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Alpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q°, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b-1. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm , price , profit b) It occurs to the managers of Alpha and Gamma that they could do a lot better by clluding. If the two firms were to collude, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm , price , profit c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that phones have a limited shelf life and become useless after one period, i.e. one period's output must be sold in the same period). Find also the optimal quantity that cheating firm want to produce, price and profit associated with this quantity. Round the discount factor to the first figure after the decimal sign (0.1, 0.2, 0.3, etc.) Cheating quantity , cheating price , cheating profit , discount factor

Alpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q°, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b-1. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm , price , profit b) It occurs to the managers of Alpha and Gamma that they could do a lot better by clluding. If the two firms were to collude, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm , price , profit c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that phones have a limited shelf life and become useless after one period, i.e. one period's output must be sold in the same period). Find also the optimal quantity that cheating firm want to produce, price and profit associated with this quantity. Round the discount factor to the first figure after the decimal sign (0.1, 0.2, 0.3, etc.) Cheating quantity , cheating price , cheating profit , discount factor

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Alpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q?, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b=1. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm , price , profit b) It occurs to the managers of Alpha and Gamma that they could do a lot better by colluding. If the two firms were to collude, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm , price , profit c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that phones have a limited shelf life and become useless after one period, i.e. one period's output must be sold in the same period). Find also the optimal quantity that cheating firm want to produce, price and profit associated with this quantity. Round the discount factor to the first figure after the decimal sign (0.1, 0.2, 0.3, etc.) Cheating quantity , cheating price , cheating profit discount factor Part C
Transcribed Image Text:Alpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q?, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b=1. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm , price , profit b) It occurs to the managers of Alpha and Gamma that they could do a lot better by colluding. If the two firms were to collude, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm , price , profit c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that phones have a limited shelf life and become useless after one period, i.e. one period's output must be sold in the same period). Find also the optimal quantity that cheating firm want to produce, price and profit associated with this quantity. Round the discount factor to the first figure after the decimal sign (0.1, 0.2, 0.3, etc.) Cheating quantity , cheating price , cheating profit discount factor Part C
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