Exam 37:Public Goods-Part B

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?

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?

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?

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?

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

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

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?

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?

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?

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?

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?

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?

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

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

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