The origins of the Marxian Transformation Problem lie in the differences between two central abstractions of classical political economy, the labour theory of value and the equalization of the rate of profit through competition among capitals. Marx proposed that these two principles could be reconciled by distinguishing the production of surplus-value through the exploitation of labour in the process of production from the realization of surplus-value through the price system, and claimed that the equalization of the rate of profit could be viewed as a redistribution of a given surplus-value among sectors. Marx's treatment can be seen as a generalization of the discussion of this problem in Smith and Ricardo. Modern criticisms of Marx's discussion claim that the labour theory of value is an unnecessary detour to the determination of prices and profit rates, and that Marx's claims that total value and surplus-value are conserved when prices equalize profit rates is unfounded. The Single-System Labour Theory of Value (SS-LTV) interpretation maintains Marx's two fundamental claims in the following formulations: (1) the price of the net product is the expression in prices (price form) of the total value-creating labour expanded during the period, and (2) total profits are the price form of surplus-value, determining the value of labour-power as unallocated purchasing power (UPP) on any set of commodities workers can buy from their wages. These properties hold for any set of prices, not specifically prices of production. The various positions in this controversy are illustrated in a mathematical formalization of the circulating capital model of production.

G. Duménil, D. Foley, "The Marxian Transformation Problem", 2008, in , The New Palgrave Dictionary of Economics, Palgrave Macmillan : London, Basingstoke.
Reproduced with permission of Palgrave Macmillan

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