I had written:
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.
In ope-l 3948, Paul Cockshott responded:
"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."
Of course K can increase, and there's no reason to assume it doesn't. But the
point is that an increase in K ("accumulation," in Frank's usage) and an
increase in the value composition, (c), are distinct things. As Frank points
out, the value compostion is determined and can be defined independently of
the absolute magnitude of K. I'll also note that Marx's discussion of
unemployment in Vol. I looks at accumulation and the composition of capital as
distinct things, which produce movements in labor demand that go in opposite
directions. Frank thus takes the same approach as Marx did when he decomposes
the change in labor demand into the (positive) change caused by accumulation
and the (negative) change caused by a rising value composition.
If there's accumulation without a change in the VCC, then labor demand rises.
If there's a rise in the VCC without accumulation, then labor demand falls.
The net impact of these two factors on labor demand depends on their relative
rates of change. That's what Marx says (actually, he deals with the OCC);
that's what Thompson says.
Since changes in K and changes in the VCC are distinct things, having indeed
opposite impacts on labor demand, it is entirely appropriate to differentiate
partially --- hold K constant --- when assessing the impact of the VCC on
labor demand, the real wage, and the profit rate, as Frank does. One just
needs to be clear --- as Frank is --- that this does not imply that anytime
the VCC rises, the profit rate cannot fall. It does imply that if the VCC
rises and the profit rate falls, the fall is NOT CAUSED by the rise in the
VCC.
I therefore disagree with Paul when he writes that "You have to take into
account however, that what matters is whether a theory accords with reality."
Frank is not proposing a "theory"; he is, in other words, not saying what
*will* happen to the VCC, K, the profit rate, etc. He is simply saying that
the simultaneist equations imply that *if* the VCC rises, then, if this rise
has any effect on the profit rate at all, it will tend to raise the profit
rate. "Tend" in the last sentence means that a rising VCC *alone* will cause
the profit rate to rise.
Andrew Kliman