The Purchasing Power of Money in an Exchange Economy

Fiat money requires no backing to be accepted at a uniquely determined positive value. I show this using an equilibrium model with realistic frictions and rational households allowed to freely interact in a competitive environment. The model portrays a modern 'cashless' economy relying on electronic payments. Monetary policy is run by a generic authority, which most closely corresponds to a consolidated banking system or monopoly central bank issuing digital currency. The policy defines the accumulation laws for nominal net worth and features two exogenous dimensions corresponding to the nominal interest rate and the rate of new net worth creation via a continuous helicopter drop. The equilibrium concept of Lucas (1978) is generalized by adding a no-arbitrage condition by which the value of money cannot fall to zero if agents know that it can be positive. The model disproves the claims that the price level is generally subject to self-fulfilling expectations or that monetary policy can be reduced to controlling the interest rate via a feedback rule. There is no role for a fiscal authority, either running a non-Ricardian policy or providing implicit backing. Models that remain silent on the nature of money can be misused to draw dramatically incorrect conclusions