The jointly optimal monetary and fiscal policy mix in a multi-sector New Keynesian model with sectoral government spending and productivity shocks entails a separation of roles: Sectoral government spending optimally adjusts to sectoral output gaps and inflation rates---a policy supported by evidence from sectoral federal procurement data. Monetary policy optimally focuses on aggregate stabilization, but deviates from a zero-inflation target; in a model calibration to the U.S., however, it effectively approximates a zero-inflation target. Because monetary policy is a blunt instrument and government spending trades off stabilization against the optimal-level public good provision, the first best is not achieved.