(c) Two profit-maximising firms, A and B, producing differentiated goods are competing in

the same market, simultaneously selecting prices pA and pB (Bertrand competition).

Profits for each firm equal the quantity it sells times the difference between the price it

charges and marginal cost. The demand schedule faced by A is q_A = 1p_A +p_B/2 and

the demand schedule faced by B is q_B = 1 p_B + p_A/2. Firm A produces the good at

a marginal cost of 1/2. Firm A's costs are known to both competitors.

(i) Suppose that firm B's marginal cost is 1/2, and that this is also known to both

competitors. Derive equilibrium prices. (3 marks)

(ii) Next suppose that firm B's marginal cost can be either 0 or 1, with equal

probabilities, and that B observes its cost before A and B select their prices, while

A does not observe firm B's marginal cost but knows that it is either zero or 1 with

equal probabilities. Derive equilibrium prices. (5 marks)

(iii) Now suppose that, as in (ii), B's marginal cost can be either 0 or 1 with equal

probabilities, but A can fully observe B's costs. Derive equilibrium prices and

expected equilibrium profits for this scenario and compare them with those obtained

under (ii). (4 marks)