Expected utility preference with the utility function

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Consider a consumer with an income of 100 dollars. There are two possible states: A good state (G) and a bad state (B). In the good state, the consumer doesn't lose any money. In the bad state, the consumer loses 75 dollars. The probability that we will be in the good state is 0.98, and hence the probability that we are in the bad state is 0.02.

Suppose the consumer has an expected utility preference with the utility function u(m) = √ m. 4

(a) Suppose the consumer can purchase insurance coverage amount I, which will be paid to the consumer in the bad state. If the consumer purchases coverage amount I, then she will have to pay a premium γI to the insurance company. This payment must be made in both states. If the insurance is actuarially fair, what should be the value of γ?

(b) At the actuarially fair price, how much insurance coverage does the consumer purchase? How much income will the consumer have in each state?

(c) Now suppose γ = 0.03. How much insurance coverage does the consumer purchase? How much income will the consumer have in each state?

Reference no: EM132414731

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