The Purchasing Power of Money in an Exchange Economy

Abstract

This paper develops a rigorously micro-founded model of money, monetary policy, and the price level. Money is issued by a generic authority in an environment portraying a modern cashless economy relying on electronic payments. The main result is that the households endogenously accept money with probability one, at a uniquely determined price level, as long as monetary policy satisfies certain sufficient conditions. The monetary policy is designed in terms of two exogenous dimensions, in equilibrium corresponding to nominal interest rate and a continuous helicopter drop of new net worth. The uniqueness of equilibrium follows from the saddle-path property of optimal spending. The model shows that the stability of the price level understood as independence of sunspots does not depend on whether the authority follows a Taylor rule, or if it can commit to a non-Ricardian (fiscal) policy. We argue that monetary models with no explicit role for money may lead to these and other incorrect conclusions.

Keywords: Money, price level, inflation, monetary policy, helicopter drop, sunspots, central bank digital currency (CBDC).

JEL Classification: E10, E31, E40, E50, E58, G12, G20.