[OPE-L:1819] Re: Temporality vs simultaneity

Gilbert Skillman (gskillman@wesleyan.edu)
Thu, 18 Apr 1996 15:54:26 -0700

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I apologize for the long lag in responding to Andrew's and John's
comments on my post 1492 re Marx's theory of the falling rate of
profit. Through the first week of May, I'll have to snatch bits of
free time where I can find them.

Andrew raises a number of interesting issues. In preparation for
subsequent (and immediately following) responses to John, for now I'm
simply going to note that Andrew did not address my final point in
1492, to the effect that Marx's account re the "tendentially falling
rate of profit" is at odds with his account in section 1 of Ch. 25 in
Volume I, where he says that inroads on the prevailing profit rate
are self-correcting, because they lead to a slowdown in the rate of
capital accumulation which restores the higher rates of profit.

Marx does not suggest that this phenomenon is limited to a setting in
which the organic composition of capital is held constant. To the
contrary, as I mentioned in my previous post, I can show that the
steady-state profit rate is independent of technical coefficients of
production and the wage rate (Paul C. has established a similar
conclusion in a short paper he has posted to his web site), so that Marx's
section one conclusion should be seen (I assert) as quite general, and manifestly
at odds with the notion that the profit rate is "tendentially falling" in any
meaningful sense.

In isolating this point I do not mean to disregard Andrew's comments.
Rather, I'm going to approach them indirectly, via my response to
John (upcoming).

In solidarity, Gil

> A reply to Gil's ope-l 1492, with reference to John Ernst's reply (ope-l
> 1493). My reply will also take up Fred's objection, similar to Gil's
> about historical cost measurement of the profit rate.
> Gil writes that the TSS interpretation is neither necessary or sufficient
> for "rehabilitating Marx's theory of the falling rate of profit," and that
> "A number of alternative postulate sets re-establish Marx's result." My
> question here is very similar to John's: what do you mean, Gil, by
> "Marx's theory" of the FRP and "Marx's result"? If you mean that one can
> show conditions under which the profit rate will fall without the TSS
> interpretation of Marx's value theory, well, of course. But that is not
> what the debate has been about.
> *Marx's* law of the FRP is that the profit rate can fall, and under certain
> circumstances, will fall, due to mechanization ITSELF. The Okishio
> theorem was never meant as a proof that the profit rate can't fall. It
> was meant as a proof that the cause can't be mechanization ITSELF; i.e.,
> given profit-maximization, blah-blah-blah, only a rise in the real wage
> rate can cause a falling profit rate. Roemer, in _Analytical Foundations
> of Marxian Economic Theory_ is *very* clear about this: "Although the
> real wage in fact does not remain fixed, the problem has been to understand
> whether a FRP can be construed to be due to technical innovation *itself*,
> independent of changes in the real wage [p. 113, my emphasis]." "The
> argument of this chapter is that there is *no hope for producing a FRP
> theory in a competitive, equilibrium environment with a constant real
> wage.
> "It must be reiterated that this does not mean that the rate of profit
> does not fall. ... The general point is this: If the rate of profit falls
> in such a changing real wage model, it is a consequence of the class
> struggle that follows [sic] technical innovation, not because of the
> innovation *itself*" [p. 132, my emphases].
> I don't fully understand what Gil's Metroeconomica paper is about, and it
> sounds interesting, but it seems to belong to the class of rising real
> wage models of the FRP. If so, it doesn't "rehabilitate" *Marx's*
> theory of the FRP.
> Roemer also states a common belief: for "a theory of a falling rate of
> profit in capitalist economies [to exist, it is necessary to] relax some of
> the *assumptions* of the stark models discussed here [Roemer's extensions
> of Okishio's model]" [Roemer AFMET, p. 132, my emphasis]. Gil has a
> similar view: "What's really at stake, it seems to me, is the legitimacy
> of the *assumptions*" [my emphasis]. What Gil is implying is that I
> (and John and Alan) haven't refuted the Okishio theorem on value-theoretic
> grounds because "Given the postulates of the theorem, the conclusion is
> logically valid. Absent a demonstration that the proof is deductively
> invalid, the theorem itself isn't refuted."
> I think I HAVE demonstrated that the proof is deductively invalid, on the
> basis of, i.e., without altering, the postulates of the theorem. The
> conclusion does NOT follow from the postulates, as I understand them.
> Let me be clear: I do not claim to refute the relevant Frobenius-Perron
> theorem upon which the Okishio theorem is based. Nor do I claim to
> find an error in Okishio's or Roemer's algebraic manipulations. I DO
> claim that they "deduce" invalid conclusions from the math.
> To explain this, I'll turn to Roemer's particularly amusing proof of the
> theorem in his "The Effect of Technological Change on the Real Wage and
> Marx's Falling Rate of Profit," _Austrailian Economic Papers 17, June
> 1978. On pp. 152-53, Roemer writes: "if technical change is introduced
> when it is cost-reducing, the final general equilibrium effect will be
> to _increase_ the rate of profit, assuming the real wage-consumption
> bundle of workers remains unchanged. (This was first shown by Okishio ...."
> Later on p. 153, Roemer begins his "proof." "The equal-profit rate equations
> for this economy are: ...
> p = (1+r)pM (2.4)
> [I'm using r instead of Roemer's Greek pi for the profit rate. M = A + bl.]
> ..
> "We shall assume that technical change is _cost-reducing at current prices_."
> [Roemer then states this symbolically in inequality (2.5)]. ... "If such a
> technique appears and is adopted, the profit rate will *immediately rise*
> in sector 1. This will encourage more firms to *enter* sector 1 from
> sector 2; prices *will be cut in competition and *eventually* a new
> equilibrium tableau *will emerge* [my emphases]:
> p* = (1+r*)p*M*" (2.4')
> [Roemer calls (2.4') "Tableau 2"]. Then he states immediately:
> "It is a theorem that is (2.5) holds then r* > r: WHICH IS TO SAY that if
> the real wage (b) remains fixed then cost-reducing technical innovations
> GIVE RISE, EVENTUALLY, to a rise in THE equilibrium rate of profit in a
> competitive situation" [p. 154, my emphases].
> Now the math simply DOES NOT support any such conclusion. In other words,
> a comparison of (2.4) and (2.4') and their associated r's permits absolutely
> no conclusion regarding the dynamic process that follows adoption of the
> new technique. Will the profit rate in sector 1 immediately rise? If so,
> Roemer doesn't show it. Can we then be sure that firms will enter sector
> 1 from sector 2? *Far* more importantly, how do we know that "eventually"
> Tableau 2 "will emerge," so that the innovation "give[s rise, eventually"
> to a rise in the equilibrium rate of profit? The rigorous Roemer certainly
> proves nothing like this. He merely substitutes a lot of dynamic language
> that conjures up an unproved adjustment to a stationary price equilibrium
> in place of a harmless and rather trivial static equilibrium comparison,
> via the untrue words "which is to say."
> I would suggest that a valid English translation of the demonstration would
> be: "Assume a static equilibrium at stationary prices, with an equalized
> profit rate. Assume a technical change that lower's some producer's costs
> at current prices. Use the new input coefficents to compute an imaginary
> set of prices and the imaginary profit rate associated with it, given the
> further assumptions that the profit rate is again equalized and that
> stationary prices then prevail. The latter, imaginary, profit rate must be
> greater than the initial one."
> Lest any of this seem to be quibbling, it is very well known that the
> stability properties of (2.4) are rather shaky. Moreover, the investiga-
> tions of stability, to my knowledge, do NOT permit technical change during
> the process of adjustment or non-adjustment to a new stationary price
> equilibrium. It is rather obvious that if techniques are *continually*
> changing, (2.4) will never be reached and thus r* and the subsequent
> rates associated with Tableaux 3, 4, ... will *remain* imaginary. And
> the TSS refutations of the Okishio theorem do rely on continual technical
> change--which the theorem DOES NOT prohibit. Indeed, to have any relevance
> to Marx's law of the FRP at all, the theorem *cannot* exclude the possibility
> of continual technical change, since Marx's Vol. III, Ch. 13 statement of
> the law clearly states that it feres to a continual rise in productivity,
> a continual rise in the composition of capital, etc ["feres" in line above
> should be "refers"].
> Once one DOES examine the dynamic set off by the technical change, one needs
> a theory of the determination of value and the profit rate. One can no
> longer *postulate* that input and output prices must be equal. So the
> physical quantities, even with a uniform profitability assumption, no longer
> are sufficient to determine the profit rate. So, in keeping with Marx--
> since, again, the Okishio theorem is supposed to be a refutation of *Marx's*
> law of the FRP--John, myself, and Alan all (independently) invoked Marx's
> theory of the determination of value by labor-time as we understand it.
> Together with continual mechanization, this can lead to a fall in the
> profit rate under conditions in which the imaginary (which Roemer calls
> "actual" at least 13 times in Ch. 5 of AFMET) Okishio profit rate must rise,
> even if EQUILIBRIUM exists in the sense that the profit rate is equalized
> each period. (Note that Roemer, in the above, *never* defines exactly
> what he means by "equilibrium." While there are good reasons to think that
> intercapitalist competition leads to a tendency for the profit rate to be
> equalized, there is really no good reason to think that any real process
> leads to stationary prices, given the results of the abovementioned
> investigations of this issue. I do not consider iterating a matrix to
> be a meaningful indication of convergence to stationary prices.)
> The most amusing aspect of Roemer's discussion in the AEP, however, is
> his almost self-parodying use of the Method of Substitutionism to try to
> link the mathematical results to Marx's law. Roemer begins (pp. 154-55)
> by quoting from Vol. III, p. 264 (Progress):
> "[Sentence 1:] No capitalist ever voluntarily introduces a new method of
> production ... so long as it reduces the rate of profit. [But he gets
> superprofit. This is because] [Sentence 6:] His method of production
> stands above the social average. [Sentence 7:] But competiton makes it
> general and subject to the general law. [Sentence 8:] There follows a
> fall in the rate of profit perhaps first in this sphere of production,
> and eventually it achieves a balance with the rest which is, therefore,
> wholly independent of the will of the capitalist."
> Roemer then begins substituting his interpretation for what Marx said,
> without even acknowledging that interpretation is involved or that
> other interpretations are possible: "Sentence seven points out that
> eventually, through competition, the new equilibrium Tableau 2 is estab-
> lished. And, finally [in sentence 8], Marx's intuition fails him, when in
> the last sentence he says that the new rate of profit r* will be less than
> r."
> Now one can argue that it is an utterly arbitrary use to language to think
> that sentence 7 can mean anything else but the stationary price equations
> (2.4') of Tableau 2, but I would find this suggestion laughable, as I would
> the related suggestion that "fall in the rate of profit" can only mean that
> r* < r, if language is being used rationally. This is particularly because,
> as Roemer notes in concluding this paragraph (p. 155): "since the general
> proof that the [sic] equilibrium profit rate r* is greater than r relies on
> the Froebenius-Perron theorems, not discovered until a generation after
> Marx's death, we may not fault him too much for his mistaken intuition."
> In other words, in order to reduce Marx to the level of a third-rate graduate
> student, Roemer says Marx was not too much at fault because he didn't know
> the math. But to attempt to tie what Marx actually claimed about the FRP
> to an otherwise irrelevant matrix algebra theorem, well, then, certainly,
> Marx was simply translating Tableau 2 into German in sentences 7 & 8.
> To summarize: the TSS refutations of the Okishio theorem are indeed
> refutations. They do NOT relax Okishio's or Roemer's *assumptions*. They
> show that Oksihio's and Roemer's *conclusions* are deductively invalid.
> And they show that, WITHOUT invoking alternate assumptions about capital-
> ists' behavior or the nature of technical change, the rate of profit can
> fall under conditions in which the Okishio/Roemer simultaneist profit rate
> must rise. These demonstrations rely crucially on Marx's theory of the
> determination of value by labor-time because, as I show, if value is not
> determined by labor-time and instead, only relative prices affect the
> profit rate, then we get the Okishio/Roemer results in the one-commodity
> case (at least).
> Finally, let me briefly address Gil's point that "as I understand Andrew's
> argument, it requires that capitalists calculate rates of profit on the
> basis of *historical* costs of capital (i.e., that capitalists fail to
> ignore sunk costs). ... Now, I doubt that this is the case ...."
> My refutation of Okishio's theorem *requires* nothing concerning how
> capitalists calculate. The Okishio theorem is meant to refute *Marx's*
> law of the FRP. My work refutes the refutation. So what is at issue
> is how MARX calculates the profit rate. Second, the TSS refutations of
> the Okishio theorem do not actually require historical cost valuation
> at all, because they do not require fixed capital. With circulating
> capital valued at pre-production reproduction (not historical) cost, and
> input prices and output prices that differ, the profit rate can fall due
> to excess of pre-production over post-production prices (values).
> But I DO think that capitalists calculate their rate of return on investment
> by using historical costs (which is not to say that they use only this
> measure). At least that's what they necessarily do if they use the
> internal rate of return formula, which is simply an application of a
> present value formula. In both versions of my refutation of Okishio, I
> follow Roemer in assuming fixed capital that lasts forever. For rate
> of return calculations, this is analytically equivalent to a consol or
> perpetual bond; it never matures, and yields a never-ending stream of
> interest payments.
> It is well known that in this case (taking the limit of the sum of the
> infinite series), the present-value determined price of the bond is
> given by
> P = C/r
> where P is price, C is the coupon interest each year, and r is the annual
> rate of return.
> Now, let's imagine a financial community of simultaneists. One of them
> buys a consol for $1000, which pays interest of $100 each year. Hence,
> r = 10%. But after a few years, the bond's price in the market has
> collapsed; its "replacement cost" is now only $500. It still gives an
> infinite stream of interest payments, so the above formula still applies.
> Being a good simultaneist, and having read Ch. 14 of Vol. III of
> _Capital_, but especially having read the Robinson-Sweezy-Okishio-et al.
> interpretations of that chapter, our investor figures that the cheapening
> of his/her asset raises his/her profit rate ("cheapening of the elements
> of constant capital"). To compute the exact amount, s/he now puts $500
> instead of $1000 for P on the left-hand side. C remains $100. And, to
> his/her delight, our simultaneist investor finds that his/her profit rate
> has doubled to 20%.
> S/he is overjoyed. And since the rest of the financial community is made
> up of simultaneists, all of them continually cheer whenever bond prices
> take a dive. They continually cheer good economic news that tends to make
> bond prices fall. And they put pressure on the central banks to inflate
> the economy, in the belief that this will lower bond prices. Since the
> central banks suck up to the financial community, we find them continually
> trying to inflate.
> And all of the simultaneist investors secretly dream at night that their
> assets become totally worthless, giving them an infinite rate of return!
> Sweet dreams
> Andrew Kliman