Bertrand's price competition in markets with fixed costs
AbstractWe 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.
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Bibliographic InfoPaper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 541.
Length: 23 pages
Date of creation: Sep 2008
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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.
Other versions of this item:
- Alejandro Saporiti & German Coloma, 2009. "Bertrand's price competition in markets with fixed costs," RCER Working Papers 549, University of Rochester - Center for Economic Research (RCER).
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-01-24 (All new papers)
- NEP-COM-2009-01-24 (Industrial Competition)
- NEP-IND-2009-01-24 (Industrial Organization)
- NEP-MIC-2009-01-24 (Microeconomics)
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