# Tax Multiplier Explained [and Tax Multiplier Formula]

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There are certain multiples or factors, such as tax multipliers, that governments and economists use to design their fiscal policies. These multiples play an important role in the GDP of a country. What is the tax multiplier? What is the tax multiplier formula?

The tax multiplier is the amplification effect of a variation in taxes on aggregate demand. The reduction in taxes has the same effect on consumption and income as a rise in government spending. Generally, the tax multiplier is smaller than the spending multiplier.

The tax multiplier refers to the multiple by which GDP or gross domestic product increases (or decreases) in response to a decrease (or increase) in taxes. The final result is that the GDP increases by a multiple of initial tax decreases.

This tax multiplier is expressed as the negative marginal propensity to consume or MPC divided by the 1 minus MPC. It is the tax multiplier type that is easier to understand. So, we will first dwell on the way it is calculated. The basic formula for a simple tax multiplier is as follows:

Tax Multiplier = (–) MPC / MPS

Read on to learn more about the tax multiplier, what it is, what it is used for, its effects on GDP, its formula, and a sample of how you can use the tax multiplier formula.

## Tax Multiplier Explained [and Tax Multiplier Formula]

What is the tax multiplier? The magnification effect of a variation in taxes on aggregate demand is the tax multiplier. The reduction in taxes has the same effect on income and consumption as a rise in government spending. But the tax multiplier is less than the spending multiplier.

The tax multiplier works as the multiple by which GDP or gross domestic product increases (or decreases) in its reaction to a decrease (or increase) in taxes. The final result is that the GDP rises by a multiple of initial decreases in taxes.

To put it in another way, the tax multiplier is an economic formula that computes the effect of the variation in tax policies on consumption and output. There is a tax multiplier formula you can use for this purpose.

### More Detailed Explanation of Tax Multiplier

Investors, economists, and governments widely use the term tax multiplier to analyze and evaluate how fiscal policy modifications in taxation impact the aggregate production of a country.

There are two types of tax multipliers, the simple and the complex tax multipliers. The multiplier they use will depend on whether the tax change affects only the consumption portion of GDP or if it affects all the elements of GDP.

#### Simple Tax Multiplier

The most commonly used is the simple tax multiplier. This TM suggests that only consumption expenditures are impacted in the aggregate production due to the changes made in the taxes imposed by the government.

The reality is, taxes that governments impose on their people affect the consumers’ disposable income. This, in turn, impacts both the people’s consumption rate and their savings.

#### Complex Tax Multiplier

On the other side of the coin, the complex multiplier suggests that a variation in the aggregate production that occurred because of a modification in government taxes impacts not only the consumption expenditures but also the aggregate expenditures.

At both micro and macro levels, taxes are generally a hot-button issue. How do the changes in government taxes affect the gross domestic product of the nation? GDP is the worth of goods and services created by a country within a certain time frame.

The measure of this effect is the tax multiplier. Generally, taxes will definitely change the consumers’ available disposable income. Any change in disposable income will definitely affect people’s savings and consumption.

So, tax multiplier is a term that represents the multiple that measures the change manifested by the gross domestic product (GDP) of a country or an economy as a result of the taxes introduced or imposed by its government.

Economists, investors, and governments use the tax multiplier as one of the metrics to evaluate and analyze the effect of the changes in policy in taxation on the level of the aggregate income of a nation.

## More on the Two Types of Tax Multipliers

Two methods are used in the calculation of tax multipliers. One involves simple calculation, and the other involves more complex computations. They are the simple tax multiplier and the complex tax multiplier.

Basically, economists use the simple method when the government’s imposed tax only affects the consumption component of the GDP. In contrast, they use the complex method when the tax changes affect all of the components of the GDP.

As you can see, the simple tax multiplier is easier to compute. But the result can still provide us with important information on the effects on a country’s economy. The complex tax multiplier uses more variables in the calculation. So, its result is a better representation of the complex nature of economics.

Both these two methods can assess the propensity of consumers to spend and save. The simple method considers only these two parameters. The variables in the calculation include marginal propensity to save or MPS and marginal propensity to consume or MPC.

So, you can express the tax multiplier in two ways:

1. Simple Tax Multiplier – in which the tax changes affect only the consumption and spending in the GDP.
2. Complex Tax Multiplier – in which the tax changes affect all the components of the GDP.

### Simple Tax Multiplier

Economists use the simple tax multiplier to measure the change in aggregate production due to changes in government taxes that impact the macroeconomy when consumption is the only induced expense. The simple tax multiplier is useful when analyzing fiscal policy changes in taxes.

This tax multiplier is expressed as the negative marginal propensity to consume or MPC divided by the 1 minus MPC. It is the tax multiplier type that is easier to understand. So, we will first dwell on the way it is calculated.

#### Simple Tax Multiplier Formula

The basic formula for a simple tax multiplier is as follows:

Tax Multiplier = (–) MPC / MPS

The simple tax multiplier formula is a negative marginal propensity to consume divided by the marginal propensity to save.

As you can see, MPC has a negative sign simply because the tax multiplier is basically a measure of an increase in national income (ΔY) by a decrease in tax receipts (ΔT). The following mathematical formula represents this relationship:

Tax Multiplier = ΔY / ΔT = (–) MPC / (1 – MPC)

The tax multiplier is always negative. When taxes go down, the demand for goods and services will increase. So, there is an inverse relationship between GDP and taxes. Conversely, when taxes go up, disposable income will decrease. That means a negative impact on the GDP.

We can still refine the simple tax multiplier formula even more. Since the marginal propensity to save or MPS has an inverse relationship to the marginal propensity to consume or MPC, we can simplify the formula slightly by expressing (1 – MPC).

So, we can express the tax multiplier formula in the following form:

TM = (–) MPC / (1 – MPC)

### Tax Multiplier Is Always Negative

The tax multiplier is always negative, while the expenditure multiplier is positive. This is because an increase in aggregate expenditure will increase the actual GDP. Additionally, an increase in taxes will reduce the actual GDP.

There is an inverse relationship between aggregate demand and taxes. When the government reduces its taxes, there will be an increase in aggregate demand. There will be a crowding-out effect when higher income leads to a rise in demand for money, causing interest rates to increase.

Again, the tax multiplier refers to the amplification effect of the change in taxes on the aggregate demand. Whether the government decreased the taxes or increase its spending, both have the same effects on income and consumption. However, the tax multiplier is less than the spending multiplier.

## Fiscal Policy Affects Taxation and the Economy

Taxation and spending are the two levers that governments use to set their fiscal policies. When governments want to expand their economies, they increase their spending or reduce taxes. They can also do both.

When government spending increases, and there’s tax reduction, there will be an increase in aggregate demand. However, the extent of the increase will depend on the spending and the tax multipliers.

The spending multiplier of governments is a figure that shows how much variation in aggregate demand will result from a known change in spending. The effect of this spending multiplier is manifested when an incremental rise in spending leads to an increase in consumption and income.

What is the tax multiplier? The tax multiplier is the amplification effect of a tax change on aggregate demand. The reduction in taxes has the same effect on consumption and income as a rise in government spending.

### Spending Multiplier Is Greater than the Tax Multiplier

But the spending multiplier is greater than the tax multiplier. The reason is that when the government is spending money, it directly buys something. That causes the full effect of the change in expenditure to be felt by the aggregate demand.

On the other hand, if the government reduces taxes, there will be an increase in disposable income. The government can save a portion of this expendable income, and they can spend some of it. The saved money will not contribute to the multiplier effect.

So, the spending multiplier of the government is greater than the tax multiplier since some of the increase in expendable income because of the lowering of taxes is not consumed. It is saved instead.

These multipliers can be expressed in the following format:

• Spending multiplier of the government: 1 (1 – MPC) or 1 MPS
• Tax multiplier: MPC (1 – MPC) – MPC) or – MPCMPS

The spending multiplier of the government is always positive, while the tax multiplier is always negative. This is due to their inverse relationship, e.g., when taxes are cut, aggregate demand increases.

### Factors That Affect Multiplier Effect of a Reduction in Taxes

The following factors affect the multiplier effect of a reduction in taxes:

1. Size or amount of the reduction in taxes,
2. Crowding out effect, and
3. Propensity to consume.

The crowding out effect happens when higher income results in an increased demand for money, resulting in an interest rate hike.

This will result in a decrease in investment spending, one of the four elements of aggregate demand. This will also mitigate the rise in aggregate demand otherwise generated by lower taxes.

An illustration will help you see the relationship between government spending multiplier and tax multiplier.

If the government gets involved in expansionary fiscal policy by cutting tax rates by 5%, it is expected to cut its total tax volume by \$290 billion. This will increase disposable income by \$290 billion.

Let us assume that there is a marginal propensity to consume of about 0.8. Consumers will spend \$232 billion on the increase in their disposable income (\$290 x 0.8).

The first round increase in consumption of \$232 billion will likely trigger another round increase of the exact amount and then another round of increase in consumption of \$185.6 billion (\$290 x 0.8 x 0.8). This can go on and on.

The ultimate result is that the GDP will increase by several initial decreases in taxes. This is the action of the tax multiplier, and its effect refers to the multiplier effect. In contrast, an increase in taxes will decrease the GDP by a multiple in the same way.

## Tax Multiplier Formulas

To repeat, there are two types of tax multipliers, the simple and the complex tax multipliers:

### Simple Tax Multiplier Formula

The formula for the simple version of the tax multiplier is as follows:

TM = MPC / MPS = MPC / 1- MPC

Where,

• TM is the simple tax multiplier;
• MPS is the marginal propensity to save; and
• MPC is marginal propensity to consume

As you can see from the formula, you can also represent MPS by the format: 1 – MPC.

### Complex Tax Multiplier Formula

When it comes to a complex tax multiplier, the assumption is that any tax change will affect all components of the GDP. The formula for complex tax multiplier is as follows:

TM = MPC / 1 – (MPC x (1-MPT) + MPI + MPG + MPM)

Wherein

• TM is the complex tax multiplier
• MPC is the marginal propensity to consume
• MPT is the marginal propensity to tax
• MPI is the marginal propensity to invest
• MPG is the marginal propensity of government expenditures; and
• MPM is the marginal propensity to import

## Conclusion: Tax Multiplier Explained [and Tax Multiplier Formula]

The magnification effect on the changes in taxes on aggregate demand refers to the tax multiplier. The decrease in taxes has the same impact on income and consumption as the rise in government spending. Typically, the tax multiplier is less than the spending multiplier.

There are two formulas for tax multipliers. One is the simple tax multiplier, and the other is the complex tax multiplier. The first one uses only two components of the GDP, while the second one uses all the components of the GDP.