# Factor Price Frontier

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_103

## 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).

### JEL Classifications

D3### Bibliography

- Bharadwaj, K. 1970. On the maximum number of switches between two production systems.
*Schweizerische Zeitschrift für Volkswirtschaft und Statistik*106 (December): 409–429.Google Scholar - Bruno, M. 1969. Fundamental duality relations in the pure theory of capital and growth.
*Review of Economic Studies*36 (January): 39–53.CrossRefGoogle Scholar - Burmeister, E., and K. Kuga. 1970. The factor price frontier, duality and joint production.
*Review of Economic Studies*37 (January): 11–19.CrossRefGoogle Scholar - Craven, J. 1979. Efficiency curves in the theory of capital: A synthesis. In
*The measurement of capital, theory and practice*, ed. K.D. Patterson and K. Schott. London: Macmillan.Google Scholar - Garegnani, P. 1970. Heterogeneous capital, the production function and the theory of distribution.
*Review of Economic Studies*37 (July): 407–436.CrossRefGoogle Scholar - Hagemann, H., and H.D. Kurz. 1976. The return of the same truncation period and reswitching of techniques in neo-Austrian and more general models.
*Kyklos*29 (December): 678–708.CrossRefGoogle Scholar - Hicks, J.R. 1965.
*Capital and growth*. Oxford: Oxford University Press.Google Scholar - Hicks, J.R. 1973.
*Capital and time, a neo-Austrian theory*. Oxford: Oxford University Press.Google Scholar - Kurz, H.D. 1986. ‘Normal’ positions and capital utilisation.
*Political Economy*2 (May): 37–54.Google Scholar - Metcalfe, J.S., and I. Steedman. 1972. Reswitching and primary input use.
*Economic Journal*82 (March): 140–157.CrossRefGoogle Scholar - Pasinetti, L.L. 1977.
*Lectures on the theory of production*. London: Macmillan.CrossRefGoogle Scholar - Ricardo, D. 1971.
*The works and correspondence of David Ricardo*, Edited by P. Sraffa in collaboration with M.H. Dobb, vol. VIII. Cambridge: Cambridge University Press.Google Scholar - Salvadori, N. 1982. Existence of cost-minimizing systems within the Sraffa framework.
*Zeitschrift für Nationalökonomie*42 (September): 281–298.CrossRefGoogle Scholar - Salvadori, N., and I. Steedman. 1985. Cost functions and produced means of production: Duality and capital theory.
*Contributions to Political Economy*4 (March): 79–90.CrossRefGoogle Scholar - Samuelson, P.A. 1957. Wages and interest: A modern dissection of Marxian economic models.
*American Economic Review*47 (December): 884–912.Google Scholar - Samuelson, P.A. 1962. Parable and realism in capital theory: The surrogate production function.
*Review of Economic Studies*29 (June): 193–206.CrossRefGoogle Scholar - Sraffa, P. 1960.
*Production of commodities by means of commodities*. Cambridge: Cambridge University Press.Google Scholar - Steedman, I. 1985. On input ‘demand curves’.
*Cambridge Journal of Economics*9 (June): 165–172.Google Scholar