Multiplier Effect

If investment were zero in Table 1, Aggregate Expenditures would consist only of consumption (C) and equilibrium income would be \$5,500 billion (point a in Figures 1 and 2). When autonomous investment of \$300 billion is injected, however, its effect is multiplied so that equilibrium income rises to \$7,000 billion (points e in both figures). The total change in income that ultimately results from this investment is five times the initial increase in spending!

You may wonder how a relatively small injection of investment (\$300 billion) so powerfully expands income (by \$1,500 billion). Multiplier processes provide the answer.

The multiplier effect occurs when one person's spending becomes someone else's income, and some of the second person's income is subsequently spent, becoming the income of a third person, and so on.

But at what income level does this spending    spending cycle stop? The answerincome  requires a bit of arithmetic.

The autonomous spending multiplier is the total change in income generated, divided by the  spending income change in autonomous spending that triggered the spending  sequence.

When investment is the source of new autonomous spending, this autonomous spending multiplier equals the ratio Y/I.

Suppose we begin with zero investment. According to Table 1, equilibrium income would be \$5,500 billion, because only at that level does planned saving also equal zero. Now suppose firms decide to invest \$100 billion in new capital goods. The workers and owners of firms that produce this new capital receive \$100 billion in additional income.

How will these workers and proprietors respond to this extra \$100 billion in income? Their mpc is 0.8 in their roles as consumers, so \$80 billion of this new income will be spent on consumer goods, and saving grows \$20 billion. When these producers spend the \$80 billion, this second round of spending adds \$80 billion to Aggregate Expenditures; National Output must rise by \$80 billion, which becomes new income to the firms providing these consumer goods and to their employees. In turn, they will spend 80 percent of the \$80 billion, or \$64 billion in income to their suppliers, and so on throughout the system.

The cumulative effect of this round-by-round spending is illustrated in Figure 3, assuming the mpc to be 0.8 so that the mps is 0.2, The multiplier in this case is 5. That the multiplier is the reciprocal of the mps is no coincidence: 1/mps =1/0.2= 5. In fact, any change in injections (e.g., either additional autonomous consumption or new investment) divided by the marginal propensity to save yields the total multiplied effect on National Output and Income.

FIGURE 3   The Multiplier Effect

An additional \$100 billion in spending in Round 1 (shown at the bottom "stair" spending multiplier income ) is subject to a spending  process, ultimately generating a total increase in income of \$500 billion when the mpc = 0.8. Each increase in spending in each round, when multiplied by the mpc, is the increase in spending for the subsequent round. When the sum of this infinite series is calculated, aggregate income grows by \$500 billion from this initial new injection of \$100 billion.

Note: Data after Round 3 are rounded to the nearest billion.

 Table 2   A Tabular Example of the Multiplier (billions of dollars) Round Increases in Expenditures Increases in Saving Initial Increase \$100 n/a Round 2 80 \$ 20 Round 3 64 16 Round 4 51 13 Round 5 41 10 Round 6 33 8 Round 7 26 7 Round 8 21 5 Round 9 17 4 Round 10 13 3 Sum of First 10 Rounds \$446 \$ 86 Sum of All Other Rounds 54 14 Total Increase in Spending (Income) \$500 Total Increase in Saving \$100 Note: Data are based on Table 1. The mpc is 0.8 and the mps is 0.2. Figures after Round 3 are rounded to the nearest dollar.

The only form of withdrawal in our simplified model is saving, so the multiplier is 1/mps. (A higher mps yields a faster

rate of withdrawal and a smaller multiplier.) Alternatively, the multiplier is the change in income divided by the change in autonomous injections, so [1]

Y       =          1         =     __1___

I                 mps                  1 - mpc

If we consider withdrawals other than saving,

autonomous                                  1

spending          =          withdrawal fraction

multiplier                     per spending round

=                           1

1 - fraction respent

and

total changes

in income         =         amount of  multiplier.injection

A mathematical derivation of this autonomous spending multiplier is provided in the optional material at the end of this chapter.

The cumulative effect of autonomous investment based on data from Table 1 is shown in Figure 4. If autonomous investment were zero, equilibrium output would be \$5,500 billion (point a). The \$300 billion in autonomous investment boosts equilibrium income and output to \$7,000 billion (point e) because the mpc of 0.8 yields a multiplier of 5 (\$300 x 5 = \$1,500; \$5,500 + \$1,500 = \$7,000).

Figure 4 here

The effect on total income from a spending injection is equal to the injection times the autonomous spending multiplier. When the mpc = 0.8, this multiplier is 5. Therefore, an injection of \$300 billion in new investment yields a total increase in income of \$1,500 billion (\$7 trillion - \$5.5 trillion).

"Real World" Multipliers?

Our simple model seems to imply an enormous multiplier—the mps is, historically, about 7 percent, suggesting a multiplier of between 14 and 15. However, the linkages between spending rounds are much looser in the real world than in this model. More sophisticated models consider other withdrawals from the spending  spending sequence.income

Withdrawals include taxes (roughly 30 percent) and other "leakages" such as imports—a case where the funds we spend go into the hands of foreign suppliers. Moreover, the full multiplier effect is felt only after all spending rounds have been completed. Realistically, only the first few rounds of spending will occur in the same year as any new injection. For all these reasons and more, statistical estimates of the value of the autonomous spending multiplier place its maximum real value at around 2—even during the Great Depression, when conditions were optimal for the multiplier to have its largest possible value.

The Great Depression: The Multiplier in Action

Brother, can you spare a dime?

A Hit Song from a 1930’s

Prosperity reigned in the "Roaring '20s," with unemployment of only 3.2 percent in 1929, but by 1933, it had soared to 25 percent—one worker in four was jobless. No one was left unscathed. Soup kitchens could not feed all the hungry people, and Wall Street windows became diving platforms for those who preferred suicide to bankruptcy. Most U.S. financial institutions teetered on the brink, threatening to collapse like rows of dominoes. Unemployment compensation and Social Security had not yet been enacted to replace temporarily-lost incomes. Economically, Americans had never faced harder times. This dismal plunge into the Great Depression during 1929–1933 is summarized in Figure 5, a Keynesian portrayal that seems fairly straightforward by today's standards, but which would have been a revelation in the early 1930s.

FIGURE 5  Saving, Investment, and Income During the Great Depression

MISSING!

These equilibrium points for the United States before and during the Great Depression illustrate the Keynesian explanation for such economic downturns. Investment spending fell by XXX billion from 1929 to 1933, causing a general collapse of spending. Keynes viewed this as the root cause of the Depression.

Source:  Economic Reports of the President, 1980–1994.

Data for the four components of Aggregate Expenditures (C, I, G, X - M) reveal that changes in net foreign spending and government purchases were quite small and largely offset each other during this period. Keynesians viewed the collapse of Gross Private Domestic Investment (DI in Figure 5) between 1929 and 1933 as the root cause of the erosion of Aggregate Spending—investment fell from \$173.3 billion to only \$28.3 billion. This \$145 billion decline in investment was echoed by a \$263 billion drop in income (from \$848.1 billion in 1929 to \$585.4 billion in 1933). Remember that the multiplier is the change in income divided by the change in injections, which in this case is roughly DY / DI. Thus, our highly simplified Keynesian model suggests a multiplier during the Great Depression of 1.81 (-263/-145= 1.81).

Government policies to combat instability have been refined considerably in the past 60 years. Most economists doubt that such a deep collapse will ever recur. How might government have flattened the Great Depression, or made it shorter? In the next few chapters, we will examine tools the government now uses to combat both recessions and inflations.

The Investment Accelerator

The multiplier process relies on the fact that any increase in autonomous spending creates income, which generates further consumer spending, creating more income, and so on. New investment may also be triggered by increased spending.

An investment accelerator exerts pressure for accelerated income growth when rising consumption and income stimulate new capital investment.

New autonomous spending causes investment to accelerate, so that Aggregate Spending is both multiplied by induced consumption and accelerated by induced investment. Thus, a change in autonomous spending may increase income by even more than the multiplier effect alone. (More sophisticated Keynesian models than any considered in this book explain how interactions between investment accelerators and multiplier processes may destabilize Aggregate Expenditures.) The effects on National Income of interactions between the multiplier and accelerator are traced in Figure 7.

FIGURE 7  Integrating an Investment Accelerator into a Keynesian System

Investment is stimulated by a change in autonomous spending (A) through the accelerator principle. This change in autonomous spending magnifies Aggregate Expenditures even more than is suggested by the multiplier process, but it also makes Aggregate Spending extremely volatile.

[1] The mpc + mps = 1, so the mps = 1 - mpc and the multiplier may also be written as 1/(1 - mpc).

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