Abstract: This paper formalizes the critical elements of a cryptocurrency within a monetary model of decentralized exchange: a blockchain to keep a history of transactions, the distributed updating of information and consensus through competitive mining. The key economic nature of these features is that mining is a public good, while double spending to defraud the cryptocurrency depends on individual incentives to reverse a particular transactions. We show that a cryptocurrency works best when the volume of transactions is large relative to the individual transaction size. The optimal design of a cryptocurrency faces a trade-off between optimizing the allocation of goods and minimizing mining costs subject to the constraint that no double spending occurs. This tradeoff is influenced by money growth, transaction fees and block size/frequency. Finally, we discuss alternative consensus protocols and show how different users prefer different designs depending on their transactions needs.