A farmer has a production function f(L) where the input is capital (L). The cost of this loan is L(1+i). The farmer also has an outside option which generates a profit of A. Suppose a farmer has N years where he can work productively, and then must retire. Each year, if he pays the loan, he may take out another loan, but, if he neglects to repay, the bank will never lend to him again. Assume L is fixed. If the bank knew how many more years the farmer could work productively, and the production function the farmer faced, what interest rate would the bank set?
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