# [OPE-L:960] Aggregating values and prices

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Mon, 5 Feb 1996 21:53:30 -0800

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In an earlier response to Alan, I questioned his assertion that
commodity exchange "conserved" an equality of aggregate commodity
prices and aggregate values, arguing that any such conclusion is
either invalid in general or the result of a definitional tautology.
Here I'd like to illustrate and extend the argument by considering
(1) a case in which the equality of aggregates is not in general guaranteed,
except by assumption, and (2) a case of such a tautological argument. I argue
that any conclusion based on the latter is incapable of supporting
the sort of *substantive* argument Alan evidently intends for it in our
"'Chapter 5" discussion.

First, consider the relevant aggregates based on the definition of
value drawn from the Kliman-Freeman-McGlone et al. "temporal single
system" approach. Under that definition the aggregate value of goods
exchanged in some period (t+1) is given by

V = (p(t)*A(t) + L(t+1))*x(t+1), where p(t) is a vector of input
commodity prices, A(t) is a matrix of "constant capital" input-output
coefficients, L(t+1) is a vector of direct labor coefficients, and
x(t + 1) is a vector of commodities exchanged in period t+1. (*)
indicates vector multiplication.

Aggregate price, on the other hand, is given by

P = p(t+1)*x(t+1).

Putting aside for the moment that L(), insofar as the entity is
commonly understood, is measured in units of labor time, and p( ),
insofar as the entity is commonly understood, is measured in money
units, there is nothing about the logic of exchange which guarantees
P=V. Indeed, as argued in an earlier post, for given V, one can vary
current-period p by changing some parameter affecting demand
conditions, causing arbitrary changes in P.

Since L() and p(), as commonly understood, are measured in different
units, it seems to me one must transform one or the other (but not both
simultaneously) to avoid an equation adding apples and oranges. But
no such transformation guarantees P=V, for similar reasons, unless

(2) Here's a case in which the aggregates are equated
tautologically. Define commodity values in some manner independent
of current-period prices, say in terms of the traditional notion of
embodied labor values. Denote the aggregate of values by V. Define
the aggregate of prices P as above. Now define the "money expression
of value" by multiplying individual values v(i) by the factor P/V.
This practice will of course guarantee equality of the aggregates of
price and [the money expression of] value---by definition. The
monetary expression of value sums to total prices because we've
defined it that way, not due to any particular logic of commodity
exchange.

Since this equation of aggregates results by definition rather than
from any special logic of commodity exchange, it seems to me necessarily
inadequate to provide a basis for criticizing my take on Marx's
*substantive* conclusion in Ch. 5, concerning the isomorphism of
surplus value appropriation to a case of price-value equivalence.

In solidarity, Gil Skillman