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Optimal mechanism design for the private supply of a public good

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  • Csapó, G.

    (Quantitative Economics)

  • Müller, R.J.

    (Quantitative Economics)

Abstract

We study the problem of finding the profit-maximizing mechanism for a monopolistic provider of a single, non-excludable public good. Our model covers the most general setting, namely, we allow for correlation in the signal distribution as well as for informational externalities in the valuations. We show that the optimal deterministic, ex-post incentive compatible, ex-post individual rational mechanism can be computed in polynomial time by reducing the problem to finding a maximal weight closure in a directed graph. Node weights in the graph correspond to conditional virtual values, while the network structure is arising from the monotonicity constraints. We discuss what can be achieved if we relax our core assumptions one by one, i.e., if we go for randomized, interim individual rational or Bayes–Nash implementable mechanisms. Finally, we demonstrate that our techniques can be adapted for the excludable public good problem as well.
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  • Csapó, G. & Müller, R.J., 2012. "Optimal mechanism design for the private supply of a public good," Research Memorandum 037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2012037
    DOI: 10.26481/umamet.2012037
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    1. Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), 2011. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 4, number 4, June.
    2. Bruce Faaland & Kiseog Kim & Tom Schmitt, 1990. "A New Algorithm for Computing the Maximal Closure of a Graph," Management Science, INFORMS, vol. 36(3), pages 315-331, March.
    3. Stephen Machin & Olivier Marie & Sunčica Vujić, 2011. "The Crime Reducing Effect of Education," Economic Journal, Royal Economic Society, vol. 121(552), pages 463-484, May.
    4. Werner Güth & Martin Hellwig, 1986. "The private supply of a public good," Journal of Economics, Springer, vol. 5(1), pages 121-159, December.
    5. Steven D. Levitt & Lance Lochner, 2001. "The Determinants of Juvenile Crime," NBER Chapters, in: Risky Behavior among Youths: An Economic Analysis, pages 327-374, National Bureau of Economic Research, Inc.
    6. Schmitz, Patrick W, 1997. "Monopolistic Provision of Excludable Public Goods under Private Information," Public Finance = Finances publiques, , vol. 52(1), pages 89-101.
    7. Paul J. Devereux & Robert A. Hart, 2010. "Forced to be Rich? Returns to Compulsory Schooling in Britain," Economic Journal, Royal Economic Society, vol. 120(549), pages 1345-1364, December.
    8. Mocan Naci & Unel Bulent, 2017. "Skill-Biased Technological Change, Earnings of Unskilled Workers, and Crime," Review of Law & Economics, De Gruyter, vol. 13(3), pages 1-46, November.
    9. Tauchen, Helen & Witte, Ann Dryden & Griesinger, Harriet, 1994. "Criminal Deterrence: Revisiting the Issue with a Birth Cohort," The Review of Economics and Statistics, MIT Press, vol. 76(3), pages 399-412, August.
    10. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
    11. Ricardo Sabates & Leon Feinstein, 2008. "Effects of government initiatives on youth crime," Oxford Economic Papers, Oxford University Press, vol. 60(3), pages 462-483, July.
    12. Brian A. Jacob & Lars Lefgren, 2003. "Are Idle Hands the Devil's Workshop? Incapacitation, Concentration, and Juvenile Crime," American Economic Review, American Economic Association, vol. 93(5), pages 1560-1577, December.
    13. Jo Blanden & Stephen Machin, 2013. "Educational Inequality and The Expansion of UK Higher Education," Scottish Journal of Political Economy, Scottish Economic Society, vol. 60(5), pages 578-596, November.
    14. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    15. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    16. Mirko Draca & Stephen Machin, 2015. "Crime and Economic Incentives," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 389-408, August.
    17. Oreopoulos, Philip, 2007. "Do dropouts drop out too soon? Wealth, health and happiness from compulsory schooling," Journal of Public Economics, Elsevier, vol. 91(11-12), pages 2213-2229, December.
    18. Lance Lochner, 2010. "Non-Production Benefits of Education: Crime, Health and Good Citizenship," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20107, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    19. Grogger, Jeff, 1998. "Market Wages and Youth Crime," Journal of Labor Economics, University of Chicago Press, vol. 16(4), pages 756-791, October.
    20. Devereux, Paul J. & Fan, Wen, 2011. "Earnings returns to the British education expansion," Economics of Education Review, Elsevier, vol. 30(6), pages 1153-1166.
    21. Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
    22. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    23. Lance Lochner, 2004. "Education, Work, And Crime: A Human Capital Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(3), pages 811-843, August.
    24. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    25. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461.
    26. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    27. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
    28. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 77-101.
    29. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.
    30. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368.
    31. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2011. "Bayesian and Dominant Strategy Implementation Revisited," Working Papers tecipa-422, University of Toronto, Department of Economics.
    32. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
    33. Jean-Claude Picard, 1976. "Maximal Closure of a Graph and Applications to Combinatorial Problems," Management Science, INFORMS, vol. 22(11), pages 1268-1272, July.
    34. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    35. Jeffrey C. Ely & Kim-Sau Chung, 2002. "Ex-Post Incentive Compatible Mechanism Design," Discussion Papers 1339, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    36. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    37. Hjalmarsson, Randi, 2008. "Criminal justice involvement and high school completion," Journal of Urban Economics, Elsevier, vol. 63(2), pages 613-630, March.
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    Cited by:

    1. van Ours, Jan C. & Williams, Jenny & Ward, Shannon, 2015. "Bad Behavior: Delinquency, Arrest and Early School Leaving," CEPR Discussion Papers 10755, C.E.P.R. Discussion Papers.
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    3. James, Jonathan & Vujić, Sunčica, 2019. "From high school to the high chair: Education and fertility timing," Economics of Education Review, Elsevier, vol. 69(C), pages 1-24.
    4. Ignacio Munyo, 2015. "The Juvenile Crime Dilemma," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(2), pages 201-211, April.
    5. Lastauskas, Povilas & Tatsi, Eirini, 2017. "Spatial Nexus in Crime and Unemployment in Times of Crisis," Working Paper Series 2/2017, Stockholm University, Swedish Institute for Social Research.
    6. James, Jonathan, 2015. "Health and education expansion," Economics of Education Review, Elsevier, vol. 49(C), pages 193-215.
    7. Rud, I & Van Klaveren, C. & Groot, W. and Maassen van den Brink, H., 2013. "Education and Youth Crime: a Review of the Empirical Literature," Working Papers 48, Top Institute for Evidence Based Education Research.
    8. Brugård, Kaja Høiseth & Falch, Torberg, 2013. "Post-compulsory education and imprisonment," Labour Economics, Elsevier, vol. 23(C), pages 97-106.
    9. van der Steeg, Marc & van Elk, Roel & Webbink, Dinand, 2015. "Does intensive coaching reduce school dropout? Evidence from a randomized experiment," Economics of Education Review, Elsevier, vol. 48(C), pages 184-197.
    10. Nguyen, Hieu T.M., 2019. "Do more educated neighbourhoods experience less property crime? Evidence from Indonesia," International Journal of Educational Development, Elsevier, vol. 64(C), pages 27-37.
    11. Janke, Katharina & Johnston, David W. & Propper, Carol & Shields, Michael A., 2020. "The causal effect of education on chronic health conditions in the UK," Journal of Health Economics, Elsevier, vol. 70(C).
    12. Janke, Katharina & Johnston, David W. & Propper, Carol & Shields, Michael A., 2018. "The Causal Effect of Education on Chronic Health Conditions," IZA Discussion Papers 11353, Institute of Labor Economics (IZA).
    13. Marc van der Steeg & Roel van Elk & Dinand Webbink, 2012. "Does intensive coaching reduce school dropout?," CPB Discussion Paper 224, CPB Netherlands Bureau for Economic Policy Analysis.
    14. Nordin , Martin, 2014. "Does Eligibility for Tertiary Education Affect Crime Rates? Quasi-Experimental Evidence," Working Papers 2014:14, Lund University, Department of Economics.
    15. Jin Xi & Haitian Xie, 2021. "Strength in Numbers: Robust Mechanisms for Public Goods with Many Agents," Papers 2101.02423, arXiv.org, revised May 2023.
    16. Lindgren, Karl-Oskar & Oskarsson, Sven & Persson, Mikael, 2016. "How does access to education influence political candidacy? Lessons from school openings in Sweden," Working Paper Series 2016:7, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    17. Aoki, Yu, 2014. "More Schooling, Less Youth Crime? Learning from an Earthquake in Japan," IZA Discussion Papers 8619, Institute of Labor Economics (IZA).

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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