Suppose an economy is characterized by the following equations:

\[
\begin{gathered}
\text { Price setting: } P=(1+m)(W / A) \\
\text { Wage setting: } W=A^{e} P^{e}(1-u)
\end{gathered}
\]

a. Solve for the unemployment rate if \(P^{e}=P\) but \(A^{e}\) does not necessarily equal \(A\). Explain the effects of \(\left(A^{e} / Aight)\) on the unemployment rate.

Now suppose that expectations of both prices and productivity are accurate.

b. Solve for the natural rate of unemployment if the markup (m) is equal to \(5 \%\).

c. Does the natural rate of unemployment depend on productivity? Explain.