Gaps and triangles

In this paper, we derive principles of optimal cyclical monetary policy in an economy without capital, with a cash-in-advance restriction on household transactions, and monopolistic firms that set prices one period in advance. The only distortionary policy instruments are the nominal interest rate and the money supply. In this environment it is feasible to undo both the cash-in-advance and price setting restrictions, but not the distortion due to monopolistic competition. We show that it is optimal to follow the Friedman rule, and thus offset the cash-in-advance restriction. We also find that, in general, it is not optimal to undo the price setting restriction, so that a simple criterion of eliminating gaps is not optimal. Sticky prices provide the planner with tools to improve upon a distorted flexible price allocation.