6) Suppose that an individual makes an income of y = $50,000. There is a probability, p that an accident will occur which will cost a = $20, 000, and %3D with probability (1 – p) the accident doesn't occur at there is no cost to the individual. The individual can purchase insurance I at a cost of $10,000 and if they do the insurance company will reimburse them for 75% of the cost of the accident. The individual is deciding whether or not to purchase the insurance. a) Consider the case where the individuals utility is given by U(net income) = p (net income with accident)+(1-p)(net income without accident) %3D Solve for the value of p that the consumer is indifferent between buying and not buying insurance. In words describe what the implications of your value of p are. b) Now suppose the individuals utility is given by U (net income) = pln [(net income with accident)]+(1–p)ln [(net income without accident)] Again solve for the value of p. How does it differ from the case in a). What is the intuition behind the result?

6) Suppose that an individual makes an income of y = $50,000. There is a probability, p that an accident will occur which will cost a = $20, 000, and %3D with probability (1 – p) the accident doesn't occur at there is no cost to the individual. The individual can purchase insurance I at a cost of $10,000 and if they do the insurance company will reimburse them for 75% of the cost of the accident. The individual is deciding whether or not to purchase the insurance. a) Consider the case where the individuals utility is given by U(net income) = p (net income with accident)+(1-p)(net income without accident) %3D Solve for the value of p that the consumer is indifferent between buying and not buying insurance. In words describe what the implications of your value of p are. b) Now suppose the individuals utility is given by U (net income) = pln [(net income with accident)]+(1–p)ln [(net income without accident)] Again solve for the value of p. How does it differ from the case in a). What is the intuition behind the result?

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter16: Information, Risk, And Insurance

Section: Chapter Questions

Problem 11RQ: What is an actuarially fair insurance policy?

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Question

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6) Suppose that an individual makes an income of y = $50, 000. There is a
probability, p that an accident will occur which will cost a =
$20, 000, and
with probability (1 – p) the accident doesn't occur at there is no cost to the
individual. The individual can purchase insurance I at a cost of $10,000 and
if they do the insurance company will reimburse them for 75% of the cost
of the accident. The individual is deciding whether or not to purchase the
insurance.
a) Consider the case where the individuals utility is given by
U(net income) = p (net income with accident)+(1-p)(net income without accident)
Solve for the value of p that the consumer is indifferent between buying and
not buying insurance. In words describe what the implications of your value
of p are.
b) Now suppose the individuals utility is given by
U (net income)
pln (net income with accident)]+(1-p)ln [(net income without accident)]
Again solve for the value of p. How does it differ from the case in a). What
is the intuition behind the result?

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