Suppose the monetary policy curve is given by $r=1\mathrm{.}5+0\mathrm{.}75,$ and the IS curve is given by $Y=13-r.$

a$.$ Calculate an expression for the aggregate demand curve.

b$.$ Calculate the real interest rate and aggregate output when the inflation rate is $2\%,3\%,$ and $4\%.$

c$.$ Draw graphs of the IS$,$ MP$,$ and $AD$ curves, labeling the points from part $($b$)$ on the appropriate graphs.