# Tax rate

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 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 $i_t$ be the taxable income.
$a = \frac{t}{i_t}$

## Marginal

A marginal tax rate is the tax rate that applies to the last unit of currency 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 $i_t$ be the taxable income.
$m = \frac{\Delta t}{\Delta i_t}$

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 on earnings, every taxpayer pays the same percentage of income, regardless of income or consumption. Some proponents of this system propose to exempt a fixed amount of earnings (such as the first $10,000) from the flat tax. 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, some argue, the individual has less incentive to earn more. This is the foundation of the Laffer curve, which claims taxable income decreases 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, but a discontinuity in tax paid can lead to positively or negatively infinite marginal rates at particular points. ## Effective The term effective tax rate has significantly different meanings when used in different contexts or by different sources. Generally it means some amount of tax divided by some amount of income or other tax base. In International Accounting Standard 12,[2] it is defined 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.[3] 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.[4] 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.[5] An effective tax rate may incorporate econometric, estimated, or assumed adjustments to actual data, or may be based entirely on assumptions or simulations.[6] ## Inclusive and 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).[7] 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.[7] 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