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Commons with increasing marginal costs: random priority versus average cost

Author

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  • Hervé Crès

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Hervé Moulin

Abstract

Indivisible units are produced with increasing marginal costs. Under average cost, each user pays average cost. Under random priority, users are randomly ordered (without bias) and successively offered to buy at the true marginal cost. Both average cost (AC) and random priority (RP) inefficiently overproduce. RP tends to overproduce less, but which game collects more surplus depends much on the demand configuration. We show that a key to compare the welfare properties of the two mechanisms is the crowding factor, i.e., the number of potential users over the number of units of output users can afford: The more crowded the commons, the more RP outperforms AC. In the quadratic cost case, beyond the threshold value of 2.4 for the crowding factor, RP strongly outperforms AC; beneath it AC only mildly outperforms RP. Thus the RP mechanism manages crowded commons better than AC.

Suggested Citation

  • Hervé Crès & Hervé Moulin, 2003. "Commons with increasing marginal costs: random priority versus average cost," Post-Print hal-03598176, HAL.
    • Handle: RePEc:hal:journl:hal-03598176
    DOI: 10.1111/1468-2354.t01-1-00102
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    References listed on IDEAS

    as
    1. Hervé Crès & Hervé Moulin, 2001. "Scheduling with Opting Out: Improving upon Random Priority," Operations Research, INFORMS, vol. 49(4), pages 565-577, August.
    2. 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.
    3. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    4. Hervé Moulin & Anna Bogomolnaia, 2002. "A simple random assignment problem with a unique solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 623-636.
    5. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    6. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    7. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
    8. Shapley, Lloyd S & Shubik, Martin, 1969. "Pure Competition, Coalitional Power, and Fair Division," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 337-362, October.
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    Cited by:

    1. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 379-405, September.
    2. Moulin, Herve, 2001. "Three Solutions to a Simple Commons Problem," Working Papers 2001-05, Rice University, Department of Economics.
    3. Moulin, Hervé, 2010. "An efficient and almost budget balanced cost sharing method," Games and Economic Behavior, Elsevier, vol. 70(1), pages 107-131, September.
    4. Bloch, Francis, 2017. "Second-best mechanisms in queuing problems without transfers:The role of random priorities," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 73-79.

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    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General

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