4. Harry\'s relationship between Utility(U) and income (Y) is represented in the

Question

4. Harry's relationship between Utility(U) and income (Y) is represented in the table below U(Y) 36 40 46 54 64 76 90 106 Y 10 12 14 16 's utility function with Y on horizontal axis and U(Y) on the vertical axis using the graph (a) Draw Harry (b) Suppose Harry is offered a gamble where with probability 0 (c) Is Harry Risk Neutral/ Risk averse/ Risk Loving? Explain. paper What is the expected utility(EU) associated receive 14. What is the expected value (EY) of this bet with the bet? in (a) approximate how much Harry would need to be paid/ pay to avoid the bet. Explain your answer

Explanation / Answer

The total utility of wealth is the satisfaction one gets from wealth. The marginal utility is the incremental utility that a person gets with each increasing unit of wealth. Insurance policy can be sold only in circumstances where there is diminishing marginal utility of wealth or income. This happens when the person is risk averse. With constant marginal utility of wealth, requiring them to pay actuarially fair premiums would leave them no better off than if they were uninsured.

For a risk averse person the disutility of losing money may exceed the utility of winning a similar amount. That is utility of an extra dollar of extra dollar of wealth is worth more if she has less money that the utility of an extra dollar if she has more. The utility from an extra dollar is called the marginal utility hence for a risk averse person the marginal utility will be decreasing. For a risk lover person the marginal utility of wealth increases with each increamental dollar and it is constant for risk neutral.

The MU for this person is given in the table below

Therefore, as the MU increases with each increamental dollar, the person is risk lover.

===============================================================

d)

The wealth that the person is need to be paid /pay is his certainty equivalant. It is the wealth associated with his expected utility. His expected utility is 68. This is associated with the income of $11. Then his certainty equivalant is $11. The person will not gamble if given $11 for sure.

Y U(Y) MU 2 36 4 40 2 6 46 3 8 54 4 10 64 5 12 76 6 14 90 7 16 106 8

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.