2. Suppose the Fed reduces the moncy supply by 5 percent.Assume the velocity of

Question

2. Suppose the Fed reduces the moncy supply by 5 percent.Assume the velocity of money is a. What happens to the aggregate demand b. Whar happens to the level of output and the price level in the short run and in the long run? Give a precise numerical c. In light of your answer to part (b), what happens to unemployment in che short run and in the long run according to Okun's law? Again, give a precise numerical answer d. What happens to the real interest rate in the short run and in the long run? (Hint: Use the model of the real interest rate in Chapter 3 to see what happens when output changes.) Here, your answer should just give the direction of the changes.

Explanation / Answer

a)

The aggregate demand curve shifts down if the Fed reduces the money supply. This result is based on the quantity equation

MV = PY

Which tells us that a decrease in money M leads to a proportionate decrease in nominal output PY (assuming of course that velocity V is fixed). For any given price level P, the level of output Y is lower, and for any given Y, P is lower.

b)

In the short run, we assume that the price level is fixed and that the aggregate supply curve is flat. In the short run, output falls but the price level doesn't change. In the long-run, prices are flexible, and as prices fall over time, the economy returns to full employment.

If we assume that velocity is constant, we can quantify the effect of the 5% reduction in the money supply. Recall from Chapter 4 that we can express the quantity equation in terms of percent changes:

ZIM/M + zall/V = LIPIP + zlY/Y

We know that in the short run, the price level is fixed. This implies that the percentage change in prices is zero and thus AM/M = AY/Y. Thus in the short run a 5 percent reduction in the money supply leads to a 5 percent reduction in output.

In the long-run we know that prices are flexible and the economy returns to its natural rate of output. This implies that in the long-run, the percentage change in output is zero and thus AM/M = AP/P. Thus in the long run a 5 percent reduction in the money supply leads to a 5 percent reduction in the price level.

c)

Okun's law refers to the negative relationship that exists between unemployment and real GDP. Okun's law can be summarized by the equation:

LIY/Y 3.5% - POI in unemployment)

That is, output mows in the opposite direction from unemployment, with a ratio of 2 to I. In the short run, when output falls, unemployment rises. Quantitative, if velocity is constant, we found that output falls 5% (relative to full employment) in the short run, so unemployment increases 2.5%. In the long run, both output and unemployment return to their natural levels, so there is no long-term change in unemployment.

d)

The national income accounts identity tells us that saving

S = Y —C — G.

Thus, when Y falk, S falls (assuming that MPC is less than one). This will cause the real interest rate to rise (see Figure 3-9 for what this would look like). When Y returns to its original long-run level, so does the real interest rate.

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