A response to Jerry's ope-l 2923 and Gil's ope-l 2925 on whether the Okishio
theorem has been refuted.
First, I wish to thank Jerry for his Diogenes-like labors in search of (E),
from which he came up empty-handed.
Second, I think we can dispense with the debate over the Okishio theorem
entirely. When I was away, I did a lot of work on the tendency of the profit
rate, and finally came up with a proof that the equilibrium rate of profit
*must* fall, given cost-reducing technical change. Here is the theorem:
The Kliman Theorem
----------------------------
The equilibrium rate of profit is determined by
e = mc^2
(1)
where e is the equilibrium profit rate, m is a positive constant, and c is the
sum of costs of production throughout the economy.
Now, if a cost-reducing technical change, evaluated at current prices, is
introduced anywhere in the economy, then
c' < c
(2)
where c' is the new sum of costs of production, and
e' = m(c')^2
(3)
is the new equilibrium profit rate.
Since c' < c, e' < e. Q.E.D.
>From the above, it should be clear that those authors who have denied the law
of the tendency of the profit rate to fall were simply wrong.
Questions:
Is this proof valid, or is it hogwash because the equilibrium profit rate is
NOT determined by e = mc^2?
Did I *define* "the equilibrium profit rate" in (1) or (3), or did I make a
falsifiable (and false) *claim* concerning the determination of its magnitude?
Is my conclusion, that "those authors who have denied the law of the tendency
of the profit rate to fall were simply wrong," a valid one?
Are we living on planet Earth, or in a Wonderland in which I'm allowed to use
words to mean whatever I want them to mean?
Gil (and Duncan, it seems) thinks that invocation of the term "equilibrium
rate of profit," together with the writing of an equation such as p =
p(A+bl)(1+r), constitutes an explicit statement of (E) or an equivalent of it.
Jerry and I (and, I presume, Alan and John) do not. One may discount my
reading by saying that I have an ax to grind on the issue, but does Jerry?
No. He went on a painstaking and time-consuming search for (E) or its
equivalent and, although he surely noticed the equations and terms like
"equilibrium profit rate" used in connection with r, didn't find it stated
explicitly. So we have a disagreement here. But that doesn't mean that it
is a matter of "opinion" whether (E) or its equivalent is stated explicitly.
The very fact that there's a disagreement on this issue is a *demonstration*
that (E) or its equivalent is *not* stated explicitly.
Gil also suggests that (E) "is the only reasonable interpretation of
'equilibrium' in the theoretical world specified by Roemer, i.e. a static
model with no monopolies, mobility barriers, transaction costs, or
heterogeneous goods." Yet, as Gil seems to recognize in his next paragraph,
when he mentions futures markets, more than the above is needed to ensure
stationary prices. In addition to the existence of futures markets for
everything, rather strong assumptions concerning the information available to
agents and the nature of their expectations need to be made, no? And even
then, Gil, doesn't neoclassical theory require a further assumption---no time
preferences---in order to ensure stationary prices?
But Gil has a legitimate point: if one specifies a "theoretical world" the
necessary consequence of which is stationary prices throughout all time, one
has also specified an equivalent to (E). Hence, if and when anyone shows that
Okishio or Roemer, in one of their major presentations of the Okishio theorem,
explicitly stated the full set of assumptions from which stationary prices
follow necessarily, then that person will have shown my claim to have refuted
the Okishio theorem to be false, even if stationary prices are not directly
invoked as an assumption.
The following by Gil is somewhat perplexing: "by allowing equilibria in which
input and output prices diverge other than by a given time discount factor,
Andrew is implicitly assuming a form of market incompleteness which requires
explicit justification, since futures markets do in fact exist in the real
capitalist world. Thus in my reading Roemer's assumptions are more clearly
spelled out than Andrew's." I'm not sure what "given" means, but unless it
means "constant," then input and output prices in my examples only diverge by
a "given time discount factor"-I have no variation in relative prices over
time. (This does not imply that the profit rate is determined by time
preferences, however.) I find it strange to read that "market incompleteness
...requires explicit justification," because *complete* futures markets do NOT
"in fact exist in the real capitalist world." The accepted procedure, which I
try to follow, is to state what one *does* assume, whereas Gil would burden me
with spelling out everything that I do *not* assume. Roemer does need to
assume stationary prices in order for the theorem to be valid, but fails to do
so explicitly. I do not need to assume complete futures markets in order to
refute the theorem, and so I do not include it as one of my assumptions.
Andrew Kliman