Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+10q+q², where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 100 - Q where Q=q1 + q2 is total output. 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 b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, 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 Cheating quantity price c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that widgets are perishable, 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.) Do not round the other responses. discount factor .profit , cheating price cheating profit
Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+10q+q², where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 100 - Q where Q=q1 + q2 is total output. 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 b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, 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 Cheating quantity price c) What minimum discount factor is required for firms to find it worthwhile to collude? (You can assume that widgets are perishable, 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.) Do not round the other responses. discount factor .profit , cheating price cheating profit
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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M11
Transcribed Image Text:Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function
given by: C(q) = 10+10q+q2, where q is number of widgets produced. The market demand for
widgets is represented by the inverse demand equation: P = 100 - Q where Q=q1 + q2 is total
output. 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 Gamma and Zeta that they could do a lot better by colluding. If the
two firms were to collude in a symmetric equilibrium, 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 widgets are perishable, 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.) Do not
round the other responses.
Cheating quantity
cheating price
cheating profit
, discount factor
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