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Optimal Nonlinear Prices for Multiproduct Monopolies

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  • Leonard J. Mirman
  • David Sibley

Abstract

In models of a multiproduct firm with increasing returns to scale, prices are not set equal to marginal costs. Ramsey prices, which are inversely proportional to the elasticity of demand when demands are independent, are usually used in this situation. An analogous pricing system has been derived for a single commodity firm charging different "marginal" prices, depending upon the amount consumed. Our main purpose is to study properties of such nonuniform price functions for a multi-product firm which faces consumers who are differentiated by a single characteristic. We show, using this simplification, that a multiproduct monopolist offers a nonuniform price schedule--analogous to the single product nonlinear price system--on a one-dimensional path, along which consumers choose their optimal bundles.

Suggested Citation

  • Leonard J. Mirman & David Sibley, 1980. "Optimal Nonlinear Prices for Multiproduct Monopolies," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 659-670, Autumn.
    • Handle: RePEc:rje:bellje:v:11:y:1980:i:autumn:p:659-670
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    Cited by:

    1. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
    2. Diego A. Restrepo-Tobón & Subal C. Kumbhakar, 2017. "A new method to decompose profit efficiency: an application to US commercial banks," Journal of Productivity Analysis, Springer, vol. 48(2), pages 117-132, December.
    3. B. H. Strulovici & T. A. Weber, 2008. "Monotone Comparative Statics: Geometric Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 641-673, June.
    4. Bing Jing & Roy Radner, 2004. "Nonconvex Production Technology and Price Discrimination," Econometric Society 2004 North American Summer Meetings 513, Econometric Society.
    5. Basov Suren, 2006. "Snobs and Quality Gaps," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-10, March.
    6. David Encaoua & Michel Moreaux, 1987. "L'analyse théorique des problèmes de tarification et d'allocation des coûts dans les télécommunications," Revue Économique, Programme National Persée, vol. 38(2), pages 375-414.
    7. Tarkka, Juha, 1994. "Implicit interest as price discrimination in the bank deposit market," Research Discussion Papers 1/1994, Bank of Finland.
    8. repec:zbw:bofrdp:1994_001 is not listed on IDEAS
    9. Nathan Berg & Jeong†Yoo Kim, 2018. "Price Discrimination in Public Healthcare," Australian Economic Papers, Wiley Blackwell, vol. 57(2), pages 181-192, June.
    10. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    11. Monteiro, Paulo K. & Page Jr., Frank H., 1998. "Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 473-502, November.
    12. Suren Basov, 2006. "Quality Gaps," Department of Economics - Working Papers Series 967, The University of Melbourne.
    13. Steven Matthews & John Moore, 1984. "Monopoly Provision of Product Quality and Warranties," Discussion Papers 585R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Justin P. Johnson & David P. Myatt, 2018. "The determinants of product lines," RAND Journal of Economics, RAND Corporation, vol. 49(3), pages 541-573, September.
    15. Guy Ho Wang, 2000. "On The Dynamic Incentive of Price-Quality Differentiation By A Monopolist Firm," International Economic Journal, Taylor & Francis Journals, vol. 14(1), pages 33-45.
    16. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-467, March.
    17. M. Kitti & H. Ehtamo, 2009. "Adjustment of an Affine Contract with a Fixed-Point Iteration," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 477-497, March.
    18. Paat Rusmevichientong & Benjamin Van Roy & Peter W. Glynn, 2006. "A Nonparametric Approach to Multiproduct Pricing," Operations Research, INFORMS, vol. 54(1), pages 82-98, February.
    19. Adam Hale Shapiro & Ana Aizcorbe, 2010. "Implications of Consumer Heterogeneity on Price Measures for Technology Goods," BEA Working Papers 0062, Bureau of Economic Analysis.
    20. Garcia, Diego, 2005. "Monotonicity in direct revelation mechanisms," Economics Letters, Elsevier, vol. 88(1), pages 21-26, July.
    21. J.C. Panzar & AW. Postlewaite, 1982. "Sustainable Outlay Schedules," Discussion Papers 626, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    22. Saeed Alaei & Hu Fu & Nima Haghpanah & Jason Hartline & Azarakhsh Malekian, 2019. "Efficient Computation of Optimal Auctions via Reduced Forms," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1058-1086, August.
    23. Jensen, Sissel, 2008. "Two-part tariffs with quality degradation," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 473-489, March.
    24. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    25. Tarkka, Juha, 1994. "Implicit interest as price discrimination in the bank deposit market," Bank of Finland Research Discussion Papers 1/1994, Bank of Finland.

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