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Question: Consider a market where there are two Cournot competitors. Market demand is given by: P = 125 - 2...

Show transcribed image text Consider a market where there are two Cournot competitors. Market demand is given by: P = 125 – 2Q_d. Each firm has zero fixed cost and a constant marginal cost of 5 for each unit produced. Total revenue for firm 1 is: TR_1 = 125q_1 – 2(q_1)^2 – 2q_1q_2, so marginal revenue for firm 1 is: MR_1 = 125 – 4q_1 – 2q_2. Similarly, for firm 2: TR_2 = 125q_2 – 2(q_2)^2 – 2q_1q_2, and marginal revenue for firm 2 is: MR_2 = 125 – 4q_2 – 2q_1. A) What are variable and total cost for each firm? What are average total and average variable cost for each firm? (The answers to these are simple equations) B) After finding the best-response functions find the Nash equilibrium quantity for each firm. What is the market price? C) What is the Nash equilibrium profit for each firm? D) Show how a cartel agreement would work assuming the two firms equally share the monopoly level of profit.

Consider a market where there are two Cournot competitors. Market demand is given by: P = 125 – 2Q_d. Each firm has zero fixed cost and a constant marginal cost of 5 for each unit produced. Total revenue for firm 1 is: TR_1 = 125q_1 – 2(q_1)^2 – 2q_1q_2, so marginal revenue for firm 1 is: MR_1 = 125 – 4q_1 – 2q_2. Similarly, for firm 2: TR_2 = 125q_2 – 2(q_2)^2 – 2q_1q_2, and marginal revenue for firm 2 is: MR_2 = 125 – 4q_2 – 2q_1. A) What are variable and total cost for each firm? What are average total and average variable cost for each firm? (The answers to these are simple equations) B) After finding the best-response functions find the Nash equilibrium quantity for each firm. What is the market price? C) What is the Nash equilibrium profit for each firm? D) Show how a cartel agreement would work assuming the two firms equally share the monopoly level of profit.