The optimal design of a central bank digital currency (CBDC) is analyzed in an environment where agents sort into cash, CBDC, and bank deposits according to their preferences over anonymity and security; and where network effects make the convenience of a payment instrument depend on the number of its users. A CBDC can be designed with attributes similar to cash or deposits, and can be interest bearing: a CBDC that closely competes with deposits depresses bank credit and output, while a cash-like CBDC may lead to the disappearance of cash. Then, the optimal CBDC design trades off bank intermediation against the social value of maintaining diverse payment instruments. When network effects matter, an interest-bearing CBDC alleviates the central bank’s tradeoff.

中央银行数字货币 (CBDC) 的优化设计是在代理人根据其对匿名性和安全性的偏好分类为现金、CBDC 和银行存款的环境中分析的；网络效应使支付工具的便利性取决于其用户数量。CBDC 可以设计为具有类似于现金或存款的属性，并且可以计息：与存款密切竞争的 CBDC 会抑制银行信贷和产出，而类似现金的 CBDC 可能会导致现金的消失。然后，最佳 CBDC 设计在银行中介与维持多种支付工具的社会价值之间进行权衡。当网络效应很重要时，计息 CBDC 可以减轻中央银行的权衡。