CHAPTER 14 QUESTIONS
How is the Phillips curve related to aggregate supply?
2. This chapter assumes that in the short run the supply of output depends on the natural level of output and on the difference between the price level and the expected price level. This relationship is expressed by the aggregate-supply equation Y = + α(P - EP). The Phillips curve expresses the tradeoff between inflation and unemployment implied by the short-run aggregate supply curve. The Phillips curve posits that inflation π depends on expected inflation Eπ, cyclical unemployment u - un, and supply shock v: π = Eπ - β(u - un) + v. Both equations imply a connection between real economic activity and unexpected changes in prices. In addition, both the Phillips curve and the short-run aggregate supply curve show that inflation and unemployment move in opposite directions.
Explain the differences between the demand pull inflation and cost push inflation
Demand-pull inflation results from high aggregate demand: the increase in demand pulls prices and output up. Cost-push inflation comes from adverse supply shocks that push up the cost of production—for example, the increases in oil prices in the mid- and late-1970s. The Phillips curve tells us that inflation depends on expected inflation, the difference between unemployment and its natural rate, and a supply shock v: π = Eπ - β(u - un) + v. The term - β(u - un) is demand-pull inflation because, if unemployment is below its natural rate (u < un), inflation rises. The supply shock v is cost-push inflation.
Explain two ways in which a recession might raise the natural rate of unemployment
One way in which a recession might raise the natural rate of unemployment is by affecting the process of job search, increasing the amount of frictional unemployment. For example, workers who are unemployed lose valuable job skills. This reduces their ability to find jobs after the recession ends because they are less desirable to firms. Also, after a long period of unemployment, individuals may lose some of their desire to work and hence reduce their search effort. Second, a recession may affect the process that determines wages, increasing structural unemployment. Wage negotiations may give greater voice to "insiders"—those who actually have jobs. Those who become unemployed become "outsiders." If insiders care more about high real wages and less about high employment, then the recession may permanently push real wages above the equilibrium level and raise the amount of structural unemployment. This permanent impact of a recession on the natural rate of unemployment is called hysteresis.
2. Suppose an economy has the Phillips curve pie= pie (lower- 1) - 0.5(u-5) a. What is the natural rate of unemployment? b. Graph the short run and long run relationships between inflation and unemployment cHow much cyclical unemployment is necessary to reduce inflation by 4 percentage points? Using Okun's law, compute the sacrifice ratio d. Inflation is running at 6 percent. The central bank wants to reduce it to 2 percent. Give two scenarios that will achieve that goal
a. The natural rate of unemployment is the unemployment rate at which the inflation rate does not deviate from the expected inflation rate. Here the expected inflation rate is last period's inflation rate. Setting the inflation rate equal to last period's inflation rate (that is, setting π = π-1), we find that the natural rate of unemployment is u = 5 percent. b. In the short run (that is, in a single period), the expected inflation rate is the inflation rate in the previous period π-1. The short-run relationship between inflation and unemployment is given by the graph of the Phillips curve: it has a slope of -0.5 and passes through the point where π = π-1 and u = 5 percent, as shown in Figure 14-1. In the long run, expected inflation equals actual inflation, so π = π-1, unemployment is at its natural rate of 5 percent, and output is at its natural level. The long-run Phillips curve is thus vertical at an unemployment rate of 5 percent. c. To reduce inflation, the Phillips curve tells us that unemployment must be above its natural rate of 5 percent. We can write the Phillips curve in the form π - π-1 = -0.5(u - 5). A fall in the inflation rate of 4 percentage points gives us π - π-1 = -4. Plugging this into the left side of the above equation, we find the needed unemployment rate as follows: -4 = -0.5(u - 5) 8 = u - 5 u = 13. Hence, a fall in inflation of 4 percentage points requires 8 percentage points of cyclical unemployment above the natural rate of 5 percent. Okun's law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 8 percentage points corresponds to a fall in GDP of 16 percentage points. The sacrifice ratio is the percentage of a year's GDP that must be forgone to reduce inflation by 1 percentage point. Dividing the 16-percentage-point decrease in GDP by the 4-percentage-point decrease in inflation, we find that the sacrifice ratio is 16/4 = 4. d. To reduce the inflation rate by 4 percentage points, one option is to have very high unemployment for a short period of time (for example, 13 percent unemployment for a single year). An alternative is to have a lower rate of unemployment for a longer period of time (for example, 7 percent unemployment for four years). Both plans bring the inflation rate down by 4 percentage points but at different speeds.
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 in Chapter 10? a. All firms have sticky prices b. The desired price does not depend on aggregate output (a=0)
In this question, we examine two special cases of the sticky-price model developed in this chapter. In the sticky-price model, all firms have a desired price p that depends on the overall level of prices P and the level of output relative to the natural level Y - . This can be expressed as p = P + a(Y - Y with dash). There are two types of firms. A fraction of firms 1 - s have flexible prices and set prices using the above equation. The remaining fraction s have sticky prices: they announce their prices in advance based on the economic conditions that they expect in the future. We assume that these firms expect output to be at its natural rate, so EY = Y with a dash. Hence, these firms set their prices equal to the expected price level: p = EP. The overall price level is a weighted average of the prices set by the two types of firms, which we can express as follows: P = sEP + (1 - s)[P + a(Y - )] sP = sEP + (1 - s)a(Y - ) P = EP + [(1 - s)a/s](Y - ). a. If all firms have sticky prices (s = 1), then the above equation implies that P = EP. That is, the aggregate price level equals the expected price level. This implies that the aggregate supply curve is horizontal in the short run, as assumed in Chapter 10. b. If the desired price does not depend on aggregate output (a = 0), then the above equation again implies that P = EP: the aggregate supply curve is horizontal in the short run, as assumed in Chapter 10.
Why might inflation be intertia?
Inflation might be inertial because of the way people form expectations. People's expectations of inflation may depend on recently observed inflation. These expectations then influence wages and prices. For example, if prices have been rising quickly, people may expect them to continue to rise quickly. These expectations are then built into wage and price contracts, so actual wages and prices rise quickly.
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?
The Phillips curve is given by π = Eπ - β(u - un) + v. If the government can lower expected inflation Eπ, then actual inflation π falls without any need for unemployment to rise above its natural rate, so there is no sacrifice. According to the rational-expectations approach, people form expectations about inflation using all available information. This includes information about current policies and expected future policies. On the one hand, if the public believes that the government is committed to reducing inflation, then expected inflation falls. On the other hand, if the public does not believe that the government is committed to the policy change, then expected inflation remains the same. Thus, according to the rational-expectations approach, the cost of reducing inflation depends on how resolute and credible the government is. How can the government make its commitment to reducing inflation more credible? One possibility is to appoint central bankers who have reputations as inflation fighters. A second possibility is for the legislature to pass a law requiring the central bank to lower inflation. A third possibility is to pass a constitutional amendment limiting monetary growth, which would have even more credibility than legislation, which is easier to change.
Under what circumstances might it be possible to reduce inflation without causing a recession
The Phillips curve relates the inflation rate to the expected inflation rate and to the difference between unemployment and its natural rate. A recession reduces inflation by raising unemployment above its natural rate. It is possible to reduce inflation without a recession, however, by reducing expected inflation. According to the rational-expectations approach, people optimally use all available information to form their expectations. Reducing expected inflation then requires, first, that the plan to reduce inflation be announced before people form expectations (e.g., before they form wage and price contracts) and, second, that people believe the announced plan will be carried out. If both requirements are met, then expected inflation will fall, and this in turn will reduce actual inflation without causing a recession.
Q FOR REVIEW Explain the two theories of aggregate supply. On what market imperfection does each theory rely? What do the theories have in common?
The two theories are the sticky price model and the imperfect information model. They both attempt to explain why output deviates from its natural level (natural level is output that is consistent with full employment of labor and capital) Both models result in an aggregate supply equation such that output deviates from its natural level Y(dash on top of Y) when the price level deviates from the expected price level: Y = Y with dash on top of it + α(P - EP). The first model is the sticky-price model. The market imperfection in this model is that prices in the goods market do not adjust immediately to changes in demand; the goods market does not clear instantaneously. If demand for a firm's goods falls, the firm may respond by reducing output, not prices. The second model is the imperfect-information model. This model assumes that there is imperfect information about prices, in that some suppliers of goods confuse changes in the price level with changes in relative prices. If a producer observes the nominal price of the firm's good rising, the producer attributes some of the rise to an increase in the relative price, even if it is purely a general price increase. As a result, the producer increases production. In both models, there is a discrepancy between what is really happening and what firms think is happening. In the sticky-price model, some firms expect prices to be at one level, and they end up at another level. In the imperfect-information model, some firms believe the relative price of their output has changed when it really has not.
An economy has the following equation for the Phillips curve: p=Ep-.5(u-6). People form expectations of inflation by taking a weighted average of the previous two years of inflation: Epie=.7pie(lower -1)+.3pie(lower -2). Okun's law for this economy is: (Y-Y(-1))/Y(-1)=3.0-2.0(u-u(-1)). The economy begins at its natural rate of unemployment with a stable inflation rate of 5%. ] a) What is the natural rate of unemployment for this economy? b) Graph the short-run tradeoff between inflation and unemployment that this economy faces. Label the point where the economy begins as point A. (Be sure to give numerical values for point A.) c) A fall in aggregate demand leads to a recession, causing the unemployment rate to rise 4 percentage points above its natural rate. On your graph in part a, label the point the economy experiences that year as point B. (Once again, be sure to give numerical values.) d) Unemployment remains at this high level for two years (the initial year described in part c and one more), after which it returns to its natural rate. Create a table showing unemployment, inflation, expected inflation, and output growth for 10 years beginning two years before the recession. (These calculations are best done on a computer spreadsheet.) e) On the same graph you used in part b, graph the short-run tradeoff the economy faces at the end of this 10-year period. Label the point where the economy finds itself as point C. (Again, use numerical values.) f) Compare the equilibrium before the recession with the new long-run (period ten) equilibrium. How much does inflation change? How many percentage points of output are lost during the transition? What is this economy's sacrifice ratio?
a. The natural rate of unemployment is the unemployment rate at which the inflation rate does not deviate from the expected inflation rate. The Phillips curve equation is π = Eπ - 0.5(u - 6). nm If π = Eπ, then the current rate of unemployment is equal to the natural rate of unemployment, which in this case is u = 6 percent. b. The economy begins in long-run equilibrium with inflation equal to expected inflation of 5 percent and unemployment equal to its natural rate of 6 percent. This is labeled as point A in Figure 14-2. Figure 14-2 c. If the unemployment rate rises 4 percentage points above its natural rate, then the current rate of unemployment is u = 10 percent. Since expected inflation has not changed, the Phillips curve gives an inflation rate of π = 5 - 0.5(10 - 6) = 3 percent. This is labeled as point B in Figure 14-2. Since expected inflation has not changed, points A and B are on the same short-run Philips curve SRPC1. d. The table below shows the unemployment rate, inflation rate, expected inflation rate, and rate of output growth for 10 years, beginning 2 years before the recession. Okay e. The reduction in the rate of inflation caused by the recession reduces the expected rate of inflation. As the expected rate of inflation falls, the Phillips curve shifts down to SRPC2, as illustrated in Figure 14-2. At the end of the 10-year period, inflation equals expected inflation of 1.92 percent, and the unemployment rate equals its natural rate of 6 percent. This is labeled as point C. f. The table shows that the long-run inflation rate falls by 3.08 percentage points. From year 2 to year 3, 8 percentage points of output are lost relative to trend growth but, from year 4 to year 5, 8 percentage points of output are gained relative to trend growth. Thus, there is no long-run sacrifice from reducing inflation here.
