Textbook Exercises ... please help Question 1Consider two identical firms (firm 1 and firm 2) that face a linear market demand curve. Each firmhas 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 2Marge's Hair Salon production function is Q = f(K, L) = K0.5 10.5 where K is the number of hair dryersand 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 productionfunction. (2.2 At the moment, Marge uses 16 labour hours and 16 hair dryers. Suppose that Marge can useany amount of either input without affecting the market costs of the inputs. If Marge increasedher 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 hercosts?2.4Given that Marge earns R12.50 for each unit produced, do her profits go up or down when sheincreases her input use by 10%?Question 3A monopolist faces the demand curve P = 18-Q, where P is measured in rands per unit and Q in thousandsof units. The monopolist has a constant average cost of R6 per unit.3.1What 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.

We have demand function P=150-0.25Q MC=0 for both the firms.

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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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Textbook Exercises ... please help

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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