You must show how you arrived at every single answer on the problem set. You will receive ZERO credit for any answer where you don't show your work.
1. You are a monopolist with the following cost and demand conditions:
Q = 50 - 0.5P
and C(Q) = 50 + Q 2
a. What is the firm's inverse demand function?
b. What is the firm's marginal revenue
c. Determine the profit-maximizing output and price and the resulting profits.
d. Graph this solution.
e. Show your profits and the deadweight loss to society in your graph.
f. Determine the actual amount of deadweight loss.
a. (2 pts) What is the firm's the profit-maximizing level of output?
b. (2 pts) What is the firm's the profit-maximizing price?
c. (1 pts) What is the firm total revenue at this level of output?
d. (1 pts) What is the firm's total cost at this level of output?
e. (2 pts) What is the firm's profit if it produces this level of output?
f. (2 pts) Is the demand elastic, inelastic, or unitary elastic at the profit- maximizing price-quantity combination?
2. (15 pts) Suppose you are a monopolist operating two plants at different locations.
Both plants produce the same product; Q1 is the quantity produced at plant 1, and Q2
is the quantity produced at plant 2. You face the following inverse demand function:
P = 500 - 2Q , where Q = Q1 + Q2 . The cost functions for the two plants are
2 2
C1 = 25 + 2Q1 ; C1 = 20 + Q2 .
a. (5 pts) What are your marginal revenue and marginal cost functions?
b. (5 pts) To maximize profits, how much should you produce at plant 1? At plant 2?
c. (3 pts) What is the price that maximizes profits?
d. (2 pts) What are the maximum profits?
3. (5 pts) If a monopolist has an own-price demand elasticity of -.8, is it maximizing profits? Explain. If the own-price demand elasticity is -2.5, how much should the monopolist mark up the price over the marginal cost?
4. (5 pts) A local dentist is the only one in town. He read an article published by the American Dental Association estimating that the elasticity of demand for the representative dentist's services is -2.5. How much should the dentist mark up her price over marginal cost?
5. (10 pts) You are the only pharmacist in a small town; the next closest drugstore is 50 miles away. The population in your town consists of young farmers and older retired families. You have noticed that the young farmers are less sensitive to price changes than the retired population. Specifically, you have found that the working population has an own price elasticity of demand of -1.5 and the retired farmers have an own price elasticity of -3. Suppose that the marginal cost of supplying the two markets is the same and equal to a constant, MC.
a. (2 pts) Are the conditions necessary for price discrimination to be an effective means of enhancing profits being met? Explain.
b. (4 pts) What is the profit-maximizing price to charge the working farmers?
c. (4 pts) What is the profit-maximizing price to charge retired farmers?
6. (10 pts) Consider a firm that faces the demand curve P = 100 - Q, and operates with a constant marginal cost of 10 for all units produced.(In this case MC=AC). Among all the possible second price discrimination schemes (with two blocks), what block tariff structure will maximize profit? In other words, what choices of P1, Q1 for the first block and P2, Q2 for the second block will maximize profit?
7. (10 pts) You have just been hired as manager of a new health spa in Retirement Village, Florida. The owner has commissioned a market study that estimates the average customer's monthly demand curve for visiting the health spa to be
Qd = 50 - .25P . The cost of operating is C(Q) = 3Q , where Q is the number of visits.
Describe the optimal two-part tariff strategy.
8. (15 pts) Suppose that Sony is trying to decide how to price a new stereo system composed of a receiver, CD player, and speakers. The company's economists have estimated that two different groups will purchase these products: students and club owners. The economists' analysis suggests that the total market for its brand of stereos consists of 10,000 students and 50,000 club owners. In addition, it is estimated that the maximum amount each group will pay for each stereo component is as follows:
|
Group
|
Receiver
|
CD Player
|
Speakers
|
|
Students
|
$250
|
$150
|
$100
|
|
Club owners
|
$200
|
$75
|
$250
|
Sony's objective is to maximize revenues, and it is considering three strategies to price its stereo components: (1) a standard strategy whereby it prices each stereo component separately; (2) first degree (perfect) price discrimination; or (3) bundling the three components together and selling only bundles containing the receiver, CD player, and speakers.
a. (5 pts) If Sony uses a standard pricing strategy, what price should it charge for the receiver, for the CD player, and for the speakers to maximize revenues? What are the revenues they will earn through this strategy?
b. (5 pts) Suppose Sony adopts a first-degree price discrimination policy. What prices should it charge to maximize revenues? What are Sony's revenues using this strategy?
c. Suppose that Sony markets the receiver, CD player, and speakers together. That is, it uses a commodity-bundle strategy such that the products are sold as one item. What price should Sony charge to maximize revenues? How much will it earn?
