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Indeterminate Output Allocations in Collusive Equilibria and Multi-plant Firms

Author

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  • Thomas Mitchell

    (S. Illinois Univ. at Carbondale)

Abstract

If n colluding oligopolists all have the cost function C(q_i) = c * q_i, then it will not be possible to uniquely allocate among the firms the monopoly output that maximizes their joint profit. Similarly, if all plants of an n-plant firm have the cost function C(q_i) = c * q_i, then it will not be possible to uniquely allocate the firm's optimal output among the n plants. This paper identifies the necessary and sufficient conditions for such "allocative indeterminacies" to occur (i.e., the conditions to be avoided).

Suggested Citation

  • Thomas Mitchell, 1995. "Indeterminate Output Allocations in Collusive Equilibria and Multi-plant Firms," Microeconomics 9507001, EconWPA.
  • Handle: RePEc:wpa:wuwpmi:9507001 Note: Type of Document - LaTeX (2.09); prepared on IBM PC; to print on HP LaserJet III (1Mb); pages: 9; figures: none. Only file FTP'ed is the TeX input file. With your Web browser, visit SIUC's Working Paper
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    References listed on IDEAS

    as
    1. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, pages 203-208.
    2. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, pages 882-888.
    3. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, December.
    4. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, pages 203-208.
    5. Kohli, Ulrich, 1993. "A Symmetric Normalized Quadratic GNP Function and the U.S. Demand for Imports and Supply of Exports," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 243-255, February.
    6. repec:mes:challe:v:31:y:1988:i:4:p:56-58 is not listed on IDEAS
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    More about this item

    Keywords

    production theory; functional forms; ind. org.;

    JEL classification:

    • D1 - Microeconomics - - Household Behavior
    • D2 - Microeconomics - - Production and Organizations
    • D3 - Microeconomics - - Distribution
    • D4 - Microeconomics - - Market Structure, Pricing, and Design

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