# [OPE-L:7134] [OPE-L:636] Re: Ajit on equilibrium and non-equilibrium

Ajit Sinha (sinha@cdedse.ernet.in)
09 Mar 99 16:09:42 IST (+0530)

To my question:
> > 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
Alan responded:
> 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
_____________________
Before I study the merits of the argument given below on its own
terms (for which I do not have time immideately) let me point out
that Alan's arguments below cannot be an answer to my question,
because in his case it is obvious that things are changing due to
changes in technology. My question was that whether the very
process of equalization of the rate of profits *itself* (that is
flow of capital from one sector to another) would change the rate
of profits compatible with the "natural prices". And if so, why and
how? Alan's introduction of a new cause suggests to me that in the
absense of this cause, i.e. when technology is held constant, Alan
would think that there is no reason for the general rate of profit
to change. Is this so? Alan! cheers, ajit sinha
_________________
>
>
> 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
> below:
>
> 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
> 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.
>
> Alan
>