Bertrand's Price Competition in Markets with Fixed Costs

Posted by D. Daniel Sokol

Alejandro Saporitiy (University of Manchester - Economics) and German Coloma (Universidad del CEMA - Economics) analyze Bertrand's Price Competition in Markets with Fixed Costs.

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 avoid-able, 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 sufficient 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.