Question

b. Suppose instead that there are three firms competing in price, and that Firm 1 has a marginal cost of 10, firm 2 has a marginal cost of 20, and firm 3 has a marginal cost of 30.As before, the lowest priced firm gets the entire market. If more than one firm has the same lowest price, they split the sales. What is an equilibrium of this game?

Answer 1

Here we have the situation that Firm 1 = c = 10, Firm 2 = c = 20, Firm 3 = c = 30. Here c is the marginal cost. Here all firms will operate with a profit motive and also the lowest price firm captures the entire market. The firms charging P=20 or more will not remain in the market as at below their prices they will make a loss and will be price out of the market. The firm with price P=10 will charge a price 10 + K where K is a small number so as to earn some profits. But as K cant be small enough and some firm can always price below it, K will be competed away and so the equilibrium will be at P=10 with the only surviving firm earning normal profits.