In a duopoly market, two firms produce the identical products, the cost function of firm 1 is: C, = 20q1, the cost function of firm 2 is: C2 2Q, here Q = q1 :20q2, the market demand function is: P = 500 – + 92. In a Bertrand model, the two firms set their price simultaneously, assume both firms do not have production capacity limits, and there is no collusion. What is the market equilibrium price and quantity? If the two firms decide to form a Cartel, i.e. they want to maximize the profit of the whole industry, and then split the production and profit evenly. What is the market price? What is the industry's total quantity produced? What is the quantity produced and profit of each firm? If firm 1 will produce at the production level from (b) for sure, what is firm 2's optimal production decision? What is firm 2's maximum profit?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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Chapter12: Price And Output Determination: Oligopoly
Section: Chapter Questions
Problem 2E
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1. In a duopoly market, two firms produce the identical products, the cost function of firm 1 is:
C1 =
20q1, the cost function of firm 2 is: C2 = 20g2, the market demand function is: P = 500 –
2Q, here Q = q1 + 92.
In a Bertrand model, the two firms set their price simultaneously, assume both firms do not
have production capacity limits, and there is no collusion. What is the market equilibrium price
and quantity?
а.
b. If the two firms decide to form a Cartel, i.e. they want to maximize the profit of the whole
industry, and then split the production and profit evenly. What is the market price? What is the
industry's total quantity produced? What is the quantity produced and profit of each firm?
If firm 1 will produce at the production level from (b) for sure, what is firm 2's optimal
production decision? What is firm 2's maximum profit?
C.
d. If the cartel eventually breaks down, and the two firms decide to set their quantities
simultaneously (Cournot model), what are the Cournot equilibrium quantity and price?
Based on the results from (b) (c) and (d), if the two firms signed a cartel agreement, which
anyone violates the cartel production quotas, the other firm will product at Cournot equilibrium
quantity forever. What is the highest market interest rate that makes the Cartel stable?
е.
says
if
Transcribed Image Text:1. In a duopoly market, two firms produce the identical products, the cost function of firm 1 is: C1 = 20q1, the cost function of firm 2 is: C2 = 20g2, the market demand function is: P = 500 – 2Q, here Q = q1 + 92. In a Bertrand model, the two firms set their price simultaneously, assume both firms do not have production capacity limits, and there is no collusion. What is the market equilibrium price and quantity? а. b. If the two firms decide to form a Cartel, i.e. they want to maximize the profit of the whole industry, and then split the production and profit evenly. What is the market price? What is the industry's total quantity produced? What is the quantity produced and profit of each firm? If firm 1 will produce at the production level from (b) for sure, what is firm 2's optimal production decision? What is firm 2's maximum profit? C. d. If the cartel eventually breaks down, and the two firms decide to set their quantities simultaneously (Cournot model), what are the Cournot equilibrium quantity and price? Based on the results from (b) (c) and (d), if the two firms signed a cartel agreement, which anyone violates the cartel production quotas, the other firm will product at Cournot equilibrium quantity forever. What is the highest market interest rate that makes the Cartel stable? е. says if
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