How to Generate Good Profit Maximization Problems

Abstract

This paper 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 in which the firm has a quadratic cost functions are structurally too simple to address a number of important mathematical and economic issues, such as the use of second-order conditions and the short run shutdown condition. Problems based on cubic cost functions are sufficiently complex to address these issues, but the additional complexity introduces other problems. Solving such problems may involve messy arithmetic and, moreover, many cubic functions 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. I address this issue by providing a simple algorithm that generates profit maximization problems that are theoretically interesting, economically plausible and computationally simple.