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A measure of the change in aggregate production caused by changes in an autonomous expenditure that shocks the macroeconomy, when consumption is the ONLY induced expenditure. The simple expenditures multiplier is the inverse of one minus the marginal propensity to consume, or more simply the inverse of the marginal propensity to save. A related multiplier is the simple tax multiplier, which measures the change in aggregate production caused by changes in taxes.
The simple expenditures multiplier measures the change in aggregate production triggered by changes an autonomous expenditure, such as investment expenditures or government purchases. The key to the simple expenditures multiplier, however, is that consumption expenditures and only consumption expenditures are induced by changes in aggregate production. As such the slope of the aggregate expenditures line is equal to the marginal propensity to consume.

This multiplier is commonly used to illustrate the basic multiplier principle, highlighting how and why a change in an autonomous expenditure, especially investment expenditures, triggers the multiplier process through induced consumption.

This simple expenditures multiplier can be derived from the simplest Keynesian model, the private sector, or two-sector Keynesian model. However, it works just as well for any model as long as consumption is the only induced component.

### The Simple Formula

The simple expenditures multiplier is the ratio of the change in aggregate production to an autonomous change in an aggregate expenditure when consumption is the only induced expenditure. This multiplier is as simple as it gets while capturing the fundamentals of the multiplier. Autonomous investment triggers the multiplier process and induced consumption provides the cumulatively reinforcing interaction between consumption, aggregate production, factor payments, and income.

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

 m = 1(1 - MPC) = 1MPS
Where MPC is the marginal propensity to consume and MPS is the marginal propensity to save.

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.

### Other Multipliers

The simple expenditures multiplier is one of several Keynesian multipliers. Other related multipliers exist based on (1) the autonomous shock and (2) assumptions concerning what is induced by the changes in aggregate production and income. Four notable multipliers are (complex) expenditures multiplier, simple tax multiplier, (complex) tax multiplier, and balanced-budget multiplier.
• (Complex) Expenditures Multiplier: The expenditures multiplier, or complex expenditures multiplier, is so named because it 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.

• Simple Tax Multiplier: The simple tax multiplier measures changes in aggregate production caused by changes in taxes when consumption is the only induced expenditure. It differs from the simple expenditures multiplier in that aggregate expenditures change by less than the change in taxes.

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

• 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.
Two other multipliers arise from the financial, or money, side of the economy. They are the deposit expansion multiplier and the money multiplier. The deposit expansion multiplier measures the change in bank deposits caused by a change in bank reserves. The money multiplier measures the change in money caused by a change in bank reserves. Both are useful in the analysis of monetary policy.

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