Suppose inflation at time t is given by _t = ^e_t + m + z - u_t, and inflationary expectations are given by ^e_t =_t-1+(1-), where 01, and is a constant.

Suppose the economy is initially at a medium-run equilibrium (defined by Y_n, u_n, and r_n). Consider the case where the government decides to reduce government expenditure (G) to decrease the deficit (holding taxes constant). Additionally, suppose the value of is consistent with the original Phillips curve relation.

i. Demonstrate the effect of a reduction in government expenditure on the IS curve and the PC in the short run.

ii. If the central bank only cares about the level of inflation, how should it respond to the fiscal consolidation? What happens to unemployment?

iii. If the central bank only cares about the inflation growth rate, how should it respond to the fiscal consolidation?

iv. If the central bank only cares about the level of output, how should it respond to the fiscal consolidation? What happens to unemployment?

v. Suppose the central bank adjusts the real interest rate to return the economy to a medium-run equilibrium consistent with a zero output gap. How does the level of inflation compare to its level before the fiscal consolidation?

Now suppose the value of is consistent with the new Phillips curve relation.

vi. Demonstrate the effect of a reduction in government expenditure on the IS curve and the PC in the short run.

vii. Suppose the central bank adjusts the real interest rate to return the economy to a medium-run equilibrium consistent with a zero output gap. How does the level of inflation compare to its level before the fiscal consolidation?

viii. What will occur if the real interest rate corresponding to the zero lower bound is greater than the new natural rate of interest, rn'? Illustrate this situation using the IS-LM-PC model.