The expenditures multiplier is actually a family of multipliers that differ based on which components of the Keynesian model are assumed to be induced by aggregate production and income. The simple expenditures multiplier, as the name suggestions, is the simplest variation and includes only induced consumption. Every other component -- investment expenditures, government purchases, taxes, exports, and imports -- are assumed to be autonomous.

More complex expenditures multipliers include different combinations of induced components, ranging all of the way up to the "complete" expenditures multiplier that realistically includes all induced components. Induced consumption, investment, and government purchases all increase the value of the expenditures multiplier. Induced taxes and imports both decrease the value of the expenditures multiplier.

The Simple Expenditures Multiplier

The formula for this simple expenditures multiplier, m, is:

m

=

1 (1 - MPC)

=

1 MPS

If, for example, the MPC is 0.75 (and the MPS is 0.25), then an autonomous $1 trillion change in investment expenditures results in a change in aggregate production of $4 trillion.

While the simple expenditures multiplier can be derived from the basic two-sector Keynesian multiplier, it also works for models with more sectors, as long as consumption is the only induced expenditure. If, for example, autonomous government purchases change by $1 trillion, then the change in aggregate production is $4 trillion, the same as with a $1 trillion change in investment expenditures. Moreover, the same change in aggregate production is realized if autonomous exports or consumption expenditures change by $1 trillion.

More Complex Expenditures Multipliers

Here is the formula for just such a multiplier, which can be labeled m[all].

m[all]

=

1 {1 - [MPC + MPI + MPG - (MPC x MPT) - MPM]}

Let's run through the cast of characters in this formula.

• MPC is the marginal propensity to consume.


• MPI is the marginal propensity to invest.


• MPG is the marginal propensity for government purchases.


• MPT is the marginal propensity to tax.


• MPM is the marginal propensity to import.

This particular expenditures multiplier formulation includes all induced components. However, several other expenditures multipliers that include different combinations of these induced components can be identified. One multiplier can include only induced consumption and induced government purchases. Another can include induced consumption, induced investment, and induced imports. The possibilities are almost endless.

Other Multipliers

• Tax Multiplier: The tax multiplier measures changes in aggregate production caused by changes in taxes. Like the expenditures multiplier this comes in several varieties, simple and complex, depending on which expenditures and other components are induced by aggregate production and income. It differs from the expenditures multiplier in that aggregate expenditures change by less than the change in taxes.


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