  Tuesday  October 19, 2021
 AmosWEB means Economics with a Touch of Whimsy! CARDINAL: A measurement based on a scale or quantitative numbers, such as 1, 5, or 357.2, that enables a comparison in magnitude. Comparability means, for example, that the difference between 5 and 2 is the same as the difference between 12 and 9. Measures such as height and weight use cardinal numbers. Most economic measures are based on cardinal numbers, including gross domestic product, unemployment rate, the price of chocolate, and the quantity of wheat produced. The benefit of cardinal measurement is the ability to directly compare one measure with another. If, for example, the price of chocolate is \$1 a pound and the price of wheat is \$4 a pound, then wheat is four times more expensive than chocolate. Ordinal measures, which involve relative ranking, is an alternative type of measure.                              SIMPLE TAX MULTIPLIER:

A measure of the change in aggregate production caused by changes in a government taxes that shocks the macroeconomy, when consumption is the ONLY induced expenditure. The simple tax multiplier is the negative marginal propensity to consume times the inverse of one minus the marginal propensity to consume. A related multiplier is the simple expenditures multiplier, which measures the change in aggregate production caused by changes in an autonomous expenditure.
The simple tax multiplier measures the change in aggregate production triggered by an autonomous change in government taxes. This multiplier is useful in the analysis of fiscal policy changes in taxes. What makes the simple tax multiplier simple 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.

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 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. 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 tax multiplier. (m[tax]), is:

 m[tax] = - MPC x 1MPS = - MPCMPS
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).

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.
Suppose, for example, that the government sector reduces taxes by \$1 trillion with the goal of stimulating aggregate production and warding off a business-cycle contraction. This tax reduction increases disposable income by \$1 trillion. The household sector spends part and saves part of this income. The division between consumption and saving is based on the marginal propensities to consume and save.

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

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) 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.
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.

 <= SIMPLE EXPENDITURES MULTIPLIER SIXTH RULE OF IGNORANCE => Recommended Citation:

SIMPLE TAX MULTIPLIER, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2021. [Accessed: October 19, 2021].

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