On the coexistence of cryptocurrency and fiat money

This paper uses a search-theoretic model to study conditions under which cryptocurrency is valued and under which it coexists with fiat money. In my model, a cryptocurrency economy is one in which private agents' decisions determine the stock of money and in which the marginal cost of producing money is increasing in the existing nominal stock. I show that the inflation rate of cryptocurrency must be zero in a stationary monetary equilibrium. This result is in sharp contrast to models with fiat money in which the stock of money is exogenously given. In fiat money economies, the inflation rate is determined by the rate of growth of the money stock. My result is also in sharp contrast with other types of private money economies, in which the inflation rate must necessarily be different from zero. In such private money economies, the cost of producing additional money does not depend on the existing nominal stock. Moreover, I show that cryptocurrency and fiat money can circulate at the same time and that the rates of return on these two assets may not be the same. Competition with cryptocurrency restricts the government's ability to over-issue fiat money and thereby might improve on pure fiat money equilibria without government commitment.& COPY; 2022 Elsevier Inc. All rights reserved.