7. The text assumes that the natural rate of interest r is a constant parameter. Suppose instead that it varies over time, so now it has to be written as rt.

a. How would this change affect the equations for dynamic aggregate demand and dynamic aggregate supply?

b. How would a shock to rt affect output, inflation, the nominal interest rate, and the real interest rate?

c. Can you see any practical difficulties that a central bank might face if rt varied over time?