The R. Crusoe Farming Corporation faces the following real/productive investment opportunity set:

F(X0，X1)=(100-X0)(1.07+0.003X0)-X1          0<=X0<=100

        where X0 represents current-period dollars and X1 corresponds to end-of-year dollars resulting from the investment in its farming operation.  There is no capital market; however, R. Crusoe has assessed his utility for current and future consumption, which is as follows:

u(X0,X1)=(X0^2)X1

        Solve for the optimal level of real investment for R. Crusoe.  [Hint: R. Crusoe’s current wealth is found by solving F(X0,X1) for X0 where X1=0]

        Using the same real investment opportunity set [F(X0,X1)] and utility function [u(X0,X1)], solve for the optimal level of real investment and the optimal level of consumption where capital markets exist and the borrowing and lending rate equals 7.5 percent.  Compare your answer to that obtained previously.