Thanks to Andrew's very explicit working out of the price equations in his
reply to my comments on Alan's essay on Okishio, I think I now understand
better the TSS position and the reason other people have so much trouble
accepting it. I don't think the issue lies in whether or not one assumes
stationarity of prices as it does in the definition of value added, or, to
put it another way, of the link between living labor and value creation.
To begin with, let me confirm Andrew's solutions of the equation he puts
forward as determining price and the path he gets for the profit rate
assuming this price path. (I think there is a typo in one step of Andrew's
analytical solution, which should read P(t) = [100 + 20t]*(0.8)^t, but I
think his final expression for r is correct given the price equation.) The
problem is whether the basic price equation is correct or not.
We are working in a 1-output circulating capital model where a units of
output available at the beginning of the period produce 1 unit of output at
the end of the period. The a units can include the workers' consumption
without loss of generality. Taking the sequence of prices for the moment as
given, the sales revenue from producing one unit of output is p(t), and the
cost of the inputs is p(t-1)a. The difference is p(t) - ap(t-1). Andrew
proposes to determine prices according to the convention that an hour of
living labor adds $1 to the value of the product by equation p(t) - ap(t)
to the living labor required to produce one unit of output, let's call it
l(t). (In the example worked out, l(t) = 20(.8)^t.)
We could write p(t) - ap(t) = p(t) - ap(t) + a(p(t)-p(t-1)). That is, the
difference between the sales price and the cost of inputs consists of two
components, the second of which represents the change in value of the
inventory of inputs through the production period. The question, which I
think is at the root of the disagreements about the FRP part of the TSS
claims, is whether this change in value due to price changes ought to be
imputed to the expenditure of living labor or not. Clearly Andrew wants to
attribute it to the living labor, since that is how he arrives at the price
equation p(t) - ap(t) = l(t). I don't agree with this. I would argue that
p(t) - ap(t) represents the value added by living labor to the output, and
that a(p(t)-p(t-1)) is a purely financial effect induced by the change in
prices. (In conventional business and national income accounting,
incidentally, this is exactly the distinction made: p(t)(1-a) is the
definition of the value added, and a(p(t)-p(t-1)) is called the "inventory
valuation adjustment", or IVA.)
Thus I would interpret the principle that the value added is imputable to
the expenditure of living labor as leading to the equation p(t)(1-a) =
l(t). In the example Andrew worked out, this leads to a constant fall in
prices at the rate of 25% a period, and to a constant money profit rate, as
I presumed in my initial comments on Alan.
We now have the advantage of being able to focus on the real point of
dispute, which is the definition of value added. This issue arises only
when prices are changing, which clarifies the importance of
non-stationarity to the TSS position. But it seems to me that the nub of
the issue is, in accounting terms, whether or not one includes the IVA in
value added, or in terms of the labor theory of value, whether or not one
attributes the change in the money value of inventories over the production
period to the expenditure of living labor.
I hope that Alan will accept my claim that excluding the IVA from value
added is not the same as assuming input prices are equal to output prices,
nor does it violate Alan's principle that the money paid for the inputs
ought to equal the money received for the inputs. In the equations we
clearly distinguish p(t) from p(t-1), so input prices are not being assumed
to be equal to output prices. The equations clearly reflect the fact that
the money paid by the capitalist for the inputs is p(t-1)a, the same as the
money received by the producers. The issue is whether or not in applying
the principle that it is living labor that adds value to the product, we
should count the IVA as part of the value added or not.
I'm suspect that this question will continue to be the subject of vigorous
debate. Let me say that at this point, having realized that this is the
core issue, I still lean toward the definition of value added that excludes
the revaluation of inventory over the production period. The reason is that
this change in money valuation has nothing to do with the expenditure of
labor in the actual production process: the inventories would have risen or
fallen in value even if they had simply been stored over the period, and
had never entered production at all. The value gained or lost through pure
price change is, in my view, a change in the value imputed to stocks of
existing commodities, not a flow of value attributable to the expenditure
of labor, analogous to the change in bond prices with the interest rate, or
a rise in land prices due to speculation.
I hope that this at least clarifies and focuses the questions at issue. Let
me also repeat my strong agreement with basic principle that the value
added ought to be attributed to the total living labor expended in
production.
Duncan
Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
(212)-854-3790
fax: (212)-854-8947
e-mail: dkf2@columbia.edu