3) (16 points) Lynn has a utility function U(W)-wa, where W is the amount of wea

Question

3) (16 points) Lynn has a utility function U(W)-wa, where W is the amount of wealth that she has. Lynn has two assets. She has $40,000 in a bank account, and she has a house worth $600,000, so her total wealth is initially S640-000. There is a 2% chance that her house is destroyed by a fire. a) Considering the probability that there is a fire, what is Lynn's Expected Wealth, E(Wy? E(W)= b) What is Lynn's Expected Utility, E(U)? E(U) = c) What is Lynn's Certainty Equivalent? d) How much would Lynn be willing to pay for fire insurance?

Explanation / Answer

a) E(w)= 0.02(600,000) + 0.98(640,000) = 12000+ 627200= $639,200

b) E(U) = 0.02(600,000)1/2 + 0.98(640,000)1/2 = 15.5 + 784 = 799.5

c) U = W1/2

799.5 = W1/2

W = 639,200.25 = C.E

d) WTP = Initial wealth - CE

WTP= 640000-639200.25 = $799.75

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