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# Marginal tax rate

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 Title: Marginal tax rate Author: World Heritage Encyclopedia Language: English Subject: Laffer curve Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Marginal tax rate

For a type of taxation system in the United Kingdom and elsewhere, see Rates (tax).

In a tax system and in economics, the tax rate describes the burden ratio (usually expressed as a percentage) at which a business or person is taxed. There are several methods used to present a tax rate: statutory, average, marginal, and effective. These rates can also be presented using different definitions applied to a tax base: inclusive and exclusive.

## Statutory

A statutory tax rate is the legally imposed rate. An income tax could have multiple statutory rates for different income levels, where a sales tax may have a flat statutory rate.[1]

## Average

An average tax rate is the ratio of the total amount of taxes paid to the total tax base (taxable income or spending), expressed as a percentage.[1]

• Let $t$ be the total tax liability.
• Let $i$ be the total tax base.
$= \frac\left\{t\right\}\left\{i\right\}$

## Marginal

A marginal tax rate is sometimes defined as the tax rate that applies to the last (or next) unit of the tax base (taxable income or spending).[1][2] That definition only holds true to the equation following when the denominator equals one unit of the tax base. In practice most decisions require the denominator to be a larger amount. The marginal tax rate equals the change in taxes divided by the change in tax base, expressed as a percentage.

• Let $t$ be the total tax liability.
• Let $i$ be the total tax base.
$= \frac\left\{\Delta t\right\}\left\{\Delta i\right\}$

With a flat tax all income is taxed at the same percentage, regardless of income or consumption. An example would be a sales tax where all purchases are taxed at the same rate. The marginal tax rate will always be that same percentage. A poll tax is a flat tax defined as a set dollar amount of tax per tax base (per person). The marginal tax would not be expressed as a percentage.

Marginal tax rates are usually calculated and used in the context of income tax in countries with progressive tax, where incremental increases in income are taxed at progressively higher rates (tax brackets ). In practice the tax denominator usually includes the taxes imposed by all levels of government who tax that tax base - federal, state, provincial, even municipal.

Public discussion of "high taxes" may refer to overall average tax rates or marginal taxes - without clarification. In countries with progressive tax rates the average rate will be lower than the marginal rate.

In economics, marginal tax rates are important because they are one of the factors that determine incentives to increase income. At higher marginal tax rates individuals may have less incentive to earn more. This is the foundation of the Laffer curve, which claims that population-wide taxable income decreases as a function of marginal tax rate, and therefore tax revenue begins to decrease after a certain point.

## Effective

The term effective tax rate has different meanings in different contexts. Generally its calculation attempts to adjust a nominal tax rate to make it more meaningful. It may incorporate econometric, estimated, or assumed adjustments to actual data, or may be based entirely on assumptions or simulations.[3]

The term is used in financial reporting to measure the total tax paid as a percentage of the company's accounting income, instead of as a percentage of the taxable income. International Accounting Standard 12,[4] define it as income tax expense or benefit for accounting purposes divided by accounting profit. In Generally Accepted Accounting Principles (United States), the term is used in official guidance only with respect to determining income tax expense for interim (e.g., quarterly) periods by multiplying accounting income by an "estimated annual effective tax rate," the definition of which rate varies depending on the reporting entity's circumstances.[5]

In U.S. income tax law, the term is used in relation to determining whether a foreign income tax on specific types of income exceeds a certain percentage of U.S. tax that would apply on such income if U.S. tax had been applicable to the income.[6]

The popular press, Congressional Budget Office, and various think tanks have used the term to mean varying measures of tax divided by varying measures of income, with little consistency in definition.[7]

Investors usually modify a statutory marginal tax rate to create the effective tax rate appropriate for their decision.

For example: If capital gains are only taxed when realized by a sale, the effective tax rate is the yearly rate that would have applied to the average yearly gain so that the resulting after-tax profit is the same as when all taxed at statutory rates on sale. It will be lower than the statutory rate because unrealized profits are reinvested without tax.

For example: When dividends are both taxed as income, and also generate a tax credit in the UK and Canadian system, the effective tax rate is the net effect of both - the net tax divided by the actual dividend's value.

For example: When contributions are made to Tax Deferred Accounts the reduced tax base will result in reduced taxes calculated at the statutory marginal rate. But the reduction in the tax base may also affect qualification for other government benefits. The difference in those benefits is added to the numerator to increase the effective marginal rate due to the contribution.

## Inclusive and exclusive

Tax rates can be presented differently due to differing definitions of tax base, which can make comparisons between tax systems confusing.


Some tax systems include the taxes owed in the tax base (tax-inclusive), while other tax systems do not include taxes owed as part of the base (tax-exclusive).[8] In the United States, sales taxes are usually quoted exclusively and income taxes are quoted inclusively. The majority of Europe, value added tax (VAT) countries, include the tax amount when quoting merchandise prices, including Goods and Services Tax (GST) countries, such as Australia and New Zealand. However, those countries still define their tax rates on a tax exclusive basis.

For direct rate comparisons between exclusive and inclusive taxes, one rate must be manipulated to look like the other. When a tax system imposes taxes primarily on income, the tax base is a household's pre-tax income. The appropriate income tax rate is applied to the tax base to calculate taxes owed. Under this formula, taxes to be paid are included in the base on which the tax rate is imposed. If an individual's gross income is $100 and income tax rate is 20%, taxes owed equals$20.

The income tax is taken "off the top", so the individual is left with $80 in after-tax money. Some tax laws impose taxes on a tax base equal to the pre-tax portion of a good's price. Unlike the income tax example above, these taxes do not include actual taxes owed as part of the base. A good priced at$80 with a 25% exclusive sales tax rate yields $20 in taxes owed. Since the sales tax is added "on the top", the individual pays$20 of tax on $80 of pre-tax goods for a total cost of$100. In either case, the tax base of $100 can be treated as two parts—$80 of after-tax spending money and \$20 of taxes owed. A 25% exclusive tax rate approximates a 20% inclusive tax rate after adjustment.[8] By including taxes owed in the tax base, an exclusive tax rate can be directly compared to an inclusive tax rate.

Inclusive income tax rate comparison to an exclusive sales tax rate:
• Let $t$ be the income tax rate. For a 20% rate, then $t = 0.20$
• Let $a$ be the rate in terms of a sales tax.
• Let $p$ be the price of the good (including the tax).
The revenue that would go to the government:
$t \times p$
The revenue remaining for the seller of the good:
$p - t \times p$
To convert the tax, divide the money going to the government by the money the company nets:
$a = \frac\left\{t \times p\right\}\left\{p - t \times p\right\} = \frac\left\{t\right\}\left\{1 - t\right\}$
Therefore, to adjust any inclusive tax rate to that of an exclusive tax rate, divide the given rate by 1 minus that rate.
• 15% inclusive = 18% exclusive
• 20% inclusive = 25% exclusive
• 25% inclusive = 33% exclusive
• 33% inclusive = 50% exclusive
• 50% inclusive = 100% exclusive