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Responsibility and cross-subsidization in cost sharing

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  • Moulin, Herve
  • Sprumont, Yves

Abstract

We propose two axiomatic theories of cost sharing with the common premise that agents demand comparable -though perhaps different- commodities and are responsible for their own demand. Under partial responsibility the agents are not responsible for the asymmetries of the cost function: two agents consuming the same amount of output always pay the same price; this holds true under full responsibility only if the cost function is symmetric in all individual demands. If the cost function is additively separable, each agent pays her stand alone cost under full responsibility; this holds true under partial responsibility only if, in addition, the cost function is symmetric. By generalizing Moulin and Shenker’s (1999) Distributivity axiom to cost-sharing methods for heterogeneous goods, we identify in each of our two theories a different serial method. The subsidy-free serial method (Moulin, 1995) is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method (Sprumont, 1998) is the only distributive method satisfying Separability and Strong Ranking. Finally, we propose an alternative characterization of the latter method based on a strengthening of Distributivity.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 55 (2006)
Issue (Month): 1 (April)
Pages: 152-188

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Handle: RePEc:eee:gamebe:v:55:y:2006:i:1:p:152-188

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. SPRUMONT, Yves, 1999. "Coherent Cost-Sharing Rules," Cahiers de recherche 9902, Universite de Montreal, Departement de sciences economiques.
  2. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
  3. Bossert, Walter, 1995. "Redistribution mechanisms based on individual characteristics," Mathematical Social Sciences, Elsevier, vol. 29(1), pages 1-17, February.
  4. Nouweland, C.G.A.M.. van den & Potters, J. & Tijs, S.H. & Zarzuelo, J., 1991. "Cores and related solution concepts for multi-choice games," Research Memorandum 478, Tilburg University, Faculty of Economics and Business Administration.
  5. Bertil Tungodden, 2001. "Responsibility and Redistribution: The Case of First Best Taxation," CESifo Working Paper Series 545, CESifo Group Munich.
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  7. Roemer,John E., 1997. "Egalitarian Perspectives," Cambridge Books, Cambridge University Press, number 9780521574457, October.
  8. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  9. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  10. Young, H Peyton, 1985. "Producer Incentives in Cost Allocation," Econometrica, Econometric Society, vol. 53(4), pages 757-65, July.
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  12. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
  13. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
  14. Moulin Herve & Shenker Scott, 1994. "Average Cost Pricing versus Serial Cost Sharing: An Axiomatic Comparison," Journal of Economic Theory, Elsevier, vol. 64(1), pages 178-201, October.
  15. Moulin, Herve & Shenker, Scott, 1999. "Distributive and Additive Costsharing of an Homogeneous Good," Games and Economic Behavior, Elsevier, vol. 27(2), pages 299-330, May.
  16. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
  17. Sharkey,William W., 1983. "The Theory of Natural Monopoly," Cambridge Books, Cambridge University Press, number 9780521271943, October.
  18. Ori Haimanko, 2000. "Value theory without symmetry," International Journal of Game Theory, Springer, vol. 29(3), pages 451-468.
  19. Sprumont, Y., 1995. "Balanced Egalitarian Redistribution of Income," Cahiers de recherche 9521, Universite de Montreal, Departement de sciences economiques.
  20. Thom Bezembinder & Hans Maassen, 2002. "Generating random weak orders and the probability of a Condorcet winner," Social Choice and Welfare, Springer, vol. 19(3), pages 517-532.
  21. Fleurbaey Marc, 1995. "Three Solutions for the Compensation Problem," Journal of Economic Theory, Elsevier, vol. 65(2), pages 505-521, April.
  22. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
  23. Marc Fleurbaey & Walter Bossert, 1996. "Redistribution and compensation (*)," Social Choice and Welfare, Springer, vol. 13(3), pages 343-355.
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Citations

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Cited by:
  1. Yves Sprumont, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Econometrica, Econometric Society, vol. 78(5), pages 1711-1748, 09.
  2. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
  3. Moulin, Herve & Vohra, Rakesh, 2003. "Characterization of additive cost sharing methods," Economics Letters, Elsevier, vol. 80(3), pages 399-407, September.
  4. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 17-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. SPRUMONT, Yves & MOULIN, Hervé, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 2005-22, Universite de Montreal, Departement de sciences economiques.
  6. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
  7. Christian Trudeau, 2013. "Minimum cost spanning tree problems with indifferent agents," Working Papers 1306, University of Windsor, Department of Economics.
  8. Edward Pearsall, 2009. "The complete incremental cost test for cross-subsidies with a sub-modular cost function," Journal of Regulatory Economics, Springer, vol. 36(3), pages 274-285, December.
  9. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer, vol. 42(2), pages 439-460, May.

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