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A Dynamic Model of Leap-Frogging Investments and Bertrand Price Competition

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  • John Rust

    (University of Maryland)

  • Bertel Schjerning

    (University of Copenhagen)

  • Fedor Iskhakov

    (University of Technology Sydney)

Abstract

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to "leapfrog" their rival and attain, at least temporarily, low-cost leadership. The model resolves a paradox about investing in the presence of Bertrand price competition: if both firms simultaneously invest in the current state-of-the-art production technology and thereby attain the same marginal cost of production, the resulting price competition drives the price down to marginal cost and profits to zero. Thus, it would seem that neither firm can profit from undertaking the cost-reducing investment, so the firms should not have any incentive to undertake cost-reducing investments if they are Bertrand price competitors. We show this simple intuition is incorrect. We formulate a dynamic model of price and investment competition as a Markov-perfect equilibrium to a dynamic game. We show that even when firms start with the same marginal costs of production there are equilibria where one of the firms invests first, and leapfrogs its opponent. In fact, there are many equilibria, with some equilibria exhibiting asymmetries where there are extended periods of time where only one of the firms does most of the investing, and other equilibria where there are alternating investments by the two firms as they vie for temporary low cost leadership. Our model provides a new interpretation of the concept of a "price war". Instead of being a sign of a breakdown of tacit collusion, in our model price wars occur when one firm leapfrogs its opponent to become the new low cost leader.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2012 Meeting Papers with number 370.

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Date of creation: 2012
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Handle: RePEc:red:sed012:370

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  1. Doraszelski, Ulrich & Escobar, Juan, 2008. "A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification," CEPR Discussion Papers 6805, C.E.P.R. Discussion Papers.
  2. Giovannetti, Emanuele, 2001. "Perpetual Leapfrogging in Bertrand Duopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 671-96, August.
  3. Rust, John, 1986. "When Is It Optimal to Kill Off the Market for Used Durable Goods?," Econometrica, Econometric Society, vol. 54(1), pages 65-86, January.
  4. Ronald L. Goettler & Brett R. Gordon, 2011. "Does AMD Spur Intel to Innovate More?," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1141 - 1200.
  5. Riordan, Michael H & Salant, David J, 1994. "Preemptive Adoptions of an Emerging Technology," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 247-61, September.
  6. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
  7. Rosenkranz, Stephanie, 1997. "Quality improvements and the incentive to leapfrog," International Journal of Industrial Organization, Elsevier, vol. 15(2), pages 243-261, April.
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