A consumer’s utility of income is given by the function ??(. ). The consumer has initial...

A consumer’s utility of income is given by the function ??(. ). The consumer has initial income $??, but risks losing $?? with probability ??. If a company offers insurance, the contract consists of coverage $?? at price $?? per dollar of coverage.

(a) Using the notation above, what is the consumer’s expected utility with insurance?

(b) Define actuarially fair insurance. What are the sufficient assumptions for insurance to be actuarially fair?

(c) Prove that, if insurance is actuarially fair, the consumer will demand full insurance coverage: ??∗ = ??.

(d) Prove that, if insurance charges a loading factor $??, such that ?? = ?? + ??, the consumer will demand less than full insurance: ??∗ < ??.

Expert Solution

Rahul Sunny answered 2 years ago

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