1. A monopolist has an (inverse) demand curve for its product of P = 30 - 6Q (where Q is in millions of units). Its total cost curve is: TC = 14 + 3Q + 3Q2. Find the profit maximizing level of output, the profit maximizing price and the monopolist's profits.
2. Suppose you have 8 customers for a good that only you produce. For simplicity, assume that the total and marginal cost of producing the good is zero. Each customer has a different willingness to pay for the good and these are listed below:
|
Customer
|
Willingness to pay
|
|
A
|
$10
|
|
B
|
9
|
|
C
|
8
|
|
D
|
7
|
|
E
|
6
|
|
F
|
5
|
|
G
|
4
|
|
H
|
3
|
a. Suppose that you cannot tell these customers apart and have to act as a simple monopolist: What is the optimal price and quantity pair? What is the total profit?
b. Suppose instead you can act as a perfect price discriminator: What is the optimal pricing scheme? What is the total profit?
c. Suppose you can only tell if a customer is one of the top four customers or one of the bottom four customers: What is the optimal pricing scheme? What is the total profit?
3. A firm that produces cars sells three types: a low quality car for $12,000, a medium quality car for $18,000 and a high quality car for $26,000. Is this evidence of this firm practicing price discrimination? Explain.
4. A monopolist produces a single good from the utilization of two plants, plant 1 and plant
2. It faces an inverse demand curve of: P = 1100 - 2Q, where Q is total quantity produced, thus Q = q1 + q2. q1 = quantity produced in plant 1 and q2 = quantity produced in plant two. Plant 1 is an older plant and has a marginal cost of production equal to 10q1. Plant 2 is newer and its marginal cost of production is 5q2. How much should this monopolist produce in total and how much will each plant be producing at the profit maximizing level of output?
5. A university has determined that its students fall into two categories when it comes to room and board demand. University planners call these two types, Sleepers and Eaters. The reservation prices for a dormitory room and the basic meal plan of the two types are as follows:
|
|
Sleepers
|
Eaters
|
|
Dorm Room
|
$5,500
|
$3,000
|
|
Meal Plan
|
$2,500
|
$6,000
|
Currently, the university offers students the option of selecting just the dorm room at
$3,000, just the meal plan at $2,500, or both for a total price of $5,500. An economic consultant advises the university to stop offering the two goods separately and, instead, to sell them only as a single, combined room and board package. Explain the consultant's strategy and determine what price the university should set for the combined product.
6. In the early 1970s, the six largest manufacturers of ready-to-eat breakfast cereals had 95 percent of the market. Over the preceding twenty years, these same manufacturers introduced over eighty new varieties of cereals. How would you evaluate this strategy from the standpoint of the Hotelling spatial model described in the lecture?