On the Coexistence of Cryptocurrency and Fiat Money

Abstract

Cryptocurrency is private money and is costly to produce. In this paper, I ask whether cryptocurrency can serve as a medium of exchange, and whether it can coexist with fiat money as a widely accepted medium of exchange. To answer these questions, I develop two search-theoretic models: a model of monetary exchange in an economy with cryptocurrency only and a model of currency competition between cryptocurrency and fiat money. In my models, profit-maximizing miners produce cryptocurrency. In the economy with cryptocurrency only, unlike fiat money models, there is no equilibrium in which the stock of cryptocurrency grows at a constant rate. In a stationary equilibrium in which cryptocurrency is valued, the stock of cryptocurrency must be constant. In the two-currency economy, cryptocurrency and fiat money differ in terms of issuers, production costs, supply rules, and degrees of acceptability in decentralized markets. Different from the traditional two-fiat money models in which currencies have the same rate of return in equilibrium, cryptocurrency and fiat money can circulate in equilibrium with different rates of return. Further, Gresham’s Law does not hold in the sense that, even if cryptocurrency is costly to produce and less acceptable, cryptocurrency can coexist with fiat money, a widely accepted asset that is costless to produce.