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History of Political Economy 32.2 (2000) 187-232
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Sraffa and the Interpretation of Ricardo:
The Marxian Dimension
Samuel Hollander *
Sraffa . . . bit out a piece of Ricardo's shirt and ran it up on a flagstaff claiming that it was all that the man had on.
--Sir John Hicks, letter dated 2 November 1978
1. Sraffa's Attributions to Ricardo
Piero Sraffa's Production of Commodities by Means of Commodities (PCMC) (1960) concerns the problem of a given physical surplus to be distributed to assure a uniform profit rate. Output levels ("gross output quantities") are included among the technological data determined outside the system along with the wage rate. (Alternatively, the profit rate may be taken as independent variable and the wage as one of the unknowns .) Assume a physical surplus in the sense of an excess of one or more commodities over the amount(s) used up as input; then the (general) profit rate (r) will be determined "through the same mechanism and at the same time as the prices of commodities" (6), for to distribute the (physical) surplus so as to assure a uniform profit rate requires [End Page 187] knowledge of prices in order to calculate the value of the means of production (which are heterogeneous products), while conversely to calculate the prices implies knowledge of r. But these propositions regarding price and profit-rate determination apply specifically to basic commodities, or commodities entering (directly or indirectly) as input into the production of all commodities, including themselves. 1 The simultaneous emergence of profit rate and prices is not the case in the so-called Standard system, where distribution has absolute priority. A brief summary of this position is in order.
Sraffa constructs a measure of value that has the property that it is itself invariable to a change in distribution, and though a change in distribution will alter its rate of exchange against other commodities produced under different technical conditions, the variation can be said not to "originate" in the measure itself but in the commodities being measured. The commodity in question is one produced with the "balancing input proportion" recurring at all stages in the vertical production process (16). 2 Although no individual commodity is likely to have the requisite characteristics, a composite commodity can be constructed--it is a weighted average of actual commodities that includes all basics and only basics (23-25)--with the property that the commodity-mix of the aggregate (gross) product is identical with the commodity-mix of the aggregate means of production. Sraffa proves, first, that any actual system can be reduced to a Standard system that describes the input-output relations relating to the sought-after composite commodity and, second, that only one such miniature system will apply (26). Finally, in the Standard system the ratio of net output to means of production (the Standard ratio R) can be specified independently of prices, since effectively we have the same physical commodity in the denominator and the numerator of the expression--the proportionate mix of commodities being the same for both. [End Page 188]
Now to the major uses of the device. First and foremost, changes in the division of the net product between wages and profits may affect relative prices in terms of the measure, but the ratio (R) of the net product to means of production in the Standard system will be unaffected; indeed, the role of the Standard system is to "give transparency to an [actual] system and render visible what was hidden" (23). 3 Second, when the net product is divided between wages and profits--these shares as well as the total consisting of the Standard commodity--then the rate of profit will equal the profit share times the Standard ratio. 4 Like the Standard ratio itself, the rate of profit in the Standard system is effectively a ratio between quantities of commodities and is therefore unaffected by movements in relative prices (22). These results may be expressed as
r = R (1 - w),
where r is the profit rate, w the share of wages...