Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W)...

Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W) indicates the natural logarithm of wealth. What is the maximum amount this individual would pay for full insurance to cover a loss of $5,000 with probability 0.10?

Solutions

Expert Solution

If insurance if bought, the total wealth in any case 20000- X

in case insurance is not bought, then

-expected total wealth = expected wealth when loss happens + expected wealth when loss doesnt happen

= probability of loss* wealth at loss + probability of no loss* wealth at no loss

= 0.1 * (20000-5000) + 0.9 *20000

=19500

For him to buy insurance, utility of 20000 - X should be greater than 19500

=> ln(20000 - X) > ln(19500)

=> 20000 - X > 19500

=> X < 500

So 500 is the maximum premium that he will pay

keosha answered 2 years ago

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