Problem Set 6 Crop Insurance 1. Suppose a farmer's utility function is: U(income) = In (income) The farmer has a 200-acre farm and earns $500,000 when there is no hail (probability=85%) and $200,000 when there is hail (probability=15%). a. What is the actuarial fair price for insurance to indemnify the farmer 100% from hail losses? b. How much more utility does the farmer get from the availability of an actuarial fair policy? c. What is the amount the farmer would pay in premiums above actuarial fair amount for insurance (i.e calculate the risk premium)? 2. Suppose a farm has 160 acres of corn in one insured basic unit with an actual production history (APH) average yield of 170 bu/ac. a. If the farmer buys 80% Yield Protection (YP) crop insurance, what would be the per acre yield guarantee? What would be the yield guarantee for the whole 160 acre unit? b. If the farmer actually harvested 18,400 bushels from the unit (an average of 115 bu/ac), what would be the YP indemnity, assuming a 100% price election of $3.88/bu? c. If instead the farmer actually harvested 22,400 bushels from the unit (an average of 140 bu/ac) and sold the corn for $3.70/bu, what would be the YP indemnity, assuming a 100% price election of $3.88/bu? 3. Suppose a farm has 200 acres of soybeans in one insured unit with an actual production history (APH) average yield of 48 bu/ac and the Revenue Protection (RP) base price is $9.17/bu. a. If the farm buys 75% Revenue Protection crop insurance, what would be the initial per acre revenue guarantee? What would be the initial revenue guarantee for the 200 acre unit? b. What is the final per acre revenue guarantee and unit guarantee if the officially announced harvest price is $10.55/bu? What if the officially announced harvest price were $8.44/bu? c. Suppose the farm actually harvests 6,000 bushels from the unit (an average of 30 bu/ac). If the officially announced harvest price is $10.55/bu, what would be the RP indemnity