Exercise 2: Cournot Oligopoly The inverse market demand is where Qielli = 0 if Q≥ 220 P(Q) = 220 Q if Q< 220 1. Suppose there are two identical firms with cost functions ci(qi) 10q; for i = {1,2}. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits in equilibrium. 2. Suppose firm 1's cost function is still c₁(91) the cost function = 10q1. Firm 2 has an avoidable fixed cost, resulting in 0 if q2 = 0 C2(92) 10q23,600 if q2 > 0. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. 3. Suppose there are nЄ IN, n > 2 identical firms with cost functions ci (qi) = 10q; for i = {1, 2,..., n}. Find the payoff functions and best responses for all firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits (as functions of n) in equilibrium. Discuss how the market price and profits react to an increase in the number of firms n. What happens in the limit as n goes to infinity?
Exercise 2: Cournot Oligopoly The inverse market demand is where Qielli = 0 if Q≥ 220 P(Q) = 220 Q if Q< 220 1. Suppose there are two identical firms with cost functions ci(qi) 10q; for i = {1,2}. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits in equilibrium. 2. Suppose firm 1's cost function is still c₁(91) the cost function = 10q1. Firm 2 has an avoidable fixed cost, resulting in 0 if q2 = 0 C2(92) 10q23,600 if q2 > 0. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. 3. Suppose there are nЄ IN, n > 2 identical firms with cost functions ci (qi) = 10q; for i = {1, 2,..., n}. Find the payoff functions and best responses for all firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits (as functions of n) in equilibrium. Discuss how the market price and profits react to an increase in the number of firms n. What happens in the limit as n goes to infinity?
Chapter29: Service-entrance Calculations
Section: Chapter Questions
Problem 3R: a. What is the ampere rating of the circuits that are provided for the small-appliance loads? _____...
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Transcribed Image Text:Exercise 2: Cournot Oligopoly
The inverse market demand is
where Qielli
=
0
if Q≥ 220
P(Q)
=
220 Q if Q< 220
1. Suppose there are two identical firms with cost functions ci(qi)
10q; for i = {1,2}. Find the payoff
functions and best responses for both firms. Identify all Nash equilibria of this game. Compute the
market price and the firms' profits in equilibrium.
2. Suppose firm 1's cost function is still c₁(91)
the cost function
=
10q1. Firm 2 has an avoidable fixed cost, resulting in
0
if q2 = 0
C2(92)
10q23,600 if q2 > 0.
Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game.
3. Suppose there are nЄ IN, n > 2 identical firms with cost functions ci (qi) = 10q; for i = {1, 2,..., n}.
Find the payoff functions and best responses for all firms. Identify all Nash equilibria of this game.
Compute the market price and the firms' profits (as functions of n) in equilibrium. Discuss how the
market price and profits react to an increase in the number of firms n. What happens in the limit as
n goes to infinity?
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