2. The cost per bushel of growing corn on a given acre of land depends partly on how intensely the land is farmed and partly on the quality of the soil, the amount of rainfall, and the length of the growing season. Suppose that the last three factors are summarized by a single index f for fertility. Suppose that the long-run total cost of producing y hundred bushels of corn on an acre of land of fertility f is c(y, f ), where c(y, f ) (1 y2 )/f for y 0 and c(0, f ) 0.

a. Write down a formula for the long-run average cost function per hundred bushels of corn from an acre of land of quality f.

b. At what level of output is long-run average cost minimized on an acre of land of quality f?

c. What is the lowest price per hundred bushels at which an acre of land of quality f will be used to produce corn?