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 firmgets a demand of 1 and the more expensive firm gets a demand of 0. If P1 = P2, each firmgets 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 <p2if P1 = p2if 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] 13:02 Tue 5 Mar个(c) How do your results compare to the equilibria of Rock, Paper, Scissors? What is the keydifference between the twTt>Question 2Two profit-maximising firms-firm 1 and firm 2-produce an identical good at no cost andsimultaneously choose their prices, which must be between 0 and 1. That is, firm 1 choosesP₁ = [0, 1] and firm 2 chooses p2 € [0, 1] (i.e., 0 ≤ P1, P2 ≤ 1). If p1p2, the cheaper firmgets a demand of 1 and the more expensive firm gets a demand of 0. If p₁ = P2, each firmgets a demand of 0.5. Firm 1 has a capacity constraint x = [0, 1] but firm 2 has no capacityconstraint. Therefore, the demands are(91,92)=(x0,للللا1 x)(min{x, 0.5), max{1 − x,0.5})(0,1)if p₁ < P2if p₁ = P2if p₁ > P2.(a) For any capacity constraint x = (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of thatgame.(b) 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 allNash equilibria of that game.(c) Repeat parts (a) and (b) for the case where x = 1. Briefly interpret your results. [max:50 words](d) Repeat parts (a) and (b) for the case where x = 0. Briefly interpret your results. [max:50 words]86%< NIS<

This is a Bertrand competition with capacity constraints. In this case, firm 1 has a capacity…

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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]

13:02 Tue 5 Mar
个
(c) How do your results compare to the equilibria of Rock, Paper, Scissors? What is the key
difference between the tw
Tt
>
Question 2
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 = [0, 1] and firm 2 chooses p2 € [0, 1] (i.e., 0 ≤ P1, P2 ≤ 1). If p1p2, 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 = [0, 1] but firm 2 has no capacity
constraint. Therefore, the demands are
(91,92)
=
(x0,
للللا
1 x)
(min{x, 0.5), max{1 − x,0.5})
(0,1)
if p₁ < P2
if p₁ = P2
if p₁ > P2.
(a) For any capacity constraint x = (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of that
game.
(b) 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.
(c) Repeat parts (a) and (b) for the case where x = 1. Briefly interpret your results. [max:
50 words]
(d) Repeat parts (a) and (b) for the case where x = 0. Briefly interpret your results. [max:
50 words]
86%
< NIS
<

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