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Consider a market with two firms whose products are identical. The market demand curve is p...

Consider a market with two firms whose products are identical. The market demand curve is p = a − bq where a > 0 and b > 0, and where q = q1 + q2. Firm i’s profits are πi(q1, q2) = pqi − cqi . Assume that the firms move in sequence, with firm 1 choosing q1 first, and then firm 2 choosing q2; however, assume firm 2 observes q1 before choosing q2.

(a) What is a Nash equilibrium in this game?

(b) Note that firm 2 will always choose a best response to q1. Therefore, firm 1 knows that if it produces q1, then total output will be q1 + r2(q1); thus it will use this information to choose q1 optimally. Find output and profits for each firm.

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