Question

. A corn farmer is considering two alternatives for selling his crop. The first is a contract where he can sell the rights to the future crop at planting. The second is to sell the crop after harvest. At harvest the farmer estimates that the price of corn will be $10 per bushel with probability 0.5 and $12 per bushel with probability 0.5. The farmer is averse to risk, and his benefit of avoiding the risk of damage to the crop while it is growing (e.g., from a tornado or flood) is worth $50,000 to him. If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels. The cost of pesticides is $20,000. The other costs associated with planting and harvesting the crop total $450,000. If the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00. Note: ($12 × 0.50 + $10 × 0.50) = $11 What will be his total cost if he uses pesticide?

Q10. If the farmer uses pesticide and decides to sell the crop at harvest, what is his expected revenue? (610000 is a wrong answer)

Q11. If the farmer uses pesticide and decides to sell the crop at harvest, what is his expected profit? (140000 is a wrong answer)

Q12. If the farmer does not use pesticide and decides to sell the crop at harvest, what is his expected revenue? (555000 is a wrong answer)

Q13. If the farmer does not use pesticide and decides to sell the crop at harvest, what is his expected profit? (105000 is a wrong answer)

Q14. Should the farmer decide to use pesticide or not? YES

Q15. What is the maximum a purchaser would be willing to pay to the farmer for the rights to the future corn crop assuming they cannot monitor the farmer after purchasing the contract? (720000 is a wrong answer)

Answer 1

		Price per bushel with Probability of 0.5	$10
		Price per bushel with Probability of 0.5	$12
		Expected Price	$11
		Expected produce if pesticide is used	60000 Bushels
		Expected produce if pesticide is not used	55000 Bushels
		Cost Of Pestiside	$20000
		Other Cost	$450000
		Expected revenue and Profit
Question 10		Revenue = 60000 (expected produce using pesticides) multiplied by 11 (expected price)	660000
		Less: Cost of Pesticide	20000
		Less: other costs	450000
Question 11		=Profit	190000
Question 12		Revenue = 55000 (expected produce without using pesticides) multiplied by 11 (expected price)	605000
		Less: other costs	450000
Question 13		=Profit	155000
Question 14		Since Expected Profit is 190000>155000 while using pesticides he should be using it.