[OPE-L:3531] Non-constant returns to scale and the LTV

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Thu Jun 22 2000 - 17:44:01 EDT

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I'd like to take a small break from the Ch. 5/"Marx's starting point"
discussion and elaborate on an issue that arose in an earlier exchange with
Rakesh (posts 3370 and 3380). In response to this clause in a passage
written by Rakesh,

>Now barring neo Ricardianism due to its untenable assumption
>of constant returns to scale (Patrick, thanks for the Freeman and Mandel
>reference, the Jesus Albarracin essay p.190-91 seems decisive....)

I responded that dropping the assumption of constant returns created at
least as many difficulties for the Marxian labor theory of value as it does
for the neo-Ricardian theory of prices of production. As Rakesh rightly
noted, my argument on this point was somewhat dense and hard to follow.
What I'd like to do here is state plainly the consequences of non-constant
returns for the labor theory of value: in a nutshell, the LTV is
invalidated once you abandon constant returns (I think it's invalid in any
case, but this drives more nails into the coffin). More specifically,
claims of the following sort, all made by Marx, are invalidated or rendered
severely problematic given one or the other bases for departing from
constant returns, *even if* we assume otherwise competitive exchange
conditions (page numbers refer to relevant passages in the Penguin edition
of Capital, unless otherwise noted):

1) The notion that socially necessary labor time is based on *average*, as
opposed to *marginal* production conditions in a given labor process (I:
129), and/or the notion that exchange on the basis of price-value
equivalence (as Marx measures "values") represents the "pure case" of
commodity exchange in some meaningful sense (problematic in any case, but
completely trashed in the absence of constant returns).+

2) The notion that commodity prices are in some sense "regulated" by their
corresponding labor values (I: 156, 168, 196, 269; III: 277, 280-81, 289;
Grundrisse, pp 136-38 in Penguin ed.) and the companion notion that labor
values somehow determine the exchange value that remains when supply and
demand are equated and thus "cancel each other out" (I: 678; III: 291, 478).

3) The stipulation, central to Marx's V. III discussion of the
transformation problem, that capitalist competition tends to equate the
*average* (as opposed to the *marginal*) rate of return across production
sectors (III: 289). Combined with point 1, this has the effect of further
disconnecting prices from values. In particular, *no* expectation can be
drawn under these circumstances about the empirical connection between
commodity prices and values, no matter what the average compositions of
capital across sectors. For example, a finding that prices and values are
virtually proportionate offers no information whatsoever about any
*substantive* connection between the two.

These points are established in the following four steps.

I) First, let's fix some terms. The issue in question concerns the
presence or absence of constant returns at the *industry* or *sectoral*
level, that is, how the average and marginal conditions of production vary
with the total level of production within a given industry or production
sector. Neither Marxian nor neoRicardian theory is premised on returns to
scale within given enterprises, and there is no necessary connection either
way between enterprise- and industry-level returns to scale.

To keep things simple, let's assume competitive, i.e. price-taking,
behavior by firms. To do otherwise introduces an additional wedge between
prices and values due to monopoly pricing. As an almost-corollary, I'll
focus just on the case of *decreasing* returns to industrial scale (DRIS),
to avoid the case of "natural monopoly"; however, many of the same claims
can be made in the case of competitive behavior on the basis of increasing
returns to industrial scale (IRIS).

There are two instances of DRIS consistent with competitive market behavior
by sellers: first, the case of "pure competition" and second, the case of
external diseconomies of industrial scale, or external diseconomies for
short. In the case of pure competition, production conditions vary across
firms in a given sector due to absolute scarcities in the productivity of
given inputs, be these "land", "labor" or "capital". It doesn't matter for
present purposes whether these scarcities are the result of natural
differences (there's only one Michael Jordan, Tiger Woods or Hank Aaron),
property rights on scarce natural assets (one firm owns exclusive rights to
the most productive titanium mine) or government-enforced patents on
process innovations. Note that all of these forms of scarcity are
consistent with price-taking behavior; this is the "right-angled input
supply curve" case I've discussed earlier.

The second case of DRIS under competitive conditions arises in the presence
of external diseconomies. Here, the more firms in an industry, the higher
are the average costs of production (i.e., the less productive are workers
under average and marginal production conditions). An example of this is
when more firms drilling for oil in a given area reduces oil pressure, and
thus the productivity of labor in *every* firm is reduced.
The common implication of these two bases for DRIS is an upward-sloping
*industry* supply curve for the relevant commodities. The key difference
between the two cases is that in the case of external diseconomies, all
firms can have the same production conditions, and thus it's possible for
all firms to earn the same level of profit, e.g. the "normal" rate of
profit obtaining under free entry and exit. In the case of pure
competition, in contrast, only the "marginal" firms--those which just
survive at going commodity prices--earn the "normal" rate of profit; all
*inframarginal firms--those with lower production costs, for any of the
reasons given above--earn higher rates of profit, *if* the firm owns the
scarce input in question. (Thus, either the firm owns the patent, or owns
the mine, or the Michael Jordan-equivalent is also the firm owner).

II) Suppose that pure competition is the basis for DRIS. Then it at least
problematic to insist, as Marx does in Ch. 1 of V. I, that socially
necessary labor time is based on the *average* conditions of production,
rather than the *marginal* conditions of production. To see one
illustration of this, suppose that we measure labor values as Marx says in
terms of *average* production conditions, and consider the so-called "pure"
case of commodity exchange (not to be confused with the neoclassical case
of "pure"--as opposed to "perfect"--competition) in which all commodities
exchange at their values.

Now if all commodities exchange on the basis of the *average* rather than
*marginal* conditions of production, as Marx insists, and DRIS is based on
conditions of pure competition, then the relatively high-cost firms in the
industry must be driven out of business, since the price they receive,
based on *average* industry production conditions, is necessarily less than
their unit cost, based on *marginal* conditions. Once the highest cost
firms are driven out, the average then adjusts, and the commodity price
then necessarily falls below the unit cost of the *next* highest cost firm,
and so on and so on until all firms are eliminated but those with the
lowest unit cost. If competitive conditions are thereby eliminated (e.g.,
there is only one such firm), the result is necessarily a monopoly; but in
any case, the prediction based on Marx's definition of value and his "pure"
case of commodity exchange is that sectoral conditions of "pure"
competition *must necessarily destroy themselves.*

But this prediction is nonsensical, as even a cursory understanding of the
model of pure competition (or of economic common sense) demonstrates.
There is no *economic* contradiction in positing an industry of
price-taking firms whose production conditions vary. If there is otherwise
free entry and exit, firms will enter the industry just until the profit of
the *marginal* firm falls to the "normal" level permitting its continued
existence in the industry; all lower-cost firms will earn rates of return
higher than this "normal" level.

Thus, since Marx's proposed measure of labor value yields an absurdity when
applied to his so called "pure" case of commodity exchange, either his
measure or the "purity" of his base case (or both) is rendered
fundamentally problematic.

It is also straightforward to show, based on related reasoning, that
virtually all of Marx's analysis in V. III, Ch. 10, where he addresses
conditions of pure competition, is fallacious. I won't go through that
demonstration here.

III) It's much easier to see the basis of point (2) above: 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).

Correspondingly, there is no single point at which supply and demand
"equate and thus cancel out", since the industry supply curve is
upward-sloping. Each commodity has an infinity of possible labor values,
depending on where supply and demand equate.

IV) With respect to point (3): If DRIS is derived from conditions of pure
competition, free entry and exit across sectors can only be expected to
equate rates of return earned by *marginal* firms; as noted above, all
*inframarginal* firms earn higher rates of return. Thus nothing whatsoever
can be stated about the *average* rates of return across sectors. This
drives an additional wedge between the determination of commodity prices
and the determination of labor values, implying no consistent relationship
whatsoever between the two regimes. One consequences is that empirical
estimates purporting to show a close correspondence between commodity
prices and their respective values have absolutely no substantive
implications for the latter's economic significance.

Things get even messier in the case of IRIS, to the extent this corresponds
to conditions of "natural monopoly" But even putting aside monopoly
considerations, point (III) above holds under IRIS: there is no meaningful
sense in which commodity prices are "regulated" by their corresponding
labor values; rather, as in the case of DRIS, both prices and values are
dependent on the level of demand for the commodity, which is necessarily
determined by factors other than the commodity's price (or labor value).

For reasons presented in our earlier Chapter 1 discussion, I think that
Marx's labor theory of value, understood as the notion that there is some
systematic or economically meaningful connection between commodity prices
and their respective labor values, is problematic in any case. But as
indicated above, dropping the condition of *universal* constant returns to
industrial scale (CRIS) really drives the nails into the LTV's coffin.

(It shouldn't be necessary, but I'll reiterate for the sake of clarity that
accepting Marx's labor theory of exploitation does not entail accepting his
labor theory of value as interpreted above.)


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