CHAPTER 35: Externalities
TRUE/FALSE
1. A trade between two people is an example of an externality.
2. The only known way to eliminate externalities is through taxes or subsidies.
3. The efficient amount of air pollution is in general independent of whether polluters or pollutees pay to
reduce pollution.
4. A Pigouvian tax on pollution is designed to collect enough revenue to pay for pollution detection by
the government.
5. If there are negative externalities in production or consumption, competitive equilibrium is unlikely to
be Pareto efficient but positive externalities enhance the efficiency of the market.
6. The “tragedy of the commons” refers to the tendency for common property to be overused.
7. If preferences are quasilinear, then the delineation of property rights has no distributional
consequences.
8. If your consumption of toothpaste produces positive externalities for your neighbors (which you
ignore), then you are consuming less toothpaste than is Pareto optimal.
9. Mobil Oil Corporation recently bought the right to emit an additional 900 pounds of noxious gas
vapors per day at its Torrance, California, refinery. This suggests that allowing pollution rights to be
marketed is likely to lead to more pollution than there would be if there were no restrictions on
polluting.
MULTIPLE CHOICE
1. A mountain village owns a common pasture where villagers graze their goats. The cost to a goat owner
of owning and caring for a goat is 4 groschens. The pasture gets overgrazed if too many goats share
the pasture. The total revenue from all goats on the common pasture is f (g) = 48g − 2g2, where g is the
number of goats on the pasture. The town council notices that total profit from the pasture is not
maximized if villagers are allowed to pasture goats for free. The council decides to allow a goat to use
the common pasture only if its owner buys it a goat license. To maximize total profit (of villagers and
council), how many groschens per goat should the council charge?
a.
12
b.
20
c.
24
d.
26
e.
22
2. The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their
neighbors’ campfires. Each camper’s utility function is U = 22f − f 2 − s, where f is the number of
hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s
is 10 times the average amount of hours that campers use their fires. The campground authority could
make all campers better off by limiting the number of hours of campfire per day for everyone. How
many hours of campfire per day should the authority allow each camper in order to make the typical
camper as well off as possible?
a.
6
b.
11
c.
4
d.
7
e.
Campers will be best off if they are free to choose their own amounts of campfire.
3. The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their
neighbors’ campfires. Each camper’s utility function is U = 17f − f 2 − s, where f is the number of
hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s
is 7 times the average amount of hours that campers use their fires. The campground authority could
make all campers better off by limiting the number of hours of campfire per day for everyone. How
many hours of campfire per day should the authority allow each camper in order to make the typical
camper as well off as possible?
a.
3
b.
6
c.
8.50
d.
5
e.
Campers will be best off if they are free to choose their own amounts of campfire.
4. The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their
neighbors’ campfires. Each camper’s utility function is U = 25f − f 2 − s, where f is the number of
hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s
is 11 times the average amount of hours that campers use their fires. The campground authority could
make all campers better off by limiting the number of hours of campfire per day for everyone. How
many hours of campfire per day should the authority allow each camper in order to make the typical
camper as well off as possible?
a.
5
b.
7
c.
12.50
d.
8
e.
Campers will be best off if they are free to choose their own amounts of campfire.
5. Two stores are located side by side. They attract customers to each other and to themselves by
advertising. The profit functions of the two stores are (45 + x2)x1 − 2x21 for store 1 and
(90 + x1)x2 − 2x22 for store 2, where x1 and x2 are total advertising expenditures by stores 1 and 2
respectively. If each store sets its advertising expenditures independently (as in Nash equilibrium),
how much would store 1 spend on advertising?
a.
$18
b.
$20
c.
$15
d.
$23
e.
None of the above.
6. Two stores are located side by side. They attract customers to each other and to themselves by
advertising. The profit functions of the two stores are (75 + x2)x1 − 2x21 for store 1 and
(105 + x1)x2 − 2x22 for store 2, where x1 and x2 are total advertising expenditures by stores 1 and 2
respectively. If each store sets its advertising expenditures independently (as in Nash equilibrium),
how much would store 1 spend on advertising?
a.
$27
b.
$29
c.
$32
d.
$24
e.
None of the above.
7. Two stores are located side by side. They attract customers to each other and to themselves by
advertising. The profit functions of the two stores are (45 + x2)x1 − 2x21 for store 1 and
(75 + x1)x2 − 2x22 for store 2, where x1 and x2 are total advertising expenditures by stores 1 and 2
respectively. If each store sets its advertising expenditures independently (as in Nash equilibrium),
how much would store 1 spend on advertising?
a.
$14
b.
$19
c.
$22
d.
$17
e.
None of the above.
8. Two stores are located side by side and attract customers to each other and to themselves by
advertising. Where x1 and x2 are the advertising expenditures of stores 1 and 2, the profits of the firms
are (48 + x2)x1 − 2(x1)2 for store 1 and (54 + x1)x2 − 2(x2)2 for store 2. Knowing these functions, one
investor buys both stores. In order to maximize his total profits, how much should he spend on
advertising for store 1?
a.
$10
b.
$26
c.
$25
d.
$35
e.
None of the above.
9. A small coffee company roasts coffee beans in its shop. The unroasted beans cost the company $2 per
pound. The marginal cost of roasting coffee beans is $(150 − 10q + q2)/100 per pound when q pounds
are roasted. The smell of roasting beans imposes costs on the company’s neighbors. The total amount
that neighbors would be willing to pay to have the shop stop roasting altogether is 5q2, where q is the
number of pounds being roasted. The company sells its output in a competitive market at $4.50 per
pound. What is the socially efficient amount of coffee for the company to roast?
a.
10 pounds.
b.
15 pounds.
c.
the square root of 10 pounds.
d.
45 pounds.
e.
None of the above.
10. Firm 1 produces output x with a cost function c1(x) = x2 + 10. Firm 2 produces output y with a cost
function c2(y, x) = y2 + x. Thus, the more that firm 1 produces, the greater are firm 2’s costs. Both firms
face competitive product markets. The competitive price of x is $20 and the competitive price of y is
$40. No new firms can enter the industry and the old ones must remain. The efficient Pigouvian tax on
the x good is
a.
$0.
b.
$1.
c.
$2.
d.
$3.
e.
$4.
11. Mike’s utility function is U(c, d, h) = 8c + 12d − d2 − 6h, where d is the number of hours per day that
he spends driving around, h is the average number of hours per day spent driving around by other
citizens of his town, and c is the amount of money he has to spend on other things than gasoline and
auto repairs. There are 1,001 identical citizens in Mike’s home town. Mike’s expenses for gasoline and
auto repairs amount to $.50 per hour for the time he spends driving. If Mike believes that his amount
of driving won’t affect the amount that others drive, how many hours per day will he choose to drive?
a.
4
b.
6
c.
8
d.
2
e.
1
12. Mike’s utility function is U(c, d, h) = 8c + 12d − d2 − 6h, where d is the number of hours per day that
he spends driving around, h is the average number of hours per day spent driving around by other
citizens of his town, and c is the amount of money he has to spend on other things than gasoline and
auto repairs. There are 1,001 identical citizens in Mike’s home town. Mike’s expenses for gasoline and
auto repairs amount to $.50 per hour for the time he spends driving. If Mike believes that his amount
of driving won’t affect the amount that others drive, how many hours per day will he choose to drive?
a.
4
b.
8
c.
2
d.
6
e.
1
13. Mike’s utility function is U(c, d, h) = 4c + 14d − d 2 − 6h, where d is the number of hours per day that
he spends driving around, h is the average number of hours per day spent driving around by other
citizens of his town, and c is the amount of money he has to spend on other things than gasoline and
auto repairs. There are 1,001 identical citizens in Mike’s home town. Mike’s expenses for gasoline and
auto repairs amount to $.50 per hour for the time he spends driving. If Mike believes that his amount
of driving won’t affect the amount that others drive, how many hours per day will he choose to drive?
a.
7
b.
8
c.
6
d.
3
e.
0.50
14. Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function,
u(m, b, B) = m + 24b − b2 − B/50, where m is the amount of macaroni (in kilograms) that he or she eats
per day, b is the number of hours that he or she spends on the beach per day, and B is the total number
of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10
per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the
amount of time that any person can spend on the beach. How many hours per day should they allow in
order to maximize the utility of a typical Marbellite?
a.
12
b.
14
c.
11
d.
15
e.
They could not possibly be made better off by legislation that limits their freedom to
choose.
15. Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function,
u(m, b, B) = m + 14b − b2 − B/50, where m is the amount of macaroni (in kilograms) that he or she eats
per day, b is the number of hours that he or she spends on the beach per day, and B is the total number
of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10
per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the
amount of time that any person can spend on the beach. How many hours per day should they allow in
order to maximize the utility of a typical Marbellite?
a.
6
b.
9
c.
10
d.
7
e.
They could not possibly be made better off by legislation that limits their freedom to
choose.
16. Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function,
u(m, b, B) = m + 14b − b2 − B/50, where m is the amount of macaroni (in kilograms) that he or she eats
per day, b is the number of hours that he or she spends on the beach per day, and B is the total number
of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10
per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the
amount of time that any person can spend on the beach. How many hours per day should they allow in
order to maximize the utility of a typical Marbellite?
a.
10
b.
7
c.
9
d.
6
e.
They could not possibly be made better off by legislation that limits their freedom to
choose.
17. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $4,000 per month.
Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the
bay is $1,000(12x − x2). If there are no restrictions on entry and new boats come into the bay until
there is no profit to be made by a new entrant, then the number of boats who enter will be X1. If the
number of boats that operate in the bay is regulated to maximize total profits, the number of boats in
the bay will be X2.
a.
X1 = 8 and X2 = 8.
b.
X1 = 4 and X2 = 2.
c.
X1 = 8 and X2 = 4.
d.
X1 = 12 and X2 = 8.
e.
None of the above.
18. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $4,000 per month.
Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the
bay is $1,000(28x − x2). If there are no restrictions on entry and new boats come into the bay until
there is no profit to be made by a new entrant, then the number of boats who enter will be X1. If the
number of boats that operate in the bay is regulated to maximize total profits, the number of boats in
the bay will be X2.
a.
X1 = 24 and X2 = 24.
b.
X1 = 28 and X2 = 16.
c.
X1 = 24 and X2 = 12.
d.
X1 = 12 and X2 = 10.
e.
None of the above.
19. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $4,000 per month.
Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the
bay is $1,000(28x − x2). If there are no restrictions on entry and new boats come into the bay until
there is no profit to be made by a new entrant, then the number of boats who enter will be X1. If the
number of boats that operate in the bay is regulated to maximize total profits, the number of boats in
the bay will be X2.
a.
X1 = 12 and X2 = 10.
b.
X1 = 28 and X2 = 16.
c.
X1 = 24 and X2 = 12.
d.
X1 = 24 and X2 = 24.
e.
None of the above.
20. An apiary is located next to an apple orchard. The apiary produces honey and the apple orchard
produces apples. The cost function of the apiary is CH(H, A) = H 2/100 − 2A and the cost function of the
apple orchard is CA(H, A) = A2/100, where H and A are the number of units of honey and apples
produced respectively. The price of honey is $1 and the price of apples is $3 per unit. Let A1 be the
output of apples if the firms operate independently, and let A2 be the output of apples if the firms are
operated by a single owner so as to maximize total profit.
a.
A1 = 75 and A2 = 150.
b.
A1 = A2 = 150.
c.
A1 = 125 and A2 = 150.
d.
A1 = 150 and A2 = 250.
e.
A1 = 50 and A2 = 150.
21. An apiary is located next to an apple orchard. The apiary produces honey and the apple orchard
produces apples. The cost function of the apiary is CH(H, A) = H 2/100 − 1A and the cost function of the
apple orchard is CA(H, A) = A2/100, where H and A are the number of units of honey and apples
produced respectively. The price of honey is $5 and the price of apples is $6 per unit. Let A1 be the
output of apples if the firms operate independently, and let A2 be the output of apples if the firms are
operated by a single owner so as to maximize total profit.
a.
A1 = 300 and A2 = 350.
b.
A1 = A2 = 300.
c.
A1 = 175 and A2 = 300.
d.
A1 = 150 and A2 = 300.
e.
A1 = 250 and A2 = 300.
22. An apiary is located next to an apple orchard. The apiary produces honey and the apple orchard
produces apples. The cost function of the apiary is CH(H, A) = H 2/100 − 3A and the cost function of the
apple orchard is CA(H, A) = A2/100, where H and A are the number of units of honey and apples
produced respectively. The price of honey is $2 and the price of apples is $7 per unit. Let A1 be the
output of apples if the firms operate independently, and let A2 be the output of apples if the firms are
operated by a single owner so as to maximize total profit.
a.
A1 = A2 = 350.
b.
A1 = 250 and A2 = 350.
c.
A1 = 175 and A2 = 350.
d.
A1 = 350 and A2 = 500.
e.
A1 = 100 and A2 = 350.
23. Peter’s utility is U(c, d, h) = 8c + 18d − d 2 − 6h, where d is the number of hours per day that he spends
driving around, h is the number of hours per day spent driving around by other people in his home
town, and c is the amount of money he has left to spend on other stuff besides gasoline and auto
repairs. Gas and auto repairs cost $.50 per hour of driving. All the people in Peter’s home town have
the same tastes. If each citizen believes that his own driving will not affect the amount of driving done
by others, they will all drive D1 hours per day. If they are all drive the same amount, they would all be
best off if each drove D2 hours per day, where
a.
D1 = 7 and D2 = 4.
b.
D1 = D2 = 7.
c.
D1 = 9 and D2 = 5.
d.
D1 = 10 and D2 = 0.
e.
D1 = 7 and D2 = 2.
24. Charlie’s utility is U(c, d, h) = 4c + 10d − d 2 − 4h, where d is the number of hours per day that he
spends driving around, h is the number of hours per day spent driving around by other people in his
home town, and c is the amount of money he has left to spend on other stuff besides gasoline and auto
repairs. Gas and auto repairs cost $.50 per hour of driving. All the people in Charlie’s home town have
the same tastes. If each citizen believes that his own driving will not affect the amount of driving done
by others, they will all drive D1 hours per day. If they are all drive the same amount, they would all be
best off if each drove D2 hours per day, where
a.
D1 = 6 and D2 = 3.
b.
D1 = 7 and D2 = 1.
c.
D1 = D2 = 4.
d.
D1 = 4 and D2 = 2.
e.
D1 = 4 and D2 = 0.
25. Peter’s utility is U(c, d, h) = 2c + 9d − d2 − 6h, where d is the number of hours per day that he spends
driving around, h is the number of hours per day spent driving around by other people in his home
town, and c is the amount of money he has left to spend on other stuff besides gasoline and auto
repairs. Gas and auto repairs cost $.50 per hour of driving. All the people in Peter’s home town have
the same tastes. If each citizen believes that his own driving will not affect the amount of driving done
by others, they will all drive D1 hours per day. If they are all drive the same amount, they would all be
best off if each drove D2 hours per day, where
a.
D1 = 4 and D2 = 1.
b.
D1 = 7 and D2 = 0.
c.
D1 = 6 and D2 = 2.
d.
D1 = D2 = 4.
e.
D1 = 4 and D2 = 0.
26. An airport is located next to a housing development. Where X is the number of planes that land per day
and Y is the number of houses in the housing development, profits of the airport are 28X − X2 and
profits of the developer are 20Y − Y2 − XY. Let H1 be the number of houses built if a single
profit-maximizing company owns the airport and the housing development. Let H2 be the number of
houses built if the airport and the housing development are operated independently and the airport has
to pay the developer the total “damages” XY done by the planes to the profits of the developer.
a.
H1 = H2 = 4.
b.
H1 = 4 and H2 = 10.
c.
H1 = 10 and H2 = 4.
d.
H1 = 6 and H2 = 9.
e.
H1 = 9 and H2 = 13.
27. An airport is located next to a housing development. Where X is the number of planes that land per day
and Y is the number of houses in the housing development, profits of the airport are 26X − X2 and
profits of the developer are 22Y − Y2 − XY. Let H1 be the number of houses built if a single
profit-maximizing company owns the airport and the housing development. Let H2 be the number of
houses built if the airport and the housing development are operated independently and the airport has
to pay the developer the total “damages” XY done by the planes to the profits of the developer.
a.
H1 = 11 and H2 = 6.
b.
H1 = H2 = 6.
c.
H1 = 8 and H2 = 10.
d.
H1 = 6 and H2 = 11.
e.
H1 = 10 and H2 = 14.
28. An airport is located next to a housing development. Where X is the number of planes that land per day
and Y is the number of houses in the housing development, profits of the airport are 36X − X2 and
profits of the developer are 42Y − Y2 − XY. Let H1 be the number of houses built if a single
profit-maximizing company owns the airport and the housing development. Let H2 be the number of
houses built if the airport and the housing development are operated independently and the airport has
to pay the developer the total “damages” XY done by the planes to the profits of the developer.
a.
H1 = 18 and H2 = 20.
b.
H1 = 21 and H2 = 16.
c.
H1 = H2 = 16.
d.
H1 = 16 and H2 = 21.
e.
H1 = 20 and H2 = 24.
29. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C
dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (36 + J )C − 2C 2 and the profits of the jeweler will be (30 + C )J − 2J 2. The clothing store
gets to choose its amount of advertising first, knowing that the jeweler will find out how much the
clothing store advertised before deciding how much to spend. The amount spent by the clothing store
will be
a.
$17.
b.
$34.
c.
$51.
d.
$8.50.
e.
$25.50.
30. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C
dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (30 + J )C − 2C 2 and the profits of the jeweler will be (24 + C )J − 2J 2. The clothing store
gets to choose its amount of advertising first, knowing that the jeweler will find out how much the
clothing store advertised before deciding how much to spend. The amount spent by the clothing store
will be
a.
$42.
b.
$14.
c.
$28.
d.
$7.
e.
$21.
31. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C
dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (18 + J )C − 2C 2 and the profits of the jeweler will be (24 + C )J − 2J 2. The clothing store
gets to choose its amount of advertising first, knowing that the jeweler will find out how much the
clothing store advertised before deciding how much to spend. The amount spent by the clothing store
will be
a.
$10.
b.
$5.
c.
$20.
d.
$30.
e.
$15.
32. Millie Bush has written a best-seller. Revenues net of production costs are $300T1/3A1/3, where T is the
number of publicity trips Millie takes and A is the number of ads for the book that appear. Millie has to
pay for all of her own publicity trips, which cost $100 each. Her publisher pays for the advertising,
which costs $100 per ad. Revenues from the book are split equally between Millie and her publisher.
Let T1 be the number of trips that Millie would choose to make in a Nash equilibrium where she
chooses the number of trips and the publisher chooses the amount of advertising. Let T2 be the number
of trips that Millie should make if trips and advertising are determined so as to maximize total profits
net of trip and ad costs.
a.
T1 = 1 and T2 = 1.
b.
T1 = 1 and T2 = 2.
c.
T1 = 2 and T2 = 1.
d.
T1 = 1 and T2 = 1/8.
e.
T1 = 1/8 and T2 = 1.
PROBLEM
1. Two firms in a grimy Ohio town produce the same product in a competitive industry. Each has an old
factory using an old technology. It still pays to operate these factories but it would not pay to expand
them. The only variable factor used by either firm is labor. Each firm pollutes the other and thus
reduces the output of the other firm. The production functions of firms A and B respectively are Q a =
L .5 a (2/3)Q b and Q b = L .5 b (1/3)Q a, where L .5 a and L .5 b are the square roots respectively of
the amount of labor used by firms A and B. The wage rate of labor is $1 and the price of the firms
output is $12.
a. If the two firms each maximize profits independently, what is their total output and how much
quasi-rents do their factories earn?
b. If someone buys them both and maximizes joint profits, how much quasi-rent is earned in total?