We introduce two new tools for relating preferences and demand to firm behavior and economic performance. The “Demand Manifold” links the elasticity and convexity of an arbitrary demand function; the “Utility Manifold” links the elasticity and con- cavity of an arbitrary utility function. Along the way we present some new families of demand functions; show how the structure of demand and preferences determine the responses of monopoly firms and monopolistically competitive industries to exogenous shocks; characterize the efficiency of a monopolistically competitive equilibrium; and present a quantitative framework for predicting the welfare effects of exogenous shocks.