove. Right?
>I don't know what Chris' problem is here. I had even pointed
>out that one process does not dominate the other in my original
>description of the processes available to the steel industry in
>my long essay.
My first problem is Rob's deliberate misrepresentation of what I
said. My second is his inability to admit his errors.
>Chris is going to have difficulty in asserting that he was
>referring to the above quoted argument of mine as a
>mathematical error, while maintaining I did not argue that
>the relevant production function is not Leontief.
Why? We agree the relevant production function is not Leontief.
I have demonstrated that you did not prove this. I am amused
by the fact that you can't admit as much.
>> Consider this "proof" :
>>
>> - A Cobb-Douglas demand function is of the form X = Y / 2Px.
>
>The point here is that the above demand function is not the
>general form that can be derived from a Cobb-Douglas utility
>function. The constant 2 should be replaced by an algebraic
>expression.
That's "the point?" That's a complete irrelevancy.
>Chris' analogy is backwards. I wrote the general form of
>a Leontief production function in my context.
Which is a specific case of a general function f(inputs), analogous
to a general demand function X( p, Y ). The analogy is exact. To
make it crystal clear:
Rob Chris
--------------------------------
min{ aL , bK} Y / 2P_x
f(L, K) X(Y, P)
>Given the general form, I argued my specific example was not
>of that form.
No, Rob, you didn't, you asserted that it's not without any sort
of argument, formal or otherwise. Essentially, you begged the
question.
>>>> Which isn't how I'm using it. I mean simply that the firm will switch
>>>> from one technique to the other.
>
>>>Again with the irony.
>
>> Huh? Rob, do you think a sentence such as, "the firm will switch from
>> process A to process B when the wage to interest ratio passes above
>> 2.3" is inherently an abuse of terminology?
>
>> Perhaps we will next argue about the definition of "is."
>
>Chris, of course, is being silly. I think, "The term 'switch point'
>has a well-defined meaning in the construction of 'factor price
>frontiers.'" Chris is abusing a technical term with a precise
>definition relevant for this thread.
Rob, read carefully now: did I use the term "switch point?" Again,
do you think it's possible to use the word "switch" without necessarily
invoking the construction of "factor price frontiers?" If I write in
another group that it's well-advised to "switch" from Fortran 77 to
Fortran 90, am I guilty of abusing terminology?
>> >My numerical example proves that it is logically possible that, in a
>> >comparison of long run positions, a higher wage may be associated with
>> >a decision by firms to adopt a more labor-intensive technique. It
>> >would seem the substitution patterns needed for downward-sloping labor
>> >demand curves, whether conditional or not, to be relevant are not
>> >necessary implications of neoclassical theory.
>
>> < slams head into desk >
>
>> OK, Rob, you state above that you don't think you're showing that
>> labour demand curves slope up, and now you relapse. [ Silliness
>> deleted. ]
>
>Nowhere in the quoted text do I say labor demand curves can slope
>up.
Stating there are "substitution patterns needed for downward-sloping
labour demand curves" necessarily implies that there existence of
"substitution patterns" which lead to demand curves with non-negative
slopes. Yet Rob has yet to present a model in which labour demand
curves can do anything but slope down. Silly, silly Rob.
>> Rob also won't directly answer the question, 'do you think that
>> counterintuitive empirical results stemming from minimum wage
>> changes are a result of the mechanism you describe.' Rob, I'm
>> simply going to tell you that no econometrician on the planet
>> would agree with that notion. Look,
>
>> dL \partial L \partial r \partial L
>> -- > 0 <==> abs ---------- < ---------- ---------- .
>> dW \partial W \partial W \partial r
>
>In my example, and, in fact, for any circulating capital technology,
>del L/del W is undefined. So however interesting Chris' explanation
>may be, it needs, at least, further development.
"Whatever." Simply because Rob makes his exposition more cumbersome
than necessary by insisting on non-differentiable technologies is
neither here nor there. The gist of the argument is adequately
summarized by the expression above -- Rob can substitute the
appropriate expressions for non-infinitesimal changes if it makes
him happier.
[ Five lengthy and completely irrelevant paragraphs deleted. ]
Rob apparently adamantly refuses to take a position on whether the
effect he outlines is responsible for counter-intuitive empirical
results with respect to changes in the minimum wage.
>> Is this likely to hold? We need for the cross-price elasticity of
>> labour demand with respect to the interest rate to be large relative
>> to the own-price elasticity, which is generally not the case, and
>> we also need the interest rate to be highly responsive to changes
>> in the minimum wage. As I already pointed out, about 2% of the
>> U.S. labour force is at the minimum wage -- even with "ratcheting"
>> and similar effects small changes in the minimum wage are simply
>> not going to push the interest rate around much, particularly when
>> we consider that U.S. rates are at least partially determined in
>> world markets. It is simply totally implausible that this effect
>> explains Card and Krueger type anomolies.
>
>So the reason why minimum wages create unemployment is not the
>introductory economics supply and demand story. Rather, it is
>the consequence of certain claims about the relative sizes of
>effects influencing the locus in my example. So much for Chris'
>logical consistency.
I have said *nothing* about why or why not minimum wages might
create unemployment (and, for Rob's information, I would use
search theory to think about _un_employment, not basic supply
and demand). What I pointed out was that there have to be some
really perverse and implausible effects occurring for Rob's story
to explain empirical anomalies with respect to the minimum wage.
> "It has been shown that if the conventional distinction between
> outputs and inputs is relaxed to allow for the existence of
> produced means of production, the laws of output supply and
> input demand break down as a result of the abrogation of the
> ceteris paribus assumption. Empirical work on a model of UK
> agriculture supports this view: evidence has been found of
> perverse aggregate supply response from a feedback effect
> induced by the use of feedgrain, an output from the cereal
> sector, as produced input in the livestock sectors, together
> with the greater responsiveness in the latter.
Again, Rob, my point is that this "feedback mechanism" is certainly
negligible in the case of minimum wage changes (particularly inter
and intra-State minimum wage changes, which is the variation most
studies of the effects of minimum wages, including Card and Krueger,
exploit to generate estimates). Would you have us believe that a
fifty cent increase in the New Jersey minimum wage would change the
U.S. interest rate enough to offset decreases in employment that
would otherwise occur in New Jersey?
>> >I have reposted exactly the same material sometimes. There are always
>> >new students of economics that need to be informed how misleading is
>> >the stuff they are being taught.
>
>> Rob -- seriously -- do you understand that when you say things like
>> this, you are insulting all the academic economists who happen to
>> read the post?
>
>No, I do not understand that.
Perhaps you should reflect on your lack of understanding. Why do you,
no, why would anyone, think that naked accusations of teaching "exploded
dogma" and "misleading" material to students wouldn't be taken as
an affront to one who teaches?
SUSUPPLY
>Who is more likely to accept Alan Sokal's
>>invitation to step out of his 21st floor apartment window, Chris or
>>me?
I know who is the more likely to be pushed out.
Patrick
Robert Vienneau
> marcel wrote:
> > Is it a matter of definition or a matter of assumption that a factor demand
> > curve must always slope downward ?
> It necessarily follows from the profit maximization hypothesis. I don't
> think it requires any additional assumptions. (It may stem simply from
> cost minimization, which is implied by profit maximization. I don't recall
> offhand.)
Non-increasing does not mean decreasing.
[...]
> Put succinctly, the labor demand curve shows the relationship of the
> quantity of labor demanded and the wage rate. If anything else changes, e.g.
> the interest rate, that isn't on the graph, the demand curve itself is going
> to shift. This may mean that in equilibrium the real wage and quantity
> demanded of labor) are positively correlated; it does not mean that, holding
> all other factors fixed, when the real wage rises the quantity demanded of
> labor also rises.
If "factors" means "factors of production," Dave is not talking about
a long run curve. If "factors" is being used in its common
English-language sense, the above claim is incoherent.
> A locus of equilibria does not trace out the demand curve, or the supply
> curve, unless one curve is shifting while the other is not moving.
Consider the locus of relevant equilibria traced out by shifting the
supply curve for labor. This locus can be upward-sloping. According
to the professional economists on this thread, it is not a demand
curve.
> Rob would
> have you believe this is news.
Leontief input-output analysis is widely applied empirically. It can
be interpreted as a long run theory of production. It can be extended
via activity analysis to consider the cost-minimizing choice of
technique in long run positions, given a technology specifying
available processes from which those techniques are constructed.
(Coefficients of production are variable in this extension.) One
can take wages as exogeneous in such analyses.
What does seem to be news to some economists is what variables
are endogeneous in such analyses.
In order to avoid discusing these analyses, some economists will
go on about a supposedly correct understanding of modeling,
dynamics, and other irrelevancies. Apparently, worrying about the
coherence of certain aspects of economic theory is not to be done.
> I've never thought about it before in the
> context of labor economics, but it should be obvious to anyone who's ever
> tried to (correctly) estimate a demand or supply function.
Before one can estimate such a function, it helps to understand
when such a function can be applicable. When one thinks about the
meaning of prices and commodities in economic theory, it is not
even clear that the notion of a long run demand curve for labor
is coherent.
Christopher Auld
>> A locus of equilibria does not trace out the demand curve, or the supply
>> curve, unless one curve is shifting while the other is not moving.
>Consider the locus of relevant equilibria traced out by shifting the
>supply curve for labor. This locus can be upward-sloping. According
>to the professional economists on this thread, it is not a demand
>curve.
It is if the demand curve doesn't shift endogenously as the supply curve
shifts -- "while the other curve is not moving."
>What does seem to be news to some economists is what variables
>are endogeneous in such analyses.
Really? Which economists are not aware that, in general equilibrium,
shocks in one market can affect other markets and produce a feedback
effect?
>In order to avoid discusing these analyses, some economists will
>go on about a supposedly correct understanding of modeling,
>dynamics, and other irrelevancies. Apparently, worrying about the
>coherence of certain aspects of economic theory is not to be done.
Gosh, I wonder who Rob is referring to here?
1. Who has been "avoiding" discussion? I seem to recall discussing
these issues with Rob over a period of many years.
2. How economists handle dynamics is not an "irrelevancy." Rob
continually tells us what economists "should know" about various
processes. He seems unphased when it's pointed out to him that
the the charicature of mainstream thought he attacks hasn't been
standard mainstream modelling practice since before I was born
(I'm 29). Personally, I am "worried" about using the tools
provided by economic and econometric theory to explain and
investigate real world phenomena. Rob seems unworried about
such low brow endeavors.
>> I've never thought about it before in the
>> context of labor economics, but it should be obvious to anyone who's ever
>> tried to (correctly) estimate a demand or supply function.
>
>Before one can estimate such a function, it helps to understand
>when such a function can be applicable. When one thinks about the
>meaning of prices and commodities in economic theory, it is not
>even clear that the notion of a long run demand curve for labor
>is coherent.
Perhaps that's one reason why such ad hoc notions of dynamics have
been abondoned in favour of explicitly dynamic models. Of course,
I apologize again for bringing up such "irrelevancies."
dav...@my-dejanews.com
little is necessary. What Chris said.
It's worth noting that no economist I'm aware of is worried about what you
suggest is the "incoherence" of partial equilibrium analysis. Do you think
your example provides one possible reason why general equilibrium and
dynamic models have become so popular in the last few decades? How
is the decision by economists to move toward these kinds of frameworks
"irrelevant" to your point? What exactly is your point?
I learned very early on in graduate school that in certain cases, partial
equilibrium analysis does not accurately describe the magnitude nor even
the direction of effects of changes in general equilibrium contexts.
Are you calling for work characterizing the circumstances in which partial
equilibrium and general equilibrium yield similar or identical results?
Are you calling for an abandonment of the use of supply and demand curves
in undergraduate education?
> it is not even clear that the notion of a long run demand curve for labor
> is coherent
No one is stopping you from estimating a reduced form regression line
through the locus of equilibria. It gets done all the time in hedonics
papers. Whether or not you could then attach a decent structural story
to the reduced form results is a different question.
marcel simkens
dav...@my-dejanews.com heeft geschreven in bericht
<7eueer$16c$1...@nnrp1.dejanews.com>...
marcel wrote:
>> I do understand the demand curve (labor or commodities) in microeconomics
but >>I have more problems with these curve in macroeconomics.
Dave wrote
>Which curve(s) trouble you? The aggregate demand curve? The demand curve
for >all the labor in an economy?
I understand the demand curve in microeconomics. Assume an economy with
only 2 commodities C1 and C2 ; a family has a budget B. If the price of C1
decrease, there is always more money available to purchase C1 by purchasing
less of C2 so that it is possible to drawn a demand curve and the quantity
of C1 will increase if the price of C1 decrease ; but ,for this case, the
aggregate demand curve does not exist because the demand for (C1 + C2) is
determined by the budget B and that is a point and not a curve.
Neither I understand the (aggregate)labor demand curve as described by
Barro.
The graph of the production function is drawn with the assumption of
diminishing marginal productivity, but these assumption can be wrong.
Example : A car producer uses the production lines only for 70 % of the
capacity. By increasing the labor input it is possible that 80 % of the
capacity is used so that the MPL will increase and not decrease.
If the level of population is constant, there are 3 possible ways to have
more labor available :
1. By decreasing the unemployment. Even if the MPL for the aggregate of
firms is decreasing, the MPL for the whole economy will increase.
2. The production is done by firms (employers) and families working for
there own account. These families will only deliver labor if the income or
the wage as employee is higher, and this is only possible if the firms have
increased their productivity.
3. By increasing the productivity, more labor is available; 200 years ago a
housewife must bear 5 children to keep the level of the population constant.
This is reduced to 2 children by improving the healthcare; and also by
developing washmachines, dishwashers, refrigerators deepfreezers etc. more
women are available for the production.
If an increase of productivity is necessary to increase the labor input, it
will be difficult to drawn a labor demand curve to labor input with a
constant level of technology.
The level of productivity is the most important exogenous variable of the
economy.
There is obviously a strong relationship between :
1. The real wage and the level of productivity
2. The real output and the level of productivity
3. The available labor and the level of productivity
If these relations do exist, it will not be possible to drawn a labor demand
curve for a determined level of technology with the real wage as abcis and
the real output as ordinate, because the level of technology is similar to
level of productivity so that for a given level of technology there is
existing only 1 value of the real wage and 1 value of the real output. This
is a point and not a curve.
I think that graphs can be misleading. Drawing a curve is similar to an
exact equation , but that last one does not exist .
Sorry for the poor English.
Robert Vienneau
I don't think your argument is related to my specific criticisms. Your
comments seem analogous to Marshall's treatment of the supply of
goods, which I only know through secondary literature:
"In Appendix H Marshall focuses on the fact that increasing returns
are due to 'extensive improvements in organization, creation of
skills' etc., which bring about changes through time that are not
reversible: economies once created can scarcely be withdrawn. He
also recognizes that irreversibilities violate the assumption,
central to the equilibrium approach, that 'if the normal production
of a commodity increases and afterwards diminishes to its old
amount, the demand and supply price will return to their old
positions' (p. 807). He argues that, if the supply is diminished,
once having been expanded, 'the supply price would not move back
by the course by which it had come', and suggests that a method
of handling irreversibilities would be to show the backward
movement by a separate curve. This treatment means, however, that
there would be no uniquely defined 'supply price' for a given
output...In fact, since along SS there are economies operating
continuously, there would be a separate curve for backward
movement at each point and the price of OM would be indeterminate,
in the sense that it would vary with every change in the *sequence*
of output levels by which it is approached. Or, to put it
differently, with every change in output, the supply curve needs
to be redrawn. Such an ever-shifting supply curve cannot be used
to determine equilibrium price and output, as it is essential for
that purpose that the supply curve should remain stable for
hypothetical movements along it. Here, *given a sequence of output
levels*, we may depict the supply price at each output level in
that sequence, taking into account irreversibilities. But such a
curve would be in the nature of an 'historical curve', and not
the one required by the theory of equilibrium price.
In the same Appendix H, Marshall suggests a way of obtaining a
'true long period normal supply curve' in the case of increasing
returns by treating 'time' as a third dimension (pp. 809-10, n. 2):
We might take a series of curves, of which the first allowed
for economies to be introduced as a result of each increase
in the scale of production during one year, a second curve
doing the same for two years...and so on. Cutting them out of
cardboard and standing them up side by side, we should obtain
a *surface*, of which the three dimensions represented amount,
price, and time respectively. If we had marked on each curve
the price corresponding to that amount for which, so far as
can be foreseen, seems likely to be the normal amount for the
year to which that curve related, then these points would form
a curve on the surface, and that curve would be a fairly true
long period normal supply curve.
There are two points to be noted about this suggestions. First, the
matter dealt with here is not one of irreversibilities but a
different one, namely that 'a suitable time to allow for the
introduction of economies appertaining to one increase in the scale
of production is not long enough for another and larger increase -
which is a matter of the time lags in reaping economies of scale.
However, the *long-period* supply curve is obtained under the
hypothesis that sufficient time is allowed for forces to work out
their full effects. Second, the supply curve is needed to *determine*,
in conjunction with the demand curve, the equilibrium price and
output, whereas what is required here are the foreseeable 'likely'
normal outputs, in order to obtain the supply curve. There are any
number of such curves, each corresponding to a sequence of likely
outputs. Indeed the exercise becomes meaningless for the theory of
equilibrium price when we see that, since the forecasts are forecasts
of equilibrium outputs, they could also be considered as forecasts
of normal quantities demanded; and the curve connecting them could
also be said to represent the long-period normal demand curve. We
are left with only one blade of the well-known pair of scissors.
Marshall, while he was acutely aware of the difficulties posed by
irreversibilities and 'the element of time' in the case of increasing
returns, nevertheless tried to present them only as 'limitations'
which qualified the results. His criticism of Pigou is directed
against Pigou's application of the statical method to the case of
increasing returns without the qualifications that he had himself
laid down. Pigou had thereby cast in a rigid form the results the
results which he himself had put forward in tentative and flexible
forms."
-- Krishna Bharadwaj, "Marshall on Pigou's _Wealth and
Welfare_," originally published in _Economica_, February
1972.
marcel simkens
Robert Vienneau wrote
Marcel,
<I don't think your argument is related to my specific criticisms. Your
comments seem <analogous to Marshall's treatment of the supply of goods,
which I only know <through secondary literature:
Robert,
I have tried to understand your essay “Upward Sloping Labor Demand Curves”,
but I am not an economist and I have not succeeded. I have been very
impressed by the long discussions between You and Chris, a professor of
economics. If 2 persons are spending so much time and energy to that
subject, you must not be surprised by my questions of message 33
Why is the Sloping of the Labor Demand Curve so important and what is the
final goal of proving that the sloping is, Or can be, upward ?
Are graphs of great use for economics ? In The General Theory, Keynes has
used only 1 graph with the footnote that it was suggested by Mr.... Harrod.
With message 35, a reply to message 34 of John J. Weatherby, I have given
more information about the second question:
I have problems with graphs if the equation is not exactly known and if they
are made by assumptions. Economic situations are very complicated and
depending On so many variables that a simple graph can be confusing.
With message 36,Dave was so kind to answer both questions and to ask for
more information about my problems with graphs. The discussion with Dave are
related to graphs and not directly to your essay.