CHAPTER 35: Externalities
MULTIPLE CHOICE
1. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 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(10x − 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.
2. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 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(21x − 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 = 16 and X2 = 16.
b.
X1 = 20 and X2 = 12.
c.
X1 = 16 and X2 = 8.
d.
X1 = 8 and X2 = 6.
e.
None of the above.
3. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $6,000 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(18x − 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 = 6 and X2 = 4.
b.
X1 = 12 and X2 = 6.
c.
X1 = 16 and X2 = 10.
d.
X1 = 12 and X2 = 12.
e.
None of the above.
4. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $6,000 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(18x − 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 = 6 and X2 = 4.
b.
X1 = 12 and X2 = 12.
c.
X1 = 12 and X2 = 6.
d.
X1 = 16 and X2 = 10.
e.
None of the above.
5. Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 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(26x − 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 = 12.
b.
X1 = 24 and X2 = 24.
c.
X1 = 12 and X2 = 10.
d.
X1 = 28 and X2 = 16.
e.
None of the above.
6. In Problem 2, suppose that the cost function of the honey farm 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 $7 and the price of apples is $5 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 profit-maximizing single owner.
a.
A1 = 125 and A2 = 250.
b.
A1 = A2 = 250.
c.
A1 = 200 and A2 = 250.
d.
A1 = 250 and A2 = 400.
e.
A1 = 350 and A2 = 250.
7. In Problem 2, suppose that the cost function of the honey farm 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 $8 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 profit-maximizing single owner.
a.
A1 = 175 and A2 = 300.
b.
A1 = 150 and A2 = 300.
c.
A1 = 300 and A2 = 350.
d.
A1 = A2 = 300.
e.
A1 = 400 and A2 = 300.
8. In Problem 2, suppose that the cost function of the honey farm 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 profit-maximizing single owner.
a.
A1 = 250 and A2 = 350.
b.
A1 = A2 = 350.
c.
A1 = 175 and A2 = 350.
d.
A1 = 350 and A2 = 500.
e.
A1 = 100 and A2 = 350.
9. In Problem 2, suppose that the cost function of the honey farm 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 $2 and the price of apples is $4 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 profit-maximizing single owner.
a.
A1 = A2 = 200.
b.
A1 = 100 and A2 = 200.
c.
A1 = 125 and A2 = 200.
d.
A1 = 200 and A2 = 250.
e.
A1 = 100 and A2 = 200.
10. In Problem 2, suppose that the cost function of the honey farm 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 $5 and the price of apples is $4 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 profit-maximizing single owner.
a.
A1 = 200 and A2 = 300.
b.
A1 = A2 = 200.
c.
A1 = 100 and A2 = 200.
d.
A1 = 150 and A2 = 200.
e.
A1 = 250 and A2 = 200.
11. In Problem 3, suppose Wilfred, a typical citizen, has the utility function
U(m, d, h) = m + 13d2 − d2 − 4h, 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 people in his home town, and
m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and
auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect
the amount of driving done by others, they will all drive D1 hours per day. If all citizens drive to
maximize the utility of a typical citizen, they will all drive D2 hours per day, where
a.
D1 = 6 and D2 = 4.
b.
D1 = D2 = 6.
c.
D1 = 8 and D2 = 5.
d.
D1 = 9 and D2 = 0.
e.
D1 = 6 and D2 = 2.
12. In Problem 3, suppose Lawrence, a typical citizen, has the utility function
U(m, d, h) = m + 7d2 − d2 − 4h, 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 people in his home town, and
m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and
auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect
the amount of driving done by others, they will all drive D1 hours per day. If all citizens drive to
maximize the utility of a typical citizen, they will all drive D2 hours per day, where
a.
D1 = 5 and D2 = 2.
b.
D1 = D2 = 3.
c.
D1 = 3 and D2 = 1.
d.
D1 = 6 and D2 = 0.
e.
D1 = 3 and D2 = 0.
13. In Problem 3, suppose Sam, a typical citizen, has the utility function U(m, d, h) = m + 13d2 − 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 people in his home town, and m is the amount of money
he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per
hour of driving. If each citizen believes that their own driving will not affect the amount of driving
done by others, they will all drive D1 hours per day. If all citizens drive to maximize the utility of a
typical citizen, they will all drive D2 hours per day, where
a.
D1 = 8 and D2 = 4.
b.
D1 = 6 and D2 = 3.
c.
D1 = D2 = 6.
d.
D1 = 9 and D2 = 0.
e.
D1 = 6 and D2 = 1.
14. In Problem 3, suppose Albert, a typical citizen, has the utility function U(m, d, h) = m + 5d2 − d2 − 2h,
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 people in his home town, and m is the amount of money
he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per
hour of driving. If each citizen believes that their own driving will not affect the amount of driving
done by others, they will all drive D1 hours per day. If all citizens drive to maximize the utility of a
typical citizen, they will all drive D2 hours per day, where
a.
D1 = 5 and D2 = 0.
b.
D1 = D2 = 2.
c.
D1 = 2 and D2 = 1.
d.
D1 = 4 and D2 = 2.
e.
D1 = 2 and D2 = 0.
15. In Problem 3, suppose Harry, a typical citizen, has the utility function U(m, d, h) = m + 7d2 − d2 − 2h,
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 people in his home town, and m is the amount of money
he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per
hour of driving. If each citizen believes that their own driving will not affect the amount of driving
done by others, they will all drive D1 hours per day. If all citizens drive to maximize the utility of a
typical citizen, they will all drive D2 hours per day, where
a.
D1 = 6 and D2 = 1.
b.
D1 = 5 and D2 = 3.
c.
D1 = D2 = 3.
d.
D1 = 3 and D2 = 2.
e.
D1 = 3 and D2 = 0.
16. 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 22X − X 2 and
profits of the developer are 26Y − Y 2 − 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 developer’s profits.
a.
H1 = H2 = 10.
b.
H1 = 10 and H2 = 13.
c.
H1 = 13 and H2 = 10.
d.
H1 = 12 and H2 = 12.
e.
H1 = 12 and H2 = 16.
17. 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 20X − X 2 and
profits of the developer are 28Y − Y 2 − 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 developer’s profits.
a.
H1 = 12 and H2 = 14.
b.
H1 = H2 = 12.
c.
H1 = 14 and H2 = 13.
d.
H1 = 14 and H2 = 12.
e.
H1 = 13 and H2 = 17.
18. 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 38X − X 2 and
profits of the developer are 28Y − Y 2 − 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 developer’s profits.
a.
H1 = H2 = 6.
b.
H1 = 14 and H2 = 6.
c.
H1 = 6 and H2 = 14.
d.
H1 = 8 and H2 = 13.
e.
H1 = 13 and H2 = 17.
19. 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 22X − 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 developer’s profits.
a.
H1 = 10 and H2 = 6.
b.
H1 = 8 and H2 = 9.
c.
H1 = 6 and H2 = 10.
d.
H1 = H2 = 6.
e.
H1 = 9 and H2 = 13.
20. 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 22X − X2 and
profits of the developer are 32Y − Y 2 − 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 developer’s profits.
a.
H1 = 16 and H2 = 15.
b.
H1 = 14 and H2 = 16.
c.
H1 = 16 and H2 = 14.
d.
H1 = H2 = 14.
e.
H1 = 15 and H2 = 19.
21. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends
C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (6 + J)C − C2 and the profits of the jeweler will be (6 + 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.
5.
b.
10.
c.
15.
d.
2.50.
e.
7.50.
22. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends
C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (18 + J)C − C2 and the profits of the jeweler will be (36 + 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.
54.
b.
9.
c.
36.
d.
18.
e.
27.
23. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends
C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (18 + J)C − C2 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.
48.
b.
16.
c.
8.
d.
32.
e.
24.
24. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends
C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (42 + J)C − C2 and the profits of the jeweler will be (54 + C)J − 2J2. 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.
74.
b.
111.
c.
18.50.
d.
37.
e.
55.50.
25. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends
C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing
store will be (24 + J)C − C2 and the profits of the jeweler will be (66 + 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.
54.
b.
81.
c.
13.50.
d.
27.
e.
40.50.