[OPE-L:3557] Re: Re: Non-constant returns to scale and the LTV

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Mon Jul 03 2000 - 20:37:50 EDT

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To the following passage from my post 3531,

>> since DRIS
>>implies an upward-sloping industry supply curve, both a commodity's market
>>price and its labor value are dependent on the level of demand, which is a
>>function of the commodity's *use value*: The higher is market demand, the
>>higher are average and marginal costs of production, the lower is the
>>average and marginal productivity of labor, and thus the higher are both
>>market prices and labor values. In no sense can it be said that commodity
>>prices are "regulated" by values, since both prices and values are
>>determined by the level of demand (not to be confused with the level of
>>*quantity demanded*, which is a function of the price. The level of
>>demand, i.e. the "demand curve", is determined by factors other than a
>>commodity's price).

Rakesh responds:

>To see how Marx, UNLIKE RICARDO, builds DEMAND into his concept of
>value,let's turn to chap 10 of vol 3. Your criticism applies to Ricardo's
>theory of value, not Marx's.

Since my original point is that sector-level non-constant returns pose at
least as much of a problem for Marx as for Ricardo, it should not be
surprising that criticisms applied to Marx *also* apply to Ricardo. But
it's completely wrong to suggest that my critique doesn't apply to Marx,
and there is perhaps no better illustration of the validity of my critique
than Marx's analysis in Chap 10 of Vol. 3, which is demonstrably a logical
mishmash virtually from beginning to end. Suffice it to say in overview
that no *valid* claim of Marx's contradicts the conclusions I established
in post 3531. In particular, the point that DRIS implies a rising industry
supply curve still stands, and in light of this fact many if not most of
Marx's claims are clearly false, as I'll show below.

Rakesh writes:

>Marx often conducts the analysis in terms of market values, instead of
>production prices. The former is applicable to independent commodity
>production (the historical reality of which I shall sidestep), the latter
>to advanced capitalist production.

That's not exactly true, since Marx asserts conditions in Ch. 10 under
which capitalist prices are "regulated" by market values; indeed the whole
point of the chapter is to show how this "regulation" takes place under
conditions of "pure" capitalist competition--about which more below.

>Marx defines market value: "Market value is to be viewed on the on the one
>hand as the average value of the commodities produced in a particular
>sphere, and on the other hand as the individual value of commodities
>produced under average conditions in the sphere in question, and forming
>the great mass of commodities." p.279 (penguin)

Although the problems with Marx's analysis start earlier in the chapter, on
p. 273 to be exact, this is not a bad place to start to note the
fundamental flaws in Marx's argument. I note that under the conditions of
pure competition allowed by Marx in this chapter, that is, market
conditions in which "the same price is paid for all commodities of the same
kind, even if these are produced under very different individual conditions
and may therefore have very different cost prices" [pp 300-301], the two
clauses in the passage cited by Rakesh are demonstrably *not equivalent*,
contrary to Marx's representation.

To see this, let (Ai, Li) respectively represent the real constant and
variable capital input requirements per unit of output for firm i in an
industry characterized by pure competition, noting that in this world these
requirements vary across firms. Now let Vi represent unit labor values of
the commodity for individual firms, and let (Am, Lm)
represent respectively the arithmetic *averages* of unit constant capital
and variable capital requirements for all firms operating in the market;
suppose there are N such firms.

The passage cited by Rakesh asserts that the sum of Vi's divided by N is
identical to the labor value under average production conditions, that is,
Lm/(1-Am). This is demonstrably *not* the case, absent a severe (and
unstated) restriction such as requiring Ai = Am for all i.

>It is easy to think of producers in terms of technical relations arrayed
>along a bell curve, so that the average line would dissect the gaussian
>distribution. The great mass of producers would be located near this line.
>However this is not necessary. It could be that the curve is skewed right
>or left, so that the average line would not dissect the curve perfectly.
>This is in part what Marx is examining this chapter, reminding us that he
>was quite aware of the idea of normal distribution (this of course goes
>back to his early study of suicide).

What he is evidently not quite aware of is that his claims are equally
invalid no matter what he assumes about the distribution of technical
conditions, so long as they vary along firms actually persisting in the
market under purely competitive conditions. Part of his confusion lies in
the failure consistently to distinguish what mainstream economists refer to
as "change in demand" and "change in quantity demanded" (or, in parallel
fashion, "change in supply" and change in quantity supplied"), as indicated
for example in the next passage cited by Rakesh; another confusion comes
from defining market values in *average* rather than *marginal* terms, as
suggested by the passage Rakesh cites above.

>Now note that Marx distinguishes between weak and strong demand in terms of
>the ability of the latter TO ENTER INTO THE DETERMINATION OF market VALUE.
>Strong demand shifts are characterized by absence of negative feedback.

>"If the demand is so strong, however, that it does not contract when price
>is determined by the value of commodities produced in the worst conditions,
>then it is these that determine the market value.

Thus, Marx's notion of "strong demand" corresponds to what is called
"price-inelastic demand" in mainstream terms. But his distinction is the
wrong one: under conditions of purely competitive equilibrium (i.e. when
supply= demand), what Marx calls market value is *always* determined by
"the worst [production] conditions", i.e. those found in the marginal firm,
the firm that just succeeds in earning the "normal" rate of return at the
going price. **This is true whether demand is "strong" in Marx's sense
[i.e price-inelastic] or not, contrary to Marx's claim.**

> This is possible only if
>demand rise above the usual level, or supply falls below this.

This does not follow. Whether or not demand is "strong", i.e.
price-inelastic, has no necessary connection to whether demand (as opposed
to quantity demanded) "rises", whether or not above the "usual" level,
whatever that means; still less does it have anything to do with shifts in

> Finally if
>the mass of commodities produced is too great to find a complete outlet at
>the MEAN market value, market value is determined by the commodities
>produced under the best conditions.

This is also not generally true. "The best conditions" are those that
obtain for the lowest-cost firm; excess supply does not generically imply
that prices will fall to the level of average costs for just this firm;
they would just be lower than the price that sustains the "marginal firm"
identified above.

By the way, another aspect of the problem with Marx's Ch. 10 analysis is
the extent to which he invokes non-equilibrium conditions such as the
above; best to get the equilibrium case straight first, and then consider
departures from that case.

>These commodities may be sold
>completely or approximately at their individual value, for instance, in
>which connection it may happen that the commodities produced under the
>worst conditions fail even to realize their cost prices, while those
>produced under average conditions realize only part of the surplus value
>they contain. What we have said here of market value holds also for the
>price of production, as soon as this takes the place of market value.
>(p.280-81; my emphasis)

>So Marx does not think it is possible to resolve the debate between Ricardo
>and Storch over whether market value or price of production is governed by
>the commodities produced under the least or most favorable conditions
>unless one considers the possibility of STRONG shifts in demand. A strong
>positive shift in demand would skew the production curve to the left and a
>strong negative one to the right. And market VALUE would thereby be

Yes, just so. And since changes in demand induce *both* changes in market
value and market price simultaneously, it cannot coherently be asserted, as
Marx does later on in the page from the passage cited by Rakesh above, that
the law of value "governs the movement" of prices. It is rather the case
that changes in demand--what mainstream economists refer to as shifts in
the entire demand schedule--lead to changes in both values and prices.

>Marx also argues that both failed to see how in the absence of such strong
>demand shifts market value would tend be determined by the bulk of
>producers in a normal distribution.

But that statement is not quite true. Market value is determined by the
marginal, i.e. "worst" production conditions under purely competitive
equilibrium; you need something stronger than a normal distribution to make
Marx's statement even *approximately* true; specifically, a near-degenerate
distribution under which the vast majority of producers produce under
average conditions. Then, and only then, the bulk of sheer numbers would
ensure that market value "tends to be" determined by average production

>Ultimately it all depends on how you define value or socially necessary
>labor time.

I agree; I'm going solely by Marx's definitions of market and individual
value in Ch. 10, as informed by his original definition in Ch. 1 of V. I.

For example, Patrick Murray quotes Carchedi: "The basic
>difference between the Marxian and the neo Ricardian notion of value is
>that that for the latter value is embodied labor and is determined by the
>technical relations of production, independent of demand." Quoted in
>Moseley, ed. Marx's Method in Capital, p. 60. In Frontiers of Poltiical
>Economy Carchedi of course pays careful attention to Marx's concept of a
>strong demand shift.
>Please also see Murray's emendation of the point on p. 50.

This doesn't really affect anything at all about my critique, since it's
based on Marx's, not Ricardo's, notion of value.

>You have isolated a problem for the Ricardian theory of labor value, not

Clearly not, as shown above and further below.

>Again, building demand into the very concept of value does not
>commit one to a subjective theory of value.

But if it doesn't, it's totally confused, as suggested by the foregoing and
buttressed by arguments to follow.

>I must ask you wherein do you think the differences lie between Ricardo's
>and Marx's labor theory of value.

What say we save that for another post. Right now I'm simply concerned
with the consequences of non-constant returns for *Marx's* labor theory of
value. As indicated in my previous post, it is rendered fundamentally
problematic by this condition. Marx's arguments in Ch. 10 do not reverse
this judgment; quite the contrary. See further details below.

>It's important to get this straight to
>ensure we do not saddle the latter with problems in the former. By the way,
>does John Roemer ever lay out what he takes Marx's critique of Ricardo to

Again, these are points for another post. My concern is the problems
specific to Marx's theory of value.

Now, to return to Marx's analysis in Ch. 10. As I mentioned above, the
problem starts earlier than p. 279. Back on the first page of Ch. 10, p.
273, Marx states that the [average] rate of profit is equalized across
spheres of production. But as I established in point 3 of my previous
post, this is not generally true under the conditions of pure competition
introduced by Marx in this chapter; capitalist competition will rather
equate *marginal* rates of return, since *inframarginal* firms can earn
arbitrarily higher rates of profit without competitive interference.

Similarly, on p. 277 Marx asserts that commodity prices fall whenever
corresponding values fall and rise whenever the latter rise. But since
values are defined by Marx in terms of *average* rather than *marginal*
production conditions, this is demonstrably not generally the case under
conditions of pure competition. Suppose an industry in purely competitive
equilibrium, such that the price is determined by the marginal firm (i.e.
that or those with the "worst" production conditions consistent with
earning a normal rate of profit). Then if the production conditions of the
*inframarginal* firms change (without making them "marginal"), the market
price will remain the same, even though market values (based on *average*
production conditions in the industry) change. So Marx's statement is false
in general.

For similar reasons, Marx's statement on p. 279 that "Only in extraordinary
situations do commodities produced under the worst conditions, or
alternatively the most advantageous ones, govern the market value" is not
accurate. Under purely competitive equilibrium conditions (that just
simply means supply= demand given that production conditions vary within
the industry), market value is *generally* governed by the worst production
conditions. It is *never* governed by the "best" conditions in
equilibrium, and even the latter are not generally relevant even if there
is excess supply.

The paragraph at the bottom of p. 279 is based on an utter confusion
between what mainstream economists call a "change in quantity demanded"
(movement along a given demand curve, induced by a change in the
commodity's price) and "change in demand" (a shift in the entire demand
curve, induced by changes in tastes, or income, or prices of other
commodities, or a combination of the foregoing; just not a change in
price). Marx writes:

"It is of no assistance to say that the sale of commodities produced under
the worst conditions shows that these are required to meet the demand. If
the price were higher than the mean market value in the case assumed, the
demand would be less."

Confusion. The "worst conditions" sustainable in purely competitive
equilibrium are dictated by the level of the demand *curve*, which is *not*
determined by price. This claim is unaffected by the fact that prices
influence *quantity demanded*. Whether or not Marx avails himself of
neoclassical terminology, he is clearly confusing logical categories in
this claim.

Consequently, it is *not* accurate to state, as Marx does on p. 281, that
"Since it is the total value of the commodities that governs the total
surplus-value... it follows that the law of value regulates the prices of

Marx's claim does not follow. It is rather the case under purely
competitive conditions that the level of demand (not quantity demanded,
note) determines the total value of commodities (by dictating the viable
"worst conditions" of production) and the total surplus value and the
prices of production, simultaneously.

After this, things *really* start getting problematic. A the bottom of p.
281, Marx writes

"Looking at the market price for identical commodities, commodities which
are identical but each produced under circumstances of a character which
varies slightly according to the individual, we may say that if this market
price is to correspond to the market value, and not diverge from it...,
then the pressures that the various sellers extert on one another must be
strong enough to put on the market the quantity of commodities...for which
the society is able to pay the market value."

We may say rather that this conclusion is economically nonsensical. Since
by definition market value is defined in terms of *average* rather than
*marginal* production conditions, it must be the case that if price=value,
the marginal firm or firms (the set of firms producing under the "worst
conditions") must be losing money, and thus eventually leave the industry.
This will change the market value, and therefore the price by Marx's
stipulation, and imply that the *new* marginal firms are next driven out of
the market. This process must continue until only the firms producing
under the "best" conditions remain, even if that means they enjoy
extranormal profits! In other words, according to Marx's analysis, a
purely competitive industry operating under the stated conditions *must*
transform itself into a monopoly or oligopoly. Nonsense.

Beginning on the next page, Marx's confusions between change in quantity
supplied (or demanded) and change in supply (or demand) *really* start to
mess things up. He writes:

" (1)If the market value changes, the conditions at which the whole mass of
commodities can be sold will also change. If the market value falls, the
social need is on average expanded..., and within certain limits the
society can absorb larger quantities of commodities. (2) If the market
value rises, the social need for the commodities contracts and smaller
quantities are absorbed. (3) Thus if supply and demand regulate market
price, or rather the departures of market price from market value, the
market value in turn regulates the relationship between demand and supply,
or the centre around which fluctuations of demand and supply make the
market price oscillate." [p. 282; enumeration of sentences added]

There are two logically distinct reasons why market value might change:
first, supply conditions might change, leading simultaneously to a shift in
the industry supply curve along a given market demand curve (and a
consequent change in price), and second, the entire demand curve might
shift along a given supply curve, leading simultaneously to a change in
market values and a change in market price. Marx's conclusion in sentence
(3) does not follow, it *cannot* follow, because the analysis in sentences
(1) and (2) deals only with the former scenario. It says nothing about the
latter, which completely invalidates the nation that "market value
regulates the relationship between demand in supply", as well as the notion
that there is some "centre" around which market prices oscillate. Given a
non-random shift in demand *the "centre" shifts, and moreover there are as
many potential "centres" as there are points along the upward-sloping
industry supply curve.*

As a consequence, his comment toward the bottom of p. 283 to the effect
that "absolutely nothing can be explained by the relationship of demand
and supply" applies more accurately to the explanatory role of market
values, since under conditions of pure competition these are strictly
dependent, not to say epiphenomenal.

My list of Marx's mistakes in Ch. 10 runs on for another page and a half,
but I think the point is clear: Marx's analysis in Ch. 10 of V. III cannot
be legitimately invoked to defend the labor theory of value against the
problems that necessarily arise once non-constant sectoral returns are
introduced. To the contrary, Marx's analysis in Ch. 10 is indicative of
the fundamental problems his value theory encounters once these conditions
are introduced.


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