On Bertrand Competition Under Not So Large an Excess of Total Capacity

We consider a homogeneous product market where, given their capacities, existing firms compete in prices. First, pricing at the constant short-run average-marginal cost - i. e., Bertrand outcome - is shown to be a Nash equilibrium of the static price game provided total capacity is sufficiently higher than the quantity demanded at a price equal to marginal cost; most importantly, the minimum amount of excess capacity that is required is quite modest when the one-firm concentration ratio is sufficiently small. Second, a study of repeated price decisions is carried out in a context where less than "fully rational" firms aim in each period at maximising current profits. The convergence result hinted at by Bertrand for a duopoly is shown to extend straightforwardly to the n-firm case: prices converge to short-run average cost under iterated best responses as well as under milder restrictions on the learning process. These results suggest that, in an unconcentrated homogenous-product industry, self-interested behaviour can easily prove "destructive" to the firms - making them not covering anything towards their fixed costs under even a modest excess of total capacity.