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Too many or too few? On the optimal number of firms in the commons

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  • Colombo, Luca
  • Labrecciosa, Paola
  • Simon, Leo K.

Abstract

In this paper, we consider common-pool non-renewable resource industries and study the socially optimal industry size. Our analysis is conducted in terms of an infinite-horizon differential game (with either open-loop or feedback strategies). We derive two main results. First, we show that there exists a unique state-independent efficiency-inducing industry size, ranging between 1 and infinity, if and only if the elasticity of the price-cost margin (capturing static market power) and the elasticity of the difference between social and private resource rents (capturing the tragedy of the commons) are the same. Second, allowing for entry/exit, we show that the regulator can set a license fee to be paid by firms to get access to the resource such that the endogenous number of firms in the equilibrium with regulated entry is socially optimal.

Suggested Citation

  • Colombo, Luca & Labrecciosa, Paola & Simon, Leo K., 2023. "Too many or too few? On the optimal number of firms in the commons," Journal of Environmental Economics and Management, Elsevier, vol. 121(C).
    • Handle: RePEc:eee:jeeman:v:121:y:2023:i:c:s0095069623000438
    DOI: 10.1016/j.jeem.2023.102825
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    References listed on IDEAS

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    1. repec:bla:econom:v:53:y:1986:i:212:p:519-27 is not listed on IDEAS
    2. Karp, Larry, 1992. "Social Welfare in a Common Property Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 353-372, May.
    3. Reinganum, Jennifer F & Stokey, Nancy L, 1985. "Oligopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 161-173, February.
    4. 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.
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    More about this item

    Keywords

    Common-pool resources; Differential games; Optimal number of firms; Oligopoly; Social welfare;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General

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