Marginal tax rate - Revision history

Vipul: /* Interval definition */

2011-08-13T05:40:10Z

Interval definition

← Older revision		Revision as of 05:40, 13 August 2011
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	This definition measures the marginal tax rate ''between'' two different but close levels of income, and is defined as the ''difference quotient'' of tax liability with respect to income. If the tax liability at income level <math>I_1</math> is <math>T_1</math>, and the tax liability at income level <math>I_2</math> is <math>T_2</math>, then the marginal tax rate is defined as:		This definition measures the marginal tax rate ''between'' two different but close levels of income, and is defined as the ''difference quotient'' of tax liability with respect to income. If the tax liability at income level <math>I_1</math> is <math>T_1</math>, and the tax liability at income level <math>I_2</math> is <math>T_2</math>, then the marginal tax rate is defined as:

	<math>\operatorname{Marginal Tax Rate} = \frac{T_2 - T_1}{I_2 - I_1} = \frac{\Delta T}{\Delta I}</math>		<math>\operatorname{Marginal} \ \operatorname{Tax} \ \operatorname{Rate} = \frac{T_2 - T_1}{I_2 - I_1} = \frac{\Delta T}{\Delta I}</math>

	===Subtleties about tax slabs===		===Subtleties about tax slabs===

Vipul: /* Definition */

2011-08-13T05:39:39Z

Definition

← Older revision		Revision as of 05:39, 13 August 2011
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	If <math>I</math> denotes the income in a given time unit (say a year) and <math>T(I)</math> is the tax liability as a function of income, then the marginal tax rate is defined as the derivative of <math>T(I)</math> with respect to <math>I</math>, i.e., it is given as:		If <math>I</math> denotes the income in a given time unit (say a year) and <math>T(I)</math> is the tax liability as a function of income, then the marginal tax rate is defined as the derivative of <math>T(I)</math> with respect to <math>I</math>, i.e., it is given as:

	<math>\operatorname{Marginal Tax Rate} = T'(I) = \frac{dT}{dI}</math>		<math>\operatorname{Marginal} \ \operatorname{Tax} \ \operatorname{Rate} = T'(I) = \frac{dT}{dI}</math>

	If the tax liability is considered to depend on many factors other than income, we use the partial derivative symbol <math>\partial T/\partial I</math> instead.		If the tax liability is considered to depend on many factors other than income, we use the partial derivative symbol <math>\partial T/\partial I</math> instead.

Vipul: Created page with "==Definition== The '''marginal tax rate''' of a given taxable entity at a given income level (per unit time) is a dimensionless quantity that measures the fraction of a slight i..."

2011-08-13T05:39:02Z

Created page with "==Definition== The '''marginal tax rate''' of a given taxable entity at a given income level (per unit time) is a dimensionless quantity that measures the fraction of a slight i..."

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==Definition==

The '''marginal tax rate''' of a given taxable entity at a given income level (per unit time) is a dimensionless quantity that measures the fraction of a slight increment of income that goes into additional taxes.

===Differential definition===

If <math>I</math> denotes the income in a given time unit (say a year) and <math>T(I)</math> is the tax liability as a function of income, then the marginal tax rate is defined as the derivative of <math>T(I)</math> with respect to <math>I</math>, i.e., it is given as:

<math>\operatorname{Marginal Tax Rate} = T'(I) = \frac{dT}{dI}</math>

If the tax liability is considered to depend on many factors other than income, we use the partial derivative symbol <math>\partial T/\partial I</math> instead.

===Interval definition===

This definition measures the marginal tax rate ''between'' two different but close levels of income, and is defined as the ''difference quotient'' of tax liability with respect to income. If the tax liability at income level <math>I_1</math> is <math>T_1</math>, and the tax liability at income level <math>I_2</math> is <math>T_2</math>, then the marginal tax rate is defined as:

<math>\operatorname{Marginal Tax Rate} = \frac{T_2 - T_1}{I_2 - I_1} = \frac{\Delta T}{\Delta I}</math>

===Subtleties about tax slabs===

* Jumps for simplicity of tax calculation: For simplicity of tax calculation, tax laws often have small slabs where the tax amount is kept constant, rather than the tax liability being a continuous function of income. For instance, in the United States, the tax liability increases in jumps at intervals of $50 for taxable income. Thus, the differential definition does not work in a strict mathematical sense, but the interval definition works well if we choose an interval that is a multiple of $50.

==Variation of marginal tax rate==

* The marginal tax rate is ''not'' a constant number but depends on the income level in general. The nature of variation is described below:

{| class="sortable" border="1"
! Type of tax !! How does the marginal tax rate vary with income? !! What can we conclude about average tax rates?
|-
| [[progressive tax]] || marginal tax rate is increasing, or non-decreasing, with respect to income. || average tax rates are increasing, and for any income level, the average tax rate is less than or equal to the marginal tax rate.
|-
| [[flat tax]] || marginal tax rate is constant with respect to income (the term ''flat tax'' is often also used for a flat tax with a base exemption, in which case the marginal tax rate is zero up to a point and then jumps to a nonzero value, at which it stays constant). || In the absence of a base exemption, the average tax rate is constant and equals the marginal tax rate.<br>In the presence of a base exemption, the average tax rate is increasing and asymptotically approaches the marginal tax rate.
|-
| [[regressive tax]] || marginal tax rate is decreasing, or non-increasing, with respect to income. || The average tax rate is decreasing, and for any income level, it is greater than or equal to the marginal tax rate.
|}

In most cases, even the case of flat and regressive taxes, the ''total'' tax liability is an increasing (or, at worst, non-decreasing) function of income, so the marginal tax rates are still ''positive'' (or, at worst, ''zero''). The terms ''progressive'' and ''regressive'' refer to the sign of the ''second derivative'' of tax liability with respect to income, not the sign of the first derivative.

Note on abrupt changes in tax rates: The marginal tax rate itself may vary continuously or in discrete jumps. For instance, if there is a basic income exemption, then the marginal tax rate up to that basic income is zero, and after that, it suddenly jumps to a nonzero value.