In the preceding example, a $50 billion increase in investment spending led to a $200 billion increase in income and output. Thus, the multiplier is 4. The multiplier (M) is the number by which any initial change in spending is multiplied to find the ultimate change in income and output.

If we know the marginal propensity to consume in our economy, we can estimate the size of the multiplier before the change in spending has run its course. Either of two simple formulas can be used:

Applying the formula to our hypothetical economy (with an MPC of 0.75), we can verify that the multiplier is indeed 4:

As we've already seen, a multiplier of 4 tells us that any increase in spending will generate an increase in equilibrium output that is four times as large. (The multiplier also works in reverse; if spending drops, we can expect equilibrium output to decline by four times as much.) Of course, the multiplier can take on different values, depending on the economy's MPC. If the MPC is 0.5, the multiplier will be 2; if the MPC is 0.8, the multiplier will be 5. As you can see, the size of the multiplier is related directly to the size of the economy's marginal propensity to consume: The larger the MPC, the larger the multiplier. This relationship exists because when the MPC is larger, a greater fraction of any increase in income is spent—meaning that more income is passed on to the next round of consumers, and the ultimate increase in GDP is larger. Studies of the U.S. economy show that the actual value of the multiplier in this country is about . (The U.S. economy's multiplier is significantly smaller than our hypothetical multiplier because taxes and spending for imports reduce the amount of income remaining to be passed on to the next household. When households pay taxes, they have less money to spend for products. Similarly, the money that goes to purchase Japanese autos and French wines leaves the country and is not available to be passed on to other U.S. consumers. The impact of taxation is discussed in the appendix to this chapter.)

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