Price of production
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A concept of Marx's in Part II of Volume III of Capital: the cost-price of a commodity (the constant and variable capital used up in making it) plus profit at the economy-wide average rate. Because capitals in different branches have different compositions, their rates of profit at first differ; but capital leaves branches with low profit rates for those with high ones, so profit rates tend to equalise into one general rate, and commodities come to sell around their prices of production rather than their values. Marx held that individual prices of production deviate from values while, for society as a whole, total prices of production equal total values and total profit equals total surplus-value, and this link became the subject of the debate over the transformation problem.
In depth
Why do the values of Volume I seem to clash with actual prices?
In Volume I of Capital the value of a commodity is the sum of the value of the means of production used up (constant capital, c), the value paid for labour-power (variable capital, v) and the surplus-value that the workers produce on top (s). Only living labour creates new value, so at an equal rate of surplus-value a branch that employs more workers, that is, one in which variable capital weighs more, yields more surplus-value for every 100 of capital advanced. A clothing workshop full of hand labour should then earn a far higher rate of profit than a steelworks that spends heavily on machines and raw materials.
Real capitalists do not think that way. Wherever they invest, they expect a profit roughly in proportion to the sum invested, and if profit rates differ greatly, money flows towards the higher one. The classical economist David Ricardo already knew well that relative prices are not proportional to the labour they contain. Marx did not hide the discrepancy; he took it head on in Part II of Volume III, "Conversion of Profit into Average Profit".
What figures did Marx use?
In Chapter 9 Marx assumes five branches of production, each with a capital of 100 and the same rate of surplus-value of 100 percent (the figures are Marx's own illustration). Their compositions are I 80c + 20v, II 70c + 30v, III 60c + 40v, IV 85c + 15v and V 95c + 5v. Surplus-value equals variable capital, so it is 20, 30, 40, 15 and 5, and the rates of profit are just as unequal: 20, 30, 40, 15 and 5 percent.
Taken together the five capitals make 500 = 390c + 110v with a total surplus-value of 110, an average of 22 for every 100: the average rate of profit is 22 percent. Marx called the price obtained by adding 22 percent to each branch's cost-price its price of production. Because his table assumes that only part of the constant capital wears out in one period, the cost-prices are 70, 81, 91, 55 and 15 and the prices of production 92, 103, 113, 77 and 37. Compared with value, I sells 2 above, IV 7 above and V 17 above, II 8 below and III 18 below. "Taken together, the commodities are sold at 2 + 7 + 17 = 26 above, and 8 + 18 = 26 below their value."
"The price of production of a commodity is equal to its cost-price plus the profit, allotted to it in per cent, in accordance with the general rate of profit." Each capitalist's profit is then no longer the surplus-value pumped out in his own workshop but a share of society's total surplus-value in proportion to the size of his capital. In Marx's words, "so far as profits are concerned, the various capitalists are just so many stockholders in a stock company in which the shares of profit are uniformly divided per 100."
How do profit rates become equal?
No one plans the equalisation; competition brings it about. In Chapter 10 Marx writes: "But capital withdraws from a sphere with a low rate of profit and invades others, which yield a higher profit." Where capital crowds in, supply grows and prices fall; where it leaves, supply shrinks and prices rise. Through this incessant outflow and influx market prices oscillate around prices of production and profit rates are pulled towards the average.
The equalisation is only ever a tendency. Within a branch, a capital producing under better than average conditions has lower costs but receives the same price of production, and so earns a surplus-profit. When that surplus-profit is tied to a natural condition that can be monopolised, such as land or a waterfall, it passes to the landowner as rent: Marx's theory of ground rent is built on the theory of prices of production.
What is preserved, and what is hidden?
Marx held that although individual prices deviate from values, the two coincide for society as a whole: "the sum of the prices of production of all commodities produced in society, the totality of all branches of production, is equal to the sum of their values." Total profit likewise equals total surplus-value. Competition only divides the surplus-value already produced; it cannot add to it.
The source of profit, however, is hidden one layer deeper. Since profit returns in proportion to the whole capital advanced, it seems to spring from the capital as a whole, machines and materials included, and the fact that living labour is its only source vanishes from the surface. Marx also knew that his own calculation still reckoned the means of production that enter the cost-price at their values, and he left the point aside: "Our present analysis does not necessitate a closer examination of this point." That passage became the starting point of the long debate over the transformation problem.
How did later research treat the theory?
Engels hinted at a historical reading in which exchange at values ruled in pre-capitalist commodity exchange and prices of production under capitalism. In the twentieth century the calculation of prices of production by simultaneous equations became standard through Bortkiewicz and Sraffa, and how it relates to Marx's procedure became the subject of the transformation debate.
Anwar Shaikh made the price of production concrete as the "regulating price" of a market: the cost-price plus profit of the "regulating capital", the one producing at the lowest reproducible cost, forms the centre towards which other firms' prices gravitate. He argued that the equalisation of profit rates is not a state of rest but a "turbulent equalisation" of perpetual overshooting and undershooting, and that what is equalised is not the average rate of profit on all existing capital but the rate of return on new investment, and he sought to show this with data for US manufacturing and across OECD countries. Emmanuel Farjoun and Moshe Machover, in Laws of Chaos, dropped the assumption of a single general rate altogether, treating profit rates as a probability distribution.