Introduction

The presence of fixed input proportions establishes a technological production ray. Economic considerations do not play so crucial a role as they do when production is subject to variable proportions. Indeed, the only two economic questions posed are: (a) should the product under consideration be produced; and (b) if so, in what quantity. All questions pertaining to the organization of production are settled on strictly technological grounds. Thus the exposition in this chapter is considerably more limited than in chapters 4 and 5 below.

Throughout the discussion several familiar terms are used. All of these are defined in detail in chapters 4 and 5; except for noting the particular circumstances of their use, we rely upon the reader's prior knowledge of their meaning.

The expansion path

When treating variable-proportions production functions, it is convenient to define and distinguish between an isocline and an expansion path. The former refers to a path along which the marginal rate of technical substitution is constant, the latter to the path along which the marginal rate of technical substitution equals the corresponding input-price ratio. The expansion path is a special isocline, of course, if all input prices are independent of the quantities of inputs used.

An isocline is strictly determined by technological conditions, while economic considerations determine the expansion path. Indeed, the latter is a path of economic efficiency in the sense that either cost is minimized for each level of output or output is maximized for each level of cost. when the production function is smoothly continuous, the expansion path is easily determined by means of the Lagrange technique for constrained extrema.