Applied Mathematics Colloquia by Bruno Strulovici: Monotone Comparative Statics: Theory and Applications

Speaker: Bruno Strulovici, Northwestern University

Title: Monotone Comparative Statics: Theory and Applications

Abstract:  Comparative statics, the study how individual decisions and equilibria react to changes in parameters of the environment, are pervasive in economics: they are used to analyze how equilibrium prices and quantities react to demand and supply shocks, to study complementarities between goods, tasks, and/or workers, to measure equality or similarity between groups, to prove equilibrium existence in auctions and supermodular games, to study the stability of matching procedures, and to predict the reaction to incoming news, among other applications.

Apart from explicit computations, early general comparative techniques relied on concavity and differentiability assumptions to track the evolution of equilibria that depended smoothly on exogenous parameters.

These assumptions, which are often violated in practice, are not needed for comparative statics. We will discuss general necessary and sufficient conditions for the global monotonicity of decision variables in optimization and equilibrium analysis and applications of monotone comparative statics techniques to a wide range of economic problems. We will cover:

1. Comparative statics for one-dimensional optimization problems
2. Supermodular games
3. Comparative statics for multi-dimensional optimization problems

Applied Mathematics Colloquium