We study optimal monetary and fiscal policies in a New Keynesian model with heterogeneous agents, incomplete markets, and nominal rigidities. Our approach uses small‐noise expansions and Fréchet derivatives to approximate equilibria quickly and efficiently. Responses of optimal policies to aggregate shocks differ qualitatively from what they would be in a corresponding representative agent economy and are an order of magnitude larger. A motive to provide insurance that arises from heterogeneity and incomplete markets outweighs price stabilization motives.