Question

4) My great-uncle died. In his will, he asked me so sell his house in Beverly Hills and share the proceeds with his nephew and with his favorite charity. Of course I care about myself but I also care about his nephew and about charity; if I receive M and the nephew receives N and charity receives C, I will derive utility M1/2N1/3C1/6. I sell the house for $1.2 Million (a) How much money should I keep for myself, how much should I give to the nephew and how much should I give to charity? (b) I forgot that I have to pay income tax of 50% on all the money I receive and the nephew has to pay income tax of 40% on all the money he receives. (I live in California and he lives in Nevada, so I have to pay state income tax and he does not.) After taking taxes into account, how much money should I keep for myself, how much should I give to the nephew and how much should I give to charity? (Hint: What is the price of money I receive? What is the price of money the nephew receives? What is the price of money the charity receives?)

Answer 1

Given that (a) The total money received from sale of the house = $ 1.2 million = 1.2 * 1000000 = $ 1200000 My utility function is U = M^1/2 N^1/3 C^1/6 where M = income that I received scale proceeds of house N = income that may nephew will received and C = income that i shall donate to charity Here coefficient of M, N and care 1/2, 1/3, and 1/6 respectively Therefore the ratio of M, N and C = 1/2: 1/3: 1/6 = 3: 2: 1 The money that i should received (M) = 1200000 * 3/6 = $ 600000 The money that i should give to my nephew = 1200000 * 1/3 = $ 400000 The money that i should give to charity = 1200000 * 1/6 = $ 200000