Suppose a farmer's utility function is u(x) = x. The farmer faces a 50% chance of having a bad year in which her revenue is $2 and a 50% chance of a good year in which her revenue is $10. The farmer's costs are $2 in every year.

(a) How much would the farmer be willing to pay for insurance that paid him $8 in the event of a bad year? (5 marks)

(b) Suppose an insurance company offered the farmer an actuarially fair insurance contract that paid $4 in the event of a bad year.

i. What would the actuarially fair price of insurance be? (5 marks)

ii. Now assume that the farmer could increase the probability of a good year by 10% by applying an extra $1 of fertilizer.

A. Suppose the insurance company could monitor fertilizer use - what would be the actuarially fair price of the $4 insurance if the farmer used the fertilizer? (5 marks)

B. If the company could not monitor fertilizer use - would the farmer use fertilizer when she is insured? Is moral hazard an issue in this contract? (5 marks)