# Encyclopedia

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, effective, effective average, and effective marginal. 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 amount of taxes paid to the tax base (taxable income or spending).[1]

To calculate the average tax rate on an income tax, divide total tax liability by taxable income:
• Let a be the average tax rate.
• Let t be the tax liability.
• Let i be the taxable income.
$a = \frac{t}{i}$

## Marginal

A marginal tax rate is the tax rate that applies to the last dollar of the tax base (taxable income or spending),[1] and is often applied to the change in one's tax obligation as income rises:

To calculate the marginal tax rate on an income tax:
• Let m be the marginal tax rate.
• Let t be the tax liability.
• Let i be the taxable income.
$m = \frac{\Delta t}{\Delta i}$

For an individual, it can be determined by increasing or decreasing the income earned or spent and calculating the change in taxes payable. An individual's tax bracket is the range of income for which a given marginal tax rate applies. The marginal tax rate may increase or decrease as income or consumption increases, although in most countries the tax rate is (in principle) progressive. In such cases, the average tax rate will be lower than the marginal tax rate: an individual may have a marginal tax rate of 45%, but pay average tax of half this amount. In a jurisdiction with a flat tax, everyone pays the same marginal tax rate. Some fixed amount of earnings (e.g., the first ten thousand dollars) is typically exempt from the flat tax, which means that not everyone pays the same average tax 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, the individual has less incentive to earn more. This is the foundation of the Laffer curve, which shows taxable income decreasing as a function of marginal tax rate, and therefore tax revenue begins to decrease after a certain point.

Public discussion of "high taxes" may refer to overall tax rates or marginal taxes.

Marginal tax rates may be published explicitly, together with the corresponding tax brackets, but they can also be derived from published tax tables showing the tax for each income. It may be calculated noting how tax changes with changes in pre-tax income, rather than with taxable income. Marginal tax rates do not fully describe the impact of taxation. A flat rate poll tax has a marginal rate of zero, while a discontinuity in tax paid can lead to positively or negatively infinite marginal rates at particular points.

## Effective

An effective tax rate refers to the actual rate, i.e., the rate existing in fact.[1] Both average and marginal tax rates can be expressed as effective tax rates.

The effective tax rate is the amount of tax an individual or firm pays when all other government tax offsets or payments are applied, divided by the tax base (total income or spending).[2] If certain groups have high degrees of tax offsets compared to other groups, their effective tax rate will be different, even where their official tax rates and marginal tax rates will be equal. The effective rate of tax can often be discussed in terms of the effective marginal rate of tax - namely the amount of effective tax paid as a percentage of the last dollar earned or spent.

### Effective average

An effective average tax rate (or average effective tax rate) may differ from an average tax rate because some measure of income other than taxable income is used. For example, the Joint Committee on Taxation typically calculates the effective average tax rate as the ratio of taxes paid to a constructed measure of "economic income".[1]

### Effective marginal

An effective marginal tax rate (or marginal effective tax rate, marginal deduction rate) may differ from a marginal tax rate because the taxpayer may be in an income range in which she/he is subject to a phase-out of some exclusion or deduction.[1] Where social security and other benefits are related to income, the combined tax and benefit effect can also be taken into account giving a result sometimes described as the marginal effective tax rate or the marginal deduction rate. If the marginal deduction rate exceeds 100%, then an increase in gross income leads to a decrease in disposable income, discouraging attempts to increase income. When this occurs for low income individuals, it is known as the "poverty trap".

## Inclusive / exclusive

Mathematically, 25% income tax out of $100 income yields the same as 33% sales tax on a$75 purchase.

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).[3] In the United States, sales taxes are quoted exclusively and income taxes are quoted inclusively. Value added tax (VAT) countries often display this tax inclusively; however, Goods and Services Tax countries do not.[4]

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.[3] 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:
$a = \frac{t \times p}{p - t \times p} = \frac{t}{1 - t}$
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

## Notes

1. ^ a b c d e f "What is the difference between statutory, average, marginal, and effective tax rates?". Americans For Fair Taxation. Retrieved 2007-04-23.
2. ^ "A statistical overview". Australian Commonwealth Government Treasury. Retrieved 2008-03-13.
3. ^ a b Bachman, Paul; Haughton, Jonathan; Kotlikoff, Laurence J.; Sanchez-Penalver, Alfonso; Tuerck, David G. (2006-11). "Taxing Sales under the FairTax – What Rate Works?". Beacon Hill Institute. Tax Analysts. Retrieved 2007-04-24.
4. ^ "Consumption Tax Topics that OECD will probably address". 1999-06. Retrieved 2007-04-23.

# Citable sentences

Up to date as of December 23, 2010

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