How to Generate Good Profit Maximization Problems

15 Pages Posted: 3 Dec 2013  

Lewis Davis

Union College - Department of Economics

Date Written: December 2, 2013


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.

Keywords: Profit maximization, perfect competition, intermediate microeconomics, cost functions, shutdown condition, constrained optimization, second-order condition.

JEL Classification: A22, C02, D21

Suggested Citation

Davis, Lewis, How to Generate Good Profit Maximization Problems (December 2, 2013). Available at SSRN: or

Lewis S. Davis (Contact Author)

Union College - Department of Economics ( email )

Schenectady, NY 12308-3107
United States

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