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Question 2 (5 marks total) Two firms are engaging in price competition. Firm 1 has the cost function c (41) = 89, for all 41 > 0 and Firm 2 has the cost function c(q:) = 2g, for all q, > 0. Firm 1 and Firm 2 charge a price of pi and p, respectively (per unit). Market demand is given by Q = 1, 200 - 2p where p = min(p, pa). If p, = pa both firms supply half of the total output Q, and if p, # po the firm with the lowest price supplies all of the output. a) Provide the definition of a Bertrand equilibrium. (1 mark) b) Consider the pair of prices (pi, pa) = (9,9). Calculate profits for both firms under these prices. (1 mark). Use your definition from part a to prove that (pi, po) = (9,9) does not form a Bertrand equilibrium (1 mark) c) Find a Bertrand equilibrium for this game. (1 mark). Use your definition from part a to prove that your answer is indeed a Bertrand equilibrium. (1 mark)