Nicholas Trachter, Francesco Lippi and Stefania Ragni
We study the optimal anticipated monetary policy in a flexible-price economy featuring heterogenous agents and incomplete markets, which give rise to a business cycle. In this setting money policy has distributional effects that depend on the state of the cycle. We parsimoniously characterize the dynamics of the economy and study the optimal regulation of the money supply as a function of the state. The optimal policy prescribes monetary expansions in recessions, when insurance is most needed by cash-poor unproductive agents. To minimize the inflationary effect of these expansions, the policy prescribes monetary contractions in good times. Although the optimal money growth rate varies greatly through the business cycle, this policy "echoes" Friedman's principle in the sense that the expected real return of money approaches the rate of time preference.