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.

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 good news though is that this economist also helps Firm Z come up with an equation that allows this firm to know how much there marginal product of labor will be when they hire different amounts of labor. That way the firm doesn't have to use the approach we discussed in class (i.e. change in Q divided by change in L) everytime Firm Z wants to know its MPL.

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