Deck 34: Extension: A: Welfare

Question 1

Suppose that Romeo has the utility function U = S ⁵_RS ²_J and Juliet has the utility function U = S ²_RS ⁵_J, where S_R is Romeo's spaghetti consumption and S_J is Juliet's.They have 42 units of spaghetti to divide between them.

A)Romeo would want to give Juliet some spaghetti if he had more than 21 units of spaghetti.
B)Romeo would want to give Juliet some spaghetti if he has more than 26 units of spaghetti.
C)Juliet would want to give Romeo some spaghetti if she has more than 28 units.
D)Romeo and Juliet would never disagree about how to divide the spaghetti.
E)Juliet would want to give Romeo some spaghetti if she has more than 30 units of spaghetti.

Answer 1

Juliet would want to give Romeo some spaghetti if she has more than 30 units of spaghetti.

Question 2

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

A)each child $2,000, even though this will buy less goods for the child in city B
B)the child in city B twice as much money as the child in city A.
C)the child in city A twice as much money as the child in city B.
D)the child in city B the same amount of money as the child in city A.
E)the child in city A the same amount of money as the child in city B.

Answer 2

each child $2,000, even though this will buy less goods for the child in city B

Question 3

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?

A)Candidate x.
B)There is a tie between x and y, with z coming in third.
C)Candidate y.
D)Candidate z.
E)There is a tie between y and z, with x coming in third.

Answer 3

Candidate x.

Question 4

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

A)the child in city B 3 times as much money as the child in city A.
B)the child in city B 1.50 times as much money as the child in city A.
C)the child in city A 3 times as much money as the child in city B.
D)each child $1,000, even though this will buy less goods for the child in city B.
E)the child in city A 1.50 times as much money as the child in city B.

Question 5

Suppose that Paul and David 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 12 apples and 20 oranges.The "fair" allocations consist of all allocations satisfying

A)A_D= A_P and O_D = O_P.
B)A_D + O_D is at least 16 and A_S + O_S is at least 16.
C)10A_P + 2O_P is at least 80 and 2A_D + 6O_D is at least 72.
D)5A_P+ O_P is at least 80 and 2A_D + 3O_D is at least 72.
E)5A_P + O_P is at least A_D + 3O_D and A_D + 3O_D is at least 5A_P + O_P.

Question 6

Suppose that Romeo has the utility function U = S ⁵_RS ²_J and Juliet has the utility function U = S ²_RS ⁵_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)Romeo and Juliet would never disagree about how to divide the spaghetti.
B)Romeo would want to give Juliet some spaghetti if he has more than 46 units of spaghetti.
C)Romeo would want to give Juliet some spaghetti if he had more than 35 units of spaghetti.
D)Juliet would want to give Romeo some spaghetti if she has more than 48 units.
E)Juliet would want to give Romeo some spaghetti if she has more than 50 units of spaghetti.

Question 7

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?

A)Candidate x.
B)Candidate y.
C)Candidate z.
D)There is a tie between x and y, with z coming in third.
E)There is a tie between y and z, with x coming in third.

Question 8

Suppose that Paul and David 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

A)A_D =A_P and O_D +O_P.
B)8A_P + 2O_P is at least 80 and 2A_D + 10O_D is at least 96.
C)4A_P + O_P is at least 80 and 2A_D + 5O_D is at least 96.
D)A_D + O_D is at least 16 and A_S + O_S is at least 16.
E)4A_P +O_P is at least A_D + 5O_D and A_D +5O_D is at least 4A_P + O_P.

Question 9

Suppose that Paul and David 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)A_D = A_P and O_D + O_P.
B)6A_P + 2O_P is at least 50 and 2A_D + 4O_D is at least 50.
C)3A_P+ O_P is at least 50 and 2A_D + 2O_D is at least 50.
D)A_D + O_D is at least 15 and A_S + O_S is at least 15.
E)3A_P + O_P is at least A_D + 2O_D and A_D + 2O_D is at least 3A_P + O_P.

Question 10

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 23 voters.3 voters rank the candidates x first, y second, and z third; 5 voters rank the candidates x first, z second, and y third; 10 rank the candidates z first, y second, and x third; and 5 voters rank the candidates y first, z second, and x third.Which candidate wins?

A)Candidate x.
B)There is a tie between x and y, with z coming in third.
C)Candidate z.
D)Candidate y.
E)There is a tie between y and z, with x coming in third.

Question 11

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?

A)Candidate y.
B)There is a tie between x and y, with z coming in third.
C)Candidate z.
D)Candidate x.
E)There is a tie between y and z, with x coming in third.

Question 12

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)the child in city B 1.50 times as much money as the child in city A.
B)the child in city A 3 times as much money as the child in city B.
C)the child in city B 3 times as much money as the child in city A.
D)each child $500, even though this will buy less goods for the child in city B.
E)the child in city A 1.50 times as much money as the child in city B.

Question 13

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)Candidate x.
B)Candidate z.
C)There is a tie between x and y, with z coming in third.
D)Candidate y.
E)There is a tie between y and z, with x coming in third.

Question 14

Suppose that Romeo has the utility function U = S ⁸_RS⁴_J and Juliet has the utility function U = S⁴_RS ⁸_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.

A)Romeo would want to give Juliet some spaghetti if he had more than 60 units of spaghetti.
B)Juliet would want to give Romeo some spaghetti if she has more than 78 units.
C)Romeo and Juliet would never disagree about how to divide the spaghetti.
D)Romeo would want to give Juliet some spaghetti if he has more than 76 units of spaghetti.
E)Juliet would want to give Romeo some spaghetti if she has more than 80 units of spaghetti.

Question 15

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

A)the child in city B 3 times as much money as the child in city A.
B)each child $1,000, even though this will buy less goods for the child in city B.
C)the child in city A 3 times as much money as the child in city B.
D)the child in city B 1.50 times as much money as the child in city A.
E)the child in city A 1.50 times as much money as the child in city B.

Question 16

Suppose that Romeo has the utility function U = S ⁶_RS⁴_J and Juliet has the utility function U = S⁴_RS ⁶_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)Romeo would want to give Juliet some spaghetti if he had more than 35 units of spaghetti.
B)Juliet would want to give Romeo some spaghetti if she has more than 40 units.
C)Romeo and Juliet would never disagree about how to divide the spaghetti.
D)Romeo would want to give Juliet some spaghetti if he has more than 38 units of spaghetti.
E)Juliet would want to give Romeo some spaghetti if she has more than 42 units of spaghetti.

Question 17

Suppose that Paul and David 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

A)5A_P + O_P is at least 94 and 2A_D + 3O_D is at least 58.
B)A_D = A_P and O_D + O_P.
C)A_D + O_D is at least 15 and A_S + O_S is at least 15.
D)10A_P + 2O_P is at least 94 and 2A_D + 6O_D is at least 58.
E)5A_P + O_P is at least A_D + 3O_D and A_D + 3O_D is at least 5A_P + O_P.

Question 18

Suppose that Romeo has the utility function U = S ³_RS¹_J and Juliet has the utility function U = S¹_RS ³_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)Romeo and Juliet would never disagree about how to divide the spaghetti.
B)Romeo would want to give Juliet some spaghetti if he had more than 18 units of spaghetti.
C)Juliet would want to give Romeo some spaghetti if she has more than 25 units.
D)Romeo would want to give Juliet some spaghetti if he has more than 23 units of spaghetti.
E)Juliet would want to give Romeo some spaghetti if she has more than 27 units of spaghetti.

Question 19

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

A)the child in city B 1.50 times as much money as the child in city A.
B)the child in city A 3 times as much money as the child in city B.
C)the child in city B 3 times as much money as the child in city A.
D)each child $2,000, even though this will buy less goods for the child in city B.
E)the child in city A 1.50 times as much money as the child in city B.

Question 20

Suppose that Paul and David 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)10A_P + 2O_P is at least 84 and 2A_D + 6O_D is at least 56.
B)5A_P + O_P is at least 84 and 2A_D + 3O_D is at least 56.
C)A_D + O_D is at least 14 and A_S + O_S is at least 14.
D)A_D + A_P and O_D + O_P.
E)5A_P + O_P is at least A_D + 3O_D and AD + 3O_D is at least 5A_P + O_P.

Question 21

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /32 and McCoy's utility is U = W_M - W²_H /32, 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

A)16 gallons and spill 20 gallons in the creek.
B)20 gallons and spill the rest in the creek.
C)8 gallons and spill 36 gallons in the creek.
D)26 gallons.
E)4 gallons and spill the rest in the creek.

Question 22

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /8 and McCoy's utility is U = W_M - W ²_H /8, 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

A)24 gallons.
B)2 gallons and spill 44 gallons in the creek.
C)4 gallons and spill 40 gallons in the creek.
D)8 gallons and spill the rest in the creek.
E)1 gallon and spill the rest in the creek.

Question 23

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /32 and McCoy's utility is U = W_M - W²_H /32, 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

A)8 gallons and spill 66 gallons in the creek.
B)16 gallons and spill 50 gallons in the creek.
C)41 gallons.
D)20 gallons and spill the rest in the creek.
E)4 gallons and spill the rest in the creek.

Question 24

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /16 and McCoy's utility is U = W_M - W²_H /16, 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)8 gallons and spill 50 gallons in the creek.
B)33 gallons.
C)12 gallons and spill the rest in the creek.
D)4 gallons and spill 58 gallons in the creek.
E)2 gallons and spill the rest in the creek.

Question 25

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /8 and McCoy's utility is U = W_M - W ²_H /8, 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

A)24 gallons.
B)4 gallons and spill 40 gallons in the creek.
C)2 gallons and spill 44 gallons in the creek.
D)8 gallons and spill the rest in the creek.
E)1 gallon and spill the rest in the creek.