Jim writes: > In the midst of his very interesting and useful thoughts on math, > Gil writes that "even if one doesn't agree with the premises of > Okishio's theorem, who would have known that Marx's claim was > inconsistent with those premises before Okishio's proof?" > > I think this example shows up some of the limitations of > mathematics as often applied to economics, though they do not > apply to math _per se_. The fact is that Okishio's premise > (constant real wages) is _not_ the same as Marx's (constant rate > of surplus-value), so that Okishio's theorem is not really a > critique of Marx. Pen-l will be glad to hear that I am not > criticizing Gil here, since I think he is familiar with the > problems arising from the conflation of the two assumptions (with > Marx's, real wages rise with productivity). What I'm commenting > on is the fact that many or even most of the writings since > Okishio ignored this confusion and even ignored John Roemer's > generalization of Okishio to a case that approximates the > constant rate of surplus-value assumption. The authors wanted to > talk about, apply, and extend Okishio's math and how it "proved" > Marx wrong. I hope that authors such as Dave Laibman (and Gil > himself & Frank Thompson) have gotten us away from the > constant-real-wage assumption. > > The moral of the story is that one has to remember that math is a > _means to an end_ (it's formalized logic) and should not become > an end in itself, replacing scholarly discussion of the subject > matter (such as actual reading of Marx) or other methods (such as > dialectics). Right on! One minor comment: Marx phrased his argument under the assumption that the rate of surplus value is held constant, but I don't read him positing this as the economically relevant condition--rather it's a simplifying assumption stipulated as a point of departure. The economically relevant condition on wages would have to be supplied by a separate story about the impact of technical changes on labor market outcomes. Roemer's argument is that there is (to him) an economically plausible story which supports the Okishio assumption, and he doesn't know of one which supports the constant-rate-of- surplus-condition. In a recent paper to which Jim refers (still in submission limbo), I establish market conditions --something like a stationary-state competitive equilibrium in a dynamic market--which support this assumption. But the point still holds: if one replaces Marx's simplifying assumption with a demonstrably market-relevant condition (long-run wages constant at the subsistence level), there is no "tendency" for the rate of profit to fall--and this is a useful result. Gil
