This paper develops a tractable model for the cryptocurrency prices based on the classical framework for rational bubbles. In the baseline equilibrium, investors hold cryptocurrency to sell them to future users. In a bubble equilibrium, investors hold cryptocurrency because they expect its price to appreciate due to future investment inflows. We establish the mathematical relationship between net investment flows and the cryptocurrency's rate of appreciation. The net investment flows required to sustain a bubble equilibrium increase in new coin issuance, the required return and the level of transactional demand, and temporarily decrease when transactional demand expands. The net investment inflows required to sustain a bubble equilibrium are, everything else equal, smaller for cryptocurrencies with a proof-of-stake than for cryptocurrencies with a proof-of-work protocol.