The Multiplier Process and Inventory Adjustment

We’ve just learned about a very important feature of the macroeconomy: when planned spending by households and firms does not equal the current aggregate output by firms, this difference shows up in changes in inventories. The response of firms to those inventory changes moves real GDP over time to the point at which real GDP and planned aggregate spending are equal. That’s why, as we mentioned earlier, changes in inventories are considered a leading indicator of future economic activity.

Now that we understand how real GDP moves to achieve income–expenditure equilibrium for a given level of planned aggregate spending, let’s turn to understanding what happens when there is a shift of the planned aggregate spending line. How does the economy move from the initial point of income–expenditure equilibrium to a new point of income–expenditure equilibrium? And what are the possible sources of changes in planned aggregate spending?

In our simple model there are only two possible sources of a shift of the planned aggregate spending line: a change in planned investment spending, IPlanned, or a shift of the aggregate consumption function, CF. For example, a change in IPlanned can occur because of a change in the interest rate. (Remember, we’re assuming that the interest rate is fixed by factors that are outside the model. But we can still ask what happens when the interest rate changes.) A shift of the aggregate consumption function (that is, a change in its vertical intercept, A) can occur because of a change in aggregate wealth—say, due to a rise in house prices. When the planned aggregate spending line shifts—when there is a change in the level of planned aggregate spending at any given level of real GDP—there is an autonomous change in planned aggregate spending.

Recall from earlier in this chapter that an autonomous change in planned aggregate spending is a change in the desired level of spending by firms, households, and government at any given level of real GDP (although we’ve assumed away the government for the time being). How does an autonomous change in planned aggregate spending affect real GDP in income–expenditure equilibrium?

TABLE 11-4

Table 11-4 and Figure 11-11 start from the same numerical example we used in Table 11-3 and Figure 11-10. They also show the effect of an autonomous increase in planned aggregate spending of 400—what happens when planned aggregate spending is 400 higher at each level of real GDP. Look first at Table 11-4. Before the autonomous increase in planned aggregate spending, the level of real GDP at which planned aggregate spending is equal to real GDP, Y*, is 2,000. After the autonomous change, Y* has risen to 3,000. The same result is visible in Figure 11-11. The initial income–expenditure equilibrium is at E1, where is 2,000. The autonomous rise in planned aggregate spending shifts the planned aggregate spending line up, leading to a new income–expenditure equilibrium at E2, where is 3,000.

The Multiplier This figure illustrates the change in Y* caused by an autonomous increase in planned aggregate spending. The economy is initially at equilibrium point E1 with an income–expenditure equilibrium GDP, , equal to 2,000. An autonomous increase in AEPlanned of 400 shifts the planned aggregate spending line upward by 400. The economy is no longer in income–expenditure equilibrium: real GDP is equal to 2,000 but AEPlanned is now 2,400, represented by point X. The vertical distance between the two planned aggregate spending lines, equal to 400, represents IUnplanned = 400—the negative inventory investment that the economy now experiences. Firms respond by increasing production, and the economy eventually reaches a new income–expenditure equilibrium at E2 with a higher level of income–expenditure equilibrium GDP, , equal to 3,000.

The fact that the rise in income–expenditure equilibrium GDP, from 2,000 to 3,000, is much larger than the autonomous increase in aggregate spending, which is only 400, has a familiar explanation: the multiplier process. In the specific example we have just described, an autonomous increase in planned aggregate spending of 400 leads to an increase in Y* from 2,000 to 3,000, a rise of 1,000. So the multiplier in this example is 1,000/400 = 2.5.

We can examine in detail what underlies the multistage multiplier process by looking more closely at Figure 11-11. First, starting from E1, the autonomous increase in planned aggregate spending leads to a gap between planned aggregate spending and real GDP. This is represented by the vertical distance between X, at 2,400, and E1, at 2,000. This gap illustrates an unplanned fall in inventory investment: IUnplanned = − 400. Firms respond by increasing production, leading to a rise in real GDP from . The rise in real GDP translates into an increase in disposable income, YD. That’s the first stage in the chain reaction. But it doesn’t stop there—the increase in YD leads to a rise in consumer spending, C, which sets off a second-round rise in real GDP. This in turn leads to a further rise in disposable income and consumer spending, and so on. And we could play this process in reverse: an autonomous fall in aggregate spending will lead to a chain reaction of reductions in real GDP and consumer spending.

We can summarize these results in an equation, where ΔAAEPlanned represents the autonomous change in AEPlanned, and , the subsequent change in income–expenditure equilibrium GDP:

Recalling that the multiplier, 1/(1 − MPC), is greater than 1, Equation 11-17 tells us that the change in income–expenditure equilibrium GDP, ΔY*, is several times as large as the autonomous change in planned aggregate spending, ΔAAEPlanned. It also helps us recall an important point: because the marginal propensity to consume is less than 1, each increase in disposable income and each corresponding increase in consumer spending is smaller than in the previous round. That’s because at each round some of the increase in disposable income leaks out into savings. As a result, although real GDP grows at each round, the increase in real GDP diminishes from each round to the next. At some point the increase in real GDP is negligible, and the economy converges to a new income–expenditure equilibrium GDP at .

The Paradox of Thrift You may recall that in Chapter 6 we mentioned the paradox of thrift to illustrate the fact that in macroeconomics the outcome of many individual actions can generate a result that is different from and worse than the simple sum of those individual actions. In the paradox of thrift, households and firms cut their spending in anticipation of future tough economic times. These actions depress the economy, leaving households and firms worse off than if they hadn’t acted virtuously to prepare for tough times. It is called a paradox because what’s usually “good” (saving to provide for your family in hard times) is “bad” (because it can make everyone worse off).

Using the multiplier, we can now see exactly how this scenario unfolds. Suppose that there is a slump in consumer spending or investment spending, or both, just like the slump in residential construction investment spending leading up to the 2007–2009 recession. This causes a fall in income–expenditure equilibrium GDP that is several times larger than the original fall in spending. The fall in real GDP leaves consumers and producers worse off than they would have been if they hadn’t cut their spending.

Conversely, prodigal behavior is rewarded: if consumers or producers increase their spending, the resulting multiplier process makes the increase in income–expenditure equilibrium GDP several times larger than the original increase in spending. So prodigal spending makes consumers and producers better off than if they had been cautious spenders.

It’s important to realize that our result that the multiplier is equal to 1/(1 − MPC) depends on the simplifying assumption that there are no taxes or transfers, so that disposable income is equal to real GDP. In the appendix to Chapter 13, we’ll bring taxes into the picture, which makes the expression for the multiplier more complicated and the multiplier itself smaller. But the general principle we have just learned—an autonomous change in planned aggregate spending leads to a change in income–expenditure equilibrium GDP, both directly and through an induced change in consumer spending—remains valid.

Extravagant spending on the part of producers and consumers makes everyone better off thanks to the multiplier process.

As we noted earlier in this chapter, declines in planned investment spending are usually the major factor causing recessions, because historically they have been the most common source of autonomous reductions in aggregate spending. The tendency of the consumption function to shift upward over time, which we pointed out earlier in the Economics in Action, “Famous First Forecasting Failures,” means that autonomous changes in both planned investment spending and consumer spending play important roles in expansions. But regardless of the source, there are multiplier effects in the economy that magnify the size of the initial change in aggregate spending.

ECONOMICS in Action: Inventories and the End of a Recession

Inventories and the End of a Recession

Avery clear example of the role of inventories in the multiplier process took place in late 2001, as that year’s recession came to an end. The driving force behind the recession was a slump in business investment spending. It took several years before investment spending bounced back in the form of a housing boom. Still, the economy did start to recover in late 2001, largely because of an increase in consumer spending—especially on durable goods such as automobiles.

Inventories and the End of a Recession Source: Bureau of Economic Analysis.

Initially, this increase in consumer spending caught manufacturers by surprise. Figure 11-12 shows changes in real GDP, real consumer spending, and real inventories in each quarter of 2001 and 2002. Notice the surge in consumer spending in the fourth quarter of 2001. It didn’t lead to a lot of GDP growth because it was offset by a plunge in inventories. But in the first quarter of 2002 producers greatly increased their production, leading to a jump in real GDP.

Quick Review

  • The economy is in income–expenditure equilibrium when planned aggregate spending is equal to real GDP.

  • At any output level greater than income–expenditure equilibrium GDP, real GDP exceeds planned aggregate spending and inventories are rising. At any lower output level, real GDP falls short of planned aggregate spending and inventories are falling.

  • After an autonomous change in planned aggregate spending, the economy moves to a new income–expenditure equilibrium through the inventory adjustment process, as illustrated by the Keynesian cross. Because of the multiplier effect, the change in income–expenditure equilibrium GDP is a multiple of the autonomous change in aggregate spending.

11-4

  1. Question 11.9

    Although economists believe that recessions typically begin as slumps in investment spending, they also believe that consumer spending eventually slumps during a recession. Explain why.

  2. Question 11.10

    1. Use a diagram like Figure 11-10 to show what happens when there is an autonomous fall in planned aggregate spending. Describe how the economy adjusts to a new income–expenditure equilibrium.

    2. Suppose Y* is originally $500 billion, the autonomous reduction in planned aggregate spending is $300 million ($0.3 billion), and MPC = 0.5. Calculate Y* after such a change.

Solutions appear at back of book.

What’s Good for America Is Good for GM

In 2009, with the economy in a steep nose-dive, the U.S. government took many measures, some of which were highly controversial. Among the most controversial was the decision to use taxpayer’s funds to bail out General Motors, which was teetering on the edge of bankruptcy. To keep the company afloat, the U.S. government gave it $49.5 billion in loans; these loans were then converted into stock, giving the government temporary ownership of 61% of the company.

General Motors—or GM, as it was often called in its heyday—was once an American icon, so dominant that in the 1950s the company’s president, who had been nominated as Secretary of Defense, famously claimed that any conflict of interest was inconceivable: “I thought what was good for our country was good for General Motors, and vice versa.”

By 2009 the fate of GM and the fate of America seemed less intertwined. Still, the case for the bailout rested crucially on the belief that GM’s problems weren’t entirely self-made, that the company was in trouble because the U.S. economy was in trouble, and that national recovery would make a big difference to the automaker’s fortune too.

On the face of it, this interdependence wasn’t entirely obvious: the 2007–2009 recession was driven by a housing bust and troubles in the banking sector, not by developments in the auto industry. But multiplier effects had indeed led to a plunge in auto sales, as shown in Figure 11-13. And sure enough, as the economy began to recover, auto sales made up most of their lost ground, with GM sharing in the industry’s resurgence.

U.S. Auto Sales, 2000–2013 Source: Federal Reserve Bank of St. Louis.

Did saving GM justify the bailout? The company’s recovery meant that taxpayers got most of their money back—but not all of it. Recall that the government loan of almost $50 billion was converted into GM stock. Over time, the government sold off its stake for roughly $40 billion—leaving taxpayers with a $10 billion loss.

Defenders of the bailout nonetheless declared it a success, because it resuscitated the U.S. auto industry and saved many jobs, not just in the auto companies and their suppliers, but in the many businesses whose sales depend on the incomes of workers employed in the auto industry. In the summer of 2009 the unemployment rate in Michigan, still America’s automotive heartland, rose above 14%—but it then began a rapid decline, falling to 7.4% by early 2014. Few would argue that the speedy recovery in employment in Michigan would have happened without the auto bailout.

In the end, GM bounced back because the U.S. economy as a whole recovered; what was good for America was indeed still good for General Motors. And what was good for General Motors was clearly good for Michigan—and maybe, arguably, for America as a whole.

QUESTIONS FOR THOUGHT

Question 11.11

Why did a national slump that began with housing affect companies like General Motors?

Question 11.12

Why was it reasonable in June 2009 to predict that auto sales would improve in the near future?

Question 11.13

How does this story about General Motors help explain how a slump in housing—a relatively small part of the U.S. economy—could produce such a deep national recession?