Exam 34:Welfare-Part A

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

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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

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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.

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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.

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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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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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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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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 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

(Multiple Choice)
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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

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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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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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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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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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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.

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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.

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Suppose that Romeo has the utility function U = S 5RS1J and Juliet has the utility function U=S1RS5J,where SR is Romeo's spaghetti consumption and SJ is Juliet's.They have 48 units of spaghetti to divide between them.

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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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