Competition over time-inconsistent consumers

How do firms respond to consumers' time inconsistency? This paper studies the optimal design of nonexclusive contracts under competition. It shows that nonexclusivity creates a stark asymmetry between immediate-costs goods and immediate-rewards goods. For immediate-cost goods nonexclusivity does not affect the equilibrium and, when consumers are sophisticated, the efficient allocation is achieved. When consumers are partially naive, the optimal sales tax may be either positive or negative and depends on parameters that are hard to estimate. In the case of immediate-rewards goods, however, the equilibrium features marginal-cost pricing and is always inefficient. Moreover, the optimal tax does not depend on the consumers' degree of naiveté and is a function of parameters that are easy to assess.