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A lump sum tax is a tax with a fixed amount that is levied on all members of a society regardless of their income levels. Each member of the society, from the richest to the poorest, is charged the same lump sum when such a tax exists. Instances of an actual lump sum tax are rare in reality, since the tax would be excessively burdensome to the poorer members of a society. Economists often use the lump sum theory as a way of showing how such a tax would help an economy to achieve maximum efficiency.
Individual taxes are usually levied depending either on the amount of income they earn or the amount of some particular product that they consume. It's usually the case that the people who make the most money in a society are taxed at the highest percentage of their income since they can afford it. Those taxes often are used in turn to benefit the poorer people in an economy. By contrast, a lump sum tax is levied upon every single member of a single society.
There are very few examples of a pure lump sum tax in existence in the world. For example, in the United Kingdom, a lump sum is charged to all those who use a television set. It doesn't matter what kind of TV it is or what kind of service the individual receives, as the tax is applicable to all TV users. Of course, even this tax is, in essence, discriminatory, since it isn't levied on those who don't have televisions.
It would be difficult for any government to levy a pure lump sum tax because of the excessive burden it would place on those citizens with the least money. For example, imagine a scenario whereby the United States would levy a $500 US Dollars (USD) on every single member of society over the age of 21. This tax could be easily handled by those making millions of dollars every year. But those who only made a small fraction of that would be hit especially hard by having to pay this amount.
The theory of a lump sum tax is often used by economists as a means of studying the ways that an economy can be more efficient. Many economists argue that charging a lump sum would be a more effective method of aiding an economy. Whereas a tax based on income might cause some workers to work at less than their maximum capability for fear of paying higher taxes, proponents of the lump sum argue that a fixed-amount tax would not impede workers' motivation in any way.