We build a model of credit card pricing that explicitly takes into account credit functionality. In the model a monopoly card network always selects an interchange fee that exceeds the level that maximizes consumer surplus. If regulators only care about consumer surplus, a conservative regulatory approach is to cap interchange fees based on retailers’ net avoided costs from not having to provide credit themselves. This always raises consumer surplus compared to the unregulated outcome, sometimes to the point of maximizing consumer surplus.

We study a continuous-time principal–agent model in which a risk-neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsizing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.