Gaps and Triangles

We derive principles of optimal short run monetary policy in a real business cycles model, with money and with monopolistic firms that set prices one period in advance. The only distortionary policy instruments are the nominal interest rates and the money supplies. In this environment it is feasible to undo both the cash in advance and the price setting restrictions. We show that the optimal allocation is achieved under the Friedman rule. We also show that, in general, it is not optimal to undo the restriction that prices are set one period in advance. Sticky prices provide the planner with tools to improve upon a distorted flexible prices allocation.