[OPE-L:7120] [OPE-L:623] Ajit on equilibrium and non-equilibrium 

Alan Freeman (a.freeman@greenwich.ac.uk)
Mon, 08 Mar 1999 08:56:32 +0000

Ajit Sinha wrote:
> Below you say that the process of profit rate equalization itself
> changes the equal rate of profit. Could you give us your reasons
> for this? Cheers, ajit sinha

Certainly. Consider a two-sector economy in which the output of I is the only
input to I and to II, in which II produces consumption goods, and in which
productivity in (I) is changing in such a way that the output of this sector
is rising as a proportion of both its inputs, and labour inputs (that is,
productivity is rising according to any acceptable definition). An example is
given below: large letters represent absolute quantities and small letters
represent coefficients

t C(I) C(II) L(I) L(II) X(I) X(II) c(I) c(II) l(I) l(II)
1 10 20 20 10 30 30 0.33 0.67 0.67 0.33
2 11 20 20 10 32 30 0.34 0.63 0.67 0.33
3 12 20 20 10 34 30 0.35 0.59 0.67 0.33
4 13 20 20 10 36 30 0.36 0.56 0.67 0.33
Two-sector economy, use-values and technical coefficients

With a real wage of 0.5, equilibrium equal-profit-rate prices and profits
yielded by this sequence, in terms of labour units as numiraire, are given

r p(I) p(II)
0.37 0.84 1
0.39 0.89 1
0.40 0.93 1
0.42 0.97 1

EPR profit rates and prices

These prices cannot be used for any actual exchange. The output of department
I from period 1 is sold for 0.84 per unit. But in the next period it is
purchased at 0.89. No known form of exchange permits the seller to receive 5
cents less than the buyer pays.

In any actual adjustment process, the output of department I must be sold for
the price at which it is purchased. Otherwise, the magnitudes we have just
calculated are not in fact prices, since they cannot constitute the basis of
actual exchanges.

If we now suppose that in period 2, goods are purchased at the prices for
which they are sold at the end of period 1, that is, for 0.84.

What now determines the profit rate in period 2? We could attempt first to
preserve the proposition that EPR profit rates predict actual profit rates,
and see what this does to prices. Let us suppose that the EPR calculation is
correct for profits, and that the profit rate of this period is 0.39. This is
also very consonant with the surplus approach, since according to this view
the profit rate should be a function of physical magnitudes alone. So it
should not be altered just because of a temporary fluctuation in price.

We must, however, in this case recalculate output prices, since input prices
are cheaper. Let us suppose that output prices are calculated as a 'markup' on
an input price of 0.84 for the produce of sector I. We then find that the
*output* prices of period 2 are different from their equilibrium magnitudes
because department I goods are relatively cheaper compared to wage goods.
Since department I is increasing its consumption of capital goods compared
with department II, the price of department I outputs sinks below its
equilibrium magnitude whilse the price of department II outputs rises above
its equilibrium magnitude: that is, they move apart or, which is the same
thing, the relative price of wage-goods in comparison with capital goods rises
faster than is predicted by the equilibrium calculation.

However the same considerations that influenced the calculation of the input
prices for period 2, must now enter into the formation of input prices in
period 3. If the prices that we just calculated are to serve as the basis of
any *actual* exchange, which is precisely what an adjustment process must
mean, then we find at the end of period 3, output prices diverge still further
from the predictions of the equilibrium calculation.

Here is the actual sequence of prices:

p(I) p(II)
0.84 1.00
0.86 1.05
0.87 1.10
0.89 1.15

Recall that the 'long-run' EPR prediction was as follows:

r p(I) p(II)
0.37 0.84 1
0.39 0.89 1
0.40 0.93 1
0.42 0.97 1

This continues indefinitely; there is no process of convergence. It is in fact
a misnomer to consider what we describe as an 'adjustment' process because it
prices do not 'adjust' to equilibrium but diverge indefinitely from the prices
predicted by the equilibrium calculation.

We could try to investigate the thesis that EPR prices and profits predict
actual prices and profits by different means. So far we have tried as hard as
we could to preserve the profit rate; we find that there is no meaningful
sense in which EPR prices can then be said to 'approximate' actual prices.
They could not act as 'centres of gravity' for actual prices. We could
alternatively suppose that EPR prices do serve as 'centres of gravity' for
actual prices, and investigate what happens to the rate of profit.

Let us suppose, therefore, that goods in each period are purchased at the
prices of the previous period and sold at the EPR prices of the current
period. In that case, we find that profit rates do not equalise; to the
contrary they diverge, and in Department II become negative after period 10;
the general profit rate, moreover, systematically diverges from the
predictions of the equilibrium calculation.

Here are the profits that result:

Dept I Dept II Total
0.441470435 0.372281323 0.403930298
0.503568522 0.320914238 0.405851725
0.559328061 0.273801847 0.408830939
0.609342268 0.230396696 0.412675332

I would conclude that no actual adjustment process is possible, given the
above very reasonable sequence of technical change, which permits goods to
exchange at the prices predicted by the EPR calculation and yields the profit
rates predicted by the EPR calculation. At least one, and probably two, of the
fundamental ideas behind the notion of 'long-run' EPR prices and profits as
predictors of actual prices and profits, must be dropped.

Either EPR prices don't predict actual prices, or EPR profits don't predict
actual profits; or both.