How to Generate Good Profit Maximization Problems

In this article, the author considers the merits of two classes of profit maximization problems: those involving perfectly competitive firms with quadratic and cubic cost functions. While relatively easy to develop and solve, problems based on quadratic cost functions are too simple to address a number of important issues, such as the use of second-order conditions and the short-run shutdown condition. Problems based on cubic cost functions are mathematically richer but often involve messy arithmetic; furthermore, many are not plausible representations of a firm's costs. Finding cubic functions that do not suffer from these drawbacks can be a time-consuming process. The author addresses this issue by providing a procedure to generate profit maximization problems that are theoretically interesting, economically plausible, and computationally simple.