Give the price and output level of international dynamos

Question

MANAGERIAL ECONOMICS AND BUSINESS

TUTORIAL SET SIX

1. Lightning company is a firm in an oligopolistic industry. Lightning faces a "kinked" demand curve for its product, which is characterized by the following equations:

Q₁ = 82 - 8P
Q₂ = 44 - 3P

Suppose further that the firm's total cost equation is

TC=8 + Q + 0.05Q²

a. Give the price and output level for lightning's product

b. Based on your answer to part a, what is the firm's profit?

c. Determine the range of values within which lightning's marginal cost may vary without affecting the prevailing price and output level

d. Based on your answer to part a, what is the firm's marginal cost? Is it consistent with your answer to part c?

e. Suppose that lightning's total cost equation changed to TC=12 + 5Q + 0.1Q² . Will the firm continue to operate at the same price and output level? If not, what price will the firm charge and how many units will it produce?

f. Based on your answer to part e, what is the lightning's profit?

2. Suppose that international dynamo is a contractor in the oligopolistic aerospace industry. International dynamo faces a "kinked" demand curve for its product, which is defined by the equations:

Q₁ = 200 - 2P
Q₂ = 60 - 0.4P

Suppose further that international dynamo has a constant marginal cost MC=$50

a. Give the price and output level of international dynamo's product.

b. Based on your answer to part a, what is international dynamo's profit?

c. Determine the range of values within which marginal cost may vary without affecting the prevailing market price and output level.

3. Supposed that an industry comprising two firms produces a homogeneous product. Consider the following demand and individual firm's cost function:

P=200 - 2(Q₁ + Q₂)
TC₁₌4Q₁
TC₂=4Q₂

a. Calculate each firm's reaction function.

b. Calculate the equilibrium price, profit maximization output levels, and profits for each firm.

c. Assume that firm 2 is a stackelberg leader and firm one is a follower. What are the equilibrium price, quantity and profits for each firm?

d. Suppose the two firms in the industry decide act jointly, what are the equilibrium price, profit maximizing level of output and total industry profit?

4. Supposed that an industry comprising two firm's producing homogeneous product. Supposed that the demand functions for two profit maximization firms in a duopolistic industry are

Q₁=50 - 0.5P₁ + 0.25P₂
Q₂=50 -0.5P₂ + 0.25P₁

Supposed, further, that the firm's total cost functions are

TC₁= 4Q₁
TC₂= 4Q₂

Where P₁ and P₂ represent the prices charged by each firm producing Q₁ and Q₂ units of output.

a. What is the inverse demand equation for this product?

b. What are the equilibrium price, profit-maximizing output levels, and profit for each firm?