Two profit-maximising firms-firm 1 and firm 2-produce an identical good at no cost and simultaneously choose their prices, which must be between 0 and 1. That is, firm 1 chooses P1 contained in [0, 1] and firm 2 chooses p2 contained in [0, 1] (i.e., 0 ≤ p1, p2 < 1). If p1< p2, the cheaper firm gets a demand of 1 and the more expensive firm gets a demand of 0. If P1 = P2, each firm gets a demand of 0.5. Firm 1 has a capacity constraint x contained in [ 0,1 ]but firm 2 has no capacity constraint. Therefore, the demands are (Q1,Q2) =( (х, 1 -х) (min{x, 0.5}, max{1 - x, 0.5}) ( (0,1) if p1 P2. For any capacity constraint x contained in (0,1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Suppose now that each firm can only choose among three possible prices: 0, 0.5, and 1; that is p1, p2 € {0,0.5, 1}. For any capacity constraint x € (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Repeat parts (a) and (b) for the case where x = 1. Briefly interpret your results. (max: 50 words] Repeat parts (a) and (b) for the case where x = 0. Briefly interpret your results. max: 50 words]
Two profit-maximising firms-firm 1 and firm 2-produce an identical good at no cost and simultaneously choose their prices, which must be between 0 and 1. That is, firm 1 chooses P1 contained in [0, 1] and firm 2 chooses p2 contained in [0, 1] (i.e., 0 ≤ p1, p2 < 1). If p1< p2, the cheaper firm gets a demand of 1 and the more expensive firm gets a demand of 0. If P1 = P2, each firm gets a demand of 0.5. Firm 1 has a capacity constraint x contained in [ 0,1 ]but firm 2 has no capacity constraint. Therefore, the demands are (Q1,Q2) =( (х, 1 -х) (min{x, 0.5}, max{1 - x, 0.5}) ( (0,1) if p1 P2. For any capacity constraint x contained in (0,1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Suppose now that each firm can only choose among three possible prices: 0, 0.5, and 1; that is p1, p2 € {0,0.5, 1}. For any capacity constraint x € (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Repeat parts (a) and (b) for the case where x = 1. Briefly interpret your results. (max: 50 words] Repeat parts (a) and (b) for the case where x = 0. Briefly interpret your results. max: 50 words]
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter9: Monopoly
Section: Chapter Questions
Problem 31P: Return to Figure 9.2. Suppose P0 is 10 and P1 is 11. Suppose a new firm with the same LRAC curve as...
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Two profit-maximising firms-firm 1 and firm 2-produce an identical good at no cost and simultaneously choose their prices, which must be between 0 and 1. That is, firm 1 chooses P1 contained in [0, 1] and firm 2 chooses p2 contained in [0, 1] (i.e., 0 ≤ p1, p2 < 1). If p1< p2, the cheaper firm
gets a demand of 1 and the more expensive firm gets a demand of 0. If P1 = P2, each firm
gets a demand of 0.5. Firm 1 has a capacity constraint x contained in [ 0,1 ]but firm 2 has no capacity constraint. Therefore, the demands are
(Q1,Q2) =( (х, 1 -х)
(min{x, 0.5}, max{1 - x, 0.5})
( (0,1)
if p1 <p2
if P1 = p2
if p1 > P2.
- For any capacity constraint x contained in (0,1) (i.e., 0 < x < 1), find all Nash equilibria of that game.
- Suppose now that each firm can only choose among three possible prices: 0, 0.5, and 1; that is p1, p2 € {0,0.5, 1}. For any capacity constraint x € (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of that game.
- Repeat parts (a) and (b) for the case where x = 1. Briefly interpret your results. (max:
50 words] - Repeat parts (a) and (b) for the case where x = 0. Briefly interpret your results. max:
50 words]
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