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Quantity Discounts for Time-Varying Consumers

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  • Miravete, Eugenio J

Abstract

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 show that the increasing hazard rate property of distributions is preserved under convolution. 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 theoretical prerequisites of the model using data directly linked to consumer types from the 1986 Kentucky telephone tariff experiment. I show that the distribution of actual calls second order stochastically dominates the distribution of expected calls, which fully supports the suggested type-varying theoretical model. Finally, I analyse 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 dominates any other pricing strategy.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 2699.

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Date of creation: Feb 2001
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Handle: RePEc:cpr:ceprdp:2699

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Related research

Keywords: Convolution Distributions; Increasing Hazard Rate; Optional Nonlinear Pricing; Quantity Discounts; Stochastic Dominance;

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References

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  1. Baron, David P. & Besanko, David, 1984. "Regulation and information in a continuing relationship," Information Economics and Policy, Elsevier, vol. 1(3), pages 267-302.
  2. Ivaldi, M. & Martimort, D., 1992. "Competition Under Nonlinear Pricing," Papers 93.288, Toulouse - GREMAQ.
  3. Caillaud, Bernard & Guesnerie, Roger & Rey, Patrick, 1989. "Noisy observation in adverse selection models," CEPREMAP Working Papers (Couverture Orange) 8921, CEPREMAP.
  4. Jean Tirole & Jean-Jaques Laffont, 1985. "Using Cost Observation to Regulate Firms," Working papers 368, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Eugenio J. Miravete, 2002. "Estimating Demand for Local Telephone Service with Asymmetric Information and Optional Calling Plans," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 943-971.
  6. Eugenio J. Miravete, 2001. "On Preservation of Increasing Hazard Rate Under Convolution," Penn CARESS Working Papers bb127ee2a4b562b26fd991e9f, Penn Economics Department.
  7. Bruno Biais & David Martimort & Jean-Charles Rochet, 2000. "Competing Mechanisms in a Common Value Environment," Econometrica, Econometric Society, vol. 68(4), pages 799-838, July.
  8. Kridel, Donald J. & Lehman, Dale E. & Weisman, Dennis L., 1993. "Option value, telecommunications demand, and policy," Information Economics and Policy, Elsevier, vol. 5(2), pages 125-144, July.
  9. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  10. Srinagesh, P., 1992. "A Dynamic Stochastic Model of choice," Papers 78, Bell Communications - Economic Research Group.
  11. Train, Kenneth E & Ben-Akiva, Moshe & Atherton, Terry, 1989. "Consumption Patterns and Self-selecting Tariffs," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 62-73, February.
  12. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, October.
  13. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  14. Miravete, Eugenio J, 1996. "Screening Consumers through Alternative Pricing Mechanisms," Journal of Regulatory Economics, Springer, vol. 9(2), pages 111-32, March.
  15. Courty, Pascal & Li, Hao, 2000. "Sequential Screening," Review of Economic Studies, Wiley Blackwell, vol. 67(4), pages 697-717, October.
  16. Miravete, Eugenio J, 2000. "Choosing the Wrong Calling Plan? Ignorance, Learning, and Risk Aversion," CEPR Discussion Papers 2562, C.E.P.R. Discussion Papers.
  17. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  18. Baron, David P & Besanko, David, 1999. "Informational Alliances," Review of Economic Studies, Wiley Blackwell, vol. 66(4), pages 743-68, October.
  19. Clay, Karen B & Sibley, David S & Srinagesh, Padmanabhan, 1992. "Ex Post vs. Ex Ante Pricing: Optional Calling Plans and Tapered Tariffs," Journal of Regulatory Economics, Springer, vol. 4(2), pages 115-38, June.
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