Distributional comparative statics.

*(English)*Zbl 1405.91118Summary: Distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters (income, wealth, productivity, information, etc.). This article develops new tools to address such issues and illustrates their usefulness in applications. The central development is a condition called quasi-concave differences, which implies concavity of the policy function in optimization problems without imposing differentiability or quasi-concavity conditions. The general take-away is that many distributional questions in economics which cannot be solved by direct calculations or the implicit function theorem, can be addressed easily with this article’s methods. Several applications demonstrate this: the article shows how increased uncertainty affects the set of equilibria in Bayesian games; it shows how increased dispersion of productivities affects output in the model of M. J. Melitz [Econometrica 71, No. 6, 1695–1725 (2003; Zbl 1154.91551)]; and it generalizes C. D. Carroll and M. S. Kimball’s result [Econometrica 64, No. 4, 981–992 (1996; Zbl 0856.90035)] on concave consumption functions to the [S. R. Aiyagari, “Uninsured idiosyncratic risk and aggregate saving”, Quart. J. Econ. 109, No. 3, 659–684 (1994; doi:10.2307/2118417)] setting with borrowing constraints.

##### MSC:

91B06 | Decision theory |

91B64 | Macroeconomic theory (monetary models, models of taxation) |

91A10 | Noncooperative games |