Consider two identical firms that face the market demand p = 180 − q, where q = q_1 + q_2 is the total output produced by the two firms, and qi (i ∈ {1, 2}) is the output of firm i. The cost function of firm i is C_i(qi) = q_2i . Suppose, firm 1 chooses the price p per unit of output first, and firm 2 will take the price p as given and make its choice of output quantity q2. (a) Carefully write down Firm 2’s optimization problem and solve it. (b) Carefully write down Firm 1’s optimization problem and solve it. (c) What is the total output quantity produces by the two firms? Which profits will the firms make??

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