## PROBLEMS AND APPLICATIONS

1. In the sticky-price model, describe the aggregate supply curve in the following special cases. How do these cases compare to the short-run aggregate supply curve we discussed in Chapter 9?

1. No firms have flexible prices (s = 1).

2. The desired price does not depend on aggregate output (a = 0).

2. Suppose that an economy has the Phillips curve

π = π–1 – 0.5(u – 0.06).

1. What is the natural rate of unemployment?

2. Graph the short-run and long-run relationships between inflation and unemployment.

3. How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? Using Okun’s law, compute the sacrifice ratio.

4. Inflation is running at 10 percent. The Fed wants to reduce it to 5 percent. Give two scenarios that will achieve that goal.

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3. According to the rational-expectations approach, if everyone believes that policymakers are committed to reducing inflation, the cost of reducing inflation—the sacrifice ratio—will be lower than if the public is skeptical about the policymakers’ intentions. Why might this be true? How might credibility be achieved?

4. Suppose that the economy is initially at a long-run equilibrium. Then the central bank increases the money supply.

1. Assuming any resulting inflation to be unexpected, explain any changes in GDP, unemployment, and inflation that are caused by the monetary expansion. Explain your conclusions using three diagrams: one for the IS–LM model, one for the AD–AS model, and one for the Phillips curve.

2. Assuming instead that any resulting inflation is expected, explain any changes in GDP, unemployment, and inflation that are caused by the monetary expansion. Once again, explain your conclusions using three diagrams: one for the IS–LM model, one for the AD–AS model, and one for the Phillips curve.

5. Assume that people have rational expectations and that the economy is described by the sticky-price model. Explain why each of the following propositions is true:

1. Only unanticipated changes in the money supply affect real GDP. Changes in the money supply that were anticipated when prices were set do not have any real effects.

2. If the Bank of Canada chooses the money supply at the same time as people are setting prices, so that everyone has the same information about the state of the economy, then monetary policy cannot be used systematically to stabilize output. Hence, a policy of keeping the money supply constant will have the same real effects as a policy of adjusting the money supply in response to the state of the economy. (This is called the policy irrelevance proposition.)

3. If the Bank of Canada sets the money supply well after people have set prices, so the Bank of Canada has collected more information about the state of the economy, then monetary policy can be used systematically to stabilize output.

6. Suppose that an economy has the Phillips curve

π = π–1 – 0.5(uun),

and that the natural rate of unemployment is given by an average of the past two years’ unemployment:

un = 0.5(u–1 + u–2).

1. Why might the natural rate of unemployment depend on recent unemployment (as is assumed in the above equation)?

2. Suppose that the Bank of Canada follows a policy to reduce permanently the inflation rate by 1 percentage point. What effect will that policy have on the unemployment rate over time?

3. What is the sacrifice ratio in this economy? Explain.

4. What do these equations imply about the short-run and long-run tradeoffs between inflation and unemployment?

7. Some economists believe that taxes have an important effect on labour supply. They argue that higher taxes cause people to want to work less and that lower taxes cause them to want to work more. Consider how this effect alters the macroeconomic analysis of tax changes.

1. If this view is correct, how does a tax cut affect the natural rate of output?

2. How does a tax cut affect the aggregate demand curve? The long-run aggregate supply curve? The short-run aggregate supply curve?

3. What is the short-run impact of a tax cut on output and the price level? How does your answer differ from the case without the labour-supply effect?

4. What is the long-run impact of a tax cut on output and the price level? How does your answer differ from the case without the labour-supply effect?

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8. Princeton economist Alan Blinder, who has served as Vice Chairman of the U.S. Federal Reserve, once wrote the following:

The costs that attend the low and moderate inflation rates experienced in the United States and in other industrial countries appear to be quite modest—more like a bad cold than a cancer on society. . . . As rational individuals, we do not volunteer for a lobotomy to cure a head cold. Yet, as a collectivity, we routinely prescribe the economic equivalent of lobotomy (high unemployment) as a cure for the inflationary cold.13

What do you think Blinder meant by this? What are the policy implications of the viewpoint Blinder is advocating? Do you agree? Why or why not?

9. Go to the website of Statistics Canada (www.statcan.ca). For each of the past five years, find the inflation rate as measured by the consumer price index (all items)—sometimes called headline inflation—and as measured by the CPI excluding food and energy—sometimes called core inflation. Compare these two measures of inflation. Why might they be different? What might the difference tell you about shifts in the aggregate supply curve and in the short-run Phillips curve?