Unit 5: Monopoly – Problems
5.1: Single-price monopoly
CORE PROBLEMS
Problem 1
The table below shows prices and corresponding quantities sold for a monopoly.
Q P TR MR TC MC
0 50 -- 4 --
1 45 10
2 40 14
3 35 16
4 30 20
5 25 26
6 20 34
7 15 44
8 10 56
a. Complete the table.
A monopolist has the cost, demand and marginal revenue functions depicted below.
a. What output maximizes the monopolist’s total profit?
b. What is marginal revenue at the profit-maximizing output? What is marginal cost? c. What price does the monopolist charge?
d. What is average total cost at the monopoly output? e. What is profit per unit at the monopoly output? f. What is the total profit at the monopoly output?
Problem 3
A profit-maximizing monopolist is earning a profit, and suddenly his fixed costs fall.
a. What happens to the monopolist’s profit-maximizing level of output? b. What happens to the monopolist’s profit-maximizing price?
SUPPLEMENTARY PROBLEMS
Problem 4
Draw demand, MR, MC and ATC curves for a monopoly that is just breaking even.
Problem 5
Firm A operates at an output level where its price and marginal cost are both equal to $50. Firm B operates at an output level where its price is $5 but its marginal cost is $3. Which firm do you think operates in a perfectly competitive market and which firm do you think is a monopoly?
Problem 6
The diagram below shows the daily demand and the marginal cost for a juice vendor, who runs the only juice bar in town.
a. Gregory wants to sell as many drinks as possible without losing money. What price and quantity does Gregory want to sell?
b. Jennifer wants to maximize revenue for the store. What price and quantity does Jennifer want to sell?
The table below describes a monopoly’s demand curve and marginal costs.
P Q TR MR TC MC
>100 0 -- 0 --
100 1 10
50 2 20
33.33 3 30
25 4 40
20 5 50
a. Complete the table.
b. What are the monopolist’s profit-maximizing price and level of output? c. How much profit does the monopolist earn?
Suppose now that the monopolist also has a fixed cost of $200 in addition to the costs already described in the table.
d. What are the monopolist’s profit-maximizing price and level of output in the short-run? e. How much profit does the monopolist earn in the short-run?
Problem 8
At first, hot dog vendors operate in a perfectly competitive market and face a price of $1.00 per hot dog. The cost schedule is shown below.
Hot Dogs TR MR TC MC
0 -- $63 --
25 $73
50 $78
75 $88
100 $103
125 $125
150 $153
175 $188
200 $233
a. Complete the table.
b. How many hot dogs will each vendor sell and what is the profit or loss?
One day, Arturo figured out that, if he were the only seller in town, he could choose the price he wanted to charge. His demand schedule is shown below. The costs are the same.
Price Hot Dogs TR MR TC MC
$6.50 0 -- $63 --
$6.00 25 $73
$5.50 50 $78
$4.00 75 $88
$3.25 100 $103
$2.75 125 $125
$2.25 150 $153
$1.75 175 $188
$1.25 200 $233
c. Complete the table.
d. How many hot dogs would Arturo sell and what price would he charge?
You are doing some consulting work for four different companies. Each company presents you with some information about the revenue and cost sides of their businesses. For each company, fill in the missing data, and then give a recommendation for the company’s course of action. Your recommendation should be one of the following.
Do nothing – Your business is already maximizing profits. Stay open, but reduce price and increase sales
Stay open, but raise price and reduce sales Shut down
FIRM A
P Q TR MR TC ATC MC
$7.00 2000 $4.00 $8000 $3.00
FIRM B
P Q TR MR TFC TVC TC AFC AVC ATC MC
$1.25 10,000 $1.00 $2000 $1.50 $1.00
FIRM C
P Q TR MR TC ATC MC
$7.00 2000 $5.00 $5.00 $5.00
FIRM D
P Q TR TC ATC MC
Problem 10
This problem is a simple example of how to apply economic reasoning to an important topic known as transfer pricing.
The web design division of Macrosoft can produce webpages at a constant marginal cost of $25 per webpage. However, the management of Macrosoft decides to charge the market rate of $45 internally for webpage design. That is, if any division of Macrosoft wants to produce webpages, then this division has to pay $45 per page to the web design division out of its own budget.
The demand for webpages at Macrosoft is shown below.
a. Show the consumer surplus (to divisions purchasing webpages) and the producer surplus (profit to the web division) on the diagram when Macrosoft sets the price at $45 per webpage. Also indicate any deadweight loss.
b. Ultimately, all the surplus in the company ends up going to Macrosoft anyway. With this in mind, what internal price should Macrosoft set in order to eliminate the deadweight loss that you identified in (a)?
c. If the price is set at the level you specified in (b), sketch the consumer surplus and the producer surplus earned by the web division.
5.2: Price discrimination and other pricing strategies
CORE PROBLEMS
Problem 1
You are thinking about tutoring students in economics and you have determined that you face the following demand curve for your services. The price is per hour of tutoring. Each student is interested in only one hour of tutoring. You view the marginal cost of your time as constant at $25 per hour.
P Students
>$40 0
$40 1
$35 2
$27 3
$26 4
$20 5
$15 6
a. Suppose that you set a single hourly price for your tutoring services and you advertise this price. How many students will you tutor and how much profit will you earn?
b. Suppose instead that you perfectly price discriminate and charge each student a different price. How many students will you tutor and how much profit will you earn.
Problem 2
A firm that writes computer programs faces many customers who have the demand cure shown below. Note that this is the demand curve for each customer. The firm’s marginal cost of writing each program is equal to $4000.
a. If the firm charges a single price per program, what is the profit-maximizing price? b. If the firm uses a two-part tariff, what are the optimal unit price 𝑝 and access fee 𝐹? c. Suppose that the firm sells the first two programs for $8000 each and then sells additional
programs for $6000 each. How many programs will each customer buy and how much profit does the firm earn? What kind of price discrimination is this?
d. If the firm perfectly price discriminates, how many programs will each customer buy and how much profit does the firm earn?
Problem 3
You run a restaurant that sells hamburgers and sodas. It costs you $2 in labor and materials to serve a hamburger and it also costs you $2 in labor and materials to serve a soda. You have two customers. Lisa is willing to pay $10 for a hamburger and $5 for a soda. Derek is willing to pay $16 for a hamburger and $1 for a soda.
a. If hamburgers and sodas are sold separately, find the best prices and compute the profit earned by your restaurant.
b. If hamburgers and sodas as sold together as a “meal deal” bundle, find the best price for the meal deal and compute the profit earned by your restaurant.
SUPPLEMENTARY PROBLEMS
Problem 4
There are 5000 residents of a community who can choose between using a Blackberry or a Raspberry mobile device. Using a Raspberry generates $50 of value per month for anyone who uses one. Using a Blackberry generates a monthly value of $(30 + 0.02𝑛), where 𝑛 is the total number of residents who use a Blackberry. The idea is that the Blackberry comes with a special messaging service, so the usefulness of Blackberry rises when more people use it.
a. What economic phenomenon is this problem an example of?
b. How many residents must already be using Blackberry in order to make it worthwhile for other customers to choose Blackberry over Raspberry?
c. The CEO of Blackberry proposes to set a high price initially for a Blackberry and then lower it as time goes on. Does this seem like a good pricing strategy? If not, explain why and propose a better strategy.
Problem 5
A farmer sells apples and oranges to 100 customers – 50 vegetarians and 50 carnivores. Each customer is interested in buying only one apple and one orange. It costs the farmer $1 to harvest an apple and $2 to harvest an orange. The table below shows what both types of customers are willing to pay for an apple and an orange.
Apple Orange
Vegetarians $5 $15
Carnivores $4 $6
a. If the farmer sells apples and oranges separately, what is the best price for an apple and how much profit does he earn from apple sales?
b. If the farmer sells apples and oranges separately, what is the best price for an orange and how much profit does he earn from orange sales?
c. If the farmer sells a bundle containing one apple and one orange, what is the best price for a bundle?
Problem 6
Thor has a monopoly selling electric chairs. There are 40 dictators interested in purchasing an electric chair. 10 of them would be willing to pay $10,000 for an electric chair. 10 of them would be willing to pay $7500. 10 of them would be willing to pay $2500 and 10 of them would be willing to pay $1000.
a. Suppose that Thor’s marginal cost is $4000 per electric chair. If he cannot price discriminate, what price will he charge and how many electric chairs will he sell?
b. Is the allocation in (a) efficient?
c. Suppose that Thor’s marginal cost is $2000 per electric chair. If he cannot price discriminate, what price will he charge and how many electric chairs will he sell?
d. Is the allocation in (c) efficient?
e. Suppose that Thor’s marginal cost is $2000 per electric chair, but that he can perfectly price discriminate. How many electric chairs will he sell?
