A mixed duopoly in interbank payment services

In this paper, we analyze theoretically the coexistence of two means of payment, such as cash and digital or electronic payments, introducing some distortions in the payments markets to understand the widespread use of cash, specially in emerging countries. Lagos and Wright (2005) theoretical approach allows us to model explicitly the frictions in the exchange process considering money as essential. We introduce in this framework theft and informality (measured by tax evasion) as factors affecting cash usage and competition with a private digital payment platform. Considering heterogeneity in the seller's side by assuming different levels of productivity we ftnd the factors that explain the use of cash or digital payments. If a public provider enters the market with a less expensive platform the fees charged by the private provider have to be adjusted to the cost level of the public platform, decreasing the use of cash in the economy.