Comparative statics and heterogeneity

This paper elucidates the role played by the heterogeneity of interactions between the endogenous variables of a model in determining the model’s behavior. It is known that comparative statics are well-behaved if these interactions are relatively small, but the formal condition imposed on the Jacobian which typically captures this idea–diagonal dominance–ignores the distribution of the interaction terms. I provide a new condition on the Jacobian—mean positive dominance—which better captures a trade-off between the size and heterogeneity of interaction terms. In accord with Samuelson’s (Foundations of economic analysis, Oxford University Press, London, 1947) correspondence principle, I also show that mean positive dominance yields stability and uniqueness results. I apply the results to provide new, or to generalize known, comparative statics results in the following settings: optimization problems, platform monopoly, normality, differentiable games including Cournot oligopoly, and competitive exchange economies.