A parent has two children named A and B and she loves both of them equally. She has a total of $1,000 to give to them.
(a) The parent’s utility function is U(a, b) = √a + √b, where a is the amount of money she gives to A and b is the amount of money she gives to B. How will she choose to divide the money?
(b) Suppose that her utility function is U(a, b) = −1/a – 1/b . How will she choose to divide the money?
(c) Suppose that her utility function is U(a, b) = loga + logb. How will she choose to divide the money?
(d) Suppose that her utility function is U(a, b) = min{a, b}. How will she choose to divide the money?
(e) Suppose that her utility function is U(a, b) = max{a, b}. How will she choose to divide the money?
(f) Suppose that her utility function is U(a, b) = a2 + b2. How will she choose to divide the money between her children? Explain why she doesn’t set her marginal rate of substitution equal to 1 in this case.