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

1. u_t - u_t-1= -0.4(g_yt - 2.5%) Okun's law ; g_yt= growth rate of the real GDP

2. _t- _t-1 = -(u_t - 3.5%) Phillips curve

3. g_yt= g_mt - _t Aggregate demand; g_mt = growth rate of money supply (nominal money)

3.1. What is the natural rate of unemployment for this economy?

3.2. Suppose that the unemployment rate is equal to the natural rate. What is the growth rate of output?

3.3. Assume further that the growth rate of the money supply equals 5.5%. What is the rate of inflation?

3.4. Why are the increases in the price level not the same as the growth rate of money?

3.5. Suppose now that the growth rate of nominal money is reduced from 5.5% to 3%, starting in year t. Calculate the value of the unemployment rate, the inflation rate and the rate of growth of the GDP at time t and compare these values to your answer from parts (a-c).