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Two firms are engaging in price competition. Firm 1 has the cost function ci(91) = 8q1 for all 41 >0 and Firm 2 has the cost function c(q2) = 2q2 for all q2 > 0. Firm 1 and Firm 2 charge a price of pi and p2 respectively (per unit). Market demand is given by Q = 1, 200 - 2p where p = min{p1, p2}. If p1 = p2 both firms supply half of the total output Q, and if p1 # p2 the firm with the lowest price supplies all of the output. a) Provide the definition of a Bertrand equilibrium. (0.5 mark) b) Consider the pair of prices (P1, p2) = (9,9). Calculate profits for both firms under these prices. (0.5 mark). Use your definition from part a to prove that (P1, P2) = (9,9) does not form a Bertrand equilibrium (1 mark) 3 c) Find a Bertrand equilibrium for this game. (0.5 mark). Use your definition from part a to prove that your answer is indeed a Bertrand equilibrium. (1 mark)