Do Factor Markets Exist?
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?
--
Robert Vienneau
r
v
i
e m
n o Whether strength of body or of mind, or wisdom,
@ c or virtue, are always found...in proportion to
d . the power or wealth of a man [is] a question
r e fit perhaps to be discussed by slaves in the
e p hearing of their masters, but highly unbecoming
a a to reasonable and free men in search of the
m c truth.
s -- Rousseau
SUSUPPLY
>This long post presents an example in which higher wages are associated
>with firms choosing to employ more workers per unit output produced.....
Who was that who was complaining about long winded posts?
Patrick
Harold
<swi...@uic.edu> wrote:
>It's really pathetic that Robert is willing to put so much effort into
>his attempt to show that others are ignorant/stupid/wrong, but won't put
>similar effort into actually learning the subject he's criticizing.
>
>I guess it's time I started on this 670!!! line post. (oh, the tedium)
>
>What do you want to bet that Robert will, yet again, make basic errors
>and resort to a Leontieff production function in an attempt to make this
>work?
>
>Robert Vienneau wrote:
[deleted]
I even how much time you must have Shawn. I answered two of Robert's
posts a long time ago, then killfiled him when I realized that he had
no concept of economics.
I really don't think you have to worry about people actually believing
his stuff, any more than they do kenfran.
[deleted]
Regards, Harold
-----
"There is nothing makes a man suspect much, more than to know
little."
---Francis Bacon, Essays, "Of Suspicion" (1597-1625).
Robert Vienneau
> It's really pathetic that Robert is willing to put so much effort into
> his attempt to show that others are ignorant/stupid/wrong, but won't put
> similar effort into actually learning the subject he's criticizing.
[ Silliness deleted. ]
> Robert Vienneau wrote:
> > 1.0 INTRODUCTION
> > This long post presents an example in which higher wages are associated
> > with firms choosing to employ more workers per unit output produced.
> Yeah, right. It didn't work for an economy, despite your having the
> entire CCC to draw material from, and you think it's going to work for a
> firm, for which the theory thereof is much better?
It's curious that Shawn manages to get the logic of the CCC completely
reversed. One of the more amusing aspects of the CCC was when Paul
Samuelson attempted to get his colleague to furnish a proof that the
illustrated, or related behavior, was impossible for the economy as a
whole. The proof was published, but it was mistaken. Samuelson
acknowledge this mistake in a symposium on capital theory in the 60s.
> > The
> > exact numeric values used are obviously unreasonable.
> Then why did you use them? Why didn't you use reasonable values? I'll
> bet your little demonstration didn't work with reasonable values.
It's difficult to work with a numeric example with N goods when N is
at all reasonably large.
I wonder why Shawn disagrees with Paul Samuelson. Of course, he will
never present the hint of a ghost of a valid argument.
> > 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?
[ Irrelevant and inapplicable proof deleted ]
Apparently the Samuelson quote did not give Shawn any ideas about
how many inputs are used in this example. I've explained to him before
the Arrow-Debreu intertemporal definition of a commodity. He's still
clueless.
> > 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.
> You said FIRMS, Robert. Now you're saying 'economy? It looks like it's
> the CCC again (yawn).
It doesn't matter if one is talking about an economy or about a vertically
integrated firm. The firm, of course, is set within an economy.
> > 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
> Did you use the (1,2,3,4...) 5 decimal places to give your argument the
> semblance of credibility? [ Silliness deleted ]
That's to say the data is given to 5 significant digits. 1/5 is exact.
> > 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
> Wow! (1,2,3,4,5,6...) 7! decimal places! Why?
Strangely enough, the data is reported here to 5 significant figures
also. So I'm being consistent. 7/20 is also exact.
Since the data is given to 5 significant digits, final answers must
be also given to, at most, 5 significant digits. Intermediate calculations
should be carried further so as to lose as little significance as
possible.
> > 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.
> Why? What stationary states are observed in reality? Can't corn be
> stored? Can't steel???
Not in this model. Discussing quantity flows in terms of stationary states
simplifies calculations for the amount of labor used per net unit output.
The point of the example works with firms growing at a constant rate of
growth, too.
> (long, dull passage cut where Robert builds his house of cards even
> higher)
Part of the point of this "long, dull passage" is to show how this
example relates to the Samuelson quote and is not addressed by Varian's
proof.
> > 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.
> Where did your prices come from???
The wage is exogeneous in my calculations, although the model can be
extended to make it endogeneous. One tenth thousand of a bushel of
corn is being used as numeraire. The price of steel and the interest
rate are endogeneous. It is left as an exercise to the reader to
determine how to find these two numbers endogeneously.
Notice that prices are only given above to 4 significant digits.
> Did you notice that corn costs only
> $5663.35 to produce?
Shawn is mistaken about costs.
[ Further mistakes deleted. ]
> How about telling you about the not so trivial point that prices are
> ENDOGENOUS in an economy?
> > 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
> Ah, you did examine costs. Of course, you make some incredible mistakes
> in the process. The cost of producing a quantity of steel is simply
> price times quantity summed over all inputs.
Shawn is confused. I had written:
All production processes in this example require a year to complete.
... [P]rocess[es] require ... inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year.
Notice above where I highlight assumptions about when inputs are paid.
In calculating costs and revenues one must translate from spot prices
obtaining at different points of time to spot and future prices all
ruling at one common point in time. The interest rate is used in
such present value calculations. Since Shawn does not calculate interest
charges, he is wrong in the following calculations:
> Or:
>
> 0.033594 * $3347 = $112.44
> 0.13328 * $6013 = $801.47
> 0.1559 * $10,000 = $1559
>
> $112.44 + $801.47 + $1559 = $2472.91 per ton.
>
> $2472.91/ton * 290.3 tons = $717,885.77
> > Revenues for the steel industry using the beta technique
> > = 290.3 x $6013 = 1,746,000
> Well, at least this part's right (sorta). Funny how Robert used seven
> decimal places earlier, but rounds off here. The actual number is:
> $1,745,573.90
Since prices are given to only 4 significant digits, the final
result of this calculation is only valid to 4 significant digits,
which I report.
> > Notice that the costs incurred in the steel industry equal the revenues
> > obtained.
> Or not.
It does if one understands arithmetic and present value calculations
correctly.
[ Silliness deleted. ]
> > Thus, the cost of operating the beta process does not exceed
> > the revenues.
> HEY! Robert didn't make a mistake this sentence!
> > Furthermore, no pure economic profits are obtained by
> > operating the beta process.
>
> Aww, I had hopes there for a minute. Robert, do you even understand the
> difference between economic and accounting profits?
Yes, and I am correct.
> > 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.
> Wanna bet?
[ Shawn repeating his mistakes - deleted. ]
> > I have not yet shown the prices under consideration are
> > equilibrium prices.
> You say that like you could...
Notice that my calculations conform to the definition of equilibrium
I gave above.
[ Shawn repeating his mistakes - deleted. ]
> ( I am sooo tired of this. Robert is truly an ignorant jackass of the
> first order.)
Hmm...
[ More of Shawn's mistakes deleted. ]
> > Accordingly, consider a different set of commodity prices and
> > interest rate for this wage.
> With no depreciation, no population growth, and no time preference, the
> interest rate will be zero. For there to be an interest rate people
> must be reluctant to exchange money now for money in the future.
Since all capital goods are used up in production in this example,
depreciation is irrelevant. I had claimed that the behavior illustrated
by my example can arise if depreciation arises:
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.
Some months ago, I had explained how to extend this example to include
time preference:
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 ) )
Find steady state equilibria for each value of gamma. Note I don't
model the goods-leisure trade-off here. Yet, at different values
of gamma, a higher wage can be associated with more labor being
employed and firms choosing to adopt the more labor-intensive
technique.
Notice that, in keeping with some formulations of neoclassical theory,
one does not need to introduce money to talk about an interest rate here.
(This is actually a hottly discussed point.)
Also notice that this extension will make all prices and the interest
rate endogeneous.
> > 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%.
> Of course reality never fazes Robert...
As Shawn noted, I opened with an appropriate caveat. Shawn never seems
to be fazed by logic.
[ Continued mistakes by Shawn - deleted. ]
> > 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?
> Uhhh, that would be basic accounting.
Shawn, of course, is mistaken.
[ Silliness deleted. ]
Shawn A. Wilson
>
> In article <365B04A...@uic.edu>, "Shawn A. Wilson" <swi...@uic.edu> wrote:
>
> > It's really pathetic that Robert is willing to put so much effort into
> > his attempt to show that others are ignorant/stupid/wrong, but won't put
> > similar effort into actually learning the subject he's criticizing.
Ya know, sometimes I wished 'unsend' worked better. Oh, well. I made a
mistake. I realized it too late and tried to unsend the message (I
thought I had). Figured I'd fix it after I got back from class.
Nobody'll notice. So much for that.
Robert's numbers were correct, he hadn't specified an interest rate, so
I didn't recognize it when it popped up in his equation. Of course, you
all understand that he's still wrong, don't you? He's just wrong for
different reasons.
>
> [ Silliness deleted. ]
>
> > Robert Vienneau wrote:
>
> > > 1.0 INTRODUCTION
>
> > > This long post presents an example in which higher wages are associated
> > > with firms choosing to employ more workers per unit output produced.
>
> > Yeah, right. It didn't work for an economy, despite your having the
> > entire CCC to draw material from, and you think it's going to work for a
> > firm, for which the theory thereof is much better?
>
> It's curious that Shawn manages to get the logic of the CCC completely
> reversed.
Actually, the logic of the CCC was that the discounted dollar cost of
acquisition is the wrong way to measure capital. Apparently, Robert has
never considered the possibility that there are OTHER ways to measure
capital. Fortunately, economists have.
> > > The
> > > exact numeric values used are obviously unreasonable.
>
> > Then why did you use them? Why didn't you use reasonable values? I'll
> > bet your little demonstration didn't work with reasonable values.
>
> It's difficult to work with a numeric example with N goods when N is
> at all reasonably large.
It still doesn't require SEVEN decimal places. The only purpose those
serve is to add an air of verisimilitude to an otherwise empty argument
(oooh, cool balloon reference there).
>
> I wonder why Shawn disagrees with Paul Samuelson. Of course, he will
> never present the hint of a ghost of a valid argument.
Well, I've never actually met Samuelson. I'm arguing with YOU. I've
never been dumb enough to fall for the old 'let's you and him fight'
ploy anyway.
>
> > > 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?
>
> [ Irrelevant and inapplicable proof deleted ]
Funny how YOUR 670 line post was perfectly relevant and inapplicable,
but MY 10 line counter-argument isn't. You couldn't deal with it, could
you? Yet you're so blinded to the possibility that you're WRONG that
you refuse to acknowledge anything that violates your worldview. I
showed you the standard proof that factor demand curves slope DOWN. I
used the one input-one output case because that's what Varian used and
you aren't worth the effort to expand it.
>
> Apparently the Samuelson quote did not give Shawn any ideas about
> how many inputs are used in this example. I've explained to him before
> the Arrow-Debreu intertemporal definition of a commodity. He's still
> clueless.
Hey, I've shown you the incredibly simple proof that factor demand
curves slope down several times now. Funny how you never address it.
If you're right, then the proof is wrong. OK then, show us where.
> > > 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.
>
> > You said FIRMS, Robert. Now you're saying 'economy? It looks like it's
> > the CCC again (yawn).
>
> It doesn't matter if one is talking about an economy or about a vertically
> integrated firm. The firm, of course, is set within an economy.
Only in your little unreality, Robert.
Trivial observation #1: economies in these discussions are usually
considered to be self contained (and nothing in your example indicated
otherwise). Firms, on the other hand, are considered NOT to be self
contined (vertically integrated or not).
> > > 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
>
> > Did you use the (1,2,3,4...) 5 decimal places to give your argument the
> > semblance of credibility? [ Silliness deleted ]
>
> That's to say the data is given to 5 significant digits. 1/5 is exact.
You say that like these figures are the output of some process. WHAT
process? Why that process? It seems that you're hiding assumptions
here to make your argument appear stronger.
>
> > > 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
>
> > Wow! (1,2,3,4,5,6...) 7! decimal places! Why?
>
> Strangely enough, the data is reported here to 5 significant figures
> also. So I'm being consistent. 7/20 is also exact.
WHAT data? Why didn't you report it?
>
> Since the data is given to 5 significant digits, final answers must
> be also given to, at most, 5 significant digits. Intermediate calculations
> should be carried further so as to lose as little significance as
> possible.
Again, WHAT DATA???
> > > The example is constructed by comparing equilibrium prices associated
> > > with stationary states for producing a net output of 1,000 bushels corn.
>
> > Why? What stationary states are observed in reality? Can't corn be
> > stored? Can't steel???
>
> Not in this model.
Then exactly WHAT is it a model of? Certainly not an economy.
Discussing quantity flows in terms of stationary states
> simplifies calculations for the amount of labor used per net unit output.
Funny how the incredibly simple Solow models (and the harder Ramsey,
Sidrauski, and Tobin models) manage to get their results without too
much effort. They also predict ALL factor prices, BTW.
> > (long, dull passage cut where Robert builds his house of cards even
> > higher)
>
> Part of the point of this "long, dull passage" is to show how this
> example relates to the Samuelson quote and is not addressed by Varian's
> proof.
Funny how you never actually address Varian's proof...
Oh, and there are other economists besides Samuelson. Solow and Tobin
even have their own Nobel prizes.
> > > 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.
>
> > Where did your prices come from???
>
> The wage is exogeneous in my calculations, although the model can be
> extended to make it endogeneous.
You claim to have a model of an economy, but wages are exogenous?
That's not a model.
> One tenth thousand of a bushel of
> corn is being used as numeraire. The price of steel and the interest
> rate are endogeneous.
Actually, your interest rate is EXOGENOUS.
It is left as an exercise to the reader to
> determine how to find these two numbers endogeneously.
Meaning that you have no idea. Let me help: they're NOT endogenous.
> Notice above where I highlight assumptions about when inputs are paid.
> In calculating costs and revenues one must translate from spot prices
> obtaining at different points of time to spot and future prices all
> ruling at one common point in time. The interest rate is used in
> such present value calculations. Since Shawn does not calculate interest
> charges, he is wrong in the following calculations:
What can I say, you pulled that interest rate out your ass and caught me
by surprise.
> Since prices are given to only 4 significant digits, the final
> result of this calculation is only valid to 4 significant digits,
> which I report.
And, since they're parameters rather than estimated values, it is
perfectly OK not to round.
> > > Furthermore, no pure economic profits are obtained by
> > > operating the beta process.
> >
> > Aww, I had hopes there for a minute. Robert, do you even understand the
> > difference between economic and accounting profits?
>
> Yes, and I am correct.
Really? Then what are the economic profits? I don't see them anywhere.
> > ( I am sooo tired of this. Robert is truly an ignorant jackass of the
> > first order.)
>
> Hmm...
Which word didn't you understand, ignorant or jackass?
> > With no depreciation, no population growth, and no time preference, the
> > interest rate will be zero. For there to be an interest rate people
> > must be reluctant to exchange money now for money in the future.
>
> Since all capital goods are used up in production in this example,
> depreciation is irrelevant. I had claimed that the behavior illustrated
> by my example can arise if depreciation arises:
It may be zero, but it's never irrelevant.
> Some months ago, I had explained how to extend this example to include
> time preference:
>
> Supplement my example with intertemporal utility-maximization.
Robert, you claimed that your example was sufficient. It's perfectly
transparent that you've concealed many parts of it from scrutiny. This
can only indicate that they don't actually hold up to scrutiny.
> Notice that, in keeping with some formulations of neoclassical theory,
> one does not need to introduce money to talk about an interest rate here.
> (This is actually a hottly discussed point.)
By who? Economists have many models with interest but without money.
> Also notice that this extension will make all prices and the interest
> rate endogeneous.
Notice further that you don't dare actually exposing your claim to
scrutiny.
Robert Vienneau
<swi...@uic.edu> wrote:
> Robert's numbers were correct, he hadn't specified an interest rate, so
> I didn't recognize it when it popped up in his equation. Of course, you
> all understand that he's still wrong, don't you? He's just wrong for
> different reasons.
It sounds like Shawn is about to present an argument. Let's see what
he has.
[ Non-substantive remarks deleted ]
Strange. There's nothing left.
SUSUPPLY
>It sounds like Shawn is about to present an argument. Let's see what
>he has.
>
>[ Non-substantive remarks deleted ]
>
>Strange. There's nothing left.
>
>
I like it, Robert. Has a lot of advantages for the beleaguered reader. No
jargon, no nearly incomprehensible notation. No denials of things actually
written.
And it conludes just where you always do. Let's have more just like it.
Patrick
PS Don't forget to send me your credit card number. I'd like to have the $100
for Thanksgiving dinner--where I'll be thanking Bill Vogt, Chris Auld, Shawn,
Kelly... for all the entertainment they've provided me these many months.
Shawn A. Wilson
>
> In article <365BB99A...@uic.edu>, "Shawn A. Wilson"
> <swi...@uic.edu> wrote:
>
> > Robert's numbers were correct, he hadn't specified an interest rate, so
> > I didn't recognize it when it popped up in his equation. Of course, you
> > all understand that he's still wrong, don't you? He's just wrong for
> > different reasons.
>
> he has.
>
> [ Non-substantive remarks deleted ]
>
> Strange. There's nothing left.
That's 'cause you deleted it, Robert.