A report on Tax, Flat tax and Income tax

Total revenue from direct and indirect taxes given as share of GDP in 2017
Top marginal tax rate of the income tax (i.e. the maximum rate of taxation applied to the highest part of income)
Pieter Brueghel the Younger, The tax collector's office, 1640
William Pitt the Younger introduced a progressive income tax in 1798.
Substitution effect and income effect with a taxation on y good.
Punch cartoon (1907); illustrates the unpopularity amongst Punch readers of a proposed 1907 income tax by the Labour Party in the United Kingdom.
Budget's constraint shift after an introduction of a lump sum tax or a general tax on consumption or a proportional income tax.
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
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.
Systems of taxation on personal income
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.
Payroll and income tax by OECD Country
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 flat tax (short for flat-rate tax) is a tax with a single rate on the taxable amount, after accounting for any deductions or exemptions from the tax base.

- Flat tax

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).

- Income tax

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

Most countries charge a tax on an individual's income as well as on corporate income.

- Tax

A flat tax system is usually discussed in the context of an income tax, where progressivity is common, but it may also apply to taxes on consumption, property or transfers.

- Flat tax

The tax systems vary greatly and can be progressive, proportional, or regressive, depending on the type of tax.

- Income tax
Total revenue from direct and indirect taxes given as share of GDP in 2017

1 related topic with Alpha

Overall
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.

Progressive tax

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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.
A caricature of William Pitt the Younger collecting the newly introduced income tax.
German marginal and average income tax rates display a progressive structure.
"Tax The Rich" banner at an International Union of Socialist Youth campaign for a financial transaction 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.
Distribution of US federal taxes from 1979 to 2013, based on CBO Estimates.

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

The term is frequently applied in reference to personal income taxes, in which people with lower income pay a lower percentage of that income in tax than do those with higher income.

The act was signed into law by President Abraham Lincoln, and replaced the Revenue Act of 1861, which had imposed a flat income tax of 3% on incomes above $800.