At 04:35 PM 4/22/97 -0700, Gil wrote: >Coincidentally, Ajit's post evoked a childhood memory of my own. My parents >took me to see a debate in which one participant made an argument for which >his opponent apparently had no effective response. Rather than expose this >fact by attempting to answer the argument directly, that opponent told some >elaborate story involving circuses, elephants on hind legs, tigers jumping >through hoops, and the like, seemingly intended (but not realized) as a >metaphor about the first debater's argument. This stratagem failed miserably. ________________ Your parents took you to see a debate? Some parents, I must say! My parents told me that if you detect a participant losing his sense of humar in a debate, you know he/she is too much on his/her backfoot. _________ Gil: > >I suppose the relevance of one or the other of our childhood memories will >presently become clear. Until then, I'll just note that Ajit ignores most of >my direct responses to his original claims (e.g., concerning the >significance of reswitching phenomena to the critique of the Walrasian >model), and so far as I can see his new points just offer additional >illustrations of my original position--that the differences he asserts >between the Walrasian and Sraffian systems are more apparent than real, >having much more to do with the different political economic concerns of >their respective exponents than with any necessary difference in the >analytical systems themselves. Also, as a preview of what's to come, I'll >reiterate my observation that mere omission shouldn't count as a point in >favor of a theory. If it did, then the claim that "stuff happens" is the >most powerful political economic model going. _____________ Ajit: The reason I ignored most of your so-called specific comments was that I wanted to draw your, as well as others, attention to some basic methodological and epistemological differences between the two theories, so that your fundamental claim that Sraffian theory is just a special case of the GE theory has simply no legs to walk on. You seem to have completely, and I think delebrately, miss my point. If this long responce, which I'm writing, does not take care of any of your "specific" claims, I'll go back to it and make sure that I respond to them. _______ Gil: > >Ajit continues: > >> I have one simple question to ask Gil, and then I might have more ;). >>Question: Arrow-Debreu commodities have many properties attached to them. >>One of them is time. So let's say we start off with the commodites for time >>zero. These commodities, by definition cannot be the products of >>commodities, ie. they could not have been produced by commodities. > >I disagree. Ajit's claim holds only if one insists that in the Arrow-Debreu >framework "time zero" *must* be interpreted literally as "the beginning of >time", or, if you'd prefer, "the beginning of market time." But in no case >that I know of is "time zero" interpreted in this way--rather it is taken to >represent "the current period" or "the initial period" of an economic >interaction under study. Of course, one can assume this without having to >pretend that current endowments fall like manna from heaven. _____________ Ajit: Your disagreement cannot nullify the logical validity of my point. I never said that time zero is GENERALLY taken to be before the beginning of production. My point was that logically you could set up a general equilibrium market before any production has taken place. Because, the theory takes ENDOWMENTS as GIVEN. This was not my original point, as a matter of fact. John Geanakoplos, who is respected enough in this area to have written the entry 'Arrow-Debreu model of GE' in the New Palgrave, makes this point. So let me quote Geanakoplos: "The Arrow-Debreu model of general equilibrium is relentlessly neoclassical; in fact it has become the paradigm of the neoclassical approach. This stems in part from its individualistic hypothesis, and its celebrated conclusions about the potential efficacy of unencumbered markets. (...). But still more telling is the fact that the assumption of a finite number of commodities (and hence of dates) forces upon the model the interpretation of the economic process as a one-way activity of converting given primary resources into final consumption goods. If there is universal agreement about when the world will end, there can be no question about the reproduction of capital stock. In equilibrium it will be run down to zero. Similarly when the world has definite beginning, so that the first market transction takes place after the ownership of all resources and techniques, and the preferences of all individuals have been determined, one cannot study the evolution of the social norms of consumption in terms of the historical development of the relations of production. ONE CERTAINLY CANNOT SPEAK ABOUT THE PRODUCTION OF ALL COMMODITIES BY COMMODITIES (SRAFFA, 1960) (SINCE AT DATE ZERO THERE MUST BE COMMODITIES WHICH HAVE NOT BEEN PRODUCED BY COMMODITIES, I.E. BY PHYSICAL OBJECTS WHICH ARE TRADED)." (pp. 57-58, emphasis added) So you can see that not only my specific point was correct but Geanakoplos is also indirectly alluding to the fundamental methodological difference between the GE and the Sraffian theory, i.e. one is linear and the other is circular. ____________ To my statement: > >> This situation cannot arise in Sraffian system because his commodities are >always >> products of commodities. Gil responds: > >Yes, by assumption, but this hardly counts as a point in favor of the >Sraffian system on descriptive grounds. ________ Ajit: By assumption of what? The assumption is that the production must be contextualized within a given mode of production. Sraffa does not talk in terms of "agents" and "endowments" and prices of "endowments" etc. He talks in terms of wages and profits, capitalists and wage-laborers. These categories will not apply in any human situation, but are specific to the capitalist mode of production. So it does count as a point in favor of Sraffa, if you understand what is meant by HISTORY. However, your further remarks suggests that you don't understand what I and probably rest of the world understands by history. We will get to that soon. ___________ Gil: First, as a descriptive matter >commodities *should* be time-indexed, as they are in the Arrow-Debreu >framework, because in fact production and circulation takes >time--commodities serving as inputs into production exist at an earlier >point of time than the commodities produced with these inputs. The Sraffian >system, of course, glosses over this distinction. If it didn't, it would >commit the same spurious "error" Ajit identifies above. More on this point >below. ___________ Ajit: Ironically, the point Gil makes above is a serious problem for the GE theory and not a problem for the Sraffian theory. Since Gil repeats this point too often, and I think it is an important point, so let me take some of your time to explain the nature of the problem. My explanation is derived from Garegnani's 'Quantity of Capital'. Let us begin with Walras' problem first. The Walrasian system begins with the assumptions that: (1) consumer preferences are given, (2) methods of production at a given technical knowledge is given, and (3) the quantity of factors of production available in the economy is given. So the total quantity of factors are given, as well as all the ways in which these factors could be combined to produce commodities are also given. The measurement of these givens must be possible independent of prices, otherwise the theory will get into circularity. Now, the 'factors' that are considered 'capital' have two characteristics: they are products and they are used for further production and wear out in a short period of time, unlike land that stays there for ever. Now these two aspects of 'capital' have two consequences: one, they have a supply price, and two, they have a rate of return which, in a competitive enviorenment, has a tendency to equalize. We will call these equalized rate of return, 'effective' rate of return as opposed to nominal rates of return, i.e. empirical rates, which may fluctuate around the 'effective' rate due to accidental factors. This second requirement creates serious problem for Walras. Suppose we start off with the assumption of zero gross savings. The prices of the hetrogeneous capital stocks is determined by their given supply. But there is no guarantee that the given configuration of capital stocks would be the one 'appropriate' to the production of the outputs required by the preferences of the consumers. In that case the equality between demand and supply of the various capital goods would require that the prices of the relatively abundant capital good fall below the level compatible with the rate of return on the supply price on the relatively scarce capital good. Thus, violating the requirement of equality of return. Garegnani further shows that this problem is not resolved by relaxing the assumption of zero gross savings. The fundamental contradiction between taking a hetrogeneous capital stocks as GIVEN and the price of capital goods determined on the basis of intensity of consumer preferences would in general violate the requirement of equal 'effective' return on capital investment. Actually, Walras himself acknowledged it and made a retreat in the 4th edition of the ELEMENTS. To quote Walras: "it is not all certain that the amount of savings ... will be adequate for the manufacturing of new fixed capital goods proper in just such quantities as will satisfy the last l equations." (Walras, [1874-7]1954, p. 308, quoted from Garegnani). There have been two different kinds of attempts to solve this problem. One has been to assume capital as a single factor so that its physical composition can be left to be solved by the equilibrium condition, i.e., to think of it as a peculier factor that could change in 'form' without changing in quantity. The second approach has been to reject the Walrasian concept of equilibrium as a 'gravitational point'. This second approach is followed by Arrow-Debreu and others. The idea of equilibrium as 'gravitational point' distinguishes between persistent forces and accidental factors. In this case the theory allows sufficient time for the repetition of the same commodities' prices. But once the idea of 'gravitational point' is given up, one cannot deny that the tendency for the rate of return to equalize would affect the composition of the GIVEN capital stocks; since accidental factors would generally keep the prices away from the prices that would gurantee the 'effective' rate of return on capital stocks. Therefore, in the Arrow-Debreu framework equilibrium must be defined for every moment of time or a very short period of time for which the quantity of given capital stocks can be taken as given endowments. This is the reason why Arrow-Debreu commodities come with a clock time or 'date' attached to them as their name tags. Now, let me point out the weaknesses this name tag creats for the theory. First of all, the Arrow-Debreu equilibra loses an important capacity of a theory to distinguish between accidental and persistent causes. And, as Garegnani suggests: "to the extent to which this is true, a purely methodological reason, quite independent of the content of the theory, arises for questioning the capacity of these equilibria to offer sufficient guidance to the behaviour of the economy." (p.49). Secondly, now it can no longer be denied that if production takes time, then prices of inputs may diverge from the prices of outputs. So, there is no guarantee that this divergence itself would not affect the behavior of the agents and therefore the equilibrium conditions. [If Andrew and Alan are listening, you should direct your fire at the Arrow-Debreu model which is a legitimate target. Sraffa is not a legitimate target for your kind of attack simply because it takes the long term view that allows repetition of prices around the gravitational point]. Third, in this dated inviorenment, the savings and investment behavior of the economy can only be taken into account by assuming a complete future markets, which is an absurd idea. Because, even theoretically (forget about practicality) it is not possible to imagine that we could know the tastes of future generations and the rest. Moreover, the Arrow-Debreu theory becomes fruitless for an analysis of changes in taste, population, and most importantly 'capital' accumulation. The concept of accumulation loses all its meaning, since at every moment of time 'capital' is taken as stocks that is independently given. Even the idea of capital accumulation is difficult to maintain! Since this response is turning much longer than I thought, I'm going to send this much first and the rest in the second batch. Cheers, ajit sinha
