# Economists Do It With Models

## Let’s Back Up A Second And Give Marginal Tax Rates Their Moment…

#### August 9th, 2016 · 4 CommentsTaxes

I got a few comments of note on my last post regarding tax deductions versus tax credits. First, from Tumblr:

Technically speaking, neither of them are wrong I suppose (though I didn’t confirm the average tax rate calculation in the first comment), but the second guy is right that some additional review and clarification is probably helpful for some people.

So allow me to start with a story that, if my household is at all representative, a number of you will be able to relate to. When I was younger (let’s say like ten or so), my grandfather explained that he needed to find some tax deductions because otherwise he’d end up in a higher tax bracket (his words, not mine). The implication from his complaint was that staying in a lower tax bracket would make him better off on net, and this seemed strange. (He later clarified, still but somewhat less incorrectly, that he just didn’t want the government taking 80% of his marginal dollar, so his main error was in not realizing that it wasn’t 1962.) Now I know that tax codes are a little silly sometimes, but even 10-year-old me was suspicious that they were so stupid as to create incentives to throw money away.

I was right to be suspicious, of course- that’s not how tax brackets work. But one thing I’ve noticed is that a lot of people have similar mistaken beliefs about how taxes are calculated. So let’s do a quick refresher- if this isn’t new to you, just forward to that friend you know we all have instead…

First, let’s take a look at some marginal tax rates (assuming you’re single, but you can see the complete set of numbers here):

• 10% for income \$0 to \$9,275
• 15% for income \$9,275 to \$37,650
• 25% for income \$37,650 to \$91,150
• 28% for income \$91,150 to \$190,150
• 33% for income \$190,150 to \$413,350
• 35% for income \$413,350 to \$415,050
• 39.6% for income \$415,050+

Let’s say you make \$50,000 per year (or, if you want to be super picky, have \$50,000 in adjusted gross income or whatever, since this is the amount that you actually pay taxes on). To find out how much you will pay in federal taxes, what you DON’T do is look up \$50,000 in the table above, get a 25% tax rate, and multiply 25% by \$50,000. If this were how things worked, then yeah, a guy making \$38,000 would in fact want to burn \$351 of income, for example. (If you don’t believe me, you can calculate and confirm that taking away 15% from \$37,649 results in a bigger number than taking 25% away from \$38,000.)

What you *do* do, instead, is more sensical but more arithmetically complicated. Again, let’s say you make \$50,000 per year. Your federal tax calculation would look like this:

• Well, I max out the \$0 to \$9,275 bracket, so I pay 10% * \$9,275 = \$927.50 for that bracket.
• I also max out the \$9,275 to \$37,650 bracket, so I pay 15% on, let’s see, \$37,650 – \$9,275 = \$28,375 of income, which comes out to \$4,256.25 for that bracket.
• I go…hm, \$50,000 – \$37,650 = \$12,350 into the \$37,650 to \$91,150 bracket, so I pay 25% * \$12,350 = \$3,087.50 for that bracket.
• Adding this all together gives me \$8,271.25 in taxes owed.

I’ll be honest with you, I didn’t particularly like working though that, but it is what it is, and we have calculators and Excel (and tax prep software) and such to help. Besides, no one has to do this very often, at least not for decision-making purposes. For example, let’s say I offer you \$1,000 to do some research for me. You can look at the tax table and immediately know that your tax rate on this incremental income will be 25% (since you were already earning \$50,000, remember), leaving you with \$750 in compensation after federal income taxes. Note that it didn’t matter that your average tax rate on the original \$50,000 of income was \$8,271.25 / \$50,000 = 16.5%, since it’s only the marginal (i.e. applied to the last dollar) tax rate of 25% that is relevant to an extra dollar of income. (This would of course get more complicated if the incremental income spanned different tax brackets, but the logic is still the same.)

The same principle holds in reverse for tax deductions- if you make \$50,000 and have a \$100 tax-deductible expenditure (ignore the standard deduction for now), your taxable income decreases by \$100 and your taxes owed decrease by \$25, in effect giving you a discount on your expenditure equal to your marginal tax rate. Note again that it was only this last tax bracket, or your marginal tax rate, that was relevant in calculating the effect of the tax deduction.

So yeah…with a progressive tax system- i.e. one with larger tax rates for higher income brackets- your marginal tax rate will be higher than your average tax rate, as you can see from the example above. (They will be the same, however, for individuals with income in the lowest tax bracket only.) So, while you mainly want to keep your marginal tax rate in mind for decision-making purposes, I guess it could make you feel better to calculate your average tax rate and be reminded that the federal government isn’t taking all of your money in income taxes. That’s FICA’s job, after all…

Tags: Taxes

### 4 responses so far ↓

• 1 David Barber // Aug 9, 2016 at 3:59 pm

The OECD does some interesting stuff with tax calculations, and I had the pleasure to work on some of it (a long time ago). I don’t remember the details, but I feel like at one point one of the European countries had on the order of 50+ tax bands. It was more like a tax schedule than tax bands. Of course, with computers it was quite easy, but I feel like educational posts like yours would be much more difficult.

• 2 plusECON // Aug 9, 2016 at 7:21 pm

Thanks for always pushing economic knowledge forward! Love your blog.

Also, you said “*do* do” haha

…I’ll go away now

• 3 What Christians should know about marginal tax rates | Acton PowerBlog // Aug 11, 2016 at 2:15 pm

[…] • Just as the marginal tax rate applies to your marginal (additional) income — the income you put in the last few buckets (brackets) — so too do tax deductions. As economist Jodi Beggs explains: […]

• 4 vmware training in pune // Dec 17, 2016 at 4:51 am

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