Privacy is a feature inherent to the use of cash for payments. With steadily increasing market shares of commercial digital payments platforms, privacy in payments may no longer be attainable in the future. In this paper, we explore the potential welfare impact of reductions in privacy in payments in a dynamic framework. In our framework, firms may use data collected through payments to price discriminate among future customers. A public good aspect of privacy in payments arises because individual customers do not bear the full cost of failing to protect their privacy. As a consequence, they may suboptimally choose not to preserve their privacy in payments. When left to market forces alone, the use of privacy-preserving means of payments, such as cash, may decline faster than is optimal. Bank topics: Digital currencies and fintech; Bank notes; Payment clearing and settlement systems; Central bank research JEL codes: E42, G28 "This [central bank digital] currency could satisfy public policy goals, such as (i) financial inclusion, (ii) security and consumer protection; and to provide what the private sector cannot: (iii) privacy in payments."