Question 2: Simultaneous quantity choice: Twofirms F1 and F2 producea homogeneous product and compete on thesame market. The market price isdescribed by the inverse demandcurve P= 11−2Q, where Q is total industry output and P is themarket price. To keep things simple, suppose that each firm canproduce either 1 or 2 units (these are the only possible choices ofproduction).Further suppose that both firms have a constantmarginal cost equal to 2, so that the total cost of firm i= 1, 2producing quantity qi∈{1,2} is given by C(qi)= 2qi. Further suppose that firms’ production choicesare 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). Findthe market price P under each ofthese possible output choices.
b. If the firms choose output levels (q1,q2), then firm 1produces and sells (only) its own output q1 at the market price Pdetermined by total output q1+q2. Firm 1’s realized profit istherefore given by π1=Pq1−2q1. Bearing in mind how(q1,q2) affect P,evaluate this profit function for each combination of outputchoices above.
c. Bearing in mind that the firms are symmetric (so that firm2’s profits are themirror image of firm 1’s), represent the payoffmatrix of this game.4. Find the Nash equilibria of this game.
