Question

Please Answer all questions and sub questions in a neat and organized fashion.

1. Nadine utility function is U(Y) = Y ^ (1/2), where Y is the anual income.

(A.) What is Nadines total utility with a $40,000 income?

(B.) Suppose there is a 20% chance that Nadine will have an injury that costs her all her income. Please calculate the EXPECTED UTILITY of income of Nadine facing this uncertainty.

(C.) Following B, ( the above question) what is the maxium premium that Nadine is willing to pay for a full coverage insurance policy?

Answer 1

1) U = Y^{​​​​​​0.5}

A) Y = 40000

Total utility =U = 40000^0.5 = 200

b) Expected utility = PU

P = Probability

U = Utility

Y = 40000

Probability of loosing = 20% = 0.2

Expected utility = 0.2*40000^0.5

EU = 0.2*200 = 40

3) Maximum premium = Probability of loss * Total income

Maximum premium = 0.2*40000 = 8000$