Question

Carol has annual income of $50,000 when healthy and there is a 10% chance that she will experience an accident. If she suffers an accident, it will cost her $20,000 in medical expenses.

a. If Carol’s utility function is U=y^0.5, what is the most she would be willing to pay for an insurance policy that would cover all her medical costs when they occur.

b. If Carol’s utility function is instead U=Y^0.1, what is the most she would be willing to pay for an insurance policy that would cover all her medical costs when they occur. How did your answer change? Provide an intuitive explanation for why this value changed the way it did when the utility function changed

Answer 1

A) the maximum amount, willing to pay for full insurance

= Initial wealth - certainty equivalent ( CE)

Now EU = .9*U(50,000) + .1*U( 30,000)

Now wealth in good state = 50,000, with probability =.9

In bad state = 50,000-20,000

= 30,000

So EU = .9*√50,000 +.1*√30,000

= 218.567

.

Now for CE:

√CE = EU

CE = (218.567)²

= 47,771.37

now Maximum WTP = 50,000 - 47,771.37

= $ 2228.63

b) U = Y ^.1

now new EU

= .9*(50,000)^.1 + .1*(30,000)^.1

= 2.9358

So, for CE

CE ^.1 = EU

CE = (2.9358)¹⁰

= 47,565.076

Thus maximum WTP = 50,000 - 47,565.076

= $ 2434.923

thus the amount willing to pay has increased,

• a concave utility function exhibits risk averse behaviour

• the more is the utility function concave, the more risk averse, the individual will be

So utility function in part b) is more bowed , hence more risk averse behaviour is exhibited as compared to a)

So being more risk averse, imply that more amount is willing to pay, to get full insurance