Each firm has sufficient capacity to supply the entire market. Hence there may be no equilibrium if each of the two firms does not have sufficient spare capacity.
The firms face identical cost curves, otherwise the one which faces lower marginal costs will always end up supplying the entire market. Assume that at given input prices, MC is constant and equal to AC.
The rival's price is taken as given.
Price competition instead of quantity competition.
The Bertrand Equilibrium:
The equilibrium is achieved when each firm's expectations about the price behaviour of its rival are realised, where the two reaction functions intersect.
Each firm must charge the same price in equilibrium, if they did not, the one that charges lower price will get all the demand. As a result, the equilibrium must be characterised by equal prices and therefore lie on a 45° line from the origin on a graph which shows price of Firm 1 on the horizontal axis and price of Firm 2 on the vertical axis.
The equilibrium price must be equal to the MC of each producer (the MCs of both producer are assumed to be identical. If the equilibrium price \(P_{e}\) > MC, and firm 1 believes that firm 2 will not alter its price in response to price cut by firm 1, then firm 1 would always cut price and eventually capture the whole market. This incentive of price cutting is eliminated only when the firms charge the same P=MC price and the industry profits are zero.
Hence Bertrand competition leads is to perfectly competitive solution. The difference is that in a Bertrand model, there is relatively small numbers of firms in the industry.
It is possible that firms will collude to avoid its zero profit equilibrium.
However, like the case of output-based cartels, the collusive equilibrium tends to be unstable.
But the extent that a price is a more easily monitored variable than output, cartel arrangements that involve price fixing may be easier for the cartel members to monitor.
Summarised from Microeconomics Estrin Laidler and Dietrich Chap 16.
