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# The Multiplier Effect Review for AP Economics (page 2)

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By McGraw-Hill Professional
Updated on Mar 2, 2011

### The Tax Multiplier

The above discussion of the public sector shows that when the government injects money into the economy (G), it multiplies by a factor of the spending multiplier. But the government can also have an impact on aggregate expenditures and real GDP by changing taxes and/or transfers.

The Multiplier Effect

Recipients of a decrease in taxes treat it as an increase in disposable income. The typical household increases consumption by a factor of the MPC and increases saving by a factor of the MPS. It is important to keep in mind that less than 100 percent of this increase in disposable income circulates through the economy because most households save a proportion of it.

Example:
The MPC is equal to .90, and the government transfers back tax revenue to consumers by sending each taxpayer a \$200 check. With an MPC = .90, \$180 is consumed and \$20 is saved. The multiplier process kicks in, but not on the entire \$200, only on the consumed portion of \$180. The multiplier being 1/.10 = 10, GDP increases by \$1800.
In other words, a \$200 change in tax policy (a tax rebate in this case) caused an \$1800 change in real GDP. This tax multiplier of 9 measures the magnitude of the multiplier process when there is a change in taxes.

The Difference in Multipliers

With an MPC = .90, the spending multiplier is 10, but the tax multiplier is smaller, Tm = 9. Why? The spending multiplier begins to work as soon as there is a change in autonomous spending (C, I, G, net exports) but the tax multiplier must first go through a person's consumption function as disposable income. In that first "round" of spending, some of those injected dollars are leakages in the form of savings. In our example above, 10 percent of those injected dollars fail to be recirculated and therefore the final multiplier effect is smaller. The relationship between the spending multiplier and the tax multiplier (Tm) is:

Tm = MPC × (Spending multiplier) = .90 × (l/ .10) = 9 in our example

Be preparedto respond to a free-response question that asks you to explain why the tax multiplier is smaller than the spending multiplier.

Example:
The MPC = .80 and the government decides to impose a \$50 increase in taxes. What happens to GDP?
Tm = .80 × Multiplier = .80 × (1/.20) = 4
Because the tax multiplier is equal to 4, we determine that GDP falls by \$200. How do we know? Because taxes were increased, disposable income falls, consumption falls, causing GDP to fall, in this case by a factor of 4.

The tax multiplier is found by:

### The Balanced-Budget Multiplier

The government both collects and spends tax revenue. In a simplified model, if the dollars spent equal the dollars collected, the budget is balanced. We have already discussed how the spending multiplier and tax multiplier are different. A quick example of a balanced budget policy illustrates what is called the balanced-budget multiplier.

Example:
The government wants to spend \$100 on a federal program and pay for it by collecting \$100 in additional taxes. The MPC = .90 in this example.

Spending Effect

The spending multiplier = 10 implies that the \$100 of new spending (G) creates a \$1000 increasein real GDP.

Taxation Effect

The tax multiplier Tm = 9 implies that a \$100 increase in taxes decreasesreal GDP by \$900.

Balanced Budget Effect

Change in real GDP = +\$1000 – \$900 = +\$100

So a \$100 increase in spending, financed by a \$100 increase in taxes, created only \$100 in new GDP. The balanced-budget multiplier is always equal to one, regardless of the MPC.

• Balanced-Budget Multiplier = 1

Review questions for this study guide can be found at:

Consumption, Saving, Investment, and the Multiplier Review Questions for AP Economics

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