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 M1/2 N13C1/6. 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

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 receive from sale proceeds of house,

                                     N= Income that my nephew will receive and

                                     C= Income that I shall donate to charity

Here coefficients of M,N and C are 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 receive (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

b) Income tax on total money that I receive from sale of my house= 50%

Therefore, net income I shall keep for myself after deducting taxes from sale of the house = 600000*.50= $300000

Net income that I shall give to my nephew after deducting taxes = 400000*.60= $240000

Net income that I shall give to charity after deducting taxes = 200000*.50= $100000