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 paper develops new tools to address such issues and illustrates their usefulness in applications. The central development is a condition called quasi-concave dierences which implies concavity of the policy function in optimization problems without imposing dierentiability 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 paper’s methods. Several applications demonstrate this: the paper shows how increased uncertainty aects the set of equilibria in Bayesian games; it shows how increased dispersion of productivities aects output in the model of Melitz (2003); and it generalizes Carroll and Kimball (1996)’s result on concave consumption functions to the Aiyagari (1994) setting with borrowing constraints.