Factor Price Frontier

Abstract

The constraint binding changes in the distributive variables, in particular the real wage rate (w) and the rate of profit (r), was discovered (though not consistently demonstrated) by Ricardo: ‘The greater the portion of the result of labour that is given to the labourer, the smaller must be the rate of profits, and vice versa’ (Ricardo 1971, p. 194). He was thus able to dispel the idea, generated by Adam Smith’s notion of price as a sum of wages and profits, that the wage and the rate of profit are determined independently of each other. Ever since the inverse relationship between the distributive variables played an important role in long-period analysis of both classical and neoclassical descent. In more recent times it was referred to by Samuelson (1957), who later dubbed it ‘factor price frontier’ (cf. Samuelson 1962). Hicks (1965, p. 140, n.1) objected that this term is unfortunate, since it is the earnings (quasi-rents) of the (proprietors of) capital goods rather than the rate of profit which is to be considered the ‘factor price’ of capital (services). A comprehensive treatment of the problem under consideration within a classical framework of the analysis, including joint production proper, fixed capital and scarce natural resources, such as land, was provided by Sraffa (1960). The relationship is also known as the ‘wage frontier’ (Hicks 1965), the ‘optimal transformation frontier’ (Bruno 1969) and the ‘efficiency curve’ (Hicks 1973). The duality of the w − r relationship and the c − g relationship, that is, the relationship between the level of consumption output per worker (c) and the rate of growth (g) in steady-state capital theory has been demonstrated by the latter two authors and in more general terms by Burmeister and Kuga (1970); for a detailed account, see Craven (1979).