Question

The following table display uncertainty due to health in Tony's monthly income:

State Probability Income Utility

Sick 0.5 2,500 U(2,500)

Healthy 0.5 4,900 U(4,900)

Let Tony's utility function be U=Y^0.5, where Y is Tony's monthly income. Moreover, let E[Y] denote Tony's expected income and E[L] denote Tony's expected loss.

A. a). Tony's expected utility from income is given by

a. 62 b. 60.83 c. 60 d. none of the above

b). calculate the maximum amount that Tony is willing to pay (over and above his expected loss E[L]) for a health insurance policy, to avoid the risk of income loss resulting from becoming sick.

a. He is not willing to pay anything in addition to E[L] because he is not risk-averse

b. 100

c. 96

d. 92

Answer 1

Probability of falling sick=p=0.50

Income in case of falling sick=$2500

Utility in case of falling sick=U(2500)=2500^0.5=50

Probability of not falling sick=1-p=1-0.50=0.50

Income in case of falling sick=$4900

Utility in case of not falling sick=U(4900)=2500^0.5=70

A. Tony's expected utility from income is given by

Tony's expected utility=p*U(2500)+(1-p)*U(4900)=0.50*50+0.50*70=60 utils

Correct option is

c. 60

B)

Expected loss=E(L)=p*(Loss in case of being sick)=0.5*(4900-2500)=$1200

Let he is willing to a maximum sum of X towards insurance.

Expected utility in case of this insurance=U(4900-X)

Expected utility with insurance should be equal to expected utility in case of no insurance.

U(4900-X)=60

(4900-X)^0.50=60

4900-X=3600

X=1300

We can see that agent is willing to pay more than expected loss to avoid risk.

Risk Premium=X-E(L)=1300-1200=$100

Correct option is

b) $100