Consider an economy that can be describes by the following three equations:

_t - _t-1 = - (u_t - 5%) Phillips curve

u_t - u_t-1 = -0.4 (g_yt - 3%) Okun's Law

g_yt = g_mt - _t Aggregate demand

1. what is the natural rate of unemployment for this economy?
2. Suppose that the unemployment rate is equal to the natural rate and that the inflation rate is 8%. What is the growth rate of output? What is the growth rate of money supply?
3. Suppose that the authorities decide to use monetary policy to reduce the inflation rate to 4% in a year 1, 2, and 3 in order to achieve the target rate of inflation? What will happen to unemployment rate and output growth in years 1, 2, and 3? Summarize your results in a table
4. Define the sacrifice ratio and compute it using your previous results.