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Nonlinear Pricing with Resale



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Nonlinear Pricing with Resale Isa E Hafaliry May 8 2007 Abstract We consider the problem of a monopolist choosing an optimal nonlinear pricing scheme facing two consumers who can resell some or all of the goods to each other in a secondary market We suppose that the valuations of the consumers are drawn independently from a continuous distribution We characterize the optimum direct mechanism and show that the monopolist can be better o or worse o as compared to the without resale case depending on the speci cs of the cost function of the monopolist and the utility functions of the consumers Keywords Nonlinear pricing Resale Mechanism Design Secondary Markets JEL Classi cation Numbers D42 D82 1 Introduction Consider the adverse selection problem of a transaction between a seller the monopolist and buyers consumers where the seller does not perfectly know how much the buyers are willing to pay for the goods Suppose also that the seller sets the terms of the contract i e a menu of quantities and prices The problem of one principal facing one agent who has private information about his type was rst analyzed by Mirrlees 1971 One monopolist and a consumer problem was then analyzed by Mussa and Rosen 1978 and Maskin and Riley 1984 among others The reader is referred to Bolton and Dewatripont 2005 La ont and Martimort 2002 and Wilson 1993 for a detailed discussion of economics of adverse selection All previous work on monopolist s problem of optimal nonlinear pricing focused either on a single consumer or on multiple consumers who cannot resell the goods to one another except for Calzolari and Pavan 2006 Calzolari and Pavan 2006 PRELIMINARY AND INCOMPLETE Comments are very welcome Department of Economics Penn State University University Park PA 16802 USA E mail isaemin psu edu y 1 recently consider a monopolist who designs an allocation rule and a disclosure policy that optimally fashion the beliefs of the participants in the secondary market They consider two consumers



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