A reply to Duncan's ope-l 5388:
Duncan writes that
"The overall rate of profit is
r(p) = (u-w)lx/(pAx + wlx) ...."
Since u = p(I-A)x/lx, this can be rewritten as
r(p) = (p[I-A]x-wlx)/(pAx + wlx).
Except for the postulate that input and output prices are determined
simultaneously, this is simply a *definition* of the profit rate. It says
nothing about determination.
Duncan: "r(p) ... in general depends on x, u, w, p, A and l, and thus depends
on the composition of output, including the production of luxury goods."
Because the expression for r(p) is simply definitional (again, except for the
postulate that input and output prices are determined simultaneously), I don't
think this inference is warranted. For instance, what meaning can be given to
the statement that r(p) "depends on x, u, w, p, A and l" when one of the
determinants, u, is itself fully determined by p, A, l, and X? This is not
directly relevant to the luxury industry issue, but I mention it to illustrate
that the appearance of a symbol on the right-hand side (RHS) of an equation
isn't enough to allow us to conclude that the thing symbolized is a
determinant of what's on the left-hand side.
More directly relevant is whether x is a determinant of r(p). If it is, then,
as Duncan says, r(p) "depends on the composition of output, including the
production of luxury goods." But again, the mere appearance of x on the RHS
isn't enough to permit this inference. To see this, assume that the profit
rate is uniform and that workers have the budget constraint w = pb. (The
sizes of the various elements of b need not be determined independent of
workers' consumption choices.) Then r(p) is still the definition of the
simultaneist profit rate but, as we all agree, the *magnitude* of r(p) is
independent of the relative sizes of the elements of x, and therefore
independent of production conditions in luxury industries. Although x appears
in the *definition* of the profit rate, the profit rate does not *depend* on x
or on production conditions in luxury industries.
To ascertain whether r(p) depends on x in the general case in which the profit
rate is not uniform, we would need to have a general simultaneist theory of
price and profit rate determination. But no such theory exists. I doubt
whether it could be constructed. In any case, at the present time,
simultaneism is capable of addressing relations of determination *only* in the
special case in which the profit rate is uniform. So the claim that the
simultaneist profit rate depends on luxury industries' production conditions
is impossible to substantiate.
Duncan: "An alternative would be to take the New Solution "value of
labor-power", 1-e = w/u, and the monetary expression of labor time, u, as
given, rather than the real wage b. Then if we assume profit rate
equalization, the full
system is:
p = (1+r)(A + wlx)
p(I-A)x = ulx
w = (1-e)u
In this system of equations, p, w, and r depend in general on u, e, and x.
This same argument goes through if e = 1 so that w = 0."
I think there are a couple of typos in the top equation. I think the correct
formulation is:
px = (1+r)(pAx + wlx), or equivalently, p = (1+r)(pA + wl).
If e = 1, so that w = 0, then p = (1+r)(pA) and, as is well known, the
magnitude of r is not affected by production conditions in luxury industries.
The lack of dependence in this case is clearly due to the postulate of
simultaneous price determination, not to the theory of wage determination,
since wages = 0.
Ciao,
Andrew Kliman