This paper is about a model of Bertrand competition in a homogeneous-good market with free entry of identical firms and variable returns to scale. If the optimum number of active firms in the market is two or more, and the number of active firms is equal to that optimum number, then Bertrand equilibrium exists for that optimum number, and it does not exist if the number of active firms is less than the optimum. The model, however, does not rule out the existence of Bertrand equilibria with more active firms than the optimum number. Finally, when the optimum number of active firms in the market is one, Bertrand equilibrium does not exist.
Bertrand equilibrium, Variable returns to scale, Free entry, Number of firms