Constrained Monopoly Pricing with Endogenous Participation Gabriel - PowerPoint PPT Presentation

Introduction Data Theory Estimation Evaluation Constrained Monopoly Pricing with Endogenous Participation Gabriel A. Basaluzzo 1 Eugenio J. Miravete 2 1 Universidad de San Andr´ es 2 University of Texas at Austin & Centre for Economic Policy Research April 1, 2009 Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda Performance of linear vs. nonlinear pricing Almost non-existing theoretical results. This is due to the technical complexity of second-degree price discrimination. This is an open empirical question in an area where there are very few contributions available. Spence (1977), Roberts (1979), Katz (1983). The Robinson-Patman Act imposes some policy restrictions to second degree price discrimination: Price discrimination of intermediate goods is forbidden (secondary line or alleged injury to rivals of the buyer). Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda What do we do in this paper? Develop a “feasible” equilibrium model of second-degree price discrimination by a monopolist where: Consumers’ intensity of preferences is private information. Consumers’ also differ in the subjective valuation of their alternative to abstain from consumption. Due to scarce data availability, we use very limited information. This is an empirical implementation of the exclusive agency model of Rochet and Stole (2002). The solution to this model may accommodate common features of current tariffs such as the existence of an allowance (something that no other model can explain). Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda � Single dimensional screening (1/3) � θ θ θ Key assumption 1 - Single crossing property: u ( q, θ ) ; u qθ ( q, θ ) > 0 . p(q) q Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda � Single dimensional screening (2/3) � θ Key assumption 2 - F ( θ ) is IHR to avoid this: f( θ ) θ Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda � Single dimensional screening (3/3) � Participation and consumption decisions are ordered by the same � variable, θ , leading to a fully separating equilibrium: T(q) q Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda � Two dimensional screening � Participation and consumption decisions are ordered by different � variables, ( t and x ). Bunching at the bottom always occurs: T(q) q Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda Main task of the paper Goal: To estimate a structural equilibrium of model of nonlinear pricing where core parameters are conditioned on observable characteristics of a cross-section of local wireless markets as well as on the particular implementation of the nonlinear tariff by each carrier in each market. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda Tariff comparison Once we have obtained the structural parameters we compare the performance of the following tariffs: Fully nonlinear tariff. Linear pricing (no quantity discounts). Flat tariff (just a monthly fee). Optimal two-part tariff. Coasian tariff (fixed fee + marginal cost). Performance evaluation includes: Profits. Welfare. Market coverage. Quantity undersupply. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda Applications What do we use our model for? Evaluation of the universal service policy: Balanced: maximize market coverage while the monopolist still breaks even. Lump-sum subsidy to ensure efficient provision. Address the importance of a second source of asymmetry of information: Rochet-Stole vs. Mussa-Rosen. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Description Market Description Data only include tariff information. Individual consumption is not available. 50 largest U.S. local cellular monopoly markets (1984-88). Monopoly is temporary and entry of competitor is exogenous. No need to model entry or entry deterrence strategies. Data include all tariff plans offered by the incumbent: Focus on tariff options defining the lower envelope of peak time. Include first and last quarter in the sample. Complemented with Census, FBI, and U.S. HCN data. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Description Table 1: Tariff Features Monthly Fee, F i Rate per Minute, p i Option No. Mean Std.Dev. Mean Std.Dev. Markets with ONE option (56 observations) 1 28.78 ( 11.50 ) 0.39 ( 0.07 ) Markets with TWO options (23 observations) ( 4.96 ) ( 0.13 ) 1 14.13 0.55 2 40.68 ( 9.40 ) 0.38 ( 0.10 ) Markets with THREE options (16 observations) ( 1.29 ) ( 0.14 ) 1 3.24 0.63 2 15.65 ( 8.62 ) 0.46 ( 0.07 ) 3 33.41 ( 18.29 ) 0.31 ( 0.10 ) Mean and standard deviations (between parentheses) of monthly fixed fees F i and rate per minute p i are measured in dollars. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation Description Table 2: Descriptive Statistics First Quarter Last Quarter Variables Mean Std.Dev. Mean Std.Dev. 1.4783 0.6909 1.6304 0.7989 PLANS 0.0679 0.0681 0.0671 0.0679 COVERAGE 4.1957 2.4094 11.5652 4.0423 TIME MKT - AGE 2.1087 3.1849 24.6087 10.5756 28.2225 3.7465 27.5302 3.3053 INCOME 26.1609 2.8513 26.2174 2.7778 COMMUTING sdv ( COMMUTING ) 16.8640 2.9783 16.8627 2.9391 3.4107 1.9115 3.0609 2.0246 RAIN 11.0500 3.0281 11.2304 2.9443 POVERTY POP - AGE 32.7543 2.8836 32.6826 2.8606 12.5500 0.2420 12.5370 0.2507 EDUCATION 18.1739 18.5320 18.3478 18.4237 TCELLS 2.6223 0.2877 2.6195 0.2878 HHSIZE sdv ( HHSIZE ) 1.4665 0.1602 1.4654 0.1604 15.8190 14.0903 15.1110 13.1091 DENSITY 6.5055 1.5614 6.4900 1.4977 OPERATE 10.8424 0.6310 9.1809 0.9526 PRIME 6.9580 1.5533 7.3320 1.6649 WAGE 0.8261 0.3832 0.8261 0.3832 BELL REGULATED 0.4783 0.5050 0.4565 0.5036 Observations 48 47 All variables defined in Appendix A. Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Fully Nonlinear Solution Principal and agents’ objective functions: Profit maximization: π ( q ) = P ( q ) − cq . Consumer surplus (linear demand): v ( t, q, x ) = tq − γ 2 q 2 − P ( q ) − x . Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Figure 1: f ( θ ) — Burr type XII density function 8 0.2 0.5 7 1.0 λ 2.0 5.0 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/t Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Figure 2: G ( x ) — Exponential distribution 1 φ = 1 φ = 2 0.9 φ = 5 0.8 0.7 0.6 1/ φ exp( − x/ φ ) 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 x Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Endogenous participation Now participation decision is different for each consumer type t . Thus, the total market penetration is given by: M ( u, t ) = Prob[ t, x ≤ u ] = G ( u ) f ( t ) � 1 λ − 1 � � �� 1 � 1 − t − t − u = 1 − exp , φ λ ( t − t ) t − t Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Monopolist’s problem The monopolist’s optimal control problem is: Z max M ( u ( t ) , t ) [ P ( q ( t )) − cq ( t )] dt , q ( t ) ,u ( t ) T u ( t ) = q ( t ) ≥ 0 , ˙ q ( t ) ≥ 0 , ˙ u ( t ) = tq ( t ) − γ 2 q 2 ( t ) − P ( q ( t )) ≥ 0 . Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Solution with optimal exclusion Bunching at the bottom is always optimal for a monopolist: » u ( t ) − 1 – u 2 0= φ exp( − φu ( t ))( t − t ) 2 ˙ + [1 − exp( − φu ( t ))] ( t − t ) [2 − ¨ u ( t )] „ 1 « − λ − 1 [1 − exp( − φu ( t ))] [ t − ˙ u ( t )] , u ( t )= q ( t ) , ˙ q ( t ) ≥ q fb ( t ) , q ( t )= q fb ( t ) . Basaluzzo-Miravete Constrained Monopoly Pricing

Introduction Data Theory Estimation Evaluation General Approximation Approximately Optimal Screening Firms offer a few tariff options to their customers. Possible existence of marketing and commercialization costs, which are in general unobservable. Foregone profits decrease rapidly with the number of tariff options offered. Firms choose the number of tariff options provided their expected profits, which depend on distribution of consumer tastes and the realization of marginal costs. Simultaneously, our computed value for these core parameters depend on the actual number of tariff options. Basaluzzo-Miravete Constrained Monopoly Pricing