Thanks very much to Andrew for his detailed response to my (2193) in (2256)
and (2259). I will also respond in two parts. This post is a response to
Andrew's Part 1 in (2256).
Andrew's argument in (2256) consists two main points: (1) what looks like a
case of pure technological change in luxury goods industries (Department 3)
also includes technological change in Departments 1 and 2; and (2) my
interpretation of the rate of profit, which is derived from aggregate
magnitudes prior to prices of production and is dependent in part on the
technical conditions in Dept. 3, is in fact equal to the Sraffian
interpretation of the rate of profit, which is determined simultaneously
with prices of production and is independent of the technical conditions in
Dept. 3. Therefore, what looks like an effect of technological change in
Dept.3 on the rate of profit is really an effect of technological change in
Dept. 1 and/or Dept. 2. I will respond to each of these two arguments in turn.
As a preliminary, I would first like to clear up an apparent
misunderstanding. Andrew comments in a couple of places that I assume that
input prices and output prices are equal "as a matter of definition," not as
a matter of convergence to equilibrium. I am not sure what is meant here by
"as a matter of definition (always true?), but my assumption is definitely
intended to refer to convergence to long-run equilibrium. I assume that
Marx's theory of prices of production in Chapter 9 of Volume 3 are long-run
equilibrium prices, and that under these conditions, and only under these
conditions, input prices and output prices are equal. Maybe I haven't been
entirely clear about this, but this is definitely what I mean.
1. Andrew's first argument presents a 3 department scheme in which all the
magnitudes (C, V, S, etc.) are industry totals. He then assumes
technological change in Dept. 3 which reduces V in Dept. 3, and thus
increases the composition of capital in Dept. 3 and in the economy as a
whole, and which therefore finally causes the rate of profit to fall.
Andrew acknowledges that this example appears to support my conclusion that
the rate of profit depends on the technical conditions in Dept. 3. However,
Andrew argues:
But don't be misled by superficial appearances. Underlying these money
aggregates is a wholly different set of technical and real wage data.
How do I know? Because Fred has stipulated that in each table, input
and output prices are equal. Given that stipulation, we can immediately
ascertain that there has been technical change in Dept. I. How?
Using the usual input/output notation (a, b, l, X), and using lowercase
p's for unit prices, we can write--even though Fred gives us no way to
determines the unit prices, specifies no physical data:
C1/P1 = p1*a1*X1/p1*X1 = a1
so that a1 = .4 in Table 1 and a1 = .4118 in Table 2.
Similarly,
V2/P2 = p2*b2*l2*X2/p2*X2 = b2*l2
so that b2*l2 = .2857 in Table 1 and b2*l2 = .2941 in Table 2.
The technological change in this example is indicated by the increases in
the physical coefficients a1 and b2. However, according to this argument,
these increases in a1 and b2 result from decreases in P1 and P2 (assuming
that C1 and V2 remain constant). The decreases in P1 and P2 are themselves
the result of the decline in the rate of profit, which is in turn caused by
the initial increase in the composition of capital in Dept. 3. In other
words, the decline in the rate of profit due to the increase in the
composition of capital in Dept. 3 may have "spillover effects" that affect
the a's and b's in other industries. Or, alternatively, it may affect the
C's and V's in other industries, which in turn would have further effects on
the rate of profit. However, these are spillover EFFECTS, which result from
a decline in the rate of profit which has already occurred. According to
the logic of Marx's theory and Andrew's example, the decline in the rate of
profit was itself caused by the technological change in Dept. 3. Andrew's
argument assumes that the decline in the rate of profit could somehow be
CAUSED by the increases in a1 and b2, but we can see that the increases in
a1 and b2 are instead EFFECTS of the decline in the rate of profit, which is
itself the result or technological change in Dept. 3 alone. This effect of
technological change in Dept. 3 on the rate of profit is present in Marx's
theory and absent in Sraffian theory.
2. Andrew's argument for his second point is an unusual one. He starts
with an algebraic tautology, into which he substitutes my equation for the
rate of profit (or rather, Andrew's interpretation of my equation for the
rate of profit; see (b) below), and which is further transformed into the
Sraffian equation for the rate of profit by means of several additional
steps. I wish Andrew had presented a more straightforward transformation of
my equation for the rate of profit into the Sraffian equation for the rate
of profit; i.e. had started with my equation for the rate of profit, then
introduced his tautology, and then derived the Sraffian interpretation for
the rate of profit. I think that this would have made it easier to follow
the crucial steps in the logic. In any case, I think that there are at
least two serious logical flaws in Andrew's argument.
a. The algebraic tautology with which Andrew begins includes the terms C1,
C2, V1, and V2, but does not include C3 and V3 (the numbers stand for
departments). Andrew assures us:
"Forget that there are no '3's' in this expression. It doesn't matter."
But how could it not matter? The main question at issue here is whether the
rate of profit depends on C3 and V3. So to introduce a tautology which does
not include C3 and V3, in effect, assumes what is to be proved. Indeed, if
C3 and V3 were substituted for C2 and V2 in this tautology, then Andrew's
final equation (2) for R would show that R depends on technical conditions
in Dept. 3 and Dept. 1, but does not depend on technical conditions in Dept.
2! Therefore, an arbitrary tautology is the basis of Andrew's conclusion
that my rate of profit is the same as the Sraffian rate of profit and does
not depend on technical conditions in Dept. 3.
b. The second logical flaw in Andrew's argument is that the equation he
introduces for "my" rate of profit is not in fact my equation for the
determination of the rate of profit. According to my interpretation, the
rate of profit is determined by the equation:
(1) R = S / (C + V)
where S, C, and V are all aggregate totals. C and V are the initial givens
in Marx's theory of the aggregate surplus-value in Volume 1 and S is the
main result of this theory.
The equation which Andrew substitutes into his tautology to represent "my"
rate of profit is instead the equation for the determination of prices of
production in each dept.:
(2) Pi = (Ci + Vi) (1 + R)
where Pi, Ci, and Vi are industry totals. Andrew's argument implicitly
assumes that R is determined by (2) because this equation is eventually
transformed into the Sraffian equation for the determination of the rate of
profit. However, according to my interpretation of Marx's theory, the rate
of profit is not determined by equation (2); i.e. the rate of profit is not
determined simultaneously with prices of production, as in Sraffian theory.
Instead, the rate of profit is determined by equation (1) and then TAKEN AS
GIVEN (as predetermined) in equation (2). If Andrew wants to transform my
equation for the rate of profit into the Sraffian equation for the rate of
profit, then he should start with (1), not with (2).
Therefore, I conclude that Andrew's demonstration that my equation for the
rate of profit is equal to the Sraffian equation is invalid\ because it is
based on two logical flaws: (1) his tautology "without "3's" assumes what is
to be proved and (2) he misinterprets my equation for the rate of profit .
On further reflection, Andrew's argument strikes me as more and more
bizarre. How could a theory that assumes that the rate of profit is
determined by aggregate magnitudes prior to the determination of individual
prices and depends in part on technical conditions in luxury goods
industries be transformed by simple algebraic manipulation into a theory
that assumes the opposite?
Therefore, I continue to argue, as in my previous post, that stationary
prices do not necessarily lead to the same quantitative results as the
Sraffian interpretation. Stationary prices lead to Sraffian results only if
the additional Sraffian assumptions are made that constant capital and
variable capital are derived from given technical conditions and real wages
and that the rate of profit is determined simultaneously with prices of
production. Andrew is so opposed to stationary prices that he cannot
believe that this is true, but I think it is, and Andrew has not yet
demonstrated otherwise.
Part II to follow soon.
In solidarity,
Fred