The Firm's Decision

In the short run, then, there are only two things that are not given in the John Bates Clark model of the firm. They are the output produced and the labor (variable) input. And that is not actually two decisions, but just one, since labor input and output are linked by the "production function." Either

the output is decided, and the labor input will have to be just enough to produce that output
or
the labor input is decided, and the output is whatever that quantity of labor can produce.

Thus, the firm's objective is to choose the labor input and corresponding output that will maximize profit.

Let's continue with the numerical example in the first part of the chapter. Suppose a firm is producing with the production function shown there, in the short run. Suppose also that the price of the output is $100 and the wage per labor-week is $500. Then let's see how much labor the firm would use, and how much output it would produce, in order to maximize profits.

The relationship between labor input and profits will look something like this:

Figure 7: Labor Input and Profits in the Numerical Example

In the figure, the green curve shows the profits rising and then falling and the labor input increases. Of course, the eventual fall-off of profits is a result of "diminishing returns," and the problem the firm faces is to balance "diminishing returns" against the demand for the product. The objective is to get to the top of the profit hill. We can see that this means hiring something in the range of four to five hundred workers for the week. But just how many?

The way to approach this problem is to take a bug's-eye view. Think of yourself as a bug climbing up that profit hill. How will you know when you are at the top?