Assignment
Consider an oligopoly market with two firms producing different products. There is only fixed cost, $20. Demand function for firm 1's product is
q1 = 18-2p1 + p2
and demand function for firm 2's product is
q2 = 18-2p2 + p1
(1) Suppose the two firms act non-cooperatively, calculate equilibrium prices p∗1 and p∗2, and equilibrium profits π∗1 and π∗2.
(2) Suppose the two firms decide to collude, calculate equilibrium prices pcol1 and pcol2, and equilibrium profits πcol1 and πcol2.
(3) Suppose each firm has two choices, either to choose the price calculated in part (1) or the price calculated in part (2).
In other words, firm 1 deviates from collusion and set price as p∗1 but firm 2 stays with the price, pcol2, then what is the π1 and π2?
(4) Based on part(1)-(3), set 2x2 game table. In each cell the first number is the profit of firm 1 and the second number is the profit of firm 2. Then find the Nash equilibrium for the game. Is the Nash equilibrium pareto efficient?