Chapter Summary

Production is any activity that creates current or future utility. A production function summarizes the relationship between inputs and outputs. The short run is defined as that period during which at least some inputs are fixed. In the two-input case, it is the period during which one input is fixed, the other freely variable.

The marginal product of a variable input is defined as the change in output brought forth by an additional unit of the variable input, all other inputs held fixed. The law of diminishing returns says that beyond some point the marginal product declines with additional units of the variable input.

The average product of a variable input is the ratio of total output to the quantity of the variable input. Whenever marginal product lies above average product, the average product will increase with increases in the variable input. Conversely, when marginal product lies below average product, average product will decline with increases in the variable input.

An important practical problem is that of how to allocate an input across two productive activities in such a way as to generate the maximum possible output. In general, two types of solutions are possible. A corner solution occurs when the marginal product of the input is always higher in one activity than in the other. In that case, the best thing to do is to concentrate all the input in the activity where it is most productive.

An interior solution occurs whenever the marginal product of the variable input, when all of it is placed in one activity, is lower than the marginal product of the first unit of the input in the other activity. In this case, the output-maximizing rule is to distribute the input across the two activities, if it is perfectly divisible, in such a way that its marginal product is the same in both. Even experienced decision makers often violate this simple rule. The pitfall to be on guard against is the tendency to equate not marginal but average products in the two activities.

The long run is defined as the period required for all inputs to be variable. The actual length of time that corresponds to the short and long runs will differ markedly in different cases. In the two-input case, all of the relevant information about production in the long run can be summarized graphically by the isoquant map. The marginal rate of technical substitution is defined as the rate at which one input can be substituted for another without altering the level of output. The MRTS at any point is simply the absolute value of the slope of the isoquant at that point. For most production functions, the MRTS will diminish as we move downward to the right along an isoquant.

A production function is said to exhibit constant returns to scale if a given proportional increase in all inputs produces the same proportional increase in output. A production function is said to exhibit decreasing returns to scale if a given proportional increase in all inputs results in a smaller proportional increase in output. And, finally, a production function is said to exhibit increasing returns to scale if a given proportional increase in all inputs causes a greater proportional increase in output. Production functions with increasing returns to scale are also said to exhibit economies of scale. Returns to scale constitute a critically important factor in determining the structure of industrial organization.

The appendix to this chapter considers several mathematical extensions of production theory. Topics covered include applications of the average-marginal distinction, specific mathematical forms of the production function, and a mathematical treatment of returns to scale in production.