Marx's analysis shows what is wrong with the Temporal Single System Interpretation, because, at any one time, there is no single system of prices, based on prices of production. The prices obtaining in each sphere, at any one time, differ from the price of production, because the actual rate of profit, in each sphere, necessarily varies from the average rate of profit. As Marx describes, in his historical elaboration of the formation of prices of production, the input prices of even non-capitalist commodity producers, are modified by the output prices of capitalist commodity producers, so that even the non-capitalist producers sell at prices that differ from exchange-values, whilst also not being prices of production either.
It is this that leads Engels, in his Supplement, to comment that, from the 15th century, the prices of commodities were no longer determined by the Marxian Law of Value, by which he actually means did not coincide with their exchange-value. But, moreover, we have seen that, as far as the prices of agricultural commodities is concerned, and the same is true for any commodity where landed property intervenes, to prevent surplus profit being competed away, the price is determined by the exchange-value, rather than the price of production, with the difference being appropriated as rent.
And, a similar situation as that given by Marx, in his historical account of the formation of prices of production, applies to all new lines of production. In other words, they start off being sold at prices that approximate exchange-values (modified because their input costs are determined by prices of production), and only after a period of competition, and capital accumulation, in that sphere, do these prices get brought increasingly closer to their price of production. As he puts it,
“... if a new branch of production comes into being in which a disproportionate amount of living labour is employed in relation to accumulated labour, in which therefore the composition of capital is far below the average composition which determines the average profit, the relations of supply and demand in this new trade may make it possible to sell its output above its cost-price, at a price approximating more closely to its actual value. Competition can level this out, only through the raising of the general level [of profit], because capital on the whole realises, sets in motion, a greater quantity of unpaid surplus-labour. The relations of supply and demand do not, in the first instance as Ricardo maintains, cause the commodity to be sold above its value, but merely cause it to be sold above its cost-price, at a price approximating to its value. The equalisation can therefore bring about not its reduction to the old level, but the establishment of a new level.” (p 435)
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