Introduction

In Chapter 8 we modeled a firm with one input and one output. In Chapter 9 we developed a more general model, with multiple inputs and one output. Both the Chapter 8 single-input/single-output and the Chapter 9 multiple-input/single-output models were long-run models, which means that the inputs were freely variable. If we assume a production function such as y = f (x 1, x 2), long-run analysis means that both x 1 and x 2 can be varied by the firm. In the short run, however, some inputs cannot be varied, because the time horizon is too short. How short is “short run” and how long is “long run” in reality depends on the facts of the firm, so our economic analysis is necessarily a little vague about the time units. However, we can be exact about what we mean by a short-run model. A short-run theory of the firm model is one in which some of the input quantities are fixed.

In this chapter we develop our short-run model. If there are n inputs, x 1, x 2, …, xn , with input prices w 1, w 2, …, wn , short run means that some of the inputs are fixed at nonzero levels, whereas others are variable. If the production function is y = f (x 1, x >2), with two inputs, short run means x2 is fixed at a nonzero level, whereas x 1 is variable. One main implication should be immediately clear: In a short-run model, the cost function has a nonzero fixed part.