Theoretical work on the price formula in eastern Europe started around 1958-60. Previously, economic texts had often asserted that under socialism the planning of prices should derive from commodity-value, but these were general and impractical proclamations, because such value (in labour terms) could not be quantified. Indeed, nobody believed that a feasible way could even be found for such a calculation. However immature, there were nevertheless valuable and long-standing fundamental concepts of the transformation problem, originating in the works of Marx (in the history of which the essay by Bortkiewicz (6) is of particular significance), and of the structural model, evolving from Walras through Leontief. Both these approaches were combined in one of the most significant of contemporary works, namely in the article by Morishima and Seton,(7) which presents an exact formula of value on the Leontief structural model.

The first formula of value dates from 1904 in the development by the Russian economist and mathematician V. K. Dmitriev (8) of Walras' model of general equilibrium. He demonstrated that labour value - in present terminology cumulative labour - can be computed as an iterative solution of an equation, relating cumulative labour costs with technical coefficients and direct labour costs.(9) It is sometimes described as a Dmitriev-Leontief equation, because an identical set of equations may be derived for cumulative labour costs from Leontief's structural model, which, however, usually envisages not an iterative solution but an inversion of a matrix. The development of the theory of linear programming, resulting in dual (shadow) prices, is also relevant, and it is in this connection that the work of Kantorovich and Novozhilov (10) is important.

Prices in terms of labour value may be computed either directly in labour units using the Dmitriev equation (thence converted into monetary units), or directly in monetary units as long as wage costs are calculated instead of direct labour costs. In the first case the problem arises of aggregating labour of different intricacy and intensity, while in the second the problem is to determine the rate of surplus product, which appears in n equations as the (n +1) variable.

The term 'average value' is usually understood in socialist countries as material and wage costs plus a profit at a uniform ad valorem rate. The 'production price' formula relates the uniform rate of profit to the value of productive assets. The so-called 'multi-channel' prices, applied in Hungary, (11) represent a combination of the formulae of value and of the production price in such a way that part of the surplus product is distributed according to wages and part according to productive assets. The shadow price formula, the 'objectively-conditioned valuation' of Kantorovich, is not discussed here, because it follows from the theory of linear programming; it is a technique of pricing scarce resources to regulate decentralized decision-makers towards a socially-optimal use of such resources. Novozhilov, finally, takes labour value as his basis and - as shown by the dual - deviates according to the degree of relative scarcity.(12)