economics 4 questions

ECON104B(Spring) HW7

∗Due Date: 5/30 (Tue.) right after the class. No late submission is allowed.

∗Print out this form, solve, and submit it. You can use back page or attach other pages (staple together).

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<Price setting oligopoly>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 − 2 p1 + p2

and demand function for firm 2’s product is

q2 = 18 − 2 p2 + 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 p col 2 , and equilibrium profits

π col 1 and π

col 2 .

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(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 col 2 , 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?

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