These are some of the important questions that the sudden rise of cryptocurrencies has brought to contemporary policy discussions. To answer these questions, we construct a model of competition among privately issued fiat currencies. We find that a purely private arrangement fails to implement an efficient allocation, even though it can deliver price stability under certain technological conditions. Currency competition creates problems for monetary policy implementation under conventional methods. However, it is possible to design a policy rule that uniquely implements an efficient allocation by driving private currencies out of the market. We also show that unique implementation of an efficient allocation can be achieved without government intervention if productive capital is introduced.