Consider the following dynamic model of an economy:

ut-ut-1 = 0.5 (gy,t - 3%) [Okun's law],

pie t -pie t-1 = 0.25 (ut = 5%) [Phillips curve]

gy,t = 5% - piet [Aggregate demand].

(a) In period 0, the economy is in a medium-run equilibrium. What are the rates of unemployment (u0), output growth (gy,0) and inflation (pie0) in the medium-run equilibrium?

(b) In period 1, the medium-run growth rate of output drops to 1%. Find period 1 rates of unemployment (u1) and inflation (pie1).

(c) What are the new medium-run rates of unemployment and inflation corresponding to 1% medium-run growth rate of output?