The simple tax multiplier differs from the simple expenditures multiplier based on how the autonomous change affects aggregate expenditures. The simple expenditures multiplier reflects the fact that a given autonomous change in an expenditure results in an equal change in aggregate expenditures.

However, for the simple tax multiplier, a given autonomous change in taxes does NOT result in an equal change in aggregate expenditures. Taxes change disposable income, which causes changes in both consumption expenditures and saving. And only consumption expenditures affect aggregate expenditures.

The Simple Formula

The formula for this simple tax multiplier. (m[tax]), is:

m[tax]

=

- MPC

x

1 MPS

=

- MPC MPS

This formula is almost identical to that for the simple expenditures multiplier. The only difference is the inclusion of the negative marginal propensity to consume (- MPC).

If, for example, the MPC is 0.75 (and the MPS is 0.25), then an autonomous $1 trillion change in taxes results in an opposite change in aggregate production of $3 trillion.

Two Differences

• First, a change in taxes causes an opposite change in the disposable income of the household sector. An increase in taxes decreases disposable income and an decrease in taxes increases disposable income. This is why the simple tax multiplier has a negative value.


• Second, the household sector reacts to the change in disposable income caused by the change in taxes by changing both consumption and saving. How much consumption changes is based on the MPC. The MPC means that for each one dollar change in taxes, consumption and thus aggregate expenditures change by a only fraction. The fraction is equal to the MPC. The reason, of course, is that the taxes affect income and income is divided between saving and taxes.

If the marginal propensity to consume is 0.75, then consumption increases by $750 billion. This $750 billion change in consumption then triggers the multiplier process much like that for an autonomous change in investment expenditures. The difference, however, is the full $1 trillion change in investment triggers the multiplier process, but only 75 percent of the change in taxes works its way into the multiplier.

Other Multipliers

• (Complex) Tax Multiplier: The tax multiplier, or complex tax multiplier, is so named because it includes other induced expenditures and components, including induced investment expenditures, induced government purchases, induced taxes, and induced exports.


• Simple Expenditures Multiplier: The simple expenditures multiplier measures changes in aggregate production caused by changes in an autonomous expenditure when consumption is the only induced expenditure. It differs from the simple tax multiplier in that the change in aggregate expenditures equal the change in the autonomous expenditure.


• (Complex) Expenditures Multiplier: The expenditures multiplier, or complex expenditures multiplier, is so named because it also includes other induced expenditures and components. At the very least it might include induced investment expenditures. However, the "complete" four-sector complex multiplier is likely to include induced government purchases, induced taxes, and induced exports, as well.


• Balanced-Budget Multiplier: The balanced-budget multiplier measures the combined impact on aggregate production of equal changes in government purchases and taxes. The simple balanced-budget multiplier has a value equal to one.