[Draft] 7 economic metatheorems: Marx with Walras

A few words are needed: the equilibrium notion used here is the same used by Marx in some chapters of Vol. 3, which is not the neoclassical nor walrasian equilibrium. We don’t purport to claim there’s a walrasian Marx at all. How then is this work talking about a relationship between Marx and Walras? The relationship is based on an elaboration produced by me, not by Marx, but using Marx’s tools and concepts. So I’m starting off from Marx, and taking his concepts and tools to fields he didn’t worked on, like price formation, or like the apparent possibility of having found a way to measure not only profit, but the surplus value contained within prices themselves, etc. Second of all, the walrasian notion of equilibrium which we uphold as being present through this elaboration or extension of Marx’s own work and concepts, is not due to supply and demand, nor does it have a Pareto efficiency at all (actually proves the opposite), nor eliminates externalities (as Sraffa criticized neoclassicism, in consonance with Marx’s own critique, but in a Ricardian form –Sraffa goes from supply and demand to production, only to understand production in terms of relative prices, physicalism, etc, just like the smithianism that Ricardo himself finally conceded when dealing with production-). This is not even imperfect competition. Even in the fluctuation we supposedly want to determinate, prices do not tend to an ideal price (which is Walras’ original formulation), whether with fully satisfied supply and demand (perfect equilibrium) or not (just as an ideal tendency, never fully met). The fluctuation is based on the profit rate, based on the equivalence between prices of production and market prices we elaborated in our earlier draft-paper (the one I linked above), and consequently, has as a limit the profit rate, the organic compositions and the socially necessary labor which determinate profit and value creation and appropriation by each respective individual firm (just like Marx). But the fluctuation is indeed walrasian in three aspects: 1) first because it involves a tendency to equilibrium around an ideal profit rate, just like in the econometric and empirical analyses on the process of equalization of the profit rate, which do show a tendency between differentials and standard deviations and profit rates just like the one between relative prices and the ideal price described by Walras. Secondly, 2) because of the walrasian concept of relative prices, and it’s similarity with Marx’s difference between the total or expanded form of value and the general form of value, as the preceding moments (in a Hegelian sense: superseded but still contained within) before the money-form of value. The relative element of walrasian relative prices is completely equivalent to this Marxist notion: individual prices which fluctuate according to their relative form, and not their equivalent form, even when there’s a general equivalent. The transition from Marx’s total or expanded form into the general form, is the difference between individual exchanges having a general equivalence but still deviating from value in each individual and accidental exchange, and individual exchanges having a general and social equivalence perfectly expressed in the commodity serving as general equivalent, to the point where commodities exchange at their value. In other words, is the form which develops once the general equivalent is not casually, individually or accidentally used in a general form, but is socially and collectively established as the general equivalent form. The difference between all commodities being equivalents between themselves through a general equivalence, with relative price fluctuations or deviations from their value, and all commodities being equivalents between themselves through a single equivalent commodity, and with prices exchanging at the precise expression of this general value. So the walrasian use of the word ‘relative’, to denominate relative prices, is not casually connected to the relative form present in Marx, but is exactly the same. In Marxist terms, we would be talking about the social qualitative form, besides substance and magnitude. The mere social juxtaposition of individual prices in their aggregate or general and equivalent form, defines their oscillation. This is a walrasian notion, even though is not determined by supply and demand only, but to this social and qualitative form (is not based on the juxtaposition of individual sellers and buyers only in circulation, but on the juxtaposition of profit rate equalization and socially necessary labour). Is not a Pareto efficient equilibrium, because this equivalence doesn’t prevent externalities in Marx: even though all aggregate value exchanged in circulation stays the same, and producers and consumers only exchange the same amounts of value from one form to the other, some profit from it and some lose individually and particularly, specially in the total or expanded form where individual and accidental exchanges still deviate from their general equivalence. But it is a form of walrasian equilibrium in the precise sense in which Marx’s general form of value, where there’s still no money-form, prices are still oscillating around their own general equivalence between themselves, and in the precise sense of prices of production deviating from aggregate prices of production, and from the average and ideal general rate of profit, in the same way as relative prices deviate or oscillate around an arithmetic mean. We can conclude that Marx’s equalization of the rate of profit is not mathematically similar to an average, but to an arithmetic mean. Is not the middle point of an equilibrium, but the average of the aggregation of all individual magnitudes, all empirically deviating from any "perfect" equilibrium, and forming just a tendency to it. In this sense and finally, 3) prices of production are perfectly contained within empirical and everyday market prices, but the long-run process of equalization is not due to the average rate of profit rate determining prices of production, but to the aggregation of all individual prices of production determining an ideal average rate of profit from which the real and empirical market prices and the production prices contained within them, deviate from. Just like socially necessary labour is not Ricardian and it’s not a ‘center’ around which value or profits oscillate, and it has no ‘natural price’ (Smith) nor ‘middle price’ (Ricardo), but actually is made of heterogeneous organic compositions juxtaposed through their social qualitative form, in the same way the average profit rate is not a real and empirical ‘center’ around which prices of production fluctuate, but just an ideal arithmetic mean towards which prices of production tend to fluctuate. This means individual market prices in their aggregate juxtaposition determinate their oscillation, and not the other way around: the general aggregate does not determinate this movement, just like individual prices of production only equalize on a long-run process (both empirically and theoretically). This means our Metatheorem 6 is just as ideal as the general profit rate itself and it’s long-run equalization. It also means the oscillation itself goes from the individual to the aggregate level, just like equalization  of the profit rate goes from short-term to a long-term cycle, and just like value-form goes from the elementary or accidental form to the money-form.