Assume that money demand takes the form

\[
\frac{M}{P}=Y\left[1-\left(r+\pi^{e}ight)ight]
\]

where \(Y=1,000\) and \(r=0.1\).

a. Assume that, in the short run, \(\pi^{e}\) is constant and equal to \(25 \%\). Calculate the amount of seignorage for each annual rate of money growth, \(\Delta \mathrm{M} / \mathrm{M}\), listed.

i. \(25 \%\)

ii. \(50 \%\)

iii. \(75 \%\)

b. In the medium run, \(\pi^{e}=\pi=\Delta \mathrm{M} / \mathrm{M}\). Compute the amount of seignorage associated with the three rates of annual money growth in part (a). Explain why the answers differ from those in part (a).