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Bertrand's price competition in markets with fixed costs

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Abstract

We analyze Bertrand's price competition in a homogenous good market with a fixed cost and an increasing marginal cost (i.e., with variable returns to scale). If the fixed cost is avoidable, we show that the non-subadditivity of the cost function at the output corresponding to the oligopoly break-even price, denoted by D(pL(n)), is su±cient to guarantee that the market supports an equilibrium in pure strategies with two or more active firms supplying at least D(pL(n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(pL(n)). As a by-product, the latter implies that the average cost cannot be decreasing over the range of outputs mentioned before. In addition, we also prove that the existence of a price-taking equilibrium is sufficient, but not necessary, for Bertrand's price competition to possess an equilibrium in pure strategies. This provides a simple existence result for the case where the fixed cost is fully unavoidable.

Suggested Citation

  • Alejandro Saporiti & German Coloma, 2008. "Bertrand's price competition in markets with fixed costs," RCER Working Papers 541, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:541
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    Cited by:

    1. Matthew Andrews & Milan Bradonjic & Iraj Saniee, 2017. "Quantifying the Benefits of Infrastructure Sharing," Papers 1706.05735, arXiv.org.
    2. Robert R. Routledge, 2009. "Testable implications of the Bertrand model," The School of Economics Discussion Paper Series 0918, Economics, The University of Manchester.

    More about this item

    JEL classification:

    • 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

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