SRAFFA'S REPRODUCTION PRICES VERSUS PRICES OF PRODUCTION: Probability and Convergence

Abstract

(ProQuest: ... denotes formulae omitted.)1.Reproduction PricesIn the first pages of Sraffa (1960), a simple two product economy producing corn and iron is introduced with the following structure:In volume I of Capital (Marx 1887), Marx used a price theory in which commodity prices are taken to be proportional to the labour required to make the commodity. He used this price theory to argue for a theory of surplus value, according to which workers were exploited of the full value created by their work. In Chapter 20 of the second volume (Marx 1974), he introduces reproduction schemes, matrices of inter-sectional flows of commodities that had to occur if the economy was to reproduce itself.The matrices have four column vectors:C constant capital, his term for expenditure on capital goods and raw materials.V variable capital, his term for expenditure on wages.S surplus or profit.O output.We give an example in Table 1.1 of a 2 x 4 matrix, with the row labelled I representing the production of capital goods and raw materials, and row II the production of consumer goods. In Marx's tables, all quantities are in terms of money rather than in terms of use values.1 For accounting reasons, the relation O = C + V + S must hold.Furthermore, Σ C = °u that is to say, consumption of capital goods equals their production, and Σ (V + S ) = O2. Together, this implies that sector I of the economy must trade O - Q in capital goods for C2 worth of consumer goods produced in sector II. So we have an equilibrium equationC2 = V + SvThis is the equilibrium condition of an economy in a stationary state where it simply reproduces itself neither growing nor shrinking. The basic analysis in this article will assume this stationary state. Real economies may grow or shrink, but the rate at which they do this is typically quite small. A developed industrial economy like the US can go long periods in which the rate of growth averages only 3% a year or less, so analysis of price systems in a stationary state is a reasonable first approximation.Although it is not done by Marx, one can in principle construct a dual table like Table 1.2 in tons of consumer goods (corn) and tons of capital goods (coal). In this case, the first column represents the coal used up productively by the two industries, and next come the consumer goods (corn) consumed by the workers and employers in the two sectors. Again we have the requirement that the total consumption and total production of each good must balance, 160 tons of corn, and 20 tons of coal.It is clear from this table that the coal industry must sell 10 tons of coal to the corn industry and get back in return 40 tons of corn, which in turn implies that the relative price of a ton of coal must be 4 times the price of a ton of corn. Referring back to the first table and comparing it with the second, we see that indeed the price of a ton of coal was £4, but a ton of corn cost only £2.50. The important point here is that given the physical table, the relative prices necessarily follow.The example is artificial in that in practice sectors I and II would each produce a whole vector of outputs, but given the constants of proportionality between the elements of these two vectors, the exchange relation between them establishes relative sectoral prices.Marx later extends the scheme to three sectors, by dividing consumer goods into necessities (IIa) which are assumed to be bought out of wage incomes and luxuries (IIb) which are bought out of property incomes. If we retain the label II for necessities and use III for luxuries, we have the three-way trade between sectors in Figure 3.1.The tables are given in money terms, much as modern national accounts are, but the assumption explicitly remained that these quantities of money are proportional to quantities of labour (Marx 1974, Chapter 21, Section 7). But in principle, other pricing structures are possible so long as they allow the trade pattern in Figure 3. …