Martin\'s utility (U) depends on his wealth (w) in the following way. He has wea
ID: 1190410 • Letter: M
Question
Martin's utility (U) depends on his wealth (w) in the following way. He has wealth of 0 units with probability 0.20 and wealth of 10 units with probability of 0.80. He therefore has utility of 0 with probability 0.20 and utility of 100 with probability of 0.80. Calculate Martin's expected utility. Plot Martin's utility as a function of wealth. Suppose Martin could purchase insurance that guaranteed Martin wealth of 10 units. With probability 0.8 Martin has wealth 10 and the insurer pays nothing. But with probability 0.2 Martin has wealth 0 and the insurer pays Martin 10. Show that the actuarially fair premium for this policy is 2 units. It follows that if Martin purchased this insurance he would have certain wealth of 8 units (the 10 units guaranteed less the premium of 2). Would Martin be willing to purchase this insurance policy? Explain your answer. There is enough information given in this question to give an unambiguous yes or no answer.Explanation / Answer
(a) Expected utility = 0.8 × u(10) + 0.2 × u(0) = (0.8 × 100) + (0.2 × 0) = 80
(b) The following figure plots utility as a function of wealth, such that the vertical axis represents utility and the horizontal axis represents wealth.
(c) Actuarially fair premium is defined as the expected loss of the insurer.
Actuarially fair premium = Expected loss of the insurer = (0.8 × 0) + (0.2 × 10) = 2
(d) In case Martin buys the insurance, his utility will be 96, as the utility of having 8 units of certain wealth is 96.
The expected utility of wealth without insurance is 80, as calculated in part (a).
Since the utility in case insurance policy is bought is greater than the expected utility of weaith without insurance, Martin would be willing to purchase the insurance policy
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.