Abstract
Consider an economic model whose equilibrium can be represented as the …xed point of a system of dierentiable equations. Using the theory of B matrices, I show that comparative statics are well-behaved if the interactions between the equations are not too large, and the negative interactions are not too varied. When there are only positive interactions, for example when strategic comple- ments prevail in a strategic setting, I prove a version of Samuleson's (1947) Correspondence Principle in that equilibrium is nondecreasing for any positive parameter shock if and only if equilibrium is exponentially stable under dis- crete time best reply dynamics. If there are only negative interactions, like when strategic substitutes prevail in a game theoretic context, I use the theory of inverse M matrices to signi…cantly relax Dixit's (1986) conditions under which comparative statics are well-behaved. For every comparative statics result I show that if the conditions apply globally then equilibrium is unique. Applications are provided to dierentiated products Cournot oligopoly, market demand with interdependent preferences, and games on …xed networks.
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