Buyer uncertainty and two-part pricing: Theory and applications

We consider two-part pricing of a service offered to risk-averse buyers subject to demand uncertainty. Buyers subscribe to the contract before resolution of the uncertainty. Sellers set two-part prices that trade off between insuring buyers against the uncertainty and the ex post deadweight loss from inefficient usage. If marginal and total benefits from the service are positively correlated (a sufficient condition is that the uncertainty not directly affect the buyer benefit), the usage charge should be set above the marginal cost of the service. If marginal and total benefits are negatively correlated, the usage charge should be set below the marginal cost. These results apply whether the seller has market power or is subject to competition. The difference between the profit-maximizing usage charge and marginal cost increases with buyer risk aversion. Our results can be extended to the case of the seller being more risk averse than the buyers. We discuss applications to pricing of beach and ski resorts, lines of credit, utility computing, and government services.