# Utility function and optimal level of consumption

An individual faces the following investment opportunity set,

## F(Y0,Y1) = (100-Y0)(1.07 + 0.0003 x Y0) - Y1 = 107 - 1.04Y0 - 0.0003Y02 - Y1 = 0

where Y0 is the current period dollars and Y1 represents the end-of-period-dollars resulting from investing in his business operation.

Question 1:

There is no capital market; however, the individual has assessed his utility function for current and future consumption,

## U(C0, C1) = C02C1

What is the optimal level of real investment? Current wealth is found by setting Y1 = 0 in F(Y0, Y1) and obtain Y0.

Question 2:

Using the same utility function and the opportunity set, solve for the optimal level of real investment and the optimal level of consumption where capital markets exists and the borrowing and lending rate equals 7.5 percent.

How do I solve such question? Normally, for a question like this, it will provide the interest rate. But there seems no interest rate provided in question 1, does it imply 0 interest rate?

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• Smoking weed is probably an enjoyable recreational activity, but some nights you should probably forego it and just read the textbook. – denesp Feb 11 at 16:51