Exam 32: A: Welfare

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?

Suppose that Paul and David from Problem 7 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

Suppose that Romeo in Problem 8 has the utility function U = S⁵_RS²_J and Juliet has the utility function U = S²_RS⁵_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.

Suppose that Romeo in Problem 8 has the utility function U = S⁵_RS²_J and Juliet has the utility function U = S²_RS⁵_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 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