Question

Question 2: Simultaneous quantity choice: Two firms F1 and F2 producea homogeneous product and compete on the same market. The market price isdescribed by the inverse demand curve P= 11−2Q, where Q is total industry output and P is the market price. To keep things simple, suppose that each firm can produce either 1 or 2 units (these are the only possible choices of production).Further suppose that both firms have a constant marginal cost equal to 2, so that the total cost of firm i= 1, 2 producing quantity q_i∈{1,2} is given by C(q_i) = 2q_i. Further suppose that firms’ production choices are simultaneous.

a. Since each firm can choose one of two possible output levels, there are four possible combinations of output choices: (q1,q2) = (1,1), (q1,q2) = (2,1),(q1,q2) = (1,2), and (q1,q2) = (2,2). Find the market price P under each ofthese possible output choices.

b. If the firms choose output levels (q1,q2), then firm 1 produces and sells (only) its own output q1 at the market price P determined by total output q1+q2. Firm 1’s realized profit is therefore given by π1=Pq1−2q1. Bearing in mind how(q1,q2) affect P, evaluate this profit function for each combination of output choices above.

c. Bearing in mind that the firms are symmetric (so that firm 2’s profits are themirror image of firm 1’s), represent the payoff matrix of this game.4. Find the Nash equilibria of this game.

Answer 1

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