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A General Solution to the Quasi Linear Screening Problem

Author

Listed:
  • Rochet, Jean-Charles
  • Carlier, Guillaume
  • Dupuis, Xavier
  • Thanassoulis, John

Abstract

We provide an algorithm for solving multidimensional screening problems which are intractable analytically. The algorithm is a primal-dual algorithm which alternates between optimising the primal problem of the surplus extracted by the principal and the dual problem of the optimal assignment to deliver to the agents for a given surplus. We illustrate the algorithm by solving (i) the generic monopolist price discrimination problem and (ii) an optimal tax problem covering income and savings taxes when citizens differ in multiple dimensions.

Suggested Citation

  • Rochet, Jean-Charles & Carlier, Guillaume & Dupuis, Xavier & Thanassoulis, John, 2024. "A General Solution to the Quasi Linear Screening Problem," TSE Working Papers 24-1537, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:129347
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    References listed on IDEAS

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    1. Philippe Chone & Guy Laroque, 2010. "Negative Marginal Tax Rates and Heterogeneity," American Economic Review, American Economic Association, vol. 100(5), pages 2532-2547, December.
    2. John Thanassoulis, 2007. "Competitive Mixed Bundling and Consumer Surplus," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(2), pages 437-467, June.
    3. Cremer, Helmuth & Pestieau, Pierre & Rochet, Jean-Charles, 2003. "Capital income taxation when inherited wealth is not observable," Journal of Public Economics, Elsevier, vol. 87(11), pages 2475-2490, October.
    4. Robin Boadway & Maurice Marchand & Pierre Pestieau & María Del Mar Racionero, 2002. "Optimal Redistribution with Heterogeneous Preferences for Leisure," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(4), pages 475-498, October.
    5. Ritva Tarkiainen & Matti Tuomala, 2007. "On optimal income taxation with heterogeneous work preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(1), pages 35-46, March.
    6. Paul Beaudry & Charles Blackorby & Dezsö Szalay, 2009. "Taxes and Employment Subsidies in Optimal Redistribution Programs," American Economic Review, American Economic Association, vol. 99(1), pages 216-242, March.
    7. Jacquet, Laurence & Lehmann, Etienne & Van der Linden, Bruno, 2013. "Optimal redistributive taxation with both extensive and intensive responses," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1770-1805.
    8. Chenghuan Sean Chu & Phillip Leslie & Alan Sorensen, 2011. "Bundle-Size Pricing as an Approximation to Mixed Bundling," American Economic Review, American Economic Association, vol. 101(1), pages 263-303, February.
    9. Henrik Jacobsen Kleven & Claus Thustrup Kreiner & Emmanuel Saez, 2009. "The Optimal Income Taxation of Couples," Econometrica, Econometric Society, vol. 77(2), pages 537-560, March.
    10. Casey Rothschild & Florian Scheuer, 2016. "Optimal Taxation with Rent-Seeking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 1225-1262.
    11. Mark Armstrong & John Vickers, 2010. "Competitive Non-linear Pricing and Bundling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 30-60.
    12. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    13. Diamond, Peter A & Mirrlees, James A, 1971. "Optimal Taxation and Public Production: I--Production Efficiency," American Economic Review, American Economic Association, vol. 61(1), pages 8-27, March.
    14. Yannis Bakos & Erik Brynjolfsson, 1999. "Bundling Information Goods: Pricing, Profits, and Efficiency," Management Science, INFORMS, vol. 45(12), pages 1613-1630, December.
    15. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    16. Emmanuel Saez, 2001. "Using Elasticities to Derive Optimal Income Tax Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(1), pages 205-229.
    17. Atkinson, A. B. & Stiglitz, J. E., 1976. "The design of tax structure: Direct versus indirect taxation," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 55-75.
    18. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-622, May.
    19. Diamond, Peter A & Mirrlees, James A, 1971. "Optimal Taxation and Public Production II: Tax Rules," American Economic Review, American Economic Association, vol. 61(3), pages 261-278, June.
    20. Hui Li, 2019. "Intertemporal Price Discrimination with Complementary Products: E-Books and E-Readers," Management Science, INFORMS, vol. 67(6), pages 2665-2694, June.
    21. Mikhail Golosov & John Hassler & Per Krusell & Aleh Tsyvinski, 2014. "Optimal Taxes on Fossil Fuel in General Equilibrium," Econometrica, Econometric Society, vol. 82(1), pages 41-88, January.
    22. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    23. Armstrong, Mark & Rochet, Jean-Charles, 1999. "Multi-dimensional screening:: A user's guide," European Economic Review, Elsevier, vol. 43(4-6), pages 959-979, April.
    24. Cremer, Helmuth & Pestieau, Pierre & Rochet, Jean-Charles, 2001. "Direct versus Indirect Taxation: The Design of the Tax Structure Revisted," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 781-799, August.
    25. Jean‐Charles Rochet & John Thanassoulis, 2019. "Intertemporal price discrimination with two products," RAND Journal of Economics, RAND Corporation, vol. 50(4), pages 951-973, December.
    26. Rochet, Jean-Charles, 2009. "Monopoly regulation without the Spence-Mirrlees assumption," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 693-700, September.
    27. Schmalensee, Richard, 1984. "Gaussian Demand and Commodity Bundling," The Journal of Business, University of Chicago Press, vol. 57(1), pages 211-230, January.
    28. Judd, Kenneth L., 1985. "Redistributive taxation in a simple perfect foresight model," Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.
    29. Jean-Charles Rochet & Lars A. Stole, 2002. "Nonlinear Pricing with Random Participation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 277-311.
    30. Tarkiainen, Ritva & Tuomala, Matti, 1999. "Optimal Nonlinear Income Taxation with a Two-Dimensional Population; A Computational Approach," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 1-16, February.
    31. Ying Gao & Wenxing Zhang, 2023. "An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function," Computational Optimization and Applications, Springer, vol. 85(1), pages 263-291, May.
    32. Casey Rothschild & Florian Scheuer, 2013. "Redistributive Taxation in the Roy Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 623-668.
    33. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    34. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    35. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    36. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    37. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 371-383.
    38. Sander Renes & Floris Zoutman, 2017. "As Easy as ABC? Multidimensional Screening in Public Finance," CESifo Working Paper Series 6301, CESifo.
    39. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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    More about this item

    Keywords

    Multidimensional screening; algorithm; numerical methods; price discrimination; optimal tax;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly

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