Two firms, A and B, engage in Bertrand price competition in a market with inverse demand given by P = 12 - Q. Firm A has a higher marginal cost: cA > cB . Whenever a firm undercuts the rival’s price, it has all the market. If a firm charges the same price as the rival, it has half of the market. If a firm charges more than the rival, it has zero market share.
(a) Suppose that cA = 8 and cB = 3. Find the Nash equilibrium of this game (pA,pB) where one of the firms charges its marginal cost
(b) Suppose that there are not 2, but n firms with different marginal costs. Any number of firms may also have equal marginal costs. Can we have a marginal cost structure where one firm earns a positive profit? Can we have a marginal cost structure where more than one firm earns a positive profit? Just explain the intuition without the math.