# [OPE-L:988] Re: Definitions and Tautologies

Allin Cottrell (cottrell@wfu.edu)
Wed, 7 Feb 1996 13:05:42 -0800

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Andrew writes:

> Allin suggests that

[the TSS equation, v(t+1) = p(t)A + L, which I'll call equation 1, AC]

> makes prices "theoretically prior" to values. Actually, it doesn't
> -- *input* prices are *temporally* prior to output values, but
> the "value" rate of profit
>
> r = (LX - p(t)bLX)/(p(t)[A+bL]X) [equation number 2, AC]
>
> enters into the determination of output prices:
>
> p(t+1) = p(t){A + bL}(1+r) [equation number 3, AC]
>
> so that the "value" rate of profit is also *temporally* prior to
> *output* prices.

Wait a minute. Substitute equation 2 for the "r" in equation 3, and what
do we get?

p(t+1) = p(t)[A + bL]{1 + [LX - p(t)bLX]/p(t)[A + bL]X}
= p(t)[A + bL] + [LX - p(t)bLX]/X
= p(t)A + p(t)bL + L - p(t)bL
= p(t)A + L

Compare with equation 1:

v(t+1) = p(t)A + L

The system of 1, 2, and 3 implies that p(t+1) = v(t+1), "price-value
equivalence". Besides, it seems that p(t+1) does not depend on the rate
of profit, however measured, in this system, but only on the previous
price-vector, the i-o coefficients and the direct labour coefficients.
Help me out -- what's happening here?

Allin Cottrell
Department of Economics
Wake Forest University