The macroeconomic effects of the indexation of wages Suppose that the Phillips curve is given by

\[
\pi_{t}-\pi_{t}^{e}=0.1-2 u_{t}
\]

where

\[
\pi_{t}^{e}=\pi_{t-1}
\]

Suppose that inflation in year \(t-1\) is zero. In year \(t\), the central bank decides to keep the unemployment rate at \(4 \%\) forever.

a. Compute the rate of inflation for years \(t, t+1, t+2\), and \(t+3\).

Now suppose that half the workers have indexed labor contracts.

b. What is the new equation for the Phillips curve?

c. Based on your answer to part (b), recompute your answer to part (a).

d. What is the effect of wage indexation on the relation between \(\pi\) and \(u\) ?