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On the Optimal Number of Firms in the Commons: Cournot vs Bertrand

  • D. Dragone
  • L. Lambertini
  • A. Palestini
  • A. Tampieri

We revisit the debate on the optimal number of firms in the commons in a differential oligopoly game in which firms are either quantity- or price-setting agents. Production exploits a natural resource and involves a negative externality. We calculate the number of firms maximising industry profits, finding that it is larger in the Cournot case. While industry structure is always inefficient under Bertrand behaviour, it may or may not be so under Cournot behaviour, depending on parameter values. The comparison of private industry optima reveals that the Cournot steady state welfare level exceeds the corresponding Bertrand magnitude if the weight of the stock of pollution is large enough.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number wp856.

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Date of creation: Dec 2012
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Handle: RePEc:bol:bodewp:wp856
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  1. Cornes, Richard & Sandler, Todd, 1983. "On Commons and Tragedies," American Economic Review, American Economic Association, vol. 73(4), pages 787-92, September.
  2. Hassan Benchekroun & Ngo Van Long, 1997. "Efficiency Inducing Taxation for Polluting Oligopolists," CIRANO Working Papers 97s-21, CIRANO.
  3. 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 353-72, May.
  4. Charles F. Mason & Stephen Polasky, 1997. "The Optimal Number of Firms in the Commons: A Dynamic Approach," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 1143-60, November.
  5. Cellini, Roberto & Lambertini, Luca & Ottaviano, Gianmarco I. P., 2004. "Welfare in a differentiated oligopoly with free entry: a cautionary note," Research in Economics, Elsevier, vol. 58(2), pages 125-133, June.
  6. Richard Cornes & Charles F. Mason & Todd Sandler, 1986. "The Commons and the Optimal Number of Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 101(3), pages 641-646.
  7. Kotaro Suzumura & Kazuharu Kiyono, 1987. "Entry Barriers and Economic Welfare," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 157-167.
  8. Kjell Sunnevåg, 2003. "Auction Design for the Allocation of Emission Permits in the Presence of Market Power," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(3), pages 385-400, November.
  9. William Novshek, 1980. "Cournot Equilibrium with Free Entry," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 473-486.
  10. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
  11. Katsoulacos, Yannis & Xepapadeas, Anastasios, 1994. "Environmental Policy Under Oligopoly with Endogenous Market Structure," CEPR Discussion Papers 955, C.E.P.R. Discussion Papers.
  12. Benchekroun, Hassan & Van Long, Ngo, 2002. "On the multiplicity of efficiency-inducing tax rules," Economics Letters, Elsevier, vol. 76(3), pages 331-336, August.
  13. Fujiwara, Kenji, 2009. "Environmental policies in a differentiated oligopoly revisited," Resource and Energy Economics, Elsevier, vol. 31(3), pages 239-247, August.
  14. Morch von der Fehr, N-H., 1991. "Tradable Emission Rights and Strategic Interaction," Memorandum 11/1991, Oslo University, Department of Economics.
  15. Sinn, Hans-Werner, 1984. "Common Property Resources, Storage Facilities and Ownership Structures: A Cournot Model of the Oil Market," Economica, London School of Economics and Political Science, vol. 51(23), pages 235-52, August.
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