Productivity and the aggregate supply curve Consider an economy in which production is given by:

\[
Y=A N
\]

Assume that price setting and wage setting are described in the following equations:

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

Recall that the relation between employment, \(\mathrm{N}\), the labor force, \(\mathrm{L}\), and the unemployment rate, \(\mathrm{u}\), is given by:

\[
N=(1-u) L
\]

a. Derive the aggregate supply curve (that is, the relation between the price level and the level of output, given the markup, the actual and expected levels of productivity, the labor force, and the expected price level). Explain the role of each variable.

b. Show the effect of an equiproportional increase in \(A\) and \(A^{e}\) (so that \(A / A^{e}\) remains unchanged) on the position of the aggregate supply curve. Explain.

c. Suppose instead that actual productivity, \(A\), increases, but expected productivity, \(A^{e}\), does not change. Compare the results in this case to your conclusions in (b). Explain the difference.