John's main point in this post is that the determination prices of
production is "A PROCESS THAT TAKES PLACE IN TIME." John, would you
please explain further just exactly what your mean by this?
1. Do you mean that Marx's determination of prices of production somehow
takes place OVER MULTIPLE PERIODS of production (as in Andrew and Ted's
interpretation)? John quotes two passages from Chapter 10 which seem to
suggest this interpretation. These passages are about the actual process
of equalization of profit rates, which takes place over successive
periods, as capital migrates from industries with lower than average rates
of profit to industries with higher than average rates of profit.
However, the actual equalization of profit rates (or the gravitation of
market prices to prices of production) is not the same thing as the
theoretical determination of prices of production. Prices of production
are theoretically determined independently of the actual process of
equalization of profit rates. Even though the actual process of
equalization takes place over multiple periods, this does not imply that
prices of production are determined in some way over multiples periods
(e.g. as in Andrew and Ted's interpretation in which new prices of
production are determined in every period for many successive periods).
2. Indeed, a review of Part 2 shows that Marx's explanation of the
determination of prices of production is presented entirely in terms of A
SINGLE PERIOD OF PRODUCTION. All of Marx's famous tables are for a single
period. All of Marx's other numerical examples in Part 2 are also for a
single period. Chapter 9 begins with the words: "AT ANY ONE GIVEN TIME
..." A few pages later (p. 258), a summary of Marx's theory of prices of
production ends with "DURING A GIVEN PERIOD OF TIME." The length of the
period of time is not always specified, but the most common period
mentioned is a year. Sometimes, Marx's examples are in terms of the
"working week" (pp. 245-46) or the "working day" (p. 248). But they are
always in terms of a single period, never for multiple, successive
periods. A single price of production or set of prices of production is
determined for this single period, not many sets of prices of production
for multiple successive periods.
According to Marx's theory, prices of production in any given period are
determined by the following equation (for each branch of production) (see
p. 265):
(1) ppd = c + v + r(c + v)
In this theory, the variables on the right-hand-side of this equation
(constant capital, variable capital, and the rate of profit) - the inputs
for this period of production - are assumed to be known. Prices of
production for this period are then determined by this equation. There
are no time subscripts in this equation because none are needed for an
analysis of a single time period.
2. Marx's discussions of causes of CHANGES of prices of production in
Part 2 are usually not put in any specific time frame. Instead, the
discussion is about the general nature of the relation between the
independent and the dependent variables in the above equation for prices
of production. The question is: what causes prices of production, the
dependent variable in equation (1), to change? It follows from the
equation (1) that, if one or more of the independent variables on the RHS
of this equation changes, then the prices of production will also change.
Hence there are three possible proximate causes of changes in prices of
production: a change of constant capital, of variable capital, or the rate
of profit. Marx argued further that all three of these possible proximate
causes are one way or another the result of changes in the productivy of
labor or the real wage. Therefore, changes in productivity or the real
wage are the ultimate causes of changes of changes of prices of
production. As we have seen, prices of production change if and only if
productivity or the real wage changes.
Marx did not say anything in these discussions of causes of changes of
prices of production about the LENGTH OF TIME required for prices of
production to change or for changes of productivity or the real wage to
bring about changes in the prices of production. The analysis is not
presented in terms of specific time periods. Rather, the discussion is
about the general nature of the relation between productivity and the real
wage, on the one hand, and prices of production, on the other hand. The
main point, again, is that prices of production change if and only if
productivity or the real wage changes.
In Chapter 11, Marx analyzed the effect of a change of wages on prices of
production (Ricardo's question). This analysis is conducted entirely in
terms of a SINGLE PERIOD of production, as in Marx's general theory of
prices of production discussed above. Marx assumed three capitals
(average composition of capital, higher than average, and lower than
average) and one period of production ("annual" is mentioned several
times). Wages are assumed to increase by 25%. This increase of wages
changes all the variables on the RHS of equation (1). As a result, new
prices of production for this period are determined for the two
non-average capitals (the price of production for the average capital
remains the same). Marx compared the new set of prices of production with
the old set of prices of production. The most interesting conclusion is
that the price of production for capitals of higher than average
composition falls, rather than rises as in Smith's cost-of-production
theory of value.
Nothing is said here about HOW LONG it takes for prices of production to
change or possible problems or obstacles in this process of change. The
method of analysis is similar to what today we would call "comparative
statics." One of the independent variables is changed and the effects on
the dependent variable are analyzed. I know comparative statics is a
dirty word among TSSers, but it seems to me that this is essentially what
Marx did Chapter 11. Are there any other interpretation of Chapter 11?
I should note that Marx's overall logical method is much much richer than
comparative statics. But when he discussed the possible causes of changes
of prices of production, he conducted essentially a simple type of
comparative static analysis.
It should also be noted that Marx's main objective in Part 2 was NOT to
derive a time series for prices of production over multiple successive
periods. Instead, Marx's objective was to demonstrate that all possible
causes of changes of productivity ultimately boil down to a change in
productivity, i.e. a change in the value of commodities. In other words,
prices of production do not contradict the labor theory of value, but
rather can be explained on the basis of the labor theory of value
(something that Smith and Ricardo and all the other economic writers
before Marx were unable to do).
For this objective, a simple kind of comparative static analysis will
suffice. One does not need to derive a time series of prices of
production in order to explain that all possible causes of changes of
prices of production boil down to a change in the values of commodities.
I would think that the derivation of a time series of prices of production
was the farthest thing from Marx's mind when he was writing Part 2.
Especially since equal rates of profit is only one aspect of the
distribution of surplus-value and there was much more for Marx to write
(indeed the rest of Volume 3) about the other forms of the distribution of
surplus-value (merchant profit, interest, and rent).
3. In any case, there is nothing in all of Marx's discussions of changes
of prices of production like John's interpretation, according to which a
one-time change of productivity results in a SEQUENCE of many changes of
prices of production in many later periods, even though productivity and
the real wage remain constant in these later periods. In Marx's
discussions, a one-time change of productivity results in a one-time
change of price(s) of production. There is a one-to-one relationship
between productivity and prices of production. If time is specified at
all, it is a single time period.
Therefore, John's attempted rescue of Andrew and Ted's interpretation must
be judged a failure. According to Andrew and Ted's interpretation, prices
of production CHANGE EVERY PERIOD, even though productivity and the real
wage remain constant, which seems clearly and explicitly to be
contradicted by Marx's texts. John's rescue attempt is to assume that a
one-time change of productivity results, not in a one-time change of
prices of production, but rather in a SEQUENCE of many different prices of
production in many successive periods into the future. With this
assumption, it could be argued that productivity changed BEFORE PERIOD 1
in Andrew and Ted's numerical examples, and that this prior change of
productivity sets in motion the continuing every-period changes of prices
of production that we observe in Andrew and Ted's examples, even though
productivity and the real wage remain constant in these later periods.
However, we have seen above that there is NOTHING in Marx's texts to
support John's interpretation of a one-time productivity change resulting
in many successive changes in prices of production.. If I have missed
something in Marx's texts, I am sure John will let me know.
I look forward to further discussion.
Fred