The Neglect of Monotone Comparative Static Methods

Abstract

Monotone methods enable comparative static analysis without the restrictive assumptions of the implicit function theorem. Ease of use and flexibility in solving comparative static and game theory problems have made monotone methods popular in the economics literature and in graduate courses, but they are still absent from undergraduate mathematical economics courses and textbooks. We illustrate the generality of monotone comparative statics relative to the implicit function approach. For example, to sign the effect of a discrete policy shift on an optimal control or choice variable, one need only check that marginal returns increase with the policy parameter. We also apply monotone methods in game theory settings. As mathematical economics courses and majors gain popularity, incorporating monotone methods into curriculum and textbooks would provide a modern treatment of comparative static analysis.

Keywords: comparative statics, monotonicity, supermodularity, mathematical economics

JEL Classification: A22, C61, C70