Dear all,
I have to thank James Devine for pointing the pen-l forum to me. This message tries to contribute to the discussion on Roemer’s theory of exploitation, and in particular it tries to reply to G. Skillman’s (pen-l 03 March 2002) detailed and thoughtful comments (not even my closest relatives read the paper so carefully!!!!!), which are the written version of long and stimulating (at least for me) verbal discussions. First, a couple of preliminary issues: a) G. Skillman’s point on the implication of my results about Marx V.I, Ch.25: my “reply” in the message forwarded by J. Devine is simply too poor to be a proper counter-argument. I am sorry, I wrote it before having subscribed to pen-l, and thus before having read the whole discussion. b) I have never thought, let alone claimed, that my results (even assuming that they are correct…) “demolish” Roemer’s theory. As a matter of intellectually honesty (and to avoid potential readers’ disappointment), I have to say that no logical flaw of Roemer’s (1981, 1982) results is found and no general impossibility theorem is proved regarding neoclassical microfoundations to Marx’s exploitation. Unless one needs space on bookshelves, Veneziani (2000) should not be in itself sufficient to throw Roemer (1981, 1982) away (my paper is much shorter than his books…) c) This is going to be a bit boring, I am afraid. Anyway, a verbal summary of the results of the paper under discussion are in J.Devine’s message (pen-l 08 March 2002). G. Skillman’s two main points are: (1) My results “qualify” Roemer’s claims, but do not cast substantial doubts on his Differential Ownership of Productive Assets (DOPA) theory of exploitation and classes, because the scarcity of productive assets is not taken into account. Roemer’s result (beyond his verbal claims) is that DOPA “plus scarcity” (to be explained later) is necessary and sufficient for exploitation. (2) Even assuming that my paper raises serious doubts on Roemer’s theory, SKILLMAN: [“to the extent it compromises Roemer's analysis, it *necessarily* also calls into question Marx's analysis of "the general law of capital accumulation" in V.I, Ch. 25 of Capital, since Veneziani's results depend on the possibility that *all* individuals, not just the rich ones, can save, a possibility that Marx evidently rules out, or at least fails to discuss.”] In this message I will only reply to (1). Details: 1) SCARCITY. Skillman: [“despite the passage from GTEC cited by Veneziani, Roemer doesn't really assert that mere differential ownership of the means of production (DOMP) is of itself sufficient for the existence of exploitation.” And then: “As Roemer quite explicitly explains elsewhere in GTEC, the means of production must also be *scarce* for exploitation to arise. In any case, his formal results on this point are unambiguous. The relevant theorem is 2.2, which asserts the equivalence of the existence of exploitation with *the possibility of positive profits* (PPP), not mere DOMP. Since, in this formal system, the profit rate is (also) a shadow price, this is equivalent to asserting the equivalence of exploitation with differential ownership of *scarce* means of production (DOSMP). So in any case, Veneziani hasn't established anything fundamental about the conditions for exploitation that Roemer didn't already assert himself.”] I have not been able to find the passage where Roemer talks about scarcity. Anyway, as far as Theorem 2.2 is concerned, neither I nor Roemer “have established anything fundamental about the conditions for exploitation” that Okishio, Morishima. etc. did not already assert. Theorem 2.2 is a version of the Fundamental Marxian Theorem: positive exploitation is equivalent to positive profits. This result is NOT put into question in the paper (although one might criticise Roemer’s definitions on a priori theoretical grounds). Actually, taking as given Roemer’s definitions, the paper “implicitly proves” a dynamic version of Theorem 2.2 in the intertemporal economy. The point is exactly to show that in Roemer’s perfectly competitive neoclassical economy, the conditions for Roemer-exploitation (and thus profits, due to Theorem 2.2) fail to hold in the long run: exploitation, and thus profits, disappear. Having said this, I do not see how the scarcity issue might change my conclusions. As regards PHYSICAL SCARCITY, Theorem 2.2 requires that there are enough resources in the economy to guarantee subsistence to all agents. Roemer stresses that this imposes a floor on endowments, but the theorem holds for any level of endowments above that level. And given that Roemer’s economy repeats itself forever (and given that capital does not depreciate) such abundance can persist forever. Moreover, my result does not depend on physical accumulation (as Skillman notes, the simple possibility of savings does the job). Hence, I assume that the issue here is not physical scarcity. If the issue is about “ECONOMIC SCARCITY,” namely the relative scarcity of capital with respect to labour, such that profits remain positive, then Skillman’s point confirms my result! I show that in Roemer’s subsistence economy exploitation and profits (thanks to Theorem 2.2) disappear. Skillman says: your result would not hold if profits remained positive. I agree. The point is that there is no mechanism guaranteeing such “scarcity” in Roemer’s models, and this “scarcity” disappears even in the absence of accumulation, so that the physical balance between labour and capital does not change in time. 2) This fact implies that my results do not simply “qualify” Roemer’s theory. Here is what Roemer says in his reply to Devine and Dymsky (Economics and Philosophy, 1992): “Consider the logical structure of the argument. In the real world we observe X (DOPA), Y (coercion in the labor process), and Z (class and exploitation). We have, if you will, an ‘empirical proposition’ that [X + Y => Z]. Now I construct a model in which the following theorem holds: [X + not Y => Z]; from this I say that X is the ‘fundamental cause’ of Z in the real world, not Y” (p.152). In the next page, he adds: “my position on the ‘fundamentalism’ of DOPA in fact goes farther than advocating the strictly logical claim advanced three paragraphs above” (p.153). There are many other statements like these about the logical status of DOPA plus competitive markets as the ONLY source of exploitation (e.g. Roemer, 1982, p.13-14, and p.42). I think they are difficult to “interpret” abstracting from what it is explicitly contained in them. In any case, at least as far as Roemer’s own interpretation of his theory is concerned, I think my point stands, and from what he writes, I think G.Skillman would agree. The aim of the paper is precisely to discuss Roemer’s LOGICAL ARGUMENT quoted above: the paper shows that maybe [X + not Y => Z] holds, but [X persistent + not Y => Z persistent] does not hold, BECAUSE of Theorem 2.2. Thus DOPA is NOT necessary and sufficient to have exploitation (and thus profits) as a persistent phenomenon. At least in a neoclassical framework one must have a mechanism to make it persistent, and trivial as it may seem, the other point of the paper is that such a mechanism is unlikely to be found in perfectly competitive neoclassical models. This result is not very surprising: Roemer obtains “persistent” exploitation by assuming away not only accumulation, which is alright in a subsistence economy, but also life-cycle savings, interpersonal credit, and intertemporal tradeoffs. Thus, here comes another conclusion of the paper: if these extremely restrictive and ad hoc assumptions, are necessary to have “persistent” exploitation, and given that these assumptions imply that Roemer’s model is very far from the Walrasian benchmark, it seems legitimate to say that the results in the paper raise serious doubts on the claim that “the neo-classical model of a competitive economy is not a bad place for Marxists to start their study of idealized capitalism” (Roemer, Analytical Marxism 1986, p.192). At the very least, one might argue that Roemer’s model does not prove this claim convincingly. 2) G. Skillman suggestion about scarcity is the following: let K be some other factor guaranteeing the “scarcity” of capital (namely, positive profits), then Roemer’s argument should be more precisely stated as: [X persistent + K persistent => Z persistent]. Well, it is difficult to disagree: since K guarantees persistent positive profits, by Theorem 2.2, this guarantees persistent exploitation. However, in this case, unless one shows that X is fundamental in the causation of K, namely that X implies K (so that in the end it is still only X that matters), the logical claim remains true: DOPA is not necessary and sufficient by itself to generate persistent exploitation and profits. Theorem 2.2 does not change this conclusion, and the claim that a perfectly competitive neoclassical model with utility maximising agents is unlikely to provide exploitation (and profits) as a persistent phenomenon. On the other hand, if K is just the statement that profits must be positive, then by Theorem 2.2. K and Z are equivalent, so that X is redundant and the statement reduces to [K persistent <=> Z persistent]. 3) ASSUMPTIONS. Given the nature of my argument, I have opted for having a model as close as possible to Roemer’s. Hence, except for the fact that agents live for more than one period and can save out of their income, all other assumptions are Roemer’s. Zero depreciation of capital goods, no capital markets, no growth in the labour force, etc. If these assumptions are not plausible, then they are not plausible in Roemer’s framework either, which is not a static framework in that the economy repeats itself over time. 4) SPECIFIC POINTS. Skillman says that the main result [“doesn't really suffice to controvert Roemer's claims, because: A) It is not shown that the rate of exploitation ever *reaches* zero in any finite period.”] Exploitation (and profits) decrease at an exponential rate: thus after 100 periods it is already virtually zero. If periods are quarters, 25 years suffice to have a basically-exploitation-free economy. Although, I agree that [“this leaves open the possibility that exploitation persists for a lifetime”] (as I say in the conclusions of the paper), it remains true that Roemer’s economies have the disturbing feature (at least from a Marxian viewpoint) that the economy has a self-correcting mechanism that leads exploitation to virtually disappear. Notice that this result is obtained with only a very small change in the Roemer’s original assumptions: it seems legitimate to infer that other changes would lead exploitation to disappear completely from the perfectly competitive neoclassical model sooner. I do not think I am particularly original on this point: this is what neoclassical economists say all the time based on their models. B) I agree with G. Skillman on the WITHIN PERIOD vs. WHOLE LIFE exploitation issue. My aim is not to show that the economy is just. And I do not say that WL exploitation is irrelevant. The theoretical importance of WP explo. is as follows: take two agents, in period 1 one is an exploiter and the other is exploited, while in period 2, roles are reversed so that “total exploitation” over the two periods is zero. Is this society “exploitation-free” (or, if you wish, would it be correct to hold that it is exploitation-free in a Marxian sense)? I doubt it, otherwise a truly Marxist policy should be to keep capitalism alive but assign capitalist and workers roles to people by a lottery. Hence the particular interest in WP explo. C) Skillman: [“Veneziani's results are based on omitting a fundamental feature of Marx's dynamic analysis, i.e. an exogenously given rate of growth in the labor force. Were this incorporated into the formal model, then persistent non-negligible rates of exploitation might be consistent with even strictly positive levels of saving. Notice the relevance of this to Roemer's basic claim: given labor force growth, capital may remain *functionally* scarce, and exploitation persist, even in the presence of accumulation.”] The assumption that there is no growth in the labour force is Roemer’s. And I am not sure about what would happen in his subsistence economy in the presence of exogenous growth of the labour force. Anyway, Skillman’s claim is equivalent to saying that K = exogenous increase in the labour force. I do not think this is the most persuasive choice of K, given that Roemer’s logical argument is based on a subsistence economy (as he argues in his reply to Devine and Dymsky), and assuming an exogenous increase in the labour force does not seem very consistent with the subsistence assumption. Moreover, once one moves to Roemer’s accumulating economies, it easily shown (and explicitly admitted by Roemer) that, due to the knife-edge property of the Leontief technology, apart from very special assumptions on the growth of the labour force, the economy breaks down after only one period. I guess this is another reason why Roemer emphasises the importance of subsistence economies. D) Skillman: [“One can also establish the persistence of exploitation due to DOSMP in a dynamic context by introducing wealth-dependent time preferences—I demonstrate this formally in a paper available on my web site.”] G.Skillman’s model is rather different from Roemer’s, thus I am not sure that it reinstates Roemer’s claims, at least not as they were formulated. Apart from this, I strongly suggest the paper (and H.Ryder’s 1985 paper in the references). Skillman continues: [“Veneziani thinks this requires altering Roemer's assertion that DOSMP is of itself sufficient for the existence of persistent exploitation. Perhaps so, but to my mind, not in a way that does fundamental violence to Roemer's result.”] Here K = heterogeneous and endogenous preferences. Although there is no doubt that if one adds enough structure (and especially heterogeneity) on agents’ preferences, profits and exploitation might persist, this does not change the conclusion that DOPA is not sufficient to generate persistent exploitation, as admitted by Skillman. Moreover I think that this choice of K does harm Roemer’s theory at least in two fundamental ways: (1) differences in preferences are the typical neoclassical argument to justify differences in wealth, and Roemer explicitly rejects this sort of argument. See for instance, the discussion about differences in rates of time preference in Roemer 1981, p.85, and Roemer, 1982, p.12. (A particularly detailed discussion is in “Free to loose”, but I do not have the reference because I left my copy in Italy!!). The reason why he does not want to have differences in preferences is that the normative status of his DOPA-based theory of exploitation would be blurred. (2) Methodologically, it is dubious that models whose results depend on specific assumptions on preferences provide proper microfoundations to Marx, who did not use such assumptions. 4) Skillman: [“Finally, Veneziani infers from his conclusions that one cannot establish the persistence of capitalist exploitation on the basis of the sort of *competitive* market conditions assumed by Roemer. But I don't see the basis for this.”] I don’t either. This is the only point in which I think there is a mere misunderstanding, probably due to my poor explanation in the paper. I do not think Marx’s theory requires a walrasian model with imperfections: exploitation does not appear thanks to monopoly power, externalities, etc. The theory should work in a competitive economy, too, at least at the highest level of abstraction. The point is not the adjective “competitive,” but the adjective “walrasian.” Once again, I do not think one can provide microfoundations to exploitation within a perfectly competitive neoclassical-walrasian model. 5) On the very last paragraph of G. Skillman’s comments: no reply, just a renewed invitation to Italy… Roberto Veneziani
