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I examine optimal monetary policy in a Lagos and Wright [A unified framework for monetary theory and policy analysis, J. Polit. Econ. 113 (2005) 463-484] model where trade is centralized and all exchange is voluntary. I identify a class of incentivefeasible policies that improve welfare beyond what is achievable with zero intervention. Any policy in this class necessarily entails a non-negative inflation rate and a strictly positive nominal interest rate. Despite the absence of a lump-sum tax instrument, there exists an incentive-feasible policy that implements the first-best allocation.

I investigate how an interest-bearing central bank digital currency (CBDC) can be expected to impact a monopolistic banking sector. My framework of analysis combines the Diamond (1965) model of government debt with the Klein (1971) and Monti (1972) model of a monopoly bank. I …nd that the introduction of a CBDC has no detrimental e¤ect on bank lending activity and may, in some circumstances, even serve to promote it. The intervention does, however, reduce monopoly bank pro…t since it induces the monopoly bank to raise its deposit rate to retain deposits that remain a relatively cheap source of funding. More attractive deposit services have the e¤ect of increasing …nancial inclusion and decreasing the demand for currency. Available theory and evidence suggests that a properly-designed CBDC is not likely to threaten …nancial stability.

I investigate how a central bank digital currency (CBDC) can be expected to impact a monopolistic banking sector. My framework of analysis combines the Diamond (1965) model of government debt with the Klein (1971) and Monti (1972) model of a monopoly bank. I find that the introduction of a CBDC has no detrimental effect on bank lending activity and may, in some circumstances, even serve to promote it. Competitive pressure leads to a higher monopoly deposit rate which reduces profit but expands deposit funding through greater financial inclusion and desired saving. An appeal to available theory and evidence suggests that a properly-designed CBDC is not likely to threaten financial stability.