Exam 32: A: Welfare

A Borda count is used to decide an election between three candidates, x, y, and z, where a score of 1 is awarded to a first choice, 2 to a second choice, and 3 to a third choice. There are 26 voters. 9 voters rank the candidates x first, y second, and z third; 9 voters rank the candidates x first, z second, and y third; 6 rank the candidates z first, y second, and x third; and 2 voters rank the candidates y first, z second, and x third. Which candidate wins?

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is U and McCoy's utility is U , where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons. The sheriff has a total of 48 gallons of confiscated whisky which he could give back to them. For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally. The sheriff should give them each

Suppose that Romeo in Problem 8 has the utility function U = S⁸_RS⁴_J and Juliet has the utility function U = S⁴_RS⁸_J, where S_R is Romeo's spaghetti consumption and S_J is Juliet's. They have 120 units of spaghetti to divide between them.

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is U and McCoy's utility is U , where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons. The sheriff has a total of 82 gallons of confiscated whisky which he could give back to them. For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally. The sheriff should give them each

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is U and McCoy's utility is U , where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons. The sheriff has a total of 48 gallons of confiscated whisky which he could give back to them. For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally. The sheriff should give them each

Suppose that Paul and David from Problem 7 have utility functions U = 4A_P + O_P and U = A_D + 5O_D, respectively, where A_P and O_P are Paul's consumptions of apples and oranges and A_D and O_D are David's consumptions of apples and oranges. The total supply of apples and oranges to be divided between them is 16 apples and 16 oranges. The "fair" allocations consist of all allocations satisfying

Suppose that Paul and David from Problem 7 have utility functions U = 3A_P + O_P and U = A_D + 2O_D, respectively, where A_P and O_P are Paul's consumptions of apples and oranges and A_D and O_D are David's consumptions of apples and oranges. The total supply of apples and oranges to be divided between them is 10 apples and 20 oranges. The "fair" allocations consist of all allocations satisfying

A parent has two children living in cities with different costs of living. The cost of living in city B is 3 times the cost of living in city A. The child in city A has an income of $3,000 and the child in city B has an income of $9,000. The parent wants to give a total of $4,000 to her two children. Her utility function is U(C_A, C_B) = C_AC_B, where C_A and C_B are the consumptions of the children living in cities A and B respectively. She will choose to give

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is U and McCoy's utility is U , where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons. The sheriff has a total of 66 gallons of confiscated whisky which he could give back to them. For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally. The sheriff should give them each

A Borda count is used to decide an election between three candidates, x, y, and z, where a score of 1 is awarded to a first choice, 2 to a second choice, and 3 to a third choice. There are 25 voters. 10 voters rank the candidates x first, y second, and z third; 7 voters rank the candidates x first, z second, and y third; 5 rank the candidates z first, y second, and x third; and 3 voters rank the candidates y first, z second, and x third. Which candidate wins?

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is U and McCoy's utility is U , where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons. The sheriff has a total of 52 gallons of confiscated whisky which he could give back to them. For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally. The sheriff should give them each

Suppose that Paul and David from Problem 7 have utility functions U = 5A_P + O_P and U = A_D + 3O_D, respectively, where A_P and O_P are Paul's consumptions of apples and oranges and A_D and O_D are David's consumptions of apples and oranges. The total supply of apples and oranges to be divided between them is 16 apples and 14 oranges. The "fair" allocations consist of all allocations satisfying

Suppose that Paul and David from Problem 7 have utility functions U = 5A_P + O_P and U = A_D + 3O_D, respectively, where A_P and O_P are Paul's consumptions of apples and oranges and A_D and O_D are David's consumptions of apples and oranges. The total supply of apples and oranges to be divided between them is 14 apples and 14 oranges. The "fair" allocations consist of all allocations satisfying

A Borda count is used to decide an election between three candidates, x, y, and z, where a score of 1 is awarded to a first choice, 2 to a second choice, and 3 to a third choice. There are 25 voters. 3 voters rank the candidates x first, y second, and z third; 10 voters rank the candidates x first, z second, and y third; 6 rank the candidates z first, y second, and x third; and 6 voters rank the candidates y first, z second, and x third. Which candidate wins?

A parent has two children living in cities with different costs of living. The cost of living in city B is 3 times the cost of living in city A. The child in city A has an income of $2,000 and the child in city B has an income of $6,000. The parent wants to give a total of $1,000 to her two children. Her utility function is U(C_A, C_B) = C_AC_B, where C_A and C_B are the consumptions of the children living in cities A and B respectively. She will choose to give

A Borda count is used to decide an election between three candidates, x, y, and z, where a score of 1 is awarded to a first choice, 2 to a second choice, and 3 to a third choice. There are 20 voters. 4 voters rank the candidates x first, y second, and z third; 5 voters rank the candidates x first, z second, and y third; 8 rank the candidates z first, y second, and x third; and 3 voters rank the candidates y first, z second, and x third. Which candidate wins?

Suppose that Romeo in Problem 8 has the utility function U = S⁶_RS⁴_J and Juliet has the utility function U = S⁴_RS⁶_J, where S_R is Romeo's spaghetti consumption and S_J is Juliet's. They have 70 units of spaghetti to divide between them.

A parent has two children living in cities with different costs of living. The cost of living in city B is 2 times the cost of living in city A. The child in city A has an income of $5,000 and the child in city B has an income of $10,000. The parent wants to give a total of $4,000 to her two children. Her utility function is U(C_A, C_B) = C_AC_B, where C_A and C_B are the consumptions of the children living in cities A and B respectively. She will choose to give

Suppose that Romeo in Problem 8 has the utility function U = S³_RS¹_J and Juliet has the utility function U = S¹_RS³_J, where S_R is Romeo's spaghetti consumption and S_J is Juliet's. They have 36 units of spaghetti to divide between them.

A parent has two children living in cities with different costs of living. The cost of living in city B is 3 times the cost of living in city A. The child in city A has an income of $3,000 and the child in city B has an income of $9,000. The parent wants to give a total of $2,000 to her two children. Her utility function is U(C_A, C_B) = C_AC_B, where C_A and C_B are the consumptions of the children living in cities A and B respectively. She will choose to give