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Question 1 Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 150 - 0.25Q, where Q = Q₁ + Q2. Find the Cournot equilibrium quantity and market price for each firm.

Question 1 Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 150 - 0.25Q, where Q = Q₁ + Q2. Find the Cournot equilibrium quantity and market price for each firm.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
Problem 1E
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Question 1 Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 150 - 0.25Q, where Q = Q₁ + Q2. Find the Cournot equilibrium quantity and market price for each firm. Question 2 Marge's Hair Salon production function is Q = f(K, L) = K0.5 10.5 where K is the number of hair dryers and L is the number of labour hours she employs. 2.1 Prove, with the aid of mathematics, the type of returns to scale exhibited by this production function. ( 2.2 At the moment, Marge uses 16 labour hours and 16 hair dryers. Suppose that Marge can use any amount of either input without affecting the market costs of the inputs. If Marge increased her use of labour hours and hair dryers by 10%, how much would her production increase? 2.3 Increasing the use of both inputs by 10% will result in Marge's costs increasing by exactly 10% If Marge increases her use of all inputs by 10%, what will increase more, her production or her costs? 2.4 Given that Marge earns R12.50 for each unit produced, do her profits go up or down when she increases her input use by 10%? Question 3 A monopolist faces the demand curve P = 18-Q, where P is measured in rands per unit and Q in thousands of units. The monopolist has a constant average cost of R6 per unit. 3.1 What are the monopolist's profit-maximising price and quantity and what is its resulting profit? 3.2 Calculate the firm's degree of monopoly power using the Lerner index.
Transcribed Image Text:Question 1 Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 150 - 0.25Q, where Q = Q₁ + Q2. Find the Cournot equilibrium quantity and market price for each firm. Question 2 Marge's Hair Salon production function is Q = f(K, L) = K0.5 10.5 where K is the number of hair dryers and L is the number of labour hours she employs. 2.1 Prove, with the aid of mathematics, the type of returns to scale exhibited by this production function. ( 2.2 At the moment, Marge uses 16 labour hours and 16 hair dryers. Suppose that Marge can use any amount of either input without affecting the market costs of the inputs. If Marge increased her use of labour hours and hair dryers by 10%, how much would her production increase? 2.3 Increasing the use of both inputs by 10% will result in Marge's costs increasing by exactly 10% If Marge increases her use of all inputs by 10%, what will increase more, her production or her costs? 2.4 Given that Marge earns R12.50 for each unit produced, do her profits go up or down when she increases her input use by 10%? Question 3 A monopolist faces the demand curve P = 18-Q, where P is measured in rands per unit and Q in thousands of units. The monopolist has a constant average cost of R6 per unit. 3.1 What are the monopolist's profit-maximising price and quantity and what is its resulting profit? 3.2 Calculate the firm's degree of monopoly power using the Lerner index.
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