English, Article, Journal or magazine article edition: Bertrand's price competition in markets with fixed costs Alejandro Saporiti; German Coloma

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Bookmark: http://trove.nla.gov.au/version/69036
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Bertrand's price competition in markets with fixed costs
Author
  • Alejandro Saporiti
  • German Coloma
Physical Description
  • preprint
Notes
  • This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly break-even price, denoted by D(pL (n)), is sufficient to guarantee that the market supports a (not necessarily symmetric) Bertrand equilibrium in pure strategies with two or more 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(p(n)).
  • Bertrand competition, cost subadditivity, fixed costs, natural monopoly.
  • RePEc:roc:rocher:549
  • 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.
  • RePEc:roc:rocher:541
Language
  • English
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