Consider a farmer who can either plant or market/consume his crop. Whatever amount he plants becomes a crop twice the size the following year. For example, if he plants seed from 2 ears of corn, he gets 4 ears of corn at harvest. Assume he starts off with 50 bushels of corn.
a. If he decides every year to market/consume half his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?
b. If he decides every year to market/consume 2/5 of his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?
c. Compare the consumption of the farmer in each of the first five years under plans a. and b.
d. Why might the results of plan b. not be realistic?