Deck 37: B: Public Goods

Question 1

Lucy and Melvin.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.

Answer 1

$10,000

Question 2

Lucy and Melvin.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.

Answer 2

$20,000

Question 3

Problem 1
An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.

-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 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.

Answer 3

110 square meters.

Question 4

Problem 1
An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.

-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 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) 120.0 square meters.
B) 245 square meters.
C) 240 square meters.
D) 120 square meters.
E) None of the above.

Question 5

Problem 1
An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.

-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 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.

Question 6

Bob and Ray .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.

Question 7

Lucy and Melvin.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 8

Lucy and Melvin.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 9

Problem 1
An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.

-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 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.

Question 10

Bob and Ray.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.

Question 11

Bob and Ray.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 =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 12

Lucy and Melvin.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 13

Bob and Ray.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 14

Problem 1
An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.

-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 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 15

Bob and Ray .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.