# Principles of Microeconomics

By Peter Else; Peter Curwen | Go to book overview

CHAPTER TEN

COSTS AND COST FUNCTIONS

Introduction

In the last chapter the costs incurred by a firm were introduced as the sum of the costs of all the inputs employed, or in symbolic terms as

 C = p1y1 + p2y2 + , . . ., pnyn, (10.1)

where C represents total costs, y1, y2, . . . yn the quantities of the various inputs employed and p1, p2, . . . pn their respective prices. Further, it was also pointed out that a profit-maximizing firm must seek to use the specific bundle of inputs that minimizes its costs, and to adjust its use of inputs, as it adjusts its output, along a particular expansion path, which is determined by the underlying production function and relative input prices. Points along that expansion path then determine the specific relationship between costs and output, constituting the firm’s cost function, which can, therefore, be expressed as

 C = F(q), (10.2)

where, adapting the basic production function expression (9.1),

q = f(y1*, y2*, . . ., yn*),

in which y1*, y2*, . . . yn* define the cost-minimizing input quantities used in the production of output, q.

As the cost function is essentially the relationship between costs and outputs along an expansion path, it is strictly defined for given input prices. This means that any change in input prices leads to a shift in the cost function, reflecting the associated change in the position of the expansion path. In practice, of course, the input prices faced by a firm may be subject to frequent change, but our main concern in this chapter is to examine the basic relationship between costs and output with given input prices. So far, however, it has been implied that each input, whether it is a labour, capital or material input, has its readily identifiable price, which constitutes the cost to the firm of using it. In fact this is not always the case, so before discussing the form of the cost function we must consider what the cost of using an input might be. But, even more fundamentally, we must start by attempting to clarify the meaning of cost that is relevant to our analysis.

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