Exam 32: Welfare-Part A

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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.

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

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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.

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

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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?

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Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = WH - W 2M / 8 and McCoy's utility is U = WM - W 2H / 8, where WH is Hatfield's whisky consumption and WM 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

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Suppose that Romeo has the utility function U = S5RS2J and Juliet has the utility function U = S1RS5J, where SR is Romeo's spaghetti consumption and SJ is Juliet's.They have 36 units of spaghetti to divide between them.

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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

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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.

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No one is meaner and uglier than Gladys.Someone is meaner and uglier than Harold.Therefore Gladys is meaner and uglier than Harold.Is this reasoning correct? If so, explain why.If not, explain why not.(Assume that people can be ranked from ugliest to least ugly by a complete transitive ordering and that there are no ties.Likewise assume that people can be ranked from meanest to least mean by a complete transitive ordering and that there are no ties.)

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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?

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Suppose that Romeo has the utility function U = S 7RS3J and Juliet has the utility function U = S 3RS7J, where SR is Romeo's spaghetti consumption and SJ is Juliet's.They have 60 units of spaghetti to divide between them.

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

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

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

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A tiny fishing village has 3 residents.Ann has a utility of 10, Bruce has a utility of 6, and Charlie has a utility of 7.If the mayor uses a Rawlsian social welfare function, the social welfare of this tiny village would be

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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?

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Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = WH - W 2M / 40 and McCoy's utility is U = WM - W 2H / 40, where WH is Hatfield's whisky consumption and WM 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

(Multiple Choice)
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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

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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

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