Question

Understanding demand for health insurance is a key to formulating good health policy. In this

question you will model how much people are willing to pay for a health insurance plan. Here

are our starting assumptions:

- the consumer has an income of $49 next year

- if he gets sick he will have to pay $40 for medicine

- he has a 20% chance of getting sick

(a) Suppose your utility function is ?(?) = √? . Calculate the consumers expected utility

assuming he cannot buy any health insurance.

(b) What is the actuarially fair price for insurance for this consumer? (If you don’t have a

calculator just set up the equation you would solve.)

(c) Suppose a health insurance plan is offered that would cost $13 but cover any expenses in case

he got sick. Would the consumer buy the plan?

(d) Calculate the risk premium that the consumer is willing to pay for health insurance.

Answer 1

@ (b) Empected utility of wealths assuming he cannot buy health insurance: Wealth if he is Walthy = 49 Probability of being healther = 80% =0.8 Wealth in the is falls sikk-49-40-9 Probability of falling sick: 20.7. 20.2 Expected utility, E[u(w)] = b[Whentary). PChealtly) +V[wock']. Psick) => E[vew)] = (49)(0-8) + (v2)(0-2) = 6.2 Actuarially fair price is the price that ma zero profile for the insurance companies. => Actuarially fair price - Enpected costs, El ECC) - ČCosthealthy) EP Chealthy) + Costsick) • P(sick) = 20), (0.8) + (40) (0.2)=8 Actuarially fair price is $8 . Excpected utility wealies willwut ünsmance = 6.2 à Corresponding level of wealth = (6.23 = $38.44 ... He would accept any risk premium that would not tower his wealth from $49 to less than $38.44 sie he would lee willing to accept any risk premium dess than $48- $38.44 Consumer's risk premium - 49-38.44 = $10.56 since $13> $10.56 consenner will not way the insurance plan at the price of $13. Risk premiere consumer is willing to pay has been calculated in part (c). ::. Consumer's risk premium - $10.56