Suppose that an economy in year t can be described by the following three equations:

ut – ut-1 = -0.4(gyt – 3%) Okun’s law

πt – πt-1 = -(ut – 5%) Phillips curve

gyt = gmt – πt Aggregate demand

a) What is the natural rate of unemployment for this economy in year t?

b) Suppose that in year t-1 and year t the unemployment rate is equal to the natural rate and that the inflation rate is 8%. What is the growth rate of output in year t? What is the growth rate of the money supply in year t?

c) Suppose that conditions are as in (b), when, in year t+1, the authorities use monetary policy to reduce the inflation rate to 4% in year t+1 and keep it there. Given this inflation rate and using the Phillips curve, what must happen to the unemployment rate in years t+1, t+2 and so on? Given the unemployment rate and using Okun’s law, what must happen to the rate of growth of output in years t+1, t+2 and so on? Given the rate of growth of output and using the aggregate demand equation, what must be the rate of nominal money growth in years t+1, t+2 and so on?