Question: A consumer has initial wealth $100 and is facing risk of losing it with probability 20%. An insurance company offers to fully cover the risk

A consumer has initial wealth $100 and is facing risk of losing it with probability 20%. An insurance company offers to fully cover the risk with the price of such insurance option $25.

(a) Will the consumer with utility u(x)=−e^−0.01x purchase the insurance?

(b) Will the consumer with utility u(x)=−e^−0.005x purchase the insurance? If the answer is different from (a), explain why.

(c) For both of the cases in (a) and (b), derive the maximum possible price of insurance that such consumer purchases the insurance option (find the price with which the consumer is indifferent between buying insurance and not buying it). How does this price depend on absolute risk aversion? Provide intuition.

(d) Calculate the risk premium for both consumers.

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Weath W 100 Probability of losing all wealth p 20 02 Price of insurance I 25 Part a Ux e 001x Let us consider the case when the consumer doesnt buy in... View full answer

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