4. (9 points} In class we talked about the fact that desired investment is sensitive to interest rates. If you actually tried to show this in the data, you'd have a hard time! In the actual data, the level of investment and the interest rate in the economy are not very strongly correlated. This problem will help explore why that might be the case, and how even if that's what we see in the data, our model may be perfectly correct! (It will also illuminate why working with these macro models is sometimes so tricky!) A. (3 pts) Suppose that the desired investment in the economy was fairly stable. That is, the desired investment function (as a function of interest rates} did not shift around very much. However, suppose that the desired savings mction in the economy was quite unstable. (I.e., it shifts very regularly.) Explain what might cause desired savings to be unstable. If this were the case, what correlation between the actual amount of investment and interest rates would you see in the macroeconomic data? (For all the parts of this question, you can't give an exact number, but tell me if the correlation will be positive, negative, zero, or you can*t tell.)