<prompt> Human: I was inspired by the post on Thursday about pervasive financial myths and in particular the thread about people misunderstanding how marginal tax brackets work. permalinkIn particular, sometimes people think that they should avoid crossing into a new tax bracket because they believe all their income will be taxed at that rate and theyll be worse off. In other words, they think theyll actually take home less after taxes.I made a graph showing tax vs income for a single person, using just the standard deduction and personal exemption, as if this really were true. This is the result.Misconception: Tax vs IncomeYou can see what people think is happening. Notice the steep jumps at the thresholds between the tax brackets. Adding one dollar at any of those points causes a huge leap in tax liability. The segments in the graph that arent vertical leaps have slopes 0.00, 0.10, 0.15, 0.25, 0.28, and so on. Those slopes correspond to the tax bracket rates. They are all pointing toward the point 10,300, 0. That is what the tax graph would look like if tax varied directly with taxable income, in the manner of this misconception.Now here is the reality.Reality: Tax vs IncomeThe graph is a series of connected segments, but there are no vertical leaps. Adding one dollar of income at any of the thresholds does increase your tax, but only by 10, 15, 25, 28, and so on. The segments again have slopes 0, 0.10, 0.15, 0.25, 0.28, and so on. But the segments arent pointing at a single point. The relationship is not direct variation. That is why the tax schedule gives an algorithm for finding tax based on taxable income, instead of just saying to multiply total taxable income by a number.Lets take a look now at what income after tax is under the misconception. Here is a graph of Income After Tax compared to Income, using the misconception that all income is taxed at your tax bracket rate.Misconception: Income After Tax vs IncomeThis graph shows an alarming sawtooth behavior at the thresholds between the tax brackets. Adding one dollar of income appears to cause a dramatic drop in take-home income. This is what people who are misunderstanding marginal tax brackets fear would happen. They are worse off if they let their income stray into the next bracket, and they need to earn quite a bit more until they are back to where they were in terms of take-home income. If tax brackets were not applied marginally the way they are, this really would happen.On this graph, the slopes are 1 - tax rate. So first we see slope of 1 between income 0 and 10,300 because there is 0 tax there. Then we see slope of 0.90 in 10 bracket, slope of 0.85 in 15 bracket, slope of 0.75 in 25 bracket, and so on.All the nonvertical segments point toward 10,300, 10,300. In this misconception, take-home varies directly with taxable income, but is subject to the sawtooth effect caused at the thresholds.Now here is the reality.Reality: Income After Tax vs IncomeThe slopes are 1 - tax rate as in the previous graph, so they are 1, 0.90, 0.85, 0.75, and so on. The segments are connected rather than having the vertical cliffs seen in the misconception. Adding one dollar of income always increases your take-home. The graph is monotonically increasing. You never are worse off by earning more income and having it get taxed at higher rates.Note: This discussion is ignoring the possible consequences of losing access to subsidies or credits, or facing AMT, based on crossing specific thresholds. There are some instances where earning more does eliminate certain assistance or expose you to more tax. If that is the reason someone is cautious about earning more, that is rational and not a misconception.Graphic update: Here is a revised graphic that I hope is an improved presentation.Gross Income and Income After Taxes single filer  <response>: Awesome, I think the third and fourth graphs more intuitively communicate the intent than the first two. 