Question

Suppose that the Phillips curve in the economy is given by (for any time t) pi t = pi t - 1 -0.5(U t -0.06) Suppose that the economy starts with an inflation rate of 0 at time t - 1 Moreover at time t the unemployment rate is at the natural level. What is the inflation rate in the economy at time t?

Answer 1

To solve this problem, we start with the Phillips curve equation given:

\[
\pi_t = \pi_{t-1} - 0.5 (U_t - 0.06)
\]

Where:
- \(\pi_t\) is the inflation rate at time \(t\).
- \(\pi_{t-1}\) is the inflation rate at time \(t-1\).
- \(U_t\) is the unemployment rate at time \(t\).

We know from the problem that:
- The inflation rate at time \(t-1\) is \(\pi_{t-1} = 0\).
- At time \(t\), the unemployment rate \(U_t\) is at the natural level. By definition, the natural level of unemployment is often denoted as \(U_n\). In this equation, it is implied that the natural rate (or level) of unemployment is \(0.06\).

Substituting these values into the Phillips curve equation:

1. Substitute \(\pi_{t-1} = 0\) and \(U_t = 0.06\):

\[
\pi_t = 0 - 0.5 (0.06 - 0.06)
\]

2. Calculate the term in parentheses:

\[
0.06 - 0.06 = 0
\]

3. Now substitute this back into the equation:

\[
\pi_t = 0 - 0.5(0) = 0
\]

Thus, the inflation rate in the economy at time \(t\) is:

\[
\pi_t = 0
\]

In conclusion, the inflation rate at time \(t\) is \(0\).