Monopolistic nonlinear pricing with consumer entry

We consider consumer entry in the canonical monopolistic nonlinear pricing model (Mussa and Rosen, 1978) wherein consumers learn their preference "types" after incurring privately known entry costs. We show that by taking into account consumer entry, the nature of optimal nonlinear pricing contracts changes significantly: compared to the benchmark without costly entry, in our model both quality distortion and market exclusion are reduced, sorting is more likely, and whenever bunching occurs, the bunching interval is necessarily smaller. Additionally, under certain conditions the monopoly solution may even achieve the first best (i.e., production efficiency). We also demonstrate that the optimal monopoly solutions can be ranked according to inverse hazard rate functions of the entry cost, which suggests an interesting dynamic for monopolistic nonlinear pricing with consumer entry.

[1]  Morton I. Kamien,et al.  Dynamic Optimization , 2020, Natural Resource Economics.

[2]  Raghuram Iyengar,et al.  Nonlinear pricing , 2022 .

[3]  Achim Wambach,et al.  Sequential Information Disclosure in Auctions , 2013, J. Econ. Theory.

[4]  I. Segal,et al.  Dynamic Mechanism Design: A Myersonian Approach , 2014 .

[5]  Diego Moreno,et al.  Auctions with heterogeneous entry costs , 2011 .

[6]  Jingfeng Lu,et al.  Entry Coordination and Auction Design with Private Costs of Information Acquisition , 2010 .

[7]  Lixin Ye,et al.  Nonlinear pricing, market coverage, and competition , 2008 .

[8]  Péter Eso,et al.  Optimal Information Disclosure in Auctions and the Handicap Auction , 2007 .

[9]  J. Vickers,et al.  Competitive Non-linear Pricing and Bundling , 2009 .

[10]  Dirk Bergemann,et al.  Information in Mechanism Design , 2005 .

[11]  Glenn Ellison,et al.  A Model of Add-On Pricing , 2003 .

[12]  Jean-Charles Rochet,et al.  Nonlinear Pricing with Random Participation , 2002 .

[13]  Mark Armstrong,et al.  Competitive price discrimination , 2001 .

[14]  Moshe Tennenholtz,et al.  Optimal auctions revisited , 1998, Artif. Intell..

[15]  Frank Verboven,et al.  Product Line Rivalry and Market Segmentation--With an Application to Automobile Optional Engine Pricing , 2003 .

[16]  J. Miguel Villas-Boas,et al.  Oligopoly with Asymmetric Information: Differentiation in Credit Markets , 1999 .

[17]  Jean-Charles Rochet,et al.  Strategic Information Gathering Before a Contract is Offered , 1998 .

[18]  P. Courty,et al.  Sequential Screening , 1998 .

[19]  Jean-Charles Rochet,et al.  Contracts and Productive Information Gathering , 1997 .

[20]  Lars Stole,et al.  Nonlinear Pricing and Oligopoly , 1995 .

[21]  Dan Levin,et al.  Equilibrium in Auctions with Entry , 1994 .

[22]  M. Petit Dynamic optimization. The calculus of variations and optimal control in economics and management : by Morton I. Kamien and Nancy L. Schwartz. Second Edition. North-Holland (Advanced Textbooks in Economics), Amsterdam and New York, 1991. Pp. xvii+377. ISBN0-444- 01609-0 , 1994 .

[23]  J. I. Ramos,et al.  Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Second Edition, Morton I. Kamien, Nancy L. Schwartz. North-Holland, Amsterdam, The Netherlands (1991), $55 , 1993 .

[24]  Guofu Tan,et al.  Entry and R & D in procurement contracting , 1992 .

[25]  Severin Borenstein,et al.  Competition and Price Dispersion in the U.S. Airline Industry , 1991, Journal of Political Economy.

[26]  Jacques Crémer,et al.  Gathering Information before Signing a Contract , 1991 .

[27]  Richard J. Gilbert,et al.  Product line rivalry with brand differentiation , 1993 .

[28]  Daniel F. Spulber Product Variety and Competitive Discounts , 1989 .

[29]  R. McAfee,et al.  Auctions with entry , 1987 .

[30]  E. Maskin,et al.  Monopoly with Incomplete Information , 1984 .

[31]  Esther Gal-Or,et al.  Quality and Quantity Competition , 1983 .

[32]  R. Vidal Dynamic optimization: The calculus of variations and optimal control in economics and management: Morton I. KAMIEN and Nancy L. SCHWARTZ Volume 4 in: Dynamic Economics: Theory and Applications, North-Holland, New York, 1981, xi + 331 pages, Dfl.90.00 , 1982 .

[33]  R. Myerson,et al.  Regulating a Monopolist with Unknown Costs , 1982 .

[34]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[35]  S. Rosen,et al.  Monopoly and product quality , 1978 .

[36]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[37]  M. L. Chambers The Mathematical Theory of Optimal Processes , 1965 .

[38]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .