The medium-run equilibrium is characterized by four conditions:

Output is equal to potential output \(Y=Y_{n}\).

The unemployment rate is equal to the natural rate \(u=u_{n}\).

The real policy interest rate is equal to the natural rate of interest \(r_{n}\) where aggregate demand equals \(Y_{n}\)

The expected rate of inflation \(\pi^{e}\) is equal to the actual rate of inflation \(\pi\).

a. If the level of expected inflation is formed so \(\pi^{e}\) equals \(\pi(-1)\), characterize the behavior of inflation in a mediumrun equilibrium.

b. If the level of expected inflation is \(\bar{\pi}\), what is the level of actual inflation in the medium-run equilibrium?

c. Write the \(I S\) relation as \(Y=C(Y-T)+I(Y, r+x)+G\). Suppose \(r_{n}\) is \(2 \%\). If \(x\) increases from 3 to \(5 \%\), how must the central bank change \(r_{n}\) to maintain the existing mediumrun equilibrium. Explain in words.

d. Suppose \(G\) increases. How must the central bank change \(r_{n}\) to maintain the existing medium-run equilibrium? Explain in words.

e. Suppose \(T\) decreases. How must the central bank change \(r_{n}\) to maintain the existing medium-run equilibrium? Explain in words.

f. Discuss: In the medium run, a fiscal expansion leads to an increase in the natural rate of interest.