__TAX MULTIPLIER:__A measure of the change in aggregate production caused by changes in government taxes. The tax multiplier is the negative marginal propensity to consume times one minus the slope of the aggregate expenditures line. The simple tax multiplier includes ONLY induced consumption. More complex tax multipliers include other induced components. Two related multipliers are the expenditures multiplier, which measures the change in aggregate production caused by changes in an autonomous aggregate expenditure, and the balanced-budget multiplier which measures the change in aggregate production from equal changes in both taxes and government purchases.

The tax 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 tax 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 tax multipliers include different combinations of induced components, ranging all of the way up to the "complete" tax 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 Tax Multiplier

The simple tax multiplier is the ratio of the change in aggregate production to an autonomous change in government taxes when consumption is the only induced expenditure. Autonomous tax changes trigger the multiplier process and induced consumption provides the cumulatively reinforcing interaction between consumption, aggregate production, factor payments, and income.The formula for this simple tax multiplier. (m[tax]), is:Where MPC is the marginal propensity to consume and MPS is the marginal propensity to save.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).

m[tax] = - MPC x 1

MPS= - MPC

MPS

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

The key feature of the simple tax multiplier that differentiates it from the simple expenditures multiplier is how taxes affect aggregate expenditures. In particular, taxes do not affect aggregate expenditures directly (as do government purchases or investment expenditures). They affect aggregate expenditures indirectly through disposable income and consumption. This gives rise to two important differences compared to the simple expenditures multiplier.- 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.

### More Complex Tax Multipliers

The simple tax multiplier assumes that consumption is the only induced component. In the real world, however, consumption is not the only induced expenditure. Investment, government purchases, taxes, and net exports (through imports) are also induced. A more complete, more realistic, and more complex multiplier includes induced components.Here is the formula for just such a multiplier, which can be labeled m[tax-all].This particular multiplier has a number of abbreviations containing the letters "MP." These are the assorted induced components, with "MP" standing for marginal propensity. In fact, the batch of abbreviations within the brackets "[]" is actually the slope of the aggregate expenditures line.Let's run through the cast of characters in this formula.

m[tax-all] = - MPC

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

- 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.

### Other Multipliers

The tax multiplier is one of several Keynesian multipliers. Two other related multipliers are expenditures multiplier and balanced-budget multiplier.- Expenditures Multiplier: The expenditures multiplier measures changes in aggregate production caused by changes in an autonomous expenditure. Like the tax 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 tax multiplier in that aggregate expenditures change by full amount of the autonomous change.
- 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.

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