Efficiency Curves in the Theory of Capital: A Synthesis

In Capital and Time Hicks (1973) introduced the ‘efficiency curve’ to capital theory. This was not new, except in name, for many authors had written previously of ‘factor price frontiers’ (Samuelson (1962)), ‘optimal transformation frontiers’ (Bruno (1969)), ‘wage frontiers’ (an earlier vintage of Hicks (1965)) and ‘w-r relationships’ (Harcourt (1972)). None of these earlier names captured the important dual nature of these curves, which relate not only the real wage to the profit rate, but also the level of consumption output per labour unit to the growth rate. This duality has been demonstrated by Hicks (1973), by Bruno (1969) and in its most general form by Burmeister and Kuga (1970), but none of these authors has exploited the expository powers of efficiency curves to the full. In this paper we shall discuss the role of these curves in many parts of steady state capital theory, including the debates on the measurement of capital and on Marxian theorems. Their usefulness is heightened by the fact that, even in the most complicated models involving joint production, an efficiency curve can be represented in two dimensions without the problems of aggregation which prevent the use of plane geometry so often in multisectoral models.