We consider debit and credit card networks. Our contribution is to introduce the role of consumer credit into these payment networks, and to assess the way this affects competition and equilibrium fees. We analyze a situation in which overdrafts are associated with current accounts and debit cards, and larger credit lines with 'grace' periods are associated with credit cards. If we just introduce credit cards, we find their merchant fees depend not only on the networks' cost of funds and the probability of default, but also on the interest rates of overdrafts. Whilst debit card merchant fees do not depend on funding costs or default risk in a debit-card only world, this changes when they start to compete with credit cards. First, debit merchant acceptance increases with the default probability, even though merchant fees increase. Second, an increase in funding costs causes a surprising increase in debit merchant fees. Effectively, the bank offering the debit card benefits from consumers maintaining a positive current account balance, when they use their credit instead of their debit card. As a result, this complementarity may lead to relatively high debit card merchant fees as the bank discourages debit card acceptance at the margin.
