A farmer has two storage facilities for grain; a modern silo and an old shed. Grain stored in the silo is perfectly preserved, but grain stored in the shed suffers a 10% loss through spillage, spoilage, and rodent damage. The farmer's current crop is 10,000 bushels. The capacity of the silo is 6,000 bushels, while the shed can store the remaining crop. Suppose grain sells today for $1 per bushel, and will sell next year for $1.21.

a. If interest rates are 10% per year, how much grain should he store in the silo?

b. If interest rates are 10% per year how much grain should he store in the shed?

c. If interest rates are 10% per year how much grain should he sell this year?

d. If interest rates are 10% per year how much grain should he sell next year?

e. What is the max present value of his wealth from the optimal decision of weather to sell or store grain if interest rates are 10% per year?

f. Above what interest rate will the farmer elect to sell all 10,000 bushels today?

g. below what interest rate will the farmer elect to store all 10,000 bushels and sell them next year?