Exam 35: Public Goods-Part B

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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 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?

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B

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 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?

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A

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?

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D

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 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?

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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?

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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

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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 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?

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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

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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 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?

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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

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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?

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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

(Multiple Choice)
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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

(Multiple Choice)
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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?

(Multiple Choice)
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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?

(Multiple Choice)
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