This research suggest a framework to estimate equilibrium models of nonlinear pricing competition using data that is readily available for many industries such as power, telecommunications, and other utilities. The basic idea behind the econometric approach is to make use of the information contained in the shape of tariffs actually offered to consumers to derive information about the distribution of consumers' usage intensity. The shape of the tariffs identifies the optimal markup that a seller charges for different quantity or quality levels to induce a population of customers to self-select according to their type, i.e., the intensity of their preferences, or their different elasticity of demand. The model thus overcomes the absence of individual consumption data, unlikely to be available for large customer markets. I consider a model of optimal nonlinear pricing, both in its monopoly and duopoly versions. Specific assumptions on demand and the distribution of consumer types allow obtaining a flexible closed form solution of the model for these different market configurations. This approach applies to cases where products are horizontally differentiated and where consumer tastes are allowed to be correlated. The prediction of the model is a quadratic tariff function that depends on observable market and firm specific characteristics. The curvature of the tariff solution is related to the hazard rate of the distribution of unobservable individual characteristics of consumers, and drives the optimal pricing rule for each purchase level. The quadratic tariff predicted by the model is then fitted to the actual nonlinear tariff of each firm in each market and time, thus allowing to estimate the structural parameters of the model, i.e., market specific demand effects, firm specific cost effects, and consumer specific unobserved heterogeneity.
While price discrimination practices are common, they have been theoretically addressed only recently. The empirical makes possible to identify the determinants of the optimal markups for different types of consumers. The major advantage of this structural approach is the possibility of conducting several policy evaluations. For instance, we could account for the gains in welfare and profits of using nonlinear pricing instead of linear pricing strategies. Perhaps the most interesting policy evaluation, given the structure of the data, could be to study the welfare effects of horizontal mergers when firms engage in nonlinear pricing. Dealing explicitly with second-degree price discrimination in a competitive as well as monopolistic environment makes possible to study not only how are efficiency gains or losses spread over different consumer types, but also whether approval decisions on horizontal mergers could be subject to restrictions on the way firms price their products.
