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

Question

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

t – t-1 = -(ut – 5%) Phillips curve

gyt = gmt – t 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?

Explanation / Answer

:a) Setting t equal to t-1te in the Phillips curve relation, we get un to be equal to 5%.

b) : In the medium run, we know that ut=un and that the growth rate of output is equal to its normal growth rate. As is evident from the Okun’s Law relation provided above, the normal growth rate is 0. So gyt=0. The AD relation then tells us what the inflation rate should be. With gyt = 0 and gmt = 6%, t must equal 6% as well.

c)Along the path abc, the inflation rate is always less than the money growth rate which is 10% after the change. Therefore along abc, the real money supply is growing. Therefore output is growing (by the AD relations), and therefore the unemployment rate is falling (by Okun’s law). As the unemployment rate falls, the inflation rate rises due to the Phillips curve relation but stays below 10% till the economy reaches point c. (b) At point c, the inflation rate is equal to the money growth rate, but unemployment is still below its natural rate, so the inflation rate continues to rise. But now the inflation rate outstrips the money growth rate, so the real money supply is falling. Along cd, the real money supply falls, therefore output growth falls (by the AD relation), and the unemployment rate increases (by Okun’s Law). At d, the unemployment rate is back to the natural rate, but inflation continues to be higher than the money growth rate. So the real money supply continues to fall, output growth continues to fall, and the unemployment rate continues to increase. But as soon as we are past d, the unemployment rate is greater than the natural rate, so now the inflation rate starts falling as well, and along the path de, the inflation rate, though falling, continues to be higher than the money growth rate, so output growth continues to fall, and the unemployment rate continues to increase.

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