Abstract
We provide a model of an endowment economy with two competing, but intrinsically worthless currencies (Dollar, Bitcoin). Dollars are supplied by a central bank to achieve its inflation target, while the Bitcoin supply grows deterministically. Our fundamental pricing equation implies in its simplest form that Bitcoin prices form a martingale. “Mutual impatience” implies absence of speculation. Price volatility therefore does not invalidate the medium-of-exchange function. Bitcoin block rewards are not a tax on Bitcoin holders: they are financed with a Dollar tax. We discuss monetary policy implications, Bitcoin production, taxation, welfare and entry, and characterize the range of equilibria.
Highlights
In December 2018, the total market capitalization of cryptocurrencies reached nearly 400 Billion U.S Dollars, equivalent to 11% of U.S base money or M1.1 One fundamental use case of currency is that it serves as a store of value
A central bank targets a stochastic inflation level for the Dollar via appropriate monetary injections, while Bitcoin production is decentralized via proof-of-work and Bitcoin supply may only increase over time
The block rewards are not a tax on Bitcoin holders. They are financed by Dollar taxes imposed by the central bank
Summary
In December 2018, the total market capitalization of cryptocurrencies reached nearly 400 Billion U.S Dollars, equivalent to 11% of U.S base money or M1.1 One fundamental use case of currency is that it serves as a store of value. The central bank controls the inflation of a traditional fiat money while the value of the cryptocurrency is uncontrolled and its supply can only increase over time. Both monies can be used for transactions. We rewrite the fundamental pricing equation to decompose today’s Bitcoin price into the expected price of tomorrow plus a correction term for risk-aversion which captures the correlation between the future Bitcoin price and a pricing kernel This formula shows, why constructing equilibria is not straightforward: since fiat currencies have zero dividends, the involved covariances cannot be constructed from more primitive as-. We generalize our key no-speculation theorem in appendix D, while E discusses additional monetary policy implications
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