Deck 37: Extension: A: Public Goods

Question 1

They are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S)M_B and Ray's utility function is U_R(S, M_R)= (2 + S)M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R 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.

Answer 1

$2,000.

Question 2

Just north of the town of Muskrat, Ontario,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 U_i(X_i, Y)= X_i - 121/Y, where X_i 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.

Answer 2

440 square meters.

Question 3

They are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S)M_B and Ray's utility function is U_R(S, M_R)= (4 + S)M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R 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.

Answer 3

$1,200.

Question 4

They are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S)M_B and Ray's utility function is U_R(S, M_R)= (3 + S)M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R 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.

Question 5

They are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S)M_B and Ray's utility function is U_R(S, M_R)= (2 + S)M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R 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.

Question 6

Lucy's utility function is 2X_L + G and Melvin's utility function is X_MG, where G is their expenditures on the public goods they share in their apartment and where X_L and X_M 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.

Question 7

Lucy's utility function is 2X_L + G and Melvin's utility function is X_MG, where G is their expenditures on the public goods they share in their apartment and where X_L and X_M 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.

Question 8

Lucy's utility function is 2X_L + G and Melvin's utility function is X_MG, where G is their expenditures on the public goods they share in their apartment and where X_L and X_M 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.

Question 9

Just north of the town of Muskrat, Ontario, 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 U_i(X_i, Y)= X_i - 144/Y, where X_i 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.

Question 10

Lucy's utility function is 2X_L + G and Melvin's utility function is X_MG, where G is their expenditures on the public goods they share in their apartment and where X_L and X_M 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.

Question 11

Just north of the town of Muskrat, Ontario, 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 U_i(X_i, Y)= X_i - 121/Y, where X_i 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.

Question 12

They are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S)M_B and Ray's utility function is U_R(S, M_R)= (3 + S)M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R 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.

Question 13

Just north of the town of Muskrat, Ontario, 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 U_i(X_i, Y)= X_i - 81/Y, where X_i 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.

Question 14

Lucy's utility function is 2X_L + G and Melvin's utility function is X_MG, where G is their expenditures on the public goods they share in their apartment and where X_L and X_M 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.

Question 15

Just north of the town of Muskrat, Ontario, 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 U_i(X_i, Y)= X_i - 121/Y, where X_i 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.