Exam 32: Welfare

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 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

Suppose that Romeo has the utility function U = S⁵_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.

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 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

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.

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is and McCoy's utility is , 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

Hatfield and McCoy burn with hatred for each other. They both consume corn whisky. Hatfield's utility function is and McCoy's utility is , 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