1.3 Module 29: The [em]AD–AS[/em] Model

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WHAT YOU WILL LEARN

  • The difference between short-run and long-run macroeconomic equilibrium
  • The causes and effects of demand shocks and supply shocks
  • How to determine if an economy is experiencing a recessionary gap or an inflationary gap and how to calculate the size of output gaps
  • How monetary policy and fiscal policy can be used to stabilize the economy

Putting the Aggregate Supply Curve and the Aggregate Demand Curve Together

From 1929 to 1933, the U.S. economy moved down the short-run aggregate supply curve as the aggregate price level fell. In contrast, from 1979 to 1980, the U.S. economy moved up the aggregate demand curve as the aggregate price level rose. In each case, the cause of the movement along the curve was a shift of the other curve. In 1929–1933, it was a leftward shift of the aggregate demand curve—a major fall in consumer spending. In 1979–1980, it was a leftward shift of the short-run aggregate supply curve—a dramatic fall in short-run aggregate supply caused by the oil price shock.

In the AD–AS model, the aggregate supply curve and the aggregate demand curve are used together to analyze economic fluctuations.

So to understand the behavior of the economy, we must put the aggregate supply curve and the aggregate demand curve together. The result is the AD–AS model, the basic model we use to understand economic fluctuations.

Short-Run Macroeconomic Equilibrium

The economy is in short-run macroeconomic equilibrium when the quantity of aggregate output supplied is equal to the quantity demanded.

The short-run equilibrium aggregate price level is the aggregate price level in the short-run macroeconomic equilibrium.

Short-run equilibrium aggregate output is the quantity of aggregate output produced in the short-run macroeconomic equilibrium.

We’ll begin our analysis by focusing on the short run. Figure 29-1 shows the aggregate demand curve and the short-run aggregate supply curve on the same diagram. The point at which the AD and SRAS curves intersect, ESR, is the short-run macroeconomic equilibrium: the point at which the quantity of aggregate output supplied is equal to the quantity demanded by domestic households, businesses, the government, and the rest of the world. The aggregate price level at ESR, PE, is the short-run equilibrium aggregate price level. The level of aggregate output at ESR, YE, is the short-run equilibrium aggregate output.

The AD–AS model combines the aggregate demand curve and the short-run aggregate supply curve. Their point of intersection, ESR, is the point of short-run macroeconomic equilibrium where the quantity of aggregate output demanded is equal to the quantity of aggregate output supplied. PE is the short-run equilibrium aggregate price level, and YE is the short-run equilibrium level of aggregate output.

We have seen that a shortage of any individual good causes its market price to rise and a surplus of the good causes its market price to fall. These forces ensure that the market reaches equilibrium. The same logic applies to short-run macroeconomic equilibrium. If the aggregate price level is above its equilibrium level, the quantity of aggregate output supplied exceeds the quantity of aggregate output demanded. This leads to a fall in the aggregate price level and pushes it toward its equilibrium level.

If the aggregate price level is below its equilibrium level, the quantity of aggregate output supplied is less than the quantity of aggregate output demanded. This leads to a rise in the aggregate price level, again pushing it toward its equilibrium level. In the discussion that follows, we’ll assume that the economy is always in short-run macroeconomic equilibrium.

We’ll also make another important simplification based on the observation that in reality there is a long-term upward trend in both aggregate output and the aggregate price level. We’ll assume that a fall in either variable really means a fall compared to the long-run trend. For example, if the aggregate price level normally rises 4% per year, a year in which the aggregate price level rises only 3% would count, for our purposes, as a 1% decline.

In fact, since the Great Depression there have been very few years in which the aggregate price level of any major nation actually declined—Japan’s period of deflation from 1995 to 2005 is one of the few exceptions. However, there have been many cases in which the aggregate price level fell relative to the long-run trend.

The short-run equilibrium aggregate output and the short-run equilibrium aggregate price level can change because of shifts of either the AD curve or the SRAS curve. Let’s look at each case in turn.

Shifts of Aggregate Demand: Short-Run Effects

The Great Depression was caused by a negative demand shock and ended by a positive demand shock.
© Bettmann/CORBIS

An event that shifts the aggregate demand curve is a demand shock.

An event that shifts the aggregate demand curve, such as a change in expectations or wealth, the effect of the size of the existing stock of physical capital, or the use of fiscal or monetary policy, is known as a demand shock. The Great Depression was caused by a negative demand shock—the collapse of wealth and of business and consumer confidence that followed the stock market crash of 1929 and the banking crises of 1930–1931. The Depression was ended by a positive demand shock—the huge increase in government purchases during World War II. In 2008, the U.S. economy experienced another significant negative demand shock as the housing market turned from boom to bust, leading consumers and firms to scale back their spending.

Figure 29-2 shows the short-run effects of negative and positive demand shocks. A negative demand shock shifts the aggregate demand curve, AD, to the left, from AD1 to AD2, as shown in panel (a). The economy moves down along the SRAS curve from E1 to E2, leading to lower short-run equilibrium aggregate output and a lower short-run equilibrium aggregate price level. A positive demand shock shifts the aggregate demand curve, AD, to the right, as shown in panel (b). Here, the economy moves up along the SRAS curve, from E1 to E2. This leads to higher short-run equilibrium aggregate output and a higher short-run equilibrium aggregate price level. Demand shocks cause aggregate output and the aggregate price level to move in the same direction.

A demand shock shifts the aggregate demand curve, moving the aggregate price level and aggregate output in the same direction. In panel (a), a negative demand shock shifts the aggregate demand curve leftward from AD1 to AD2, reducing the aggregate price level from P1 to P2 and aggregate output from Y1 to Y2. In panel (b), a positive demand shock shifts the aggregate demand curve rightward, increasing the aggregate price level from P1 to P2 and aggregate output from Y1 to Y2.

Shifts of the [em]SRAS[/em] Curve

An event that shifts the short-run aggregate supply curve is a supply shock.

An event that shifts the short-run aggregate supply curve, such as a change in commodity prices, nominal wages, or productivity, is known as a supply shock. A negative supply shock raises production costs and reduces the quantity producers are willing to supply at any given aggregate price level, leading to a leftward shift of the short-run aggregate supply curve. The U.S. economy experienced severe negative supply shocks following disruptions to world oil supplies in 1973 and 1979.

In contrast, a positive supply shock reduces production costs and increases the quantity supplied at any given aggregate price level, leading to a rightward shift of the short-run aggregate supply curve. The United States experienced a positive supply shock between 1995 and 2000, when the increasing use of the Internet and other information technologies caused productivity growth to surge.

The effects of a negative supply shock are shown in panel (a) of Figure 29-3. The initial equilibrium is at E1, with aggregate price level P1 and aggregate output Y1. The disruption in the oil supply causes the short-run aggregate supply curve to shift to the left, from SRAS1 to SRAS2. As a consequence, aggregate output falls and the aggregate price level rises, an upward movement along the AD curve. At the new equilibrium, E2, the short-run equilibrium aggregate price level, P2, is higher, and the short-run equilibrium aggregate output level, Y2, is lower than before.

A supply shock shifts the short-run aggregate supply curve, moving the aggregate price level and aggregate output in opposite directions. Panel (a) shows a negative supply shock, which shifts the short-run aggregate supply curve leftward and causes stagflation—lower aggregate output and a higher aggregate price level. Here the short-run aggregate supply curve shifts from SRAS1 to SRAS2, and the economy moves from E1 to E2. The aggregate price level rises from P1 to P2, and aggregate output falls from Y1 to Y2. Panel (b) shows a positive supply shock, which shifts the short-run aggregate supply curve rightward, generating higher aggregate output and a lower aggregate price level. The short-run aggregate supply curve shifts from SRAS1 to SRAS2, and the economy moves from E1 to E2. The aggregate price level falls from P1 to P2, and aggregate output rises from Y1 to Y2.

Stagflation is the combination of inflation and stagnating (or falling) aggregate output.

The combination of inflation and falling aggregate output shown in panel (a) has a special name: stagflation, for “stagnation plus inflation.” When an economy experiences stagflation, it’s very unpleasant: falling aggregate output leads to rising unemployment, and people feel that their purchasing power is squeezed by rising prices. Stagflation in the 1970s led to a mood of national pessimism. It also, as we’ll see shortly, poses a dilemma for policy makers.

A positive supply shock, shown in panel (b), has exactly the opposite effects. A rightward shift of the SRAS curve, from SRAS1 to SRAS2, results in a rise in aggregate output and a fall in the aggregate price level, a downward movement along the AD curve. The favorable supply shocks of the late 1990s led to a combination of full employment and declining inflation. That is, the aggregate price level fell compared with the long-run trend. This combination produced, for a time, a great wave of national optimism.

Producers are vulnerable to supply shocks caused by dramatic changes in oil prices.
Bloomberg via Getty Images

The distinctive feature of supply shocks, both negative and positive, is that, unlike demand shocks, they cause the aggregate price level and aggregate output to move in opposite directions.

There’s another important contrast between supply shocks and demand shocks. As we’ve seen, monetary policy and fiscal policy enable the government to shift the aggregate demand curve, meaning that governments are in a position to create the kinds of shocks shown in Figure 29-2. It’s much harder for governments to shift the aggregate supply curve. Are there good policy reasons to shift the aggregate demand curve? We’ll turn to that question soon. First, however, let’s look at the difference between short-run macroeconomic equilibrium and long-run macroeconomic equilibrium.

Long-Run Macroeconomic Equilibrium

The economy is in long-run macroeconomic equilibrium when the point of short-run macroeconomic equilibrium is on the long-run aggregate supply curve.

Figure 29-4 combines the aggregate demand curve with both the short-run and long-run aggregate supply curves. The aggregate demand curve, AD, crosses the short-run aggregate supply curve, SRAS, at ELR. Here we assume that enough time has elapsed that the economy is also on the long-run aggregate supply curve, LRAS. As a result, ELR is at the intersection of all three curves—SRAS, LRAS, and AD. So short-run equilibrium aggregate output is equal to potential output, YP. Such a situation, in which the point of short-run macroeconomic equilibrium is on the long-run aggregate supply curve, is known as long-run macroeconomic equilibrium.

Here the point of short-run macroeconomic equilibrium also lies on the long-run aggregate supply curve, LRAS. As a result, short-run equilibrium aggregate output is equal to potential output, YP. The economy is in long-run macroeconomic equilibrium at ELR.

To see the significance of long-run macroeconomic equilibrium, let’s consider what happens if a demand shock moves the economy away from long-run macroeconomic equilibrium. In Figure 29-5, we assume that the initial aggregate demand curve is AD1 and the initial short-run aggregate supply curve is SRAS1. So the initial macroeconomic equilibrium is at E1, which lies on the long-run aggregate supply curve, LRAS. The economy, then, starts from a point of short-run and long-run macroeconomic equilibrium, and short-run equilibrium aggregate output equals potential output at Y1.

In the long run the economy is self-correcting: demand shocks have only a short-run effect on aggregate output. Starting at E1, a negative demand shock shifts AD1 leftward to AD2. In the short run the economy moves to E2 and a recessionary gap arises: the aggregate price level declines from P1 to P2, aggregate output declines from Y1 to Y2, and unemployment rises. But in the long run nominal wages fall in response to high unemployment at Y2, and SRAS1 shifts rightward to SRAS2. Aggregate output rises from Y2 to Y1, and the aggregate price level declines again, from P2 to P3. Long-run macroeconomic equilibrium is eventually restored at E3.

Now suppose that for some reason—such as a sudden worsening of business and consumer expectations—aggregate demand falls and the aggregate demand curve shifts leftward to AD2. This results in a lower equilibrium aggregate price level at P2 and a lower equilibrium aggregate output level at Y2 as the economy settles in the short run at E2. The short-run effect of such a fall in aggregate demand is what the U.S. economy experienced in 1929–1933: a falling aggregate price level and falling aggregate output.

There is a recessionary gap when aggregate output is below potential output.

Aggregate output in this new short-run equilibrium, E2, is below potential output. When this happens, the economy faces a recessionary gap. A recessionary gap inflicts a great deal of pain because it corresponds to high unemployment. The large recessionary gap that had opened up in the United States by 1933 caused intense social and political turmoil. And the devastating recessionary gap that opened up in Germany at the same time played an important role in Hitler’s rise to power.

The economy is self-correcting in the long run.
Robert Adrian Hillman/Shutterstock

But this isn’t the end of the story. In the face of high unemployment, nominal wages eventually fall, as do any other sticky prices, ultimately leading producers to increase output. As a result, a recessionary gap causes the short-run aggregate supply curve to gradually shift to the right. This process continues until SRAS1 reaches its new position at SRAS2, bringing the economy to equilibrium at E3, where AD2, SRAS2, and LRAS all intersect. At E3, the economy is back in long-run macroeconomic equilibrium; it is back at potential output Y1 but at a lower aggregate price level, P3, reflecting a long-run fall in the aggregate price level. The economy is self-correcting in the long run.

What if, instead, there was an increase in aggregate demand? The results are shown in Figure 29-6, where we again assume that the initial aggregate demand curve is AD1 and the initial short-run aggregate supply curve is SRAS1, so that the initial macroeconomic equilibrium, at E1, lies on the long-run aggregate supply curve, LRAS. Initially, then, the economy is in long-run macroeconomic equilibrium.

Starting at E1, a positive demand shock shifts AD1 rightward to AD2, and the economy moves to E2 in the short run. This results in an inflationary gap as aggregate output rises from Y1 to Y2, the aggregate price level rises from P1 to P2, and unemployment falls to a low level. In the long run, SRAS1 shifts leftward to SRAS2 as nominal wages rise in response to low unemployment at Y2. Aggregate output falls back to Y1, the aggregate price level rises again to P3, and the economy self-corrects as it returns to long-run macro economic equilibrium at E3.

There is an inflationary gap when aggregate output is above potential output.

Now suppose that aggregate demand rises, and the AD curve shifts rightward to AD2. This results in a higher aggregate price level, at P2, and a higher aggregate output level, at Y2, as the economy settles in the short run at E2. Aggregate output in this new short-run equilibrium is above potential output, and unemployment is low in order to produce this higher level of aggregate output. When this happens, the economy experiences an inflationary gap. As in the case of a recessionary gap, this isn’t the end of the story.

In the face of low unemployment, nominal wages will rise, as will other sticky prices. An inflationary gap causes the short-run aggregate supply curve to shift gradually to the left as producers reduce output in the face of rising nominal wages. This process continues until SRAS1 reaches its new position at SRAS2, bringing the economy into equilibrium at E3, where AD2, SRAS2, and LRAS all intersect. At E3, the economy is back in long-run macroeconomic equilibrium. It is back at potential output, but at a higher price level, P3, reflecting a long-run rise in the aggregate price level. Again, the economy is self-correcting in the long run.

To summarize the analysis of how the economy responds to recessionary and inflationary gaps, we can focus on the output gap, the percentage difference between actual aggregate output and potential output. The output gap is calculated as follows:

The output gap is the percentage difference between actual aggregate output and potential output.

Our analysis says that the output gap always tends toward zero.

The economy is self-correcting when shocks to aggregate demand affect aggregate output in the short run, but not in the long run.

If there is a recessionary gap, so that the output gap is negative, nominal wages eventually fall, moving the economy back to potential output and bringing the output gap back to zero. If there is an inflationary gap, so that the output gap is positive, nominal wages eventually rise, also moving the economy back to potential output and again bringing the output gap back to zero. So in the long run the economy is self-correcting: shocks to aggregate demand affect aggregate output in the short run but not in the long run.

!world_eia!SUPPLY SHOCKS VERSUS DEMAND SHOCKS IN PRACTICE

How often do supply shocks and demand shocks, respectively, cause recessions? The verdict of most, though not all, macroeconomists is that recessions are mainly caused by demand shocks. But when a negative supply shock does happen, the resulting recession tends to be particularly severe.

Let’s get specific. Officially there have been twelve recessions in the United States since World War II. However, two of these, in 1979–1980 and 1981–1982, are often treated as a single “double-dip” recession, bringing the total number down to eleven. Of these eleven recessions, only two—the recession of 1973–1975 and the double-dip recession of 1979–1982—showed the distinctive combination of falling aggregate output and a surge in the price level that we call stagflation.

In each case, the cause of the supply shock was political turmoil in the Middle East—the Arab–Israeli war of 1973 and the Iranian revolution of 1979—that disrupted world oil supplies and sent oil prices skyrocketing. In fact, economists sometimes refer to the two slumps as “OPEC I” and “OPEC II,” after the Organization of Petroleum Exporting Countries, the world oil cartel. A third recession that began in 2007 and lasted until 2009 was at least partially exacerbated, if not at least partially caused, by a spike in oil prices.

So eight of eleven postwar recessions were purely the result of demand shocks, not supply shocks. The few supply-shock recessions, however, were the worst as measured by the unemployment rate. Figure 29-7 shows the U.S. unemployment rate from 1948 through 2011, with the dates of the 1973 Arab–Israeli war and the 1979 Iranian revolution highlighted. Some of the highest unemployment rates since World War II came after these big negative supply shocks.

Source: Bureau of Labor Statistics.

There’s a reason the aftermath of a supply shock tends to be particularly severe for the economy: macroeconomic policy has a much harder time dealing with supply shocks than with demand shocks. Indeed, the reason the Federal Reserve was having a hard time in 2008, as described in the section-opening story, was the fact that in early 2008 the U.S. economy was in a recession partially caused by a supply shock (although it was also facing a demand shock). We’ll see in a moment why supply shocks present such a problem.

Macroeconomic Policy

We’ve just seen that the economy is self-correcting in the long run: it will eventually trend back to potential output.

Most macroeconomists believe, however, that the process of self-correction typically takes a decade or more. In particular, if aggregate output is below potential output, the economy can suffer an extended period of depressed aggregate output and high unemployment before it returns to normal.

This belief is the background to one of the most famous quotations in economics: John Maynard Keynes’s declaration, “In the long run we are all dead.” Economists usually interpret Keynes as having recommended that governments not wait for the economy to correct itself. Instead, it is argued by many economists, but not all, that the government should use fiscal policy to get the economy back to potential output in the aftermath of a shift of the aggregate demand curve.

Stabilization policy is the use of government policy to reduce the severity of recessions and rein in excessively strong expansions.

This is the rationale for active stabilization policy, which is the use of government policy to reduce the severity of recessions and rein in excessively strong expansions.

Can stabilization policy improve the economy’s performance? As we saw in Figure 28-4, the answer certainly appears to be yes. Under active stabilization policy, the U.S. economy returned to potential output in 1996 after an approximately five-year recessionary gap. Likewise, in 2001, it also returned to potential output after an approximately four-year inflationary gap. These periods are much shorter than the decade or more that economists believe it would take for the economy to self-correct in the absence of active stabilization policy. However, the ability to improve the economy’s performance is not always guaranteed. It depends on the kinds of shocks the economy faces.

Policy in the Face of Demand Shocks

Imagine that the economy experiences a negative demand shock, like the one shown by the shift from AD1 to AD2 in Figure 29-5. As we know, fiscal policy shifts the aggregate demand curve. If policy makers react quickly to the fall in aggregate demand, they can use monetary or fiscal policy to shift the aggregate demand curve back to the right. And if policy were able to perfectly anticipate shifts of the aggregate demand curve and counteract them, it could short-circuit the whole process shown in Figure 29-5. Instead of going through a period of low aggregate output and falling prices, the government could manage the economy so that it would stay at E1.

Why might a policy that short-circuits the adjustment shown in Figure 29-5 and maintains the economy at its original equilibrium be desirable? For two reasons: First, the temporary fall in aggregate output that would happen without policy intervention is a bad thing, particularly because such a decline is associated with high unemployment. Second, price stability is generally regarded as a desirable goal. So preventing deflation—a fall in the aggregate price level—is a good thing.

Does this mean that policy makers should always act to offset declines in aggregate demand? Not necessarily. Some policy measures to increase aggregate demand, especially those that increase budget deficits, may have long-term costs in terms of lower long-run growth.

Furthermore, in the real world policy makers aren’t perfectly informed, and the effects of their policies aren’t perfectly predictable. This creates the danger that stabilization policy will do more harm than good; that is, attempts to stabilize the economy may end up creating more instability. We’ll describe the long-running debate over macroeconomic policy in later modules. Despite these qualifications, most economists believe that a good case can be made for using macroeconomic policy to offset major negative shocks to the AD curve.

Should policy makers also try to offset positive shocks to aggregate demand? It may not seem obvious that they should. After all, even though inflation may be a bad thing, isn’t more output and lower unemployment a good thing? Again, not necessarily. Most economists now believe that any short-run gains from an inflationary gap must be paid back later. So policy makers today usually try to offset positive as well as negative demand shocks. For reasons we’ll explain later, attempts to eliminate recessionary gaps and inflationary gaps usually rely on monetary rather than fiscal policy. But how should macroeconomic policy respond to supply shocks?

Responding to Supply Shocks

In panel (a) of Figure 29-3 we showed the effects of a negative supply shock: in the short run such a shock leads to lower aggregate output but a higher aggregate price level. As we’ve noted, policy makers can respond to a negative demand shock by using monetary and fiscal policy to return aggregate demand to its original level. But what can or should they do about a negative supply shock?

In contrast to the case of a demand shock, there are no easy remedies for a supply shock. That is, there are no government policies that can easily counteract the changes in production costs that shift the short-run aggregate supply curve. So the policy response to a negative supply shock cannot aim to simply push the curve that shifted back to its original position.

In 2008, stagflation made for difficult policy choices for the Federal Reserve chairman at the time, Ben Bernanke.
AP Photo/Manuel Balce Ceneta

And if you consider using monetary or fiscal policy to shift the aggregate demand curve in response to a supply shock, the right response isn’t obvious.

Two bad things are happening simultaneously: a fall in aggregate output, leading to a rise in unemployment, and a rise in the aggregate price level. Any policy that shifts the aggregate demand curve helps one problem only by making the other worse. If the government acts to increase aggregate demand and limit the rise in unemployment, it reduces the decline in output but causes even more inflation. If it acts to reduce aggregate demand, it curbs inflation but causes a further rise in unemployment.

It’s a trade-off with no good answer. In the end, the United States and other economically advanced nations suffering from the supply shocks of the 1970s eventually chose to stabilize prices even at the cost of higher unemployment. But being an economic policy maker in the 1970s, or in early 2008, meant facing even harder choices than usual.

Module 29 Review

Solutions appear at the back of the book.

Check Your Understanding

  1. Describe the short-run effects of each of the following shocks on the aggregate price level and on aggregate output.

    • a. The government sharply increases the minimum wage, raising the wages of many workers.

    • b. Solar energy firms launch a major program of investment spending.

    • c. Congress raises taxes and cuts spending.

    • d. Severe weather destroys crops around the world.

  2. A rise in productivity increases potential output, but some worry that demand for the additional output will be insufficient even in the long run. How would you respond?

  3. Suppose someone says, “Using monetary or fiscal policy to pump up the economy is counterproductive—you get a brief high, but then you have the pain of inflation.”

    • a. Explain what this means in terms of the AD–AS model.

    • b. Is this a valid argument against stabilization policy? Why or why not?

  4. In 2008, in the aftermath of the collapse of the housing bubble and a sharp rise in the price of commodities, particularly oil, there was much internal disagreement within the Fed about how to respond, with some advocating lowering interest rates and others contending that this would set off a rise in inflation. Explain the reasoning behind each of these views in terms of the AD–AS model.

Multiple-Choice Questions

  1. Question

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  2. Question

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  3. Question

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Refer to the graph for questions 4 and 5.

  1. Question

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  2. Question

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Critical-Thinking Question

Question 1.2

Draw a graph to illustrate an economy in the midst of an inflationary gap. Explain and illustrate why the economy will eventually return to long-run equilibrium.

PITFALLS: WHERE’S THE DEFLATION?

WHERE’S THE DEFLATION?

The AD–AS model tells us that either a negative demand shock or a positive supply shock should lead to a fall in the aggregate price level—that is, it should lead to deflation. But, how often does deflation actually occur?

Rarely. Since 1949, an actual fall in the aggregate price level has been a rare occurrence in the United States. Similarly, most other countries have had little or no experience with deflation. Japan, which experienced sustained mild deflation in the late 1990s and the early part of the next decade, is the big (and much discussed) exception. What happened to deflation?

The basic answer is that since World War II economic fluctuations have largely taken place around a long-run inflationary trend. Before the war, it was common for prices to fall during recessions, but since then negative demand shocks have largely been reflected in a decline in the rate of inflation rather than an actual fall in prices. For example, the rate of consumer price inflation fell from more than 3% at the beginning of the 2001 recession to 1.1% a year later, but it never went below zero. All of this changed during the recession of 2007–2009. The negative demand shock that followed the 2008 financial crisis was so severe that, for most of 2009, consumer prices in the United States indeed fell. But the deflationary period didn’t last long: beginning in 2010, prices again rose, at a rate of between 1% and 4% per year.

To learn more, see pages 297–301, especially Figure 29-5.