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 (1947) correspondence principle, I also show that mean positive dominance yields stability and uniqueness results. Applications are provided to optimization problems, differentiable games, and competitive exchange economies.