[OPE-L:3948] Re: Frank Thompson's Theorem

Paul Cockshott (wpc@cs.strath.ac.uk)
Wed, 8 Jan 1997 01:33:04 -0800 (PST)

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>Now, Frank puts forth a "Minimal Assumption" that a fall in demand for labor
>either leads to a fall in or does not affect, i.e., does not lead to a rise
>in, the real wage rate. Thus, defining the elasticity of the real wage with
>respect to labor demand as e, we have
>e = w~/L~ > or = 0.
>We can then rewrite (1) as
>w~ = K~ - c~ - (1/e)w~, or, equivalently,
>w~ = [e/(1+e)]*[K~ - c~]
>so that a rise in c, the value composition, leads to a fall in the real wage
>rate w if e > 0 and to no change in the real wage if e = 0, if K is held
>constant. In other words, the partial derivative of w with respect to c is
>negative if e > 0, and is zero if e = 0.

This depends upon the assumption that K is constant. Why should
we assume this. The historical periods in Britain in which the
organic compostion has risen have sometimes, though not always,
been associated with rising total capital stock.

During the 1950-1970 period capital stock and organic composition
both rose and the profit rate fell. In the period 79-89 the organic
composition rose whilst the capital stock remained stagnant or declining.
In this latter period, your restriction of Franks theorem appears to hold
good, the
rate of surplus value rose, and for lower paid workers the real
wage fell. The consequence was that the rate of profit rose.

In the prior period as well, Franks theorem seems to apply, but
now in its full form - allowing K to rise.

>Now, if the Okishio theorem were true, i.e., if the simultaneist
>interpretations were correct, then any fall in the real wage would lead the
>equilibrium (i.e., uniform) profit rate to rise, given profit-maximizing
>behavior and viable technical change. Hence, if e > 0, then a rise in the VCC
>lowers the real wage and therefore raises the profit rate, and if e = 0, a
>rise in the VCC has no effect on the real wage and therefore no effect on the
>profit rate.
>This is a beautiful example of the incompatibility of Marx's value theory and
>simultaneism. Frank's theorem does not carry over to the successivist
>interpretation, because for us, and Marx, the profit rate can fall when the
>real wage rate falls.

You have to take into account however, that what matters is whether a theory
accords with reality. Franks theorem accords with what I observe to have
occured in the historical record.
Paul Cockshott