A report on Progressive tax, Tax and Taxable income

Average tax rates by income groups in France, the United Kingdom, and the United States, 1970 (left) and 2005 (right). Taxes were more progressive in 1970 than in 2005.
Total revenue from direct and indirect taxes given as share of GDP in 2017
A caricature of William Pitt the Younger collecting the newly introduced income tax.
Pieter Brueghel the Younger, The tax collector's office, 1640
German marginal and average income tax rates display a progressive structure.
Substitution effect and income effect with a taxation on y good.
"Tax The Rich" banner at an International Union of Socialist Youth campaign for a financial transaction tax.
Budget's constraint shift after an introduction of a lump sum tax or a general tax on consumption or a proportional income tax.
The function which defines the progressive approach to an income tax, may be mathematically defined as a piecewise function. In every piece (tax bracket), it must be computed cumulatively, considering the taxes which had already been computed to the previous tax brackets. Pictured is the effective income tax for Portugal in 2012 and 2013.
The Laffer curve. In this case, the critical point is at a tax rate of 70%. Revenue increases until this peak, then it starts decreasing.
Distribution of US federal taxes from 1979 to 2013, based on CBO Estimates.
General government revenue, in % of GDP, from social contributions. For this data, the variance of GDP per capita with purchasing power parity (PPP) is explained in 20% by social contributions revenue.
Egyptian peasants seized for non-payment of taxes. (Pyramid Age)
Public finance revenue from taxes in % of GDP. For this data, the variance of GDP per capita with purchasing power parity (PPP) is explained in 32% by tax revenue.
Diagram illustrating deadweight costs of taxes

A progressive tax is a tax in which the tax rate increases as the taxable amount increases.

- Progressive tax

Taxable income refers to the base upon which an income tax system imposes tax.

- Taxable income

Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes are progressive based on brackets of annual income amounts.

- Tax

Many systems impose tax at different rates for differing types (e.g., capital gains or salaries) or levels of income (e.g., graduated rates).

- Taxable income

For example, a person in the U.S. who earned US$10000 US of taxable income (income after adjustments, deductions, and exemptions) would be liable for 10% of each dollar earned from the 1st dollar to the 7,550th dollar, and then for 15% of each dollar earned from the 7,551st dollar to the 10,000th dollar, for a total of US$1122.50.

- Progressive tax

It is used to illustrate the concept of taxable income elasticity (that taxable income will change in response to changes in the rate of taxation).

- Tax
Average tax rates by income groups in France, the United Kingdom, and the United States, 1970 (left) and 2005 (right). Taxes were more progressive in 1970 than in 2005.

1 related topic with Alpha

Overall
Top marginal tax rate of the income tax (i.e. the maximum rate of taxation applied to the highest part of income)

Income tax

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Top marginal tax rate of the income tax (i.e. the maximum rate of taxation applied to the highest part of income)
William Pitt the Younger introduced a progressive income tax in 1798.
Punch cartoon (1907); illustrates the unpopularity amongst Punch readers of a proposed 1907 income tax by the Labour Party in the United Kingdom.
General government revenue, in % of GDP, from personal income taxes. For this data, the variance of GDP per capita with purchasing power parity (PPP) is explained in 27 % by tax revenue
Systems of taxation on personal income
Payroll and income tax by OECD Country

An income tax is a tax imposed on individuals or entities (taxpayers) in respect of the income or profits earned by them (commonly called taxable income).

The tax rate may increase as taxable income increases (referred to as graduated or progressive tax rates).