CHAPTER 37: Public Goods
MULTIPLE CHOICE
1. Just north of the town of Muskrat, Ontario, in Problem 1, is the town of Brass Monkey, population
4,500. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single
private good, Labatt Ale. Everyone’s utility function is Ui(Xi, Y) = Xi − 81/Y, where Xi is the number of
bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is $1
per bottle. The cost of the skating rink to the city is $5 per square meter. Everyone has an income of at
least $5,000. What is the Pareto efficient size for the town skating rink?
a.
270 square meters.
b.
390 square meters.
c.
195 square meters.
d.
545 square meters.
e.
None of the above.
2. Just north of the town of Muskrat, Ontario, in Problem 1, is the town of Brass Monkey, population
800. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single private
good, Labatt Ale. Everyone’s utility function is Ui(Xi, Y) = Xi − 121/Y, where Xi is the number of
bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is $1
per bottle. The cost of the skating rink to the city is $8 per square meter. Everyone has an income of at
least $5,000. What is the Pareto efficient size for the town skating rink?
a.
230 square meters.
b.
110 square meters.
c.
225 square meters.
d.
115 square meters.
e.
None of the above.
3. Just north of the town of Muskrat, Ontario, in Problem 1, is the town of Brass Monkey, population
12,800. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single
private good, Labatt Ale. Everyone’s utility function is Ui(Xi, Y) = Xi − 121/Y, where Xi is the number
of bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is
$1 per bottle. The cost of the skating rink to the city is $8 per square meter. Everyone has an income of
at least $5,000. What is the Pareto efficient size for the town skating rink?
a.
560 square meters.
b.
885 square meters.
c.
280 square meters.
d.
440 square meters.
e.
None of the above.
4. Just north of the town of Muskrat, Ontario, in Problem 1, is the town of Brass Monkey, population
700. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single private
good, Labatt Ale. Everyone’s utility function is Ui(Xi, Y) = Xi − 121/Y, where Xi is the number of
bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is $1
per bottle. The cost of the skating rink to the city is $7 per square meter. Everyone has an income of at
least $5,000. What is the Pareto efficient size for the town skating rink?
a.
110 square meters.
b.
115 square meters.
c.
230 square meters.
d.
225 square meters.
e.
None of the above.
5. Just north of the town of Muskrat, Ontario, in Problem 1, is the town of Brass Monkey, population
700. Brass Monkey, like Muskrat, has a single public good, the town skating rink and a single private
good, Labatt Ale. Everyone’s utility function is Ui(Xi, Y) = Xi − 144/Y, where Xi is the number of
bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is $1
per bottle. The cost of the skating rink to the city is $7 per square meter. Everyone has an income of at
least $5,000. What is the Pareto efficient size for the town skating rink?
a.
120 square meters.
b.
245 square meters.
c.
240 square meters.
d.
120 square meters.
e.
None of the above.
6. Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob’s utility function is UB(S,
MB) = (1 + S)MB and Ray’s utility function is UR(S, MR) = (3 + S)MR, where S = 0 if they don’t get the
sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to
spend on their private consumptions. Bob has a total of $2,000 to spend on the sofa and other stuff.
Ray has a total of $1,600 to spend on the sofa and other stuff. The maximum amount that they could
pay for the sofa and still arrange to both be better off than without it is
a.
$2,100.
b.
$533.33.
c.
$750.
d.
$1,400.
e.
$2,800.
7. Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob’s utility function is UB(S,
MB) = (1 + S)MB and Ray’s utility function is UR(S, MR) = (2 + S)MR, where S = 0 if they don’t get the
sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to
spend on their private consumptions. Bob has a total of $2,000 to spend on the sofa and other stuff.
Ray has a total of $3,000 to spend on the sofa and other stuff. The maximum amount that they could
pay for the sofa and still arrange to both be better off than without it is
a.
$3,000.
b.
$1,500.
c.
$2,000.
d.
$1,050.
e.
$4,000.
8. Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob’s utility function is UB(S,
MB) = (1 + S)MB and Ray’s utility function is UR(S, MR) = (3 + S)MR, where S = 0 if they don’t get the
sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to
spend on their private consumptions. Bob has a total of $1,200 to spend on the sofa and other stuff.
Ray has a total of $4,000 to spend on the sofa and other stuff. The maximum amount that they could
pay for the sofa and still arrange to both be better off than without it is
a.
$1,333.33.
b.
$1,600.
c.
$850.
d.
$2,400.
e.
$3,200.
9. Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob’s utility function is UB(S,
MB) = (1 + S)MB and Ray’s utility function is UR(S, MR) = (4 + S)MR, where S = 0 if they don’t get the
sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to
spend on their private consumptions. Bob has a total of $800 to spend on the sofa and other stuff. Ray
has a total of $4,000 to spend on the sofa and other stuff. The maximum amount that they could pay
for the sofa and still arrange to both be better off than without it is
a.
$1,000.
b.
$1,200.
c.
$1,800.
d.
$650.
e.
$2,400.
10. Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob’s utility function is UB(S,
MB) = (1 + S)MB and Ray’s utility function is UR(S, MR) = (2 + S)MR, where S = 0 if they don’t get the
sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to
spend on their private consumptions. Bob has a total of $1,200 to spend on the sofa and other stuff.
Ray has a total of $1,200 to spend on the sofa and other stuff. The maximum amount that they could
pay for the sofa and still arrange to both be better off than without it is
a.
$1,500.
b.
$600.
c.
$1,000.
d.
$550.
e.
$2,000.
11. Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 160H, where H is the
number of hours they work per year. Their utility functions are, respectively, UB(CB, H) = CB −
0.01H2 and UC(CC, H) = CC − 0.04H2, where CB and CC are their private goods consumptions and H is
the number of hours they work per year. If they find a Pareto optimal choice of hours of work and
income distribution, the number of hours they work per year is
a.
1,700.
b.
2,400.
c.
1,600.
d.
750.
e.
850.
12. Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 256H, where H is the
number of hours they work per year. Their utility functions are, respectively, UB(CB, H) = CB − 0.04H2
and UC(CC, H) = CC − 0.04H2, where CB and CC are their private goods consumptions and H is the
number of hours they work per year. If they find a Pareto optimal choice of hours of work and income
distribution, the number of hours they work per year is
a.
2,400.
b.
1,600.
c.
1,700.
d.
750.
e.
850.
13. Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 72H, where H is the
number of hours they work per year. Their utility functions are, respectively, UB(CB, H) = CB − 0.03H2
and UC(CC, H) = CC − 0.03H2, where CB and CC are their private goods consumptions and H is the
number of hours they work per year. If they find a Pareto optimal choice of hours of work and income
distribution, the number of hours they work per year is
a.
600.
b.
700.
c.
900.
d.
250.
e.
350.
14. Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 192H, where H is the
number of hours they work per year. Their utility functions are, respectively, UB(CB, H) = CB − 0.02H2
and UC(CC, H) = CC − 0.04H2, where CB and CC are their private goods consumptions and H is the
number of hours they work per year. If they find a Pareto optimal choice of hours of work and income
distribution, the number of hours they work per year is
a.
750.
b.
2,400.
c.
1,700.
d.
1,600.
e.
850.
15. Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 140H, where H is the
number of hours they work per year. Their utility functions are, respectively, UB(CB, H) = CB − 0.03H2
and UC(CC, H) = CC − 0.02H2, where CB and CC are their private goods consumptions and H is the
number of hours they work per year. If they find a Pareto optimal choice of hours of work and income
distribution, the number of hours they work per year is
a.
1,400.
b.
2,100.
c.
1,500.
d.
650.
e.
750.
16. Recall Lucy and Melvin from Problem 6. Lucy’s utility function is 2XL + G and Melvin’s utility
function is XMG, where G is their expenditures on the public goods they share in their apartment and
where XL and XM are their respective private consumption expenditures. The total amount they have to
spend on private goods and public goods is $24,000. They agree on a Pareto optimal pattern of
expenditures in which the amount that is spent on Lucy’s private consumption is $9,000. How much
do they spend on public goods?
a.
$5,000
b.
$10,000
c.
$7,050
d.
$2,500
e.
There is not enough information here to be able to determine the answer.
17. Recall Lucy and Melvin from Problem 6. Lucy’s utility function is 2XL + G and Melvin’s utility
function is XMG, where G is their expenditures on the public goods they share in their apartment and
where XL and XM are their respective private consumption expenditures. The total amount they have to
spend on private goods and public goods is $33,000. They agree on a Pareto optimal pattern of
expenditures in which the amount that is spent on Lucy’s private consumption is $9,000. How much
do they spend on public goods?
a.
$8,550
b.
$4,000
c.
$8,000
d.
$16,000
e.
There is not enough information here to be able to determine the answer.
18. Recall Lucy and Melvin from Problem 6. Lucy’s utility function is 2XL + G and Melvin’s utility
function is XMG, where G is their expenditures on the public goods they share in their apartment and
where XL and XM are their respective private consumption expenditures. The total amount they have to
spend on private goods and public goods is $39,000. They agree on a Pareto optimal pattern of
expenditures in which the amount that is spent on Lucy’s private consumption is $9,000. How much
do they spend on public goods?
a.
$9,550
b.
$20,000
c.
$5,000
d.
$10,000
e.
There is not enough information here to be able to determine the answer.
19. Recall Lucy and Melvin from Problem 6. Lucy’s utility function is 2XL + G and Melvin’s utility
function is XMG, where G is their expenditures on the public goods they share in their apartment and
where XL and XM are their respective private consumption expenditures. The total amount they have to
spend on private goods and public goods is $21,000. They agree on a Pareto optimal pattern of
expenditures in which the amount that is spent on Lucy’s private consumption is $6,000. How much
do they spend on public goods?
a.
$5,550
b.
$10,000
c.
$2,500
d.
$5,000
e.
There is not enough information here to be able to determine the answer.
20. Recall Lucy and Melvin from Problem 6. Lucy’s utility function is 2XL + G and Melvin’s utility
function is XMG, where G is their expenditures on the public goods they share in their apartment and
where XL and XM are their respective private consumption expenditures. The total amount they have to
spend on private goods and public goods is $24,000. They agree on a Pareto optimal pattern of
expenditures in which the amount that is spent on Lucy’s private consumption is $6,000. How much
do they spend on public goods?
a.
$6,000
b.
$3,000
c.
$6,050
d.
$12,000
e.
There is not enough information here to be able to determine the answer.