A Corn Farmer Is Considering Two Alternatives for Selling His

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 .5 and $12 per bushel with probability .5.The farmer is averse to risk,and is willing to pay $50,000 to avoid the risk of damage to the crop while it is growing (e.g.,from a tornado or flood).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.
a.If the farmer decides to sell the crop at harvest will he be better off using pesticides or not using them? What is the farmer's expected profit in each case?
b.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? Defend your answer.
c.Which alternative: (1)sale of rights prior to planting or (2)selling the crop after harvest yields the maximum expected benefit for the farmer considering his level of risk aversion?
[this question is inspired by a question originally written by Sal March]