ONLY CASE 3 PLEASE
All questions in this homework assignment are based on the following information about a donor (person 1), who is considering giving money to a recipient (person 2). The donor has the following utility function: 4 = a + m + bm + 2x95 where m;: total money received by person i from all sources x,: amount of donor's endowment allocated to person i 1;: person i's endowment, 1 = x2 + x2 = 145, 12 = 5 a, b, c > 0: fixed parameters The sections below correspond to different cases involving different values for the fixed parameters of the donor's utility function and refer to the donor's optimization problem under these differing assumptions. Assume m = x, except where otherwise indicated. Case 1: a=6, b = 2, c= 0 1. What kind of preferences does the donor have (what is this case called)? 2. What is the donor's marginal utility from keeping money du, / dx, (express in terms of x,)? Hint: first use substitution so as to express u, as a function of xy, and then take the derivative. 3. What is the donor's marginal utility from giving money to the recipient du / dx, ? 4. What is the donor's optimal gift to the recipient, x i.e., what gift maximizes the donor's utility)? Case 2: a = 0.5 = 2, c = 0 5. What kind of preferences does the donor have (what is this case called)? 6. What is the marginal utility from keeping money (express in terms of x,)? 7. What is the marginal utility from giving money (express in terms of x)? 8. What is the optimal gift to the recipient, x;? Case 3: a = 6, h = 2, c=3 9. What is this case called? 10. What is the marginal utility from keeping money (express in terms of x;)? 11. What is the marginal utility from giving money (express in terms of X, )? Case 4:96.bc=0 12. What is this case called? 13. What is the marginal utility from keeping money (express in terms of x)? 2 All questions in this homework assignment are based on the following information about a donor (person 1), who is considering giving money to a recipient (person 2). The donor has the following utility function: 4 = a + m + bm + 2x95 where m;: total money received by person i from all sources x,: amount of donor's endowment allocated to person i 1;: person i's endowment, 1 = x2 + x2 = 145, 12 = 5 a, b, c > 0: fixed parameters The sections below correspond to different cases involving different values for the fixed parameters of the donor's utility function and refer to the donor's optimization problem under these differing assumptions. Assume m = x, except where otherwise indicated. Case 1: a=6, b = 2, c= 0 1. What kind of preferences does the donor have (what is this case called)? 2. What is the donor's marginal utility from keeping money du, / dx, (express in terms of x,)? Hint: first use substitution so as to express u, as a function of xy, and then take the derivative. 3. What is the donor's marginal utility from giving money to the recipient du / dx, ? 4. What is the donor's optimal gift to the recipient, x i.e., what gift maximizes the donor's utility)? Case 2: a = 0.5 = 2, c = 0 5. What kind of preferences does the donor have (what is this case called)? 6. What is the marginal utility from keeping money (express in terms of x,)? 7. What is the marginal utility from giving money (express in terms of x)? 8. What is the optimal gift to the recipient, x;? Case 3: a = 6, h = 2, c=3 9. What is this case called? 10. What is the marginal utility from keeping money (express in terms of x;)? 11. What is the marginal utility from giving money (express in terms of X, )? Case 4:96.bc=0 12. What is this case called? 13. What is the marginal utility from keeping money (express in terms of x)? 2
