ECON 2103 PS10

Wing Yan Lee (2096 3442)

5. Consider the relationship between monopoly pricing and price elasticity of demand.
a. Explain why a monopolist will never produce a quantity at which the demand curve is
inelastic. (Hint: If demand is inelastic and the firm raises its price, what happens to total
revenue and total costs?)

Where the demand curve is inelastic, raising the price would cause the price to increase to a
larger extent than the decrease in quantity sold, so the total revenue would increase. Thus, a
firm will always choose to maximize its profit by producing at the maximum quantity where
demand is elastic.

b. Draw a diagram for a monopolist, precisely labeling the portion of the demand curve
that is inelastic. (Hint: The answer is related to the marginal-revenue curve.)
c. On your diagram, show the quantity and price that maximize total revenue.
6. You live in a town with 300 adults and 200 children, and you are thinking about putting
on a play to entertain your neighbors and make some money.

A play has a fixed cost of $2,000, but selling an extra ticket has zero marginal cost. Here
are the demand schedules for your two types of customer:

Price Adults Children

$10 0 0

9 100 0

8 200 0

7 300 0

6 300 0

5 300 100

4 300 200

3 300 200

2 300 200

1 300 200

0 300 200

a. To maximize profit, what price would you charge for an adult ticket? For a child’s
ticket? How much profit do you make?

To maximize profit, you would charge $7 for an adult ticket at $4 for a child’s ticket. You make a
profit of $900

b. The city council passes a law prohibiting you from charging different prices to
different customers. What price do you set for a ticket now? How much profit do you
make?

You set the price of a ticket as $7 to maximize your profit, making $100.
c. Who is worse off because of the law prohibiting price discrimination? Who is better
off? (If you can, quantify the changes in welfare.)

You are worse off because you make a smaller profit, customers are also worse off because
less people will enjoy the play. No one is better off.

Loss in producer surplus = $4*200 = $800

Loss in consumer surplus = ($5-$4)*100 = $100

d. If the fixed cost of the play were $2,500 rather than $2,000, how would your answers to
parts (a), (b), and (c) change?

If the fixed cost of the play were $2500, the profit you make in (a) would be $400, while in (b),
your revenue would be less than the cost of the play, so you would choose to not put on the
play.

Loss in producer surplus = $400

Loss in consumer surplus = ($9-$7)*100 + ($8-$7)*200 + ($5-$4)*100 = $500

7. The residents of the town Ectenia all love economics, and the mayor proposes building
an economics museum. The museum has a fixed cost of $2,400,000 and no variable
costs. There are 100,000 town residents, and each has the same demand for museum
visits:

QD = 10 - P, where P is the price of admission.

a. Graph the museum’s average-total-cost curve and its marginal-cost curve. What kind
of market would describe the museum?

The museum would be a club good since it is excludable but nonrival in consumption.
b. The mayor proposes financing the museum with a lump-sum tax of $24 and then
opening the museum to the public for free. How many times would each person visit?
Calculate the benefit each person would get from the museum, measured as consumer
surplus minus the new tax.

Each person would visit 10 times.

Consumer surplus = $(10*10/2) = $50
Benefit each person would get = $50 - $24 = $26

c. The mayor’s anti-tax opponent says the museum should finance itself by charging an
admission fee. What is the lowest price the museum can charge without incurring
losses? (Hint: Find the number of visits and museum profits for prices of $2, $3, $4, and
$5.)

Price Number of visits Museum profits

$2 8 - 800,000

3 7 - 300,000

4 6 0

5 5 100,000

The lowest price the museum can charge is $4.

d. For the break-even price you found in part (c), calculate each resident’s consumer
surplus. Compared with the mayor’s plan, who is better off with this admission fee, and
who is worse off? Explain.

Consumer surplus = $(4*6/2) = $12

Compared with the mayor’s plan, the admission fee leads consumers to be worse-off since each
resident gets a lower consumer surplus. No one is better off as the museum breaks even either
way.

e. What real-world considerations absent in the problem above might justify an

admission fee?

The operating costs of the museum have not been considered. The operating cost of the
museum might vary with the number of visitors. For example, the museum may have to hire
more people to maintain order if the number of visitors increases. In such a case, the museum
should charge residents money based on the number of admissions, which could be achieved
by charging admission fees.
8. Henry Potter owns the only well in town that produces clean drinking water. He faces
the following demand, marginal-revenue, and marginal- cost curves:
Demand: P = 70 - Q
Marginal Revenue: MR = 70 - 2Q
Marginal Cost: MC = 10 + Q

a. Graph these three curves. Assuming that Mr. Potter maximizes profit, what quantity
does he produce? What price does he charge? Show these results on your graph.

He produces 20 units of water and charges $50

b. Mayor George Bailey, concerned about water consumers, is considering a price ceiling
10 percent below the monopoly price derived in part (a). What quantity would be
demanded at this new price? Would the profit-maximizing Mr. Potter produce that
amount? Explain. (Hint: Think about marginal cost.)

When the price is $45, the quantity demanded is 25 units of water. Mr. Potter maximizes his
profit by producing at a quantity where marginal cost is equal to marginal revenue, which is still
20 units of water, so Mr. Potter would not produce the amount of water demanded.
c. George’s Uncle Billy says that a price ceiling is a bad idea because price ceilings
cause shortages. Is he right in this case? What size shortage would the price ceiling
create? Explain.

In this case he is right, as seen in (b), the price ceiling creates a shortage of 5 units of water.

d. George’s friend Clarence, who is even more concerned about consumers, suggests a
price ceiling 50 percent below the monopoly price. What quantity would be demanded at
this price? How much would Mr. Potter produce? In this case, is Uncle Billy right? What
size shortage would the price ceiling create?

When the price is $25, the quantity demanded is 45 units of water. Due to the price ceiling, Mr.
Potter would be unable to receive any more than $25 by selling any additional units of water, so
his maximum marginal revenue is $25. Thus, he continues to produce at the quantity where
marginal cost equals to marginal revenue, which is 15 units of water.

In this case, Uncle Billy is also right, the price ceiling would create a shortage of 30 units of
water.
9. Only one firm produces and sells soccer balls in the country of Wiknam, and as the
story begins, international trade in soccer balls is prohibited.
The following equations describe the monopolist’s demand, marginal revenue, total cost,
and marginal cost:

Demand: P = 10 - Q
Marginal Revenue: MR = 10 - 2Q
Total Cost: TC = 3 + Q + 0.5 Q2
Marginal Cost: MC = 1 + Q,

where Q is quantity and P is the price measured in Wiknamian dollars.

a. How many soccer balls does the monopolist produce? At what price are they sold?
What is the monopolist’s profit?

The monopolist produces 3 soccer balls, they are sold at a price of $7.

b. One day, the King of Wiknam decrees that henceforth there will be free trade—either
imports or exports—of soccer balls at the world price of $6. The firm is now a price taker
in a competitive market. What happens to domestic production of soccer balls? To
domestic consumption? Does Wiknam export or import soccer balls?

The domestic production of soccer balls remains the same. The firm’s marginal cost and
marginal revenue of producing soccer balls remains unchanged, and the firm continues to
maximize its revenue by producing at a quantity where marginal cost is equal to marginal
revenue.

The demand for soccer balls would increase to 4 balls due to the decrease in price. Since the
local firm does not produce enough soccer balls to satisfy the demand for them, Wiknam
imports soccer balls.

c. In our analysis of international trade in Chapter 9, a country becomes an exporter

when the price without trade is below the world price and an importer when the price
without trade is above the world price. Does that conclusion hold in your answers to
parts (a) and (b)? Explain.

The conclusion holds true. The price without trade is $7, which is above the world price of $6.
As seen in part (b), Wiknam becomes an importer.
d. Suppose that the world price was not $6 but, instead, happened to be exactly the same
as the domestic price without trade as determined in part (a). Would allowing trade have
changed anything in the Wiknamian economy? Explain. How does the result here
compare with the analysis in Chapter 9?

Allowing trade would not have changed anything in the Wiknamian economy, as the quantity of
soccer balls demanded remains the same, and local production of soccer balls remains
unaffected.

This also proves the analysis in chapter 9. Since the price without trade is neither higher nor
lower than the world price, the country does not become an importer, nor an exporter.

10. Based on market research, a film production company in Ectenia obtains the
following information about the demand and production costs of its new DVD:

Demand: P = 1,000 - 10Q

Total Revenue: TR = 1,000Q - 10Q2
Marginal Revenue: MR = 1,000 - 20Q
Marginal Cost: MC = 100 + 10Q,

where Q indicates the number of copies sold and P is the price in Ectenian dollars.

a. Find the price and quantity that maximize the company’s profit.

The profit maximizing quantity is found when marginal revenue is equal to marginal cost, so it is
30 copies. The profit maximizing price is the maximum amount consumers are willing to pay for
the profit maximizing quantity of goods, so it is $700.

b. Find the price and quantity that would maximize social welfare.

Social welfare is maximized when the price and quantity is at the point where the marginal cost
curve and demand curve intersect. At that point, the quantity is 45 copies and the price is $550.

c. Calculate the deadweight loss from monopoly.

Deadweight loss = ½($700-550)*(45-30) = $1125

d. Suppose, in addition to the costs above, the director of the film has to be paid. The
company is considering four options:

i. a flat fee of 2,000 Ectenian dollars.

ii. 50 percent of the profits.
iii. 150 Ectenian dollars per unit sold.
iv. 50 percent of the revenue.

For each option, calculate the profit-maximizing price and quantity. Which, if any, of
these compensation schemes would alter the deadweight loss from monopoly? Explain.

For option i and ii, profit-maximizing price and quantity remains the same as marginal cost and
marginal revenue are unaffected

For option iii, the new equation for the marginal cost curve is MC = 100 + 160Q, so the
profit-maximizing quantity would be 5 copies, and the corresponding profit-maximizing price
would be $950.

Deadweight loss for (iii) = ½($950-$550)*(45-5) = $8000

For option iv, the new equation for the total revenue would be TR = 500Q - 5Q2, so the new
equation for marginal revenue would be its derivative, MR = 500 - 10Q. Thus, the
profit-maximizing quantity would be 45 copies, and the corresponding profit-maximizing price
would be $550. Coincidentally, that is the quantity and price where social welfare is maximized,
so the deadweight loss would be 0.