Question

1, 2, assume that the individual`s utility function is given by:

$Dp8d0wf21Da-B2oSNg05W_GlfeLrWW6jSbK0hcTq$

1. An individual with an income of 1000 is considering the purchase of a risky asset for $250. There is a 40% chance the asset will earn $1000 and a 60% chance it will be worthless.

1. Will the individual purchase this asset?

2. What is the cost of risk for this individual if the asset is purchased?

3. How much will the cost of risk be if a 2nd identical person is brought in to help purchase the asset?

2. Another individual is considering purchasing insurance to protect his or her home from a potential flood. There is a 20% chance of a flood. If the flood occurs, it will cost $25,000 to repair the damage. The individual begins with $60,000 in income.

1. If the individual is offered insurance at a price of $5000, will he or she purchase it?

2. What is the maximum this individual would be willing to pay for insurance?

3. Repeat part b) for damages of $5000 and $50000. Explain the different prices in the context of a risk averse individual.

Answer 1

Solution: Given U = UI W income = 1000 risky offet = 8250 = 40.3. Ceara $1000) = 60.4 (worthless @ Individual purchase this affet or not: ECx) = (cooo +100 – 250) *0.4+ (100d – 250) *0.61 = $1150 : utility from the cement wealth is 1000? = 3116] and from the risky asset is (1150) 12 = (33.9. greater, since the utility from buying affet is he will buy the affet. cost of risk for this individual is affect is purchased; → it is the expected logs. Cies ECL) = 0.4 61000-250) +0.6(250) =1150]

© cost of risk be it and identical person is brought into help purchase the affet: It will remain unchanged. [ (2) Giren o=FI flood - 20-1. Chance repair = 825,000 income = $ 60,000 @ Individual is offered insurance at a price of $ 5000, enchale or not will purchase or not: go to chance of flood = p=0.2 ECX) = 0.9 (G0000 – 25000) +0.8 (80ooo) = 0.2 (35000) +0.8Goooo) = 7000 + 48000 = (55000] ECL) = 0:2 (25000) + 0.8(0) = 5200

If individual is offered insurance at price of $5000, he will purchase it since the actuarially fair premium is the expected loss and here both are same. (b) maximam the individual would be willing to pay for insurance is : The most the one can pay for the insurance is the difference between the initial wealth and certainity Equivalent. Here the certainty equivalent income is the certain amount of income that gives the same expected utility to the onsures of his oncertain income. utility in case of geflood = (6oooog's = 244.94 In case of floud = (60000 – 25000)'!2 - (35000)005 = 187,08

Expecfed utility = 60.2) (187.08) +0.8) (R44.99 = 37.416 +195-952 • 0 = 933 368 Certainity equivalent is given af 233.368 = (1) 0.5 ". ID 54460.6234 Hence may ant of infurance paying = 6000-54460 = SJ40 @ for damage of $5000 and 850000 the different prices in context of risk querse individual: → If damage is '50000, wilty in case of pfo flood - C60000)0:5 = qu4.94 If flood = ( 60000-50000305 = (10000) 05 = 100 Expected utility = (-a) (100) + (0.8) (244.99) = 20+ 1951952 U = 215.952

Certainity equivalent is given as: 215.952 = (I) 0.5 :. I = 46635.2663 ?: max amt of insurance will be paying = 60000 4.6635 = 13365) max amit of insurance i. As amount of damase increase also rises - o