Assume that Firm Z buys varying quantities of labor from a market with many buyers and sellers, and that the laborers hired by this firm are combined with fixed amounts of capital to produce t-shirts with pictures of Sponge Bob on the front. In our analysis below, we want to see how many units of labor the firm will hire if they hire labor one unit at a time.

Assume further that Firm Z has a totally smart economist come up with a production function that tells this firm how many units of shirt can be produced after hiring a certain number of workers.

The production function (described above) and equation for MPL are as follows: