Hi, Steve. You write: > >I disagree that Sraffa's critique of marginalist theory can be dismissed >either because: > >"the"un-marginalist" Sraffian "result" about the relation between wage and >profit rates arises in part from begging the question of how these prices >(and they are indeed prices, in addition to representing claims on total >product) are determined in their respective markets" > >or because > >"The standard Sraffian model presumes that Leontief (fixed-coefficient, >constant returns to scale) production conditions obtain universally. >Whether this condition reasonably describes actual capitalist economies is >a matter of debate, but in analytical terms it is extremely restrictive. In >particular, Leontief can be understood as the limiting case of a more >general constant elasticity of substitution production function, and in >every instance of this function *except* the limit as the elasticity >parameter approaches infinity, factors are substitutable at the margin, and >thus "marginalist" considerations would presumptively apply." > >On the first point, Sraffa's objective was in part to show that a precursor >to the marginalist theory of income distribution--that the quantity of >capital was a measurable entity--was wrong. You can't have a marginal >productivity theory of income distribution--so that income equals marginal >product--if there is no way in which the amount of the factor can be >measured independently of its reward. Sraffa doesn't so much beg the >question as show that the answer to that question can't be "marginal >productivity". Up to the last comment, I agree with this wholeheartedly! As I said, reading Sraffa as refuting "marginalist theory" depends on how one interprets that notion. If it is taken to mean broadly that marginal considerations inform economic outcomes, then I think Sraffa simply begs the question by, among other things, failing to model outcomes in labor and capital markets. But if "marginalist theory" is interpreted as the (much more specific) "marginal productivity theory of capital (and perhaps labor) income," then I agree. As I noted, reswitching can be shown to occur using a fully elaborated neoclassical GE model; the marginal productivity theory of capital income is thus not an intrinsic feature of the general neoclassical system, though of course neoclassicists might not have been so willing to acknowledge this in the absence of the Sraffian challenge. I should reiterate here that I put Sraffa relatively high up on my list of contributors to modern PE, and the legitimate and important insight you address here is one of the main reasons for that placement. >Secondly, though the Leontief IO matrix is a "restrictive assumption", it >is also the linear component of any more general nonlinear production >technology (it's just the first term [Jacobian] in a Taylor series >expansion). Since the linear component of any nonlinear system dominates >the nonlinear in the proximity of equilibrium, what applies to a Leontief >IO system will apply to any more general technology in the same region. The mathematical truth in this, which I endorse, nevertheless does not rebut my point that in all cases but the limit of CES production, to which the Leontief system corresponds, substitution among factors (and thus potential "marginalist" considerations) arise, perhaps with indefinitely large elasticities of substitution, even "in the proximity of equilibrium"---indeed, *particularly* "in the proximity of equilibrium," because this is exactly the region in which marginalist comparative static analysis applies. >Since neoclassical economics is obsessed with equilibrium, the defence that >a more general production system applies in general is NO DEFENCE. Again, I question whether the neoclassical system can legitimately considered any more "obsessed" with equilibrium than the Sraffian system. The latter presupposes that the law of one price obtains universally, and implicitly, that the set of prices thus rendered are not simply transitory in the context of its theoretical representation of capitalism (otherwise why study it?). Even if you don't choose to call this representation an "equilibrium," it is formally equivalent to it. >This is an elementary point from differential/difference equation >mathematics, but it is something that few economists appreciate. It also >leads to a result most Sraffians aren't aware of--that the equilibrium of a >Leontief production system with spot prices is unstable. This result was >derived back in the 1960s, but again most economists of all persuasions >don't seem to appreciate its import. I don't understand this point--"unstable" with respect to what perturbations? Gil >Cheers, >Steve >At 05:26 AM 7/02/2002 Thursday, you wrote: >>Who has advanced our understanding of capitalism since Marx? I think it is >>impossible to answer this question briefly. When I try, I start with a >>short list of "the usual suspects" (though my list might differ from that >>of others on OPE-L, perhaps.....), and then find myself immediately >>branching out to recognize the related efforts of many others who have >>contributed small but important insights. Like Gary, I put Sraffa >>relatively high up on my list, but not exactly for the reasons he gives. >>Here's why: >> >>Gary writes: >> >> >I would have to say Sraffa (surprise!), mainly for showing that the >> classical >> >P.E. tradition running through Ricardo to Marx is robust: i.e. its >>fundamental >> >insights regarding value and distribution hold up when the problematic >> labor >> >value analysis is discarded. He also pointed the way to a critique of the >> >marginalist theory that displaced classical and Marxian P.E. >> >>To me, the validity of the latter statement depends strongly on what one >>means by "marginalist" theory. >>Speaking broadly, I would say that Sraffa's "critique" of marginalist >>theory is only achieved by arbitrarily dismissing or obscuring realistic >>conditions under which "marginal" considerations *might* plausibly arise. >>Three examples: >> >>1) Capitalism universally features markets for financial capital and labor >>power in addition to markets for commercially produced commodities, but the >>former are not incorporated into formal Sraffian analysis. Thus the >>"un-marginalist" Sraffian "result" about the relation between wage and >>profit rates arises in part from begging the question of how these prices >>(and they are indeed prices, in addition to representing claims on total >>product) are determined in their respective markets. >> >>2) The standard Sraffian model presumes that Leontief (fixed-coefficient, >>constant returns to scale) production conditions obtain universally. >>Whether this condition reasonably describes actual capitalist economies is >>a matter of debate, but in analytical terms it is extremely restrictive. >>In particular, Leontief can be understood as the limiting case of a more >>general constant elasticity of substitution production function, and in >>every instance of this function *except* the limit as the elasticity >>parameter approaches infinity, factors are substitutable at the margin, and >>thus "marginalist" considerations would presumptively apply. >> >>3) The standard Sraffian model also imposes rather stringent market >>conditions, without providing any formal grounds for understanding when and >>why they might obtain. In particular, it is assumed that the "law of one >>price" holds throughout, even in the (otherwise unanalyzed!) markets for >>capital and labor power. If you were to ask what sort of economic behavior >>would make this strong condition tenable, the only answer I know of would >>be arbitrage: market participants taking advantage of non-cost-based price >>differentials by shifting their choices of quantities demanded and >>supplied. But arbitrage is a form of optimizing behavior, and what's more >>it necessarily involves optimizing *at the margin*--otherwise price >>differentials would not be driven to zero, as the Sraffian model presumes. >>So if the model implicitly presumes marginalist optimizing behavior here, >>on what legitimate grounds does it categorically rule this behavior out in >>other plausible contexts? >> >>[Related thought experiment: Marx's analytical "base case," employed >>subsequent to V. I Ch. 5 of Capital, presumes that commodity prices are >>proportional to their respective values. Sraffian analysis replaces this >>basic scenario with one in which the law of one price obtains universally, >>but commodities typically do not exchange at their respective values. As >>Marx notes in the last footnote of Ch. 5, neither representation describes >>actual capitalist market outcomes. On what grounds *intrinsic to the >>theory* could one justify invoking the Sraffian in preference to the >>Marxian base case? ] >> >>Moreover, and more importantly, "marginalist" analysis, in the sense of >>taking derivatives of production, cost, or utility functions, is not the >>essence of *neoclassical* theory as it has developed in the 20th century. >>Which leads me to the next point: >> >> >The contribution was both positive and critical: he gave us a reason to >> stick >> >with classical P.E. (the theory holds up) and a reason to ditch >> neoclassical >> >theory (it DOESN'T hold up). >> >>I don't see this claim at all, since by the second welfare theorem, any >>market outcome generated by the Sraffian model could be supported as a >>solution of a neoclassical general equilibrium market model, and moreover >>one with Leontief production for which no derivatives are taken anywhere >>(so no "marginalist" conditions arise, in that limited sense). Thus any >>valid *positive* outcome emerging from the Sraffian model (as opposed to >>the "results" that emerge from simply failing to incorporate certain >>real-world markets or implicit behavioral assumptions) can also be >>demonstrated with the appropriately specified neoclassical general >>equilibrium model, with the important difference that in the latter the >>grounds for restrictive conditions such as the "law of one price" emerge >>from explicitly stated underlying conditions (conditions, by the way, that >>are never ruled out by Marx or Sraffa). For example, as Mas-Colell has >>demonstrated, one can readily generate "reswitching" phenomena in a >>standard neoclassical GE model. >> >>In light of this, I wonder how Sraffian analysis can be used to demonstrate >>that neoclassical theory "doesn't hold up," or for that matter that >>classical theory "holds up" any better. >> >>Gil >
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