An economy has the following \(A D\) and \(A S\) curves.

\[
\begin{array}{ll}
A D \text { curve } & Y=400+25(M / P) . \\
A S \text { curve } & Y=Y_{f}+15\left(P-P^{e}\right) .
\end{array}
\]

Here, \(Y_{f}=500\) and \(M=160\).

a. Suppose that \(P^{e}=40\). What are the equilibrium values of the price level, \(P\), and output, \(Y\) ? The solutions for \(P\) in this part and in part (b) are multiples of 5.

b. Money supply (M) increases unexpectedly to 500 . Since the increase is unanticipated, \(P^{e}\) remains at 40 . What are the equilibrium values of the price level, \(P\), and output, \(Y\) ?

c. The Fed announces that the money supply will be increased to \(M=500\), which the public believes. Now what are the equilibrium values of the price level, \(P\), the expected price level, \(P^{e}\), and output, \(Y\) ?