280 ❖ Chapter 15/Monopoly
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
c. If the government were to build the bridge, it should set price equal to marginal cost to
be efficient. Since marginal cost is zero, the government should not charge people to use
the bridge.
Figure 5
5. Larry wants to sell as many drinks as possible without losing money, so he wants to set
quantity where price (demand) equals average total cost, which occurs at quantity
Q
L and
marginal revenue equals zero, at quantity
QC
and price
PC
. Moe wants to maximize profits,
Figure 6
6. a. Figure 7 shows the firm’s average-total-cost curve and marginal-cost curve. (The
marginal-cost curve is a horizontal line at $0 because there are no variable costs.)
Because average total cost falls continuously as output rises, this firm is a natural
monopoly.
Demand
Quantity of Crossings
800,000
Price
$8
Area
= 1/2 x 8 x 800,000
= $3,200,000
Chapter 15/Monopoly ❖ 281
Figure 7
Figure 8
c. The table below shows the total revenue and profit for the town at various prices:
Price
Qd per resident
Profit
$2
8
-800,000
3
7
-300,000
4
6
0
5
5
100,000
d. At a price of $4, each consumer would earn consumer surplus equal to ½ 6 6 = $18.
(See Figure 9.) Consumers would be worse off. The town would gain revenue of $24 per
person, but it would not offset the drop in consumer surplus. Therefore, there would be
a deadweight loss.
282 ❖ Chapter 15/Monopoly
Figure 9
e. In the real world, it is unlikely that all residents have the same demand. Thus, an
admission price would push more of the cost on those who would use the museum.
7. a. A monopolist always produces a quantity at which demand is elastic. If the firm produced
a quantity for which demand was inelastic and the firm raised its price, quantity would
b. As Figure 10 shows, another way to see this is to note that on an inelastic portion of the
can never be on the inelastic portion of the demand curve. Total revenue is maximized
where marginal revenue is equal to zero (
QTR
on Figure 10).
Figure 10
Chapter 15/Monopoly ❖ 283
8. a. The profit-maximizing outcome is the same as maximizing total revenue in this case
because there are no variable costs. The total revenue from selling to each type of
consumer is shown in the following tables:
Price
Quantity of Adult
Tickets
Total Revenue from Sale
of Adult Tickets
10
0
0
9
100
900
8
200
1,600
7
300
2,100
6
300
1,800
5
300
1,500
4
300
1,200
3
300
900
2
300
600
1
300
300
0
300
0
Price
Quantity of Child
Tickets
Total Revenue from Sale
of Child Tickets
10
0
0
9
0
0
8
0
0
7
0
0
6
0
0
5
100
500
4
200
800
3
200
600
2
200
400
1
200
200
0
200
0
To maximize profit, you should charge adults $7 and sell 300 tickets. You should charge
children $4 and sell 200 tickets. Total revenue will be $2,100 + $800 = $2,900. Because
total cost is $2,000, profit will be $900.
b. If price discrimination were not allowed, you would want to set a price of $7 for the
tickets. You would sell 300 tickets and profit would be $100.
c. The children who were willing to pay $4 but will not see the show now that the price is
$7 will be worse off. The producer is worse off because profit is lower. Total surplus is
lower. There is no one that is better off.
d. In (a) total profit would be $400. In (b), there would be a $400 loss. There would be no
change in (c).
284 ❖ Chapter 15/Monopoly
9 a. The monopolist would set marginal revenue equal to marginal cost and then substitute
the profit-maximizing quantity into the demand curve:
10 – 2
Q
= 1 +
Q
9 = 3
Q
Q
= 3
P
= 10 –
Q
= $7
Total revenue =
P
Q
= ($7)(3) = $21
Total cost = 3 + 3 + 0.5(9) = $10.5
Profit = $21 – $10.5 = $10.5
b. The firm becomes a price taker at a price of $6 and no longer has monopoly power. In a
competitive equilibrium, the price equals marginal cost so,
10 –
Q
= 1 +
Q
10 = 1 + 2
Q
9 = 2
Q
Q
= 4.5
P = 5.5
The firm will export soccer balls because the world price is greater than the domestic
price (in the absence of monopoly power). As Figure 11 shows, domestic production will
rise to 5 soccer balls, domestic consumption will rise to 4, and exports will be 1.
Figure 11
c. The price actually falls even though Wiknam will now export soccer balls. Once trade
begins, the firm no longer has monopoly power and must become a price taker.
However, the world price of $6 is greater than the competitive equilibrium price ($5.50)
so the country exports soccer balls.
d. Yes. The country would still export balls at a world price of $7. The firm is a price taker
and no longer is facing a downward-sloping demand curve. Thus, it is now possible to
sell more without reducing price.
Chapter 15/Monopoly ❖ 285
10. a. Figure 12 shows the firm’s demand, marginal revenue, and marginal cost curves. The
firm’s profit is maximized at the output where marginal revenue is equal to marginal cost.
Therefore, setting the two equations equal, we get:
1,000 – 20
Q
= 100 + 10
Q
900 = 30
Q
Q
= 30
The monopoly price is
P
= 1,000 – 10
Q
= 700 Ectenian dollars.
Figure 12
b. Social welfare is maximized where price is equal to marginal cost:
1,000 – 10
Q
= 100 + 10
Q
900 = 20
Q
Q
= 45
At an output level of 45, the price would be 550 Ectenian dollars.
c. The deadweight loss would be equal to (0.5)(15)(300) = 2,250 Ectenian dollars.
d. i. A flat fee of 2000 Ectenian dollars would not alter the profit-maximizing price or
quantity. The deadweight loss would be unaffected.
ii. A fee of 50 percent of the profits would not alter the profit-maximizing price or
quantity. The deadweight loss would be unaffected.
iii. The marginal cost of production would rise by 150 Ectenian dollars if the director
was paid that amount for every unit sold. The new marginal cost would be 100 +
10
Q
+ 150. The new profit-maximizing output would be 25, the marginal cost at
that level would be 500, and the price would rise to 750. The deadweight loss
would be smaller. With the new marginal cost function, the quantity at which
social welfare is maximized changes. Now, price is equal to marginal cost when
Q
= 37.5:
1,000 – 10
Q
= 250 + 10Q
750 = 20
Q
Q
= 37.5
286 ❖ Chapter 15/Monopoly
As a result, the deadweight loss would be equal to (0.5)(37.5-25)(750-500) =
1,562.50 Ectenian dollars rather than 2,250 Ectenian dollars.
iv. If the director is paid 50 percent of the revenue, then total revenue is 500
Q
–
5
Q
2. Marginal revenue becomes 500 – 10
Q
. The profit-maximizing output level
will be 20 and the price will be 800 Ectenian dollars. The deadweight loss will be
greater.
11. a. Figure 13 shows the cost, demand, and marginal-revenue curves for the monopolist.
Without price discrimination, the monopolist would charge price
PM
and produce quantity
QM
.
Figure 13
c. If the monopolist can perfectly price discriminate, it produces quantity
QC
, and has profit
equal to X + Y + Z.
e. A monopolist would pay the fixed cost that allows it to discriminate as long as Y + Z (the
increase in profits) exceeds C (the fixed cost).
f. A benevolent social planner who cared about maximizing total surplus would want the
g. The monopolist has a greater incentive to price discriminate (it will do so if Y + Z > C)
than the social planner (she would allow it only if Z > C). Thus if Z < C but
Y + Z > C, the monopolist will price discriminate even though it is not in society’s best
interest.