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A farmer has 400 bushel of wheat, and he can covert wheat this year (x1) into wheat next year (x2) using the farming technology x2 = 50√x1 . All prices are expected to remain constant between this year and next. On the other hand, the farmer has the following inter-temporal utility function: U(c0, c1) ≡ log ??0 + log ??1
(a) Suppose there is no capital market. Then describe and solve the farmer's maximization program.
(b) Suppose that the farmer can borrow and lend at 25 percent per annum. How much wheat should he plant? What are his consumption opportunities now? Why is his investment decision now independent of his tastes?
(c) How much wheat should the farmer borrow and lend at a zero market rate of interest?
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