Fiscal consolidation at the Zero Lower Bound

Suppose the economy is operating at the zero lower bound forthe nominal policy rate; there is a large government deficit and theeconomy is operating at potential output in period t. A newly electedgovernment vows to cut spending and reduces the deficit in periodt + 1, period t + 2 and subsequent periods.

a. Show the effects of the policy on output in period t + 1.

b. Show the effects of the policy on the change in inflation inperiod t + 1.

c. If expected inflation depends on past inflation, then whathappens to the real policy rate in period t + 2? How willthis affect output in period t + 3?

d. How does the zero lower bound on nominal interest ratesmake a fiscal consolidation more difficult?