Alejandro, I found an earlier and a bit longer draft of my Encyclopedia entry on the transformation problem, which I'm puting up on ope-l in three instalment. This one is the first one. I hope this will give you some answer to your questions, at least for the time being. About other papers, i'll get back to you. Thanks for your interest. Cheers, ajit sinha Transformation Problem by Ajit Sinha One of the central theses of Marx in Capital is that the basic macro variables of a capitalist economy are determined by the socio-historical factors rather than the market forces. The appearance of the dominance of market forces in a capitalist economy was characterised by Marx as "commodity fetishism". Though commodity fetishism is an important aspect of the capitalist culture, Marx's attempt was to penetrate through this appearance and reveal to the world the real relations of capitalism that hide behind the market appearances. The relation of 'values' to 'prices of production', which has come to be known as the transformation problem, was simply an attempt to show that how the real capitalist relation of exploitation expressed by the concepts of 'value' and 'surplus value' hides behind the market appearances of 'prices' and 'profits'. A theory of prices is essentially related to the question of bourgeois accounting. A competitive capitalist system 'requires' that the rate of profit must be equal across the sectors in the economy. The problem is to find a basis of accounting the profit and the investment such that the condition of equal rate of profit is satisfied. Marx arrived at this theoretical problem much later in his theory. In the first two volumes of Capital he worked out an analysis of the capitalist mode of production on the basis of a non-bourgeois accounting. He reduced every commodity to the direct and indirect labour-time needed to produce the commodity and called it the value of the commodity. Value was treated as the social substance of capitalist economy, akin to the concept of the mass of a physical object in physics. At the first stage, Marx assumed that commodities exchange in proportion to their values. This made it possible for him to show that all the non-wage income must be the result of the unpaid labour-time performed by the wage labourers. However, the assumption of commodities exchanging in proportion to their values would in general violate the condition of capitalist competition. For as long as the organic composition of capital (ie. the ratio of constant to variable capital, where constant capital refers to the value of machines and raw materials that is used up in production and variable capital refers to the value of the wage goods consumed by the workers during the production period) are different in different sectors, the exchange of commodities in proportion to their values would imply that the rate of profit in the lower organic composition of capital sectors would be higher than the rate of profit in the higher organic composition of capital sectors. This would instigate a migration of capital from higher occ sectors to lower occ sectors raising the prices of commodities produced by higher occ sectors vis-a-vis the commodities produced by the lower occ sectors. Thus the exchange ratios of commodities must diverge from their value ratios to bring about the condition of the equal rate of profit across sectors. What exchange ratios would guarantee the equal rate of profit across sectors, and how are they related to value and surplus value was the problem Marx tried to solve in the chapter IX of Capital volume three. The core of Marx's argument was that the gross output that is thrown in circulation after a period of production is equivalent to its total value as its substance, and this substance has three basic divisions: constant capital (C), variable capital (V), and surplus value (S). These three divisions of the substance are independent of particular exchange ratios of commodities: the size of the constant capital is determined by the prevalent technology, the size of the variable capital(ie. the real wage basket) by the social and historical factors, and the size of the surplus value by the length of the working day or the class struggle. However, these three determinations are not uni-causal but interdependent on each other. Prices or exchange ratios of commodities play a role in redistributing the substance of surplus value among the capitalist class to ensure the condition of competition. As Marx wrote: "The various different capitals here are in the position of shareholders in a join-stock company, in which the dividends are evenly distributed for each 100 units." (Capital III, p. 258). Marx's contention was that the question of prices is solely concerned with bourgeois accounting, where the issue is exchange between capitalists. As far as the exchange between wo/man and nature and capital and labour are concerned, they are determined independent of the price accounting. Marx's solution to the problem of prices and the equal rate of profit was simple. He aggregated the total surplus value produced in the economy (S), and divided it by the aggregate of constant plus variable capitals (C+V). The ratio S/(C+V) [or sum of si /sum of (ci +vi )] was declared to be the 'average rate of profit' (P) of the system. Given P, the prices of production of any commodity i (pi ) was simply derived by marking up the sector's capital investment in terms of its value [ie. (ci +vi )] by its average share in the total profit, ie. pi = (ci +vi ) + P(ci +vi ). Marx's method of calculating the average or the equal rate of profit and the prices of production ensured that the total prices would be equal to the total value, and the total profits would be equal to the total surplus value in the system [ie. Sum of pi = sum of li , where li = (ci +vi +si ), and sum of P(ci +vi ) = sum of si ]. These two results confirm Marx's basic proposition that even though in a competitive capitalist economy the exchange ratios of commodities differ from their value ratios (ie. pi /pj is not = li /lj ), the basic division of the economy into C, V, and S remains intact and prices seem to only redistribute the total surplus value among the capitalist class. The reader should note that Marx's "prices of production" are not empirical 'market prices' but rather the 'ideal prices' that would hold when the rate of profits are equal in all sectors. It was considered the gravitational point towards which the market prices gravitated due to the competitive forces, given the technological and distributional parameters determined from outside the market forces. Marx did not have the notion of demand and supply schedules, which happens to be the foundation of the present day orthodox theory of prices (see Garegnani, 1976). As it is quite clear, Marx's two invariance postulates, ie. Sum of pi = Sum of li and sum of P(ci +vi ) = sum of si , are the direct result of his definition of 'average rate of profit'. Defining P = sum of si /sum of (ci +vi ) implies sum of P(ci +vi ) = sum of si and sum of pi = sum of (ci +vi +si ). Later, in 1906-7, Bortkiewicz pointed out that Marx's determination of the 'average rate of profit' was improper. He argued that in Marx's formulation the inputs are calculated as labour-values whereas the outputs are calculated as prices of production, this implies an inconsistent accounting practice. A consistent formulation of the problem must use the same accounting procedure on both sides of the equations. Thus Marx's average rate of profit was wrong because the total capital investment cannot be taken as equal to sum of (ci +vi ) a priori. Therefore, the average rate of profit was an unknown in the system. Moreover, he showed that once the problem is consistently formulated the system turns out to be short of one equation for the complete determinancy of the prices of production, and when an invariance condition, ie. some postulate about the relation of value to prices of production, is added to the system then Marx's two aggregative results, in general, would not hold simultaneously. Since Marx had presented his two results as sort of a proof of the correctness of his value analysis, Bortkiewicz's results inevitably turned it into a 'problem'. Hence the transformation 'problem'. Alejandro Ramos wrote: > Ajit in #3900: > > "First of all, the determination of what you call the "m" is the central > problem with Marx's transformation problem." > > What is your definition of "Marx's transformation problem"? It seems to me > that there is not an universal agreement about what is understood by this. > > Why is the determination of "m" the "central problem" of this... "problem"? > > "That's why assuming that the value of m is "given" can never be taken > as a solution to the problem, and particularly when it is added that not only > the real m is unknown but is unknowable." > > So, this problem would not belong to the realm of science? What is this, > then?? > > "This simply confirms the Steedman critique." > > Do you mean the "redundancy" issue here? > > Alejandro > > P.S. If you're very busy, you can perhaps post any of your writings (cited > in another post) regarding this matter. It's obvious that for people like > me it's really impossible to get a copy in another way.
This archive was generated by hypermail 2b29 : Tue Oct 31 2000 - 00:00:07 EST