Many central banks are contemplating whether to issue a central bank digital currency (CBDC). A CBDC has certain potential benefits, including the possibility that it can bear interest. However, using a CBDC is costly for agents. I study the optimal monetary policy when only cash, only a CBDC, or both cash and a CBDC are available to agents. If the cost of using a CBDC is not too high, more efficient allocations can be implemented by using a CBDC than using cash, and the first best can be achieved. Having both cash and a CBDC available may result in lower welfare than in the cases where only cash or only a CBDC is available. The welfare gains of introducing a CBDC are estimated under various scenarios for the United States and Canada. For example, if the cost of using a CBDC relative to cash is around 0.25% of the transaction value, introducing a CBDC can lead to an increase of 0.12%-0.21% consumption for the United States and 0.04%-0.07% for Canada.

许多中央银行正在考虑是否发行中央银行数字货币（CBDC）。CBDC具有某些潜在的好处，包括它可能会引起人们的兴趣。但是，使用CBDC对于代理来说是昂贵的。当代理商只能使用现金，只有CBDC或同时有现金和CBDC时，我研究最优货币政策。如果使用CBDC的成本不太高，则使用CBDC可以比使用现金实现更有效的分配，并且可以实现最佳效果。与仅现金或仅CBDC的情况相比，拥有现金和CBDC的情况可能会导致福利降低。在美国和加拿大的各种情况下，估计引入CBDC的福利收益。例如，如果相对于现金使用CBDC的成本约为交易价值的0.25％，