Andrew has argued that Alan demonstrates on pp. 13-16 of his Boston
paper that "simultaneously determined prices CANNOT function as long-
run center-of-gravity prices." I argue that Alan's argument has nothing
to do with whether or not Sraffian equilibrium prices can function as
long-run center-of-gravity prices
Alan's argument is in two main parts:
1. When there is technical change, Sraffian equilibrium prices cannot serve
as the basis of actual exchange.
2. Even if Sraffian prices are modified to make it possible for them to
serve as the basis of actual exchange, these modified Sraffian prices will
violate at least one of the fundamental principles of Sraffian theory.
Hence, Sraffian equilibrium prices cannot serve as the regulator of any
actual sequence of exchanges.
I will briefly discuss below each of these two arguments in turn.
1. ALAN'S FIRST ARGUMENT:
Alan's first argument asks "a simple question: under what circumstances
can Sraffian (equilibrium) prices form the actual basis of exchange?"
Alan's answer to this question is that, when there is technical change,
Sraffian equilibrium prices cannot serve as the basis of actual exchange.
When there is technical change, both input prices and output prices change
in the next period (and continue to be equal to each other). Therefore,
the Sraffian input prices of a given period will not be equal to the Sraffian
output prices of the previous period, when there is technical change. Alan
concludes from this that these Sraffian equilibrium prices cannot serve as
the basis of actual exchange in these circumstances. There cannot be an
actual exchange in which the price paid by the buyer (the input prices
in period 2) is not equal to the price received by the seller (the output
prices is in period 1). In other words, Sraffian equilibrium prices
cannot be equal to actual market prices, when there is technical change.
MY RESPONSE: This argument has nothing to do with whether or not Sraffian
equilibrium prices can function as long-run center-of-gravity prices
for actual market prices. It is not necessary for Sraffian equilibrium prices
to be the actual market prices in any given period in order to function
as the long-run center-of-gravity prices for market prices over successive
periods. Even though Sraffian equilibrium prices cannot actually exist as
market prices in successive periods when there is technical change, they
can still nonetheless function as long-run center-of-gravity prices around
which actual market prices fluctuate, both before and after the technical
change.
Long-run center-of-gravity prices seldom actually exist as market prices.
That is the nature of long-run center-of-gravity prices - that they do not
actually exist as market prices in every period, but exist only as the
long-run average of actual market prices. And, when there is technical
change (as in Alan's example), long-run center-of-gravity prices will
never exist as actual market prices in the next period after the technical
change. Technical change creates disequilibrium, which initiates a process
of adjustment to the new equilibrium. But these new equilibrium prices
can still function as long-run center-of-gravity prices in subsequent
periods, even though they cannot actually exist as market prices in the
next period after technical change.
Therefore, Alan's first argument does not demonstrate that Sraffian
equilibrium prices cannot function as long-run center-of-gravity prices. It
demonstrates only that Sraffian equilibrium prices cannot exist as actual
market prices in the period following technical change. I do not disagree
with Alan's argument; it is trivial. But it is also irrelevant to Andrew's
claim that Sraffian equilibrium prices cannot function as long-run
center-of-gravity prices.
2. ALAN'S SECOND ARGUMENT:
Alan's second argument modifies Sraffian prices so that they COULD
form the basis of actual exchange by assuming that the input prices of the
current period are equal to the output prices of the preceding period. He
then determines the modified Sraffian output prices in two different
ways, and shows that, in both cases, the modified Sraffian prices will
violate at least one of the fundamental principles of Sraffian theory.
Therefore, Alan concludes that Sraffian equilibrium prices cannot serve as
the regulator of even these modified Sraffian prices (that could form the
basis of an actual sequence of exchanges).
2.1 FIRST ASSUMPTION
In Alan's first modification of Sraffian prices, he assumes that the
output prices continue to be the Sraffian equilibrium prices. Since input
prices are no longer equal to output prices in the same period, profits
have to be recalculated as the difference between Sraffian (equilibrium)
output prices and the modified Sraffian input prices. This leads to the
result that profit rates diverge across sectors - thereby contradicting the
Sraffian principle of equal rates of profit.
MY RESPONSE:
Alan's argument ASSUMES THAT THERE IS NO TRANSFER OF CAPITAL from sectors
with lower rates of profit to sectors with higher rates of profit. In
Alan's example, sector 2 continues to use the same quantity of inputs to
produce the same quantity of outputs period after period, even though the
rate of profit in sector 2 is falling sharply and the rate of profit
in sector 1 is rising. There is no transfer of capital out of the low
profit rate sector 2 to the high profit rate sector 1. Hence it is not
surprising that the rates of profit in the two sectors diverge! The very
process through which rates of profit are equalized across sectors - the
transfer of capital - is assumed away in the argument !!
Thus, this is not an argument that Sraffian equilibrium prices cannot
function as long-run center-of-gravity prices. It is only an argument that,
when there is technical change in some sectors and no transfer of capital
between sectors, then rates of profit will diverge across sectors.
2.2 SECOND ASSUMPTION
In Alan's second modification of Sraffian prices, he assumes that the
rate of profit is equal in both sectors and recalculates the output prices
by adding a markup yielding this rate of profit to the modified input prices
(i.e. last year's output prices, rather this year's output prices). This
leads to the result that the modified Sraffian prices diverge radically
from the Sraffian equilibrium prices. Hence, Alan concludes that
Sraffian equilibrium prices cannot serve as regulator of "actual prices".
MY RESPONSE
What Alan calls "actual prices" are not real market prices. Instead they
are Alan's modified Sraffian prices. Alan's modified Sraffian prices are
assumed to have EQUAL rates of profit; real market prices generally have
UNEQUAL rates of profit. Unequal rates of profit will in general lead
to transfers of capital from sectors with low rates of profit to sectors with
high rates of profit, which in turn will tend to equalize profit rates. By
assuming that his "actual prices" already have equal rates of profit, Alan
has is in effect once again assumed away the process that both brings
about the real equalization of profit rates and also makes the long-run
equilibrium prices function as the centers-of-gravity of real market prices -
the transfer of capital across sectors.
Hence, once again, this is not an argument that Sraffian equilibrium prices
cannot function as long-run center-of-gravity prices of real market prices.
This is only an argument that Sraffian equilibrium prices cannot serve as
the "regulator" of Alan's modified Sraffian prices, which assume equal
rates of profit, and hence are completely different from real market prices,
with their unequal rates of profit.
In conclusion, Andrew's claim - that Alan's arguments demonstrate that
Sraffian equilibrium prices cannot function as long-run center-of-gravity
prices - is wrong. Alan's first argument demonstrates only that Sraffian
equilibrium prices cannot exist as real market prices is in the period after
technical change. Alan's second argument assumes away the very process
through which Sraffian equilibrium prices function as long-run center-of-
gravity prices - the transfer of capital.
In previous posts, I have argued that essentially the opposite of
Andrew's argument is true. ONLY simultaneously determined prices
(i.e. prices in which input prices are equal to output prices) can function
as long-run center-of-gravity prices, at least with respect to Marx's
concept of price of production.
I have argued (with substantial textual evidence) that one of the
characteristics of Marx's concept of price of production is that they
change if and ONLY IF productivity or the real wage changes. This
characteristic is contradicted by the temporal determination of prices of
production, which keep changing every period, even though productivity
and the real wage remain constant, as Andrew and Ted's numerical
examples clearly show. Therefore, the temporal interpretation of Marx's
concept of price of production cannot be correct. Instead, this fourth
characteristic of Marx's prices of production is satisfied ONLY IF input
prices are equal to output prices, i.e. only if input prices are valued is in
current reproduction costs. In other words, Marx's prices of production,
as long-run center-of-gravity prices, require that input prices are valued in
current reproduction costs, and in this sense require simultaneous
determination, and are incompatible with temporal determination (which
results in prices of production that change every period, even though
productivity and the real wage remain constant).
I look forward to Andrew's and Alan's responses to my arguments and to
further discussions with anyone interested.
Comradely,
Fred