Assume that expected inflation remains equal to the central bank's target rate of inflation. In the discussion of the Phillips curve, it was noted that expected inflation was, for some time, equal to lagged inflation and was not anchored by the central bank's target rate of inflation. This question considers the implications of these two assumptions about expected inflation for the effects of a permanent change in demand, given unchanged monetary policy.

The permanent change in demand studied in this question is an increase in consumer confidence where the parameter " \(a\) " takes a larger value.

One assumption is that the level of expected inflation equals lagged inflation and so changes over time. The other assumption is that the level of expected inflation is anchored to the central bank's target rate of inflation and never changes Begin in medium-run equilibrium where actual and expected inflation equals \(2 \%\) in period \(t\). Suppose there is an increase in consumer confidence in period \((t+1)\).

Parts (a), (b) and (c) assume expected inflation in each period equals lagged inflation from the previous period. For example, in period \((t+2) \pi_{t+2}^{e}=\pi_{t+1}\) and in period \((t+1), \pi_{t+1}^{e}=\pi_{t}\).

a. How does the IS curve shift from period t to period \((\mathrm{t}+1)\) ? What is the value of expected inflation in period t? How does the short-run equilibrium output and inflation rate in period \((t+1)\) compare to the equilibrium output and inflation rate in period \(t\) if the central bank does not change the real policy rate from period to period \((t+1)\) ?

b. Now advance the economy to the period \((t+2)\) equilibrium under the assumption that \(\pi_{t+2}^{e}=\pi_{t+1}\) and consumer confidence remains high. If the central bank leaves the real policy rate unchanged will inflation be higher or lower in period \((t+2)\) than in period \((t+1)\) ?

c. What do you conclude about the central bank policy of keeping the real policy rate unchanged in period \((t+2)\) ? Is it sustainable?

Parts (d), (e) and (f) assume expected inflation remains equal to target inflation, so \(\pi^{e}=\bar{\pi}\) in all periods.

d. Consider the period \((t+1)\) equilibrium given the assumption that \(\pi^{e}=\bar{\pi}\). If the central bank leaves the real policy rate unchanged, how does inflation in period \((t+1)\) compare to inflation in period \(t\) ? Is output higher or lower in period \((t+1)\) than in period \(t\) ?

e. Consider the period \((t+2)\) equilibrium given the assumption that \(\pi_{t+2}^{e}=\bar{\pi}\). If the central bank leaves the real policy rate unchanged, how does actual inflation in period \((t+2)\) compare to inflation in period \((t+1)\) ? Is output higher or lower in period \((t+2)\) than in period \((t+1)\) ?

f. Explain why the policy choice to maintain the real policy rate at the original level in period \((t+1)\) is not a sustainable policy?
Comparing the economic outcomes in parts (a), (b) and (c) to the economic outcomes in (d), (e) and (f).

g. Compare the inflation, expected inflation and output outcomes in part (a), (b) and (c) to that in parts (d), (e) and (f).
h. Which assumption about expected inflation, do you think is more realistic. Discuss.