Question

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 5% loss through spillage, spoilage, and rodent damage. The farmer’s current crop is 20,000 bushels. The capacity of the silo is 12,000 bushels, while the shed can store the remaining crop. Suppose grain sells today for $4 per bushel, and will sell next year for $4.40. If interest rates are 8%, how much grain should he store in the silo? In the shed? How much grain should he sell this year? Next year? What is the maximum present value of his wealth from the optimal decision of whether to sell or store grain?

Answer 1

Farmer’s current crop is 20,000 bushels.

Capacity of the silo is 12,000 bushels.

Grain stored in the shed suffers a 5% loss through spillage, spoilage, and rodent damage.

Grains in shed = 8000*(1 - 5%)

= 7600 bushels

Farmer should store 12,000 bushels in silo and 7,600 bushels in shed for the next year.