Deck 34: A: Welfare

Question 1

Suppose that Paul and David have utility functions U = 4A 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 18 apples and 18 oranges.The fair allocations consist of all allocations satisfying the following conditions.

A) A_D + A_P and O_D + O_P.
B) 8A_P + 2O_P is at least 90 and 2A_D +6O_D is at least 72.
C) 4A_P +O_P is at least 90 and 2A_D +3O_D is at least 72.
D) A_D + O_D is at least 18 and A_S +O_S is at least 18.
E) 4A_P + O_P is at least A_D +3O_D and A_D +3O_D is at least 4A_P + O_P.

Answer 1

8A_P + 2O_P is at least 90 and 2A_D +6O_D is at least 72.

Question 2

A Borda count is used to decide an election between 3 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 14 voters.6 voters rank the candidates x first,y second,and z third;3 voters rank the candidates x first,z second,and y third;3 voters rank the candidates z first,y second,and x third;2 voters rank the candidates y first,z second,and x third.Which candidate wins?

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

Answer 2

Candidate x.

Question 3

Suppose that Romeo has the utility function U =S⁵_RS²_J and Juliet has the utility function U =S¹_RS⁵_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 would want to give Juliet some spaghetti if he had more than 18 units of spaghetti.
B) Juliet would want to give Romeo some spaghetti if she had more than 28 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 had more than 26 units of spaghetti.
E) Juliet would want to give Romeo some spaghetti if she had more than 30 units of spaghetti.

Answer 3

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

Question 4

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 orange.The total supply of apples and oranges to be divided between them is 20 apples and 14 oranges.The "fair" allocations consist of all allocations satisfying the following conditions.

A) 4A_P+O_P is at least 94 and 2A_D+5O_D is at least 90.
B) A_D + O_D is at least 17 and A_S +O_S is at least 17.
C) A_D + A_P and O_D + O_P.
D) 8A_P + 2O_P is at least 94 and 2A_D +10O_D is at least 90.
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 5

If allocation x is Pareto optimal and allocation y is not,then everyone is at least as well off with x as with y,and someone is better off with x than with y.

Question 6

A Borda count is used to decide an election between 3 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 29 voters.10 voters rank the candidates x first,y second,and z third;3 voters rank the candidates x first,z second,and y third;8 voters rank the candidates z first,y second,and x third;8 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 7

A parent has two children living in cities with different costs of living.The cost of living in city B is 4 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 $12,000.The parent wants to give a total of $1,000 to her two children.Her utility function is U(C A,C B)= C A C 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 $500,even though this will buy less goods for the child in city B.
B) the child in city B 4 times as much money as the child in city A.
C) the child in city A 4 times as much money as the child in city B.
D) the child in city B 2 times as much money as the child in city A.
E) the child in city A 2 times as much money as the child in city B.

Question 8

In a pure exchange economy if the initial allocation is Pareto optimal,then competitive equilibrium is fair.

Question 9

An allocation that is worse for somebody than the initial allocation cannot be Pareto optimal.

Question 10

A Borda count is used to decide an election between 3 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 28 voters.5 voters rank the candidates x first,y second,and z third;10 voters rank the candidates x first,z second,and y third;4 voters rank the candidates z first,y second,and x third;9 voters rank the candidates y first,z second,and x third.Which candidate wins?

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

Question 11

An allocation is fair if whenever one person envies another,the envied person does not envy the envier.

Question 12

Mr.Angst has two children,Dick and Jane.Dick is a slow learner and Jane is very bright.If Mr.Angst spends $X per month on Dicks education,Dick will score a total of X/2 points on his SAT tests.If Mr.Angst spends $Y per month on Janes education,she will score a total of 2Y on her SAT tests.Mr.Angst has a utility function U(D,J)=min{D,J},where D is Dicks SAT score and J is Janes SAT score.To maximize his utility,he will spend

A) equal amounts of money on the two children.
B) 4 times as much money on Dick's education as on Jane's.
C) 4 times as much money on Jane's education as on Dick's.
D) between 1 and 2 times as much money on Dick's education as on Jane's.
E) between 1 and 2 times as much money on Jane's education as on Dick's.

Question 13

Suppose that Paul and David have utility functions U = 4A P + O P and U = A D + 4O 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 20 apples and 12 oranges.The fair allocations consist of all allocations satisfying the following conditions.

A) A_D +A_P and O_D + O_P.
B) 8A_P + 2O_P is at least 92 and 2A_D +8O_D is at least 68.
C) 4A_P + O_P is at least 92 and 2A_D +4O_D is at least 68.
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 + 4O_D and A_D +4O_D is at least 4A_P+ O_P.

Question 14

According to Arrow's impossibility theorem,it is impossible to find a social ordering that is complete,reflexive,and transitive.

Question 15

The utility possibilities frontier is the boundary of the production possibilities set.

Question 16

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 $2,000 to her two children.Her utility function is U(C A,C B)= C A C 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 $1,000,even though this will buy less goods for the child in city B.
B) the child in city B 3 times as much money as the child in city A.
C) the child in city B 1.50 times as much money as the child in city A.
D) the child in city A 3 times as much money as the child in city B.
E) the child in city A 1.50 times as much money as the child in city B.

Question 17

In a pure exchange economy,if an allocation is Pareto efficient,it is impossible to have two people who prefer each other's consumption bundles to their own.

Question 18

If a social welfare function is an increasing function of each person's utility,then every allocation that maximizes this social welfare function must be a Pareto optimum.

Question 19

In a competitive equilibrium,no matter how different their preferences may be,no two people with the same income will envy each other's consumption bundles.

Question 20

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

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 / 40 and McCoy's utility is U = W_M -W ²_H / 40,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 60 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) 30 gallons.
B) 20 gallons and spill 20 gallons in the creek.
C) 24 gallons and spill the rest in the creek.
D) 10 gallons and spill 40 gallons in the creek.
E) 5 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 28 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) 14 gallons.
B) 4 gallons and spill 20 gallons in the creek.
C) 2 gallons and spill 24 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 / 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 58 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) 2 gallons and spill 54 gallons in the creek.
B) 4 gallons and spill 50 gallons in the creek.
C) 29 gallons.
D) 8 gallons and spill the rest in the creek.
E) 1 gallon and spill the rest in the creek.

Question 24

Suppose that Romeo has the utility function U = S ⁵_RS¹_J and Juliet has the utility function U=S¹_RS⁵_J,where S_R is Romeo's spaghetti consumption and S_J is Juliet's.They have 48 units of spaghetti to divide between them.

A) Juliet would want to give Romeo some spaghetti if she had more than 38 units.
B) Romeo would want to give Juliet some spaghetti if he had more than 24 units of spaghetti.
C) Romeo and Juliet would never disagree about how to divide the spaghetti.
D) Romeo would want to give Juliet some spaghetti if he had more than 36 units of spaghetti.
E) Juliet would want to give Romeo some spaghetti if she had more than 40 units of spaghetti.

Question 25

Suppose that Romeo has the utility function U = S ⁷_RS³_J and Juliet has the utility function U= S ³_RS⁷_J,where S_R is Romeo's spaghetti consumption and S_J is Juliet's.They have 60 units of spaghetti to divide between them.

A) Romeo would want to give Juliet some spaghetti if he had more than 30 units of spaghetti.
B) Romeo would want to give Juliet some spaghetti if he had more than 38 units of spaghetti.
C) Romeo and Juliet would never disagree about how to divide the spaghetti.
D) Juliet would want to give Romeo some spaghetti if she had more than 40 units.
E) Juliet would want to give Romeo some spaghetti if she had more than 42 units of spaghetti.