Paper # Author Title  
When a monopolist asks consumers to choose a particular nonlinear tariff option, consumers do not completely know their type. Their valuations of the good and/or optimal quantity purchases are only fully realized after the optional tariff has been subscribed. In order to characterize the menu of optimal nonlinear tariffs when consumers demands are stochastic, I assume that the distributions of the different components of consumers’ types are log–concave to prove that the convolution distribution of these components is increasing hazard rate. This result, together with very weak assumptions on demand (common to standard nonlinear pricing), ensures that the continuum of optional nonlinear tariffs is characterized by quantity discounts. I test nonparametrically the model using data directly linked to consumer types from the 1986 Kentucky telephone tariff experiment. I show that the distri- bution of actual calls second order stochastically dominates the distribution of expected calls, which fully supports the suggested type–varying theoretical model. Finally, I analyze possible welfare effects of the introduction of optional tariffs and their relative expected profitability using the empirical distribution of consumer types in two local exchanges with differentiated calling patterns. The evidence suggests that a menu of optional two–part tariffs dominate any other pricing strategy. Download Paper
The increasing hazard rate (IHR) property of distributions of asymmetric information parameters play a critical role in characterizing a separating Perfect Bayesian–Nash Equilibria in screening problems. This paper studies sufficient conditions on these distributions for IHR to be preserved under convolution. When different sources of asymmetric information aggregate into a single scalar, these preservation results prove very useful in designing alternative optimal mechanisms. The paper proves that if the distributions of all convoluting parameters are IHR the resulting distribution is also IHR. This result does not necessarily requires that the corresponding densities have to be log–concave. Download Paper
This paper studies a class of multidimensional screening models where different type dimensions lie on the real line. The paper applies preservation results of totally positive functions to show that some critical properties of the distributions of asymmetric information parameters, such as increasing hazard rate, monotone likelihood ratio, and unimodality are preserved under convolution and/or composition. Under some general conditions, these preservation results also provide a natural ordering of alternative screening mechanisms. These results explain the optimality of bundling solutions in a wide range of economic models based on distributional features of the informational parameters involved. Download Paper