Question #65972

Sita expects her future earnings to be worth rs. 100. If she falls ill, her expected future earning will be rs 25. There is a belief that she may fall ill with probability of 2/3 while the probability of remaining in good health is 1/3 . Let her utility function be given as U(y)=Y1/2. Suppose that an insurance company offers to fully insure sita against loss of earnings caused by illness against an actuarially fair premium.
(a) Will sita accepts the insurance. Explain.
(b) What is the maximum amount that sita would pay for the insurance?

Expert's answer

Future earnings - Rs. 100, p = 1/3

If she falls ill - Rs. 25, p = 2/3

U(y) =y1/2

(a) Sita may accept the insurance, if the probability of illness is too high and the insurance payment is affordable. As p = 2/3, Sita will accept the insurance.

(b) The maximum amount that Sita would pay for the insurance can be calculated according to probabilities:

i(max) = 100*1/3 + 25*2/3 = 33.33 + 16.67 = 50

If she falls ill - Rs. 25, p = 2/3

U(y) =y1/2

(a) Sita may accept the insurance, if the probability of illness is too high and the insurance payment is affordable. As p = 2/3, Sita will accept the insurance.

(b) The maximum amount that Sita would pay for the insurance can be calculated according to probabilities:

i(max) = 100*1/3 + 25*2/3 = 33.33 + 16.67 = 50

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