A reply to Jerry's ope-l 2413:
I agree, of course, that assumptions must be chosen carefully, in order
not to assume away phenomena inappropriately. If I remember, Solow
coined the term "crucial assumptions," ones that are not just
simplifications, but which alter basic conclusions. One doesn't want
results to follow from crucial assumptions. But there are TWO ways of
guarding against this: (a) don't make assumptions; the more seriously
this is taken, the less you can say about anything. (b) don't draw
conclusions insofar as they are merely results of particular assumptions.
When I need to illustrate something, numerically or algebraically, I
always have to make additional assumptions that are not part of the
general conception ("model"). Otherwise, there's no illustration.
I see no problem there as long as I don't claim that particular results
which follow from the particular assumptions have general validity.
On the other hand, I can't agree with Jerry about ensuring that assumptions
are appropriate to the "level of abstraction," because I don't know what
that term means. I realize Jerry didn't invent it. I've heard and read it
a lot, but I really don't know what it means. It also raises my "watch
out" antennae, because I see it used so as to paper over contradictions
in the user's thinking: X is true at A level of abstraction, not-X is
true at B level of abstraction.
The result of a FRP under conditions in which the Okishio theorem says
it can't fall do NOT depend on zero wages. Not at all. In two published
papers and one forthcoming one, I don't assume wages are zero and get the
same qualitative results. I of course do not use r = s/NDFC in these
papers--wages and material costs are included in the denominator. What
*may* depend on the zero-wage and/or zero material cost assumption is the
equivalence of s/(c+v) (surplus-value of the period divided by the
historical cost of capital) and the internal rate of return. Then
again, it may not. I haven't checked it out.
Regarding Marx's assumption that workers live on air, I think Jerry and
I simply haven't been communicating clearly enough. I produced 2 quotes
in ope-l 2307 in which Marx does assume wages are zero and derives
conclusions concerning the rate of profit. I think it is undeniable that
in *those* passages, Marx is assuming zero wages. I don't think Jerry
disagrees with that. I think Jerry is saying that the passages do not
support a claim that Marx's law of the FRP or his entire discussion of
the FRP are based on that assumption. I agree, and I didn't make that
claim. Marx *did* make this assumption sometimes, however, even though
it does not correspond with "the facts," in order to draw theoretical
conclusions. So have I.
I too would like to see more discussion of Marx's reproduction schema,
including discussion of Marx's demolition of trickle-down theory. The
key in my view is that the schema of expanded reproduction show that
Dept. I is not just a supplier of "intermediate goods" that get used to
expand the production of consumer goods. Rather, there is an increase
in means of production to produce means of production, ad infinitum.
I.e., "production for production's sake." This BTW used to be well
known. Luxemburg understood it very well, and this was the main reason
she rejected Marx's analysis of capitalist accumulation in a closed, 2-
class capitalist society. Why did she reject it? Although Marx proved
accumulation was possible without foreign trade and "third persons"
buying up the surplus, Luxemburg DISMISSED THE PROOF BECAUSE THE CONDITIONS
IT ASSUMES DO NOT CORRESPOND TO "REALITY." But that is irrelevant,
no basis for rejecting it, unless it can be shown that other,
real world, things invalidate the implications of the schema. Neither
Luxemburg nor anyone else has done so. But she used the lack of
correspondence to "reality" to reassert her dogma that production must
"ultimately" be production for the purpose of consumption. Why?
Production for production's sake is irrational (ah, that's precisely the
point. Who says capitalism is rational?) In _Theory of Capitalist
Development_, Sweezy repeats the same dogma.
Andrew Kliman