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Curiosity 4.2: What Is The Multiplier?
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A formal definition of the multiplier is
the change in the equilibrium level of income per change in government spending.
(The equilibrium level of income, discussed in appendix A, is that income level at which aggregate demand for goods and services equals aggregate supply of goods and services.) It is calculated as
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where
D
GDP is the change in equilibrium income resulting from a change in government spending of size
D
G.
A common use of the multiplier is to enable calculation of the increase in government spending that is needed to push the economy to a desired income level. Suppose, for example, that we wish to increase the income level by $10 billion, and the multiplier is 4. From the definition of the multiplier we obtain 4 = 10/
D
G,
implying that the required
D
G
= $2.5 billion.
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This example of a multiplier of 4 should not be taken literally. The multiplier value varies across countries and within a single country over time. Furthermore, its actual value is difficult to measure. As will be seen in chapter 7, some economists believe its value is very small, perhaps less than one.
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To be careful, we should really call the multiplier the income multiplier with respect to government spending," so as not to confuse it with other multipliers, but we follow tradition and call it "the" multiplier, seldom using the quotes. Many other multipliers exist, all giving the change in something of interest per change in something over which we have control. Some examples are the income multiplier with respect to the money supply, giving the change in equilibrium income per change in the money supply, and the employment multiplier with respect to the tax rate, giving the change in equilibrium employment per change in the tax rate. The latter multiplier should be negative because an increase in the tax rate should decrease disposable income and thus lower consumption demand, decreasing aggregate demand for goods and services.
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this renewal is shrinking, so this iterative process eventually dies out. The numerical example began with $8 billion excess demand. This led to an income increase of $8 billion, which in turn caused aggregate demand to increase, but by less than $8 billion. Why? Consumers use part of any increase in income to pay extra taxes and augment savings, causing the increase in consumption demand to fall well short of $8 billion. In this numerical example, consumption increases by 70 percent of the income increase. The next time the economy cycles through this iterative process, income increases again, but by less than $8 billion, and the third time through it increases by still less, as shown in the numerical example.
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This process is also illustrated in figure 4.2 where the economy begins at income level $700 billion, experiences an increase in government spending of $8 billion, and then moves over time to a higher income level, eventually reaching an income of $726.7 billion.
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Because of the renewal of aggregate demand, the ultimate increase in national income resulting from the $8 billion increase in government spending is more than $8 billion. If we had continued the iterative calculations in our numerical example, the ultimate cumulative increase in income would have turned out to be $26.7 billion. In this example, each dollar
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