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

Okun's law: Ut - Ut - 1 = 0.4(gyt - 3%) Philips curve: t = t - 1 = - (Ut - 5%) Aggregate demand: gyt = gmt - t i)

What is the natural rate of unemployment for this economy?

Suppose that the unemployment rate is equal to the natural rate, and that inflation rate is 8%. What is the growth rate output? What is the growth rate of the money supply?

Suppose that conditions are as in (b), when in year t, the authorities use monetary policy to reduce the inflation rate to 4% in year t and keep it there. Given this inflations rate and using the Philips curve, what must happen to the unemployment rate in years t, t + 1, and t + 2?

Given the unemployment rate and using Okun's law, what must happen to the rate of growth of output in years t, t + 1 and t + 2?

Given the rate of growth of output and using the aggregate demand equation, what must be the rate of nominal growth in years t, t +1 and t + 2?