Equilibrium Conditions for Efficient Rent Seeking: The Nash-Cournot Solution

  • David L. Cleeton

Abstract

Tullock presents a model of the rent-seeking behavior of risk-neutral individuals. This model has sparked the interest of a number of researchers1 and the literature has expanded Tullock’s model in a variety of directions. This article sets out the original problem in the formal framework of a Nash-Cournot game. While only part of Tullock’s original article looks at rent seeking in the Nash-Cournot framework, this framework is a useful way to summarize the analysis of rent-seeking behavior. I will show that many of the problems addressed by other authors can be seen more clearly when one works through the detailed results of Tullock’s model using the Nash-Cournot equilibrium concept.2 I will also show the pedagogical value of using this unifying framework to study rent-seeking behavior, and I will present an important result concerning the possibility of overdissipation as stated in Tullock’s original model.

Keywords

Expected Profit Rent Seeker Cournot Equilibrium Monopoly Rent Marginal Cost Curve 
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Notes

  1. I would like to thank Joseph Jadlow, David Schap, Gordon Tullock, and a referee from The Quarterly Review of Economics and Business for helpful comments on this topic.Google Scholar
  2. 1.
    See Corcoran [1], Corcoran and Karels [2], Higgins, Shughart, and Tollison [4], Hillman and Katz [5], Jadow [6], Rogerson [7], and Tullock [9, 10] for various specifications of the model. For an alternative model, which argues that rents may be dissipated in the form of nonprice competition, see Gifford [3].Google Scholar
  3. 2.
    Other game theoretic solutions to the rent-seeking problem can be found in those articles cited in note 1. While some of these formulations extend outside of the Nash-Cournot equilibrium framework, they all begin their modeling by using the Nash-Cournot solution as the point of departure.Google Scholar
  4. 3.
    Tullock [9], p. 97, reports that the second-order conditions are not met when R N/(N— 2). His statement is incorrect, and the inequality should be reversed.Google Scholar
  5. 4.
    Corcoran [1] and Corcoran and Karels [2] attempt to rationalize a similar result based on a zero expected profit condition that is driven by entry and exit. The result obtained here is independent of the number of rent seekers and depends only on a rational participation rule for risk-neutral individuals.Google Scholar
  6. 5.
    These results can be derived directly from partial differentiation of the equation C = R(N-1)1 N. Holding N fixed, C increases with Rat a fixed rate equal to (N-1) IN. Holding R fixed, C increases with Nat a decreasing rate. The cross partial is positive.Google Scholar
  7. 6.
    The solutions proposed by Corcoran and Karels [2] to obtain a rent-seeking ratio equal to + 1, such as bet splitting and so-called preemptory betting, depend on strategic behavior on the part of individuals and, thus, do not fit into the Nash-Cournot equilibrium framework.Google Scholar
  8. 7.
    Whether these secondary rent-seeking costs are observed depends on whether the incumbents in the primary rent-seeking competition actually sell their “participation rights” or simply treat the value of those rights as an opportunity cost of remaining in the primary rent-seeking competition.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • David L. Cleeton

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