7. Two firms produce identical goods, with a production cost of c> 0 per unit. Each firm sets a nonnegative price (p₁ and 2). All consumers buy from the firm with the lower price, if p1 # P2. Half of the consumers buy from each firm if p₁ = P2. D is the total demand. Profit of firm i is: 0 if pi > p; (no one buys from firm i); Pi-c DPC if p₁ = p; (Half of customers buy from firm i); 2 D(pic) if pi < p; (All customers buy from firm 2) Find the pure strategy Nash equilibrium: a) Both firms set p = 0. b) Firm 1 sets p = 0, and firm 2 sets p = c. c) Both firms set p = c. d) No pure strategy Nash equilibrium exists.

Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter24: Price-searcher Markets With High Entry Barriers
Section: Chapter Questions
Problem 13CQ
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7. Two firms produce identical goods, with a production cost of c> 0 per unit.
Each firm sets a nonnegative price (p₁ and p₂).
All consumers buy from the firm with the lower price, if p₁ ‡ p2. Half of the consumers buy from each firm if p₁ = P2.
D is the total demand.
Profit of firm i is:
0 if pi > Pj (no one buys from firm i);
pi-c
●
Die if p₁ = p; (Half of customers buy from firm i);
2
D(pic) if pi < p; (All customers buy from firm i)
Find the pure strategy Nash equilibrium:
a) Both firms set p = 0.
b) Firm 1 sets p = 0, and firm 2 sets p = c.
c) Both firms set p = c.
O d) No pure strategy Nash equilibrium exists.
Transcribed Image Text:7. Two firms produce identical goods, with a production cost of c> 0 per unit. Each firm sets a nonnegative price (p₁ and p₂). All consumers buy from the firm with the lower price, if p₁ ‡ p2. Half of the consumers buy from each firm if p₁ = P2. D is the total demand. Profit of firm i is: 0 if pi > Pj (no one buys from firm i); pi-c ● Die if p₁ = p; (Half of customers buy from firm i); 2 D(pic) if pi < p; (All customers buy from firm i) Find the pure strategy Nash equilibrium: a) Both firms set p = 0. b) Firm 1 sets p = 0, and firm 2 sets p = c. c) Both firms set p = c. O d) No pure strategy Nash equilibrium exists.
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