1) Chapter 8, problem #1 2) You are the manager of a monopoly, and your demand and cost functions are given by P = 300 – 2.5Q and C(Q)=1000 + 2.5Q2. a. At what price and quantity are firm’s profits maximized? b. What are profits given the price and quantity you found in part a? c. What is the own price elasticity of demand at the profit-maximizing price and quantity combination? Is demand inelastic, elastic, or unit elastic? d. At what price and quantity are the firm’s revenues maximized? e. Calculate the maximum revenues (given what you found in part d). f. What is the own price elasticity of demand at the revenue-maximizing price and quantity combination? Is demand inelastic, elastic, or unit elastic? 3) Chapter 8, problem #5 4) Chapter 8, problem #7 5) You are the manager of a firm which produces according to the cost function C(Q) = 75+5Q2. Determine the profit maximizing output and price and the level of profits. Discuss what (if anything) will happen to profits in the long run, if: a. You are in a perfectly competitive market and price other firms charge is $25. b. You are a monopolist and inverse demand for your product is given by P = 250-2.5Q. c. You are in a monopolistically competitive market and inverse demand for your product is given by P = 250 – 2.5Q. 6) Chapter 8, problem #15 7) Given P = 50 – ( Q1+Q2), C1=6Q1, and C2=10Q2 in a homogenous-product Cournot duopoly. a. Find the reaction functions for each firm. b. Calculate each firm’s equilibrium output. c. Calculate the equilibrium market price. d. Calculate the profit for each firm in equilibrium. 8) Chapter 9, problem #4 9) Consider a Bertrand Oligopoly consisting of 3 firms that produce an identical product at a marginal cost of $100. The inverse market demand for this product is 1000-4Q. a. What is the equilibrium output level in this market? b. What is the equilibrium market price? c. What are the profits of each firm? 10) Chapter 9, problem #9 11) Chapter 9, problem #16 12) Chapter 9, problem #18

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Problem Set #5

1) Chapter 8, problem #1

2) You are the manager of a monopoly, and your demand and cost functions are given by P = 300 –

2.5Q and C(Q)=1000 + 2.5Q2.

a.

At what price and quantity are firm’s profits maximized?

b.

What are profits given the price and quantity you found in part a?

c.

What is the own price elasticity of demand at the profit-maximizing price and quantity

combination? Is demand inelastic, elastic, or unit elastic?

d.

At what price and quantity are the firm’s revenues maximized?

e.

Calculate the maximum revenues (given what you found in part d).

f.

What is the own price elasticity of demand at the revenue-maximizing price and

quantity combination? Is demand inelastic, elastic, or unit elastic?

3) Chapter 8, problem #5

4) Chapter 8, problem #7

5) You are the manager of a firm which produces according to the cost function C(Q) = 75+5Q2.

Determine the profit maximizing output and price and the level of profits. Discuss what (if

anything) will happen to profits in the long run, if:

a.

You are in a perfectly competitive market and price other firms charge is $25.

b.

You are a monopolist and inverse demand for your product is given by P = 250-2.5Q.

c.

You are in a monopolistically competitive market and inverse demand for your product

is given by P = 250 – 2.5Q.

6) Chapter 8, problem #15

7) Given P = 50 – ( Q1+Q2), C1=6Q1, and C2=10Q2 in a homogenous-product Cournot duopoly.

a.

Find the reaction functions for each firm.

b.

Calculate each firm’s equilibrium output.

c.

Calculate the equilibrium market price.

d.

Calculate the profit for each firm in equilibrium.

8) Chapter 9, problem #4

9) Consider a Bertrand Oligopoly consisting of 3 firms that produce an identical product at a

marginal cost of $100. The inverse market demand for this product is 1000-4Q.

a.

What is the equilibrium output level in this market?

b.

What is the equilibrium market price?

c.

What are the profits of each firm?

10) Chapter 9, problem #9

11) Chapter 9, problem #16

12) Chapter 9, problem #18

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