# On the Uniqueness of Optimal Prices Set by Monopolistic Sellers

## Author Info

• van den Berg, Gerard J

## Abstract

This paper considers price determination by monopolistic sellers who know the distribution of valuations among the potential buyers. We derive a novel condition under which the optimal price set by the monopolist is unique. In many settings, this condition is easy to interpret, and it is valid for a very wide range of distributions of valuations. The results carry over to the optimal minimum price in independent private value auctions. In addition, they can be fruitfully applied in the analysis of quantity discount price policies.

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## Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5166.

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Handle: RePEc:cpr:ceprdp:5166

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## Related research

Keywords: auction; hazard price; hazard rate; local maxima; minimum price; monopoly; quantity discount; regularity; reservation price;

Other versions of this item:

Find related papers by JEL classification:
• D42 - Microeconomics - - Market Structure and Pricing - - - Monopoly
• D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
• L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
• L42 - Industrial Organization - - Antitrust Issues and Policies - - - Vertical Restraints; Resale Price Maintenance; Quantity Discounts

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## References

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1. Majumder, Amita & Chakravarty, Satya Ranjan, 1990. "Distribution of Personal Income: Development of a New Model and Its Application to U.S. Income Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 189-96, April-Jun.
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8. Elmar WOLFSTETTER, 1994. "Auctions: An Introduction," SFB 373 Discussion Papers 1994,13, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
9. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
10. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-90, October.
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12. Wolfstetter,Elmar, 2000. "Topics in Microeconomics," Cambridge Books, Cambridge University Press, number 9780521645348.
13. Esteban, Joan M, 1986. "Income-Share Elasticity and the Size Distribution of Income," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(2), pages 439-44, June.
14. Laffont, Jean-Jacques & Maskin, Eric, 1980. "Optimal reservation price in the Vickery auction," Economics Letters, Elsevier, vol. 6(4), pages 309-313.
15. Steven A. Matthews, 1995. "A Technical Primer on Auction Theory I: Independent Private Values," Discussion Papers 1096, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
16. Russell W. Cooper, 2002. "Estimation and Identification of Structural Parameters in the Presence of Multiple Equilibria," NBER Working Papers 8941, National Bureau of Economic Research, Inc.
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## Citations

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Cited by:
1. Tarasov, Alexander, 2009. "Consumer Preferences in Monopolistic Competition Models," MPRA Paper 19990, University Library of Munich, Germany.
2. Ivanov, Maxim, 2009. "Niche market or mass market?," Economics Letters, Elsevier, vol. 105(3), pages 217-220, December.
3. Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho$$ -concavity," Economic Theory, Springer, vol. 53(3), pages 591-603, August.
4. repec:dgr:uvatin:2007041 is not listed on IDEAS

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