Question 1. Consider the market for bikes. Suppose it is a perfectly competitive market. The market demand for bikes is given by the equation PD (Q)=110 - 5Q and the market supply for bikes is given by the equation Ps (Q).5 + 2Q.
A firm faces costs given by the total cost function TC(Q)=2.5Q2 +130 . Its marginal cost curve is given by MC(Q) = 5Q .
(a) What is the profit-maximizing quantity for this firm?
(b) What profit/loss does the firm earn (specify if it is a profit or loss)?
(c) What are the fixed costs for this firm?
(d) What should this firm do in the short-run? Explain.
(e) Suppose the fixed costs of the firm decreased, what would happen to the profit-maximizing quantity? Clearly explain your reasoning.
Question 2. Consider the market for scooters. Suppose it is a (single-price) monopolistic market. The market demand for scooters is given by the equation PD (Q) =100 -8Q . The firm faces costs given by the total cost function TC(Q) = 3Q2 + 34Q +10 and marginal cost functionMC(Q). 6Q+ 34.
(a) Draw the firm's problem. Your graph should include (ATC, MC, MR, D).
(b) Calculate the profit maximizing quantity of this firm. Show it on your graph.
(c) What profit does the firm earn?
(d) Calculate the deadweight loss generated by this monopoly.
Question 3. Suppose that a monopoly faces a demand curve P = 30 - 2Q and its marginal cost curve is MC =Q
(a) Plot the average revenue, marginal revenue and marginal cost curves for this monopoly.
(b) Find the profit maximizing price and output for this monopoly.
(c) Find the consumer surplus, the producer surplus, the total surplus and the deadweight loss in the (monopolized) market.
(d) Find the competitive price and quantity (as if the above marginal cost curve represents the market supply curve).
(e) Find the consumer surplus, the producer surplus and total surplus in the competitive market.
(f) Plot a graph on which you illustrate the monopoly equilibrium, the competitive equilibrium and the deadweight loss due to the monopoly.
Question 4. Suppose that Kerasotes Crown Village Theaters Cinema is a local monopoly. It estimated the following demand curves for different groups of customers:
|
Adults
|
P =12
|
- 2Q
|
|
Children
|
P = 8
|
- 3Q
|
|
Students
|
P =10
|
- 4Q
|
The marginal cost of the cinema is $2 per customer.
(a) What is the marginal revenue in each submarket?
(b) What price should the cinema charge in each of the submarkets if its goal is to maximize profits?
Question 5. The following table shows the profits of two producers of pancakes for various combinations of prices that each firm might charge.
|
Aunt Jemima
|
|
Hungry Jack
|
|
$1
|
$2
|
$3
|
$4
|
|
$1
|
20, 40
|
25, 50
|
30, 40
|
35, 30
|
|
$2
|
25, 50
|
30, 60
|
35, 50
|
40, 40
|
|
$3
|
30, 60
|
35, 70
|
30, 60
|
45, 50
|
|
$4
|
25, 70
|
30, 80
|
40, 75
|
35, 70
|
a. Does "Hungry Jack" have a dominant strategy? f he does, find it.
b. Does "Aunt Jemima" have a dominant strategy? If she does, find it.
c. In this game there is a unique Nash equilibrium (in pure strategies). Find it and prove that it is indeed Nash equilibrium.
d. Choose one outcome other than the Nash equilibrium and show why it is not Nash equilibrium.
e. Is the Nash equilibrium in this game Pareto optimal? Prove your answer.