Question

I need help with part c & d!

Kisk Pooling Ollante Pobabilities of those outcomes used as J U U possible out 9 Spreoding the Spreading the risk of a payout over a lo group of people 2. Suppose that there are two possible states, completel of $80,000 if they remain completely healthy. H here are two possible states, completely healthy and ill. Consider an individual who has an income textbook and represents the total (actual) and expected wy remain completely healthy. Hint: The diagram below is similar to figure 7.4 on page 222 in your u represents the total (actual) and expected utility of income for this individual under uncertainty to a. Calculate the expected income for this in the expected income for this individual if the probability of illness is 10% where illness results in the Toss of 1 year's income (580,000). Label this amount on income (580,000). Label this amount on your diagram as Elyl). Calculate the expected utility for under these circumstances as well. Label this amount on your diagram as E(ul). Very briefly explain what these amounts represent. AU. (80) =1000 AUZ(O) = OU Pr=.9 Pz. Y, = 80.000 Ey=pi. Y, + P2 • Y₂ Because I live in a :980.000+ (-10) World of uncertianty. "Ey = 72,000 My best guess for now moch my income will be is $72,000 + my best 6.9.100) +(1:0) guess for how much my Utilities will be is 900 EU ={P.•AU.) + (P2 - AU, Y₂=0 [EU =90

Answer 1

Ansewring part c. and d. as you asked

c. The most amount of money this individual would be willing to pay for insurance coverage will be equal to $20,000. Since the person is indifferent between a guaranteed income of $60,000 and an expected income of $72,000(With a 90% chance of $80,000 and a 10% chance of 0 income), he would be willing to pay atmost 20,000$ out of his income of $80,000 to get a guaranteed income of $60,000 and avoid the second scenario. He will not pay more than 20,000$ as then his guaranteed income will reduce from 60,000$ and his utility will go below 90(As seen in the last pic) which is what it would have been in both the previous cases(guaranteed income of $60,000 on the total utility line or expected utility of $72,000 on the expected utility line)

d. Relative to the situation described, the person would be willing to pay more for for insurance coverage if the probability of illness were higher. Let's say the probability of illness was 20%, the expected income will be 0.8*80,000+0.2*0=$64,000 and its expected utliity along the expected utility will be at 80(Since it's linear). This will coincide with a point on the total utility curve with a guaranteed income of less than $60,000, let's say $45,000 (This is just an example, I can't predict this from the graph and it's not linear either) so he would be willing to pay 80,000-45,000=35,000$ for the insurance coverage to get a guaranteed income of 45,000$ if the probability of illness were higher.

Hope it's clear. Do ask for any clarifications required.