Solve each of the following problems and be sure to show all of the steps involved in obtaining your solution.
1. Suppose the monetary policy curve is $r = 2.2 + 0.8\pi$ and that the IS curve is $Y = 18.5 - 0.8r$.
(a) Find the expression for the aggregate demand curve.
(b) Calculate aggregate output when the inflation rate is 1%, 1.5%, and 2%.
(c) Plot the aggregate demand curve and identify the points where inflation equals 1%, 1.5%, and 2% on your plot.