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 p^col₁ and p^col₂, and equilibrium profits π^col₁ and π^col₂.

(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, p^col₂, 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?