Algebraic Optimization: Marginal Analysis Without Calculus

Abstract

Teaching students to conduct marginal analysis before they have studied calculus is a major challenge in introductory economics courses.  This paper offers a simple algebraic approach to optimization that allows students to extract explicit marginal revenue and marginal cost functions from quadratic total revenue and total cost functions.  For first- or second-degree polynomials, the algebraic results are identical to those derived from differential calculus.  The technique offers students a deeper understanding of the profit maximization process than can be obtained from spreadsheets and other conventional teaching methods. The resulting functions can be used to develop related insights regarding issues such as deadweight loss and competitive market adjustments.  Numerical examples of monopoly and perfect competition are used to illustrate the algebraic optimization technique.