Constrained Pricing of Monopolies with Endogenous Participation

We present a flexible model of monopoly nonlinear pricing with endogenous participation decisions of heterogeneous consumers. We use computing intensive methods to fit the solution of this model to many nonlinear tariffs offered by incumbent monopolists in several early local U.S. cellular telephone markets. For each market, numerical solutions of two–point boundary problems identify the marginal cost, average price sensitivity of demand, marginal consumer type, and indexing parameters governing the distribution of the two-dimensional type components. The sources of identification are the position, shape, and allowance of free minutes that defines each tariff offered by monopolists as well as a measure of market penetration in each cellular market during the first and last quarter of monopoly regime. We use the distribution of these structural parameters across markets and time to evaluate the magnitude of the inefficient provision of goods due to asymmetric information, the importance of bunching of different consumer types, and the empirical relevance of random participation constraints. We use these structural parameters to provide a first performance comparison —profits and welfare— of nonlinear tariffs relative to linear, optimal two-part, Coasian marginal cost-plus fixed fee, and flat tariffs. We furthermore evaluate the potential welfare gains of alternative policies such as implementing a universal service requirement or allowing a second identical cellular telephone carrier. Finally, we also conduct a descriptive analysis of the sample variation of all structurally identified variables conditional on the observable characteristics of markets and cellular carriersNonlinear Pricing; Random Participation;Bucket Tariffs; Quantity Underprovision; Nonlinear vs. Restricted Pricing; Universal Service; Divestiture