# Linear Inequalities in Two Variables

## Graph inequalities like 2x + 3 < y on the coordinate plane

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At the Margins

Source: http://www.flickr.com/photos/58719682@N07/6916702992

With the national debt rising, the federal government needs more money to meet its obligations and may need to raise taxes in the near future. Nobody enjoys paying income taxes, but it’s the cost of being part of our society. However, we can’t just keep raising taxes forever. If the tax rate becomes too high, people might stop working, decreasing the government’s tax revenue. As a result, Congress might collect less in taxes than it needed originally. So how does the government determine how high to raise taxes?

#### Last Dollars and the Value of Time

The United States has a progressive tax system, which means that people who earn higher incomes pay a higher percentage of those incomes in taxes. We divide people into tax brackets based on their income. The part of your earnings that falls within a bracket gets taxed at that bracket’s rate. So, for instance, in 2013, a single woman paid a 10% tax on the first $8,700 she earned. On her earnings that fell between$8,701 and $35,350, she paid a 15% tax. The tax rate increases with higher incomes. Economists think a lot about these marginal tax rates, or tax rates on the last dollar of income earned. Currently, the top tax bracket contains people who earn over$400,000 a year. They pay a tax rate of 39.6% on every dollar they earn over the $400,000 limit. Credit: Quinn Mattingly Source: http://www.flickr.com/photos/terminalnomadphotograhy/2179617521/ License: CC BY-NC 3.0 Can the top tax rate discourage high earners from working more? Probably. If people had to pay 100% tax on every dollar they earned above$400,000, there’d be no point in working once you earned \$399,999 dollars in a year. During World War II, the top American tax rate was raised to 94%, but it was sold as a patriotic contribution to the war effort. Today, economists disagree over how high taxes can go without discouraging work and the most effective tax rates are still debated.

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