Marginal tax rates: why they make sense

All righty kids, today we’re going to talk about diminishing marginal utility and taxes. For now I’m leaving comments on, but if things get too political we’ll be shutting them off. This is about the simple theory.

Above you see a nice figure of what economists generally think people’s utility curves look like with respect to income. Ignore the exact numbers– pretend they’re in zubwats instead of dollars and you don’t know the zubwat to dollars exchange rate.  (I certainly still get quite a bit of additional happiness from an extra 100 even when I have 1000… but in zubwats, an additional hundred isn’t so much).

First off, utility is just another word for happiness.  If you have no money, an additional 100 zubwats makes a HUGE difference in your quality of life.  But, as you become wealthier and wealthier, say you have 1000 zubwats, an additional 100 zubwats isn’t such a big deal.

Let’s think of this in terms of dollars.  You can probably think of a time when an additional $10 was kind of a big deal.  It meant you got to eat something other than ramen.  Today, hopefully, $10 isn’t such a big boost, and not just because of inflation.  $10 to Bill Gates would be nothing.

$1 is worth more to me than to Bill Gates.  $1 is worth more to my students than it is to me.  And $1 is worth more to a single mom working minimum wage than it is to the majority of my students.

So if we want to keep people equally happy, we really shouldn’t have a poll tax, the kind of tax where everybody just gives the same dollar amount.  The single mom wouldn’t be able to feed her kids, my students would get into bigger student debt, I’d be annoyed, and Bill Gates wouldn’t even notice.  Poll taxes seem fair in terms of dollar amount, but they’re unfair in terms of utility.  And isn’t happiness what matters?

Ok, well, how about a flat tax?  Everybody pays 10% just like God intended (not that 10% of everybody would actually make anywhere near as much money as the current system, but you can put in your own %).  Well, that isn’t going to work either.  A flat tax is essentially a straight line sloping upward.  So if you made $100, your tax would be $10.  If you made $1000, your tax would be $100 and so on.  You see that diminishing marginal utility curve?  You notice how it is curved and not flat?  Even if you subtracted off the same percent tax for everybody, it would still hurt the people with more money less than it hurts the people with less money.  And think about it.  Someone with an income of $10K simply cannot afford to lose $1K and still eat (much less feed a family).  Someone with $100K can pretty easily lose $10K.  The difference between $1,000,000 and 900,000 is really only rounding error to someone with an income of a million.  Sure, that $100,000 seems a lot to those of us who don’t make six figures, but to the person with an income of a million it actually hurts less to pay that 100K than it hurts the $100K person to pay the $10K or the $10,000 person to pay a mere $1K.

(Note:  there are more complicated “flat taxes” that are really more like step taxes that don’t quite have this problem, just with a continuous step instead of brackets, so each additional dollar is taxed a little more than the dollar before it.  These are actually thought highly of by some well-regarded economists.  But that’s not what a couple of the leading candidates for president are advocating.  They don’t want any “progressivity.”)

And that is why progressive taxes, in which additional dollars earned are taxed more then previous dollars earned (or:  those with high incomes are taxed at higher rates than those with small incomes), are actually more “fair” than poll taxes or flat taxes.  We’re trying to do our best to equalize happiness, not money.  It’s all because of diminishing marginal utility.  Each additional dollar is worth less to us than the dollar before it.

The question of how progressive a tax should be, and where we should put the brackets– those are big open questions.  Policy is not easy.  But we know that zero progressivity is not the answer if we want to minimize the pain and maximize utility.  Zero progressivity is just not fair.


32 Responses to “Marginal tax rates: why they make sense”

  1. First Gen American Says:

    I guess I’m a fan of a flat tax that starts at a certain income threshold. I surely expect to pay more in taxes than my elderly mom and disabled people. On the same token, I don’t want to be paying exponentially more. There has to be a balance between high income people paying extra but not so much that it dissuades them from earning a higher salary. Having everyone above a certain limit pay the same percent seems fair to me. Also, as it’s structured today seems kind of unfair. My mom didn’t qualify for no tax status until she retired completely despite making minimum wage. Even with her rental income, she still rolled up at poverty level AND paid taxes. So who are all these 40%+ of people who pay no taxes at all? Is it just because they have better accountants, or are in more debt? Why should that be rewarded?

    On the high end, larger income presumably comes with larger amounts of personal time spent and taking bigger risks, so if taxing gets to the point where the return on your personal investment doesn’t make sense because you’re going to be taxed at some astronomical level, I’d think that would have a negative impact on innovation and growth. Also, larger salaries mean more tax revenues, so putting a negative incentive in place to earning more seems dumb to me.

    I don’t know if it would be that hard to draw a line in the sand since there is already data on the people who pay no tax today. I’m sure there will be a few outliers, but I think simplifying the tax code would be good on so many levels. Even the cost savings from the administration of monitoring and policing taxpayers would be huge. I don’t know if any politicians have the guts to make any changes that large though.

    • nicoleandmaggie Says:

      By having a top bracket that is currently what people have. Nobody in this country gets charged more than 35%.

      Do keep in mind, though that for the first X you make you’re still charged at the original bracket. People aren’t going to go from making 379,151 to zero just because they’re now in the top bracket. Only the 379,151th dollar is charged at the 35% rate. The 379,150th is still only at the 33% rate. The 174,400th dollar is only at the 28% rate and so on. It isn’t like their entire income gets charged at the top rate, only the dollars above the bracket.

      Re: negative incentive. How negative an incentive the tax is varies by where you are on the marginal utility curve. People with more income can withstand a higher loss without as big a loss in utility. It is also likely that some people who are working at these huge incomes are pretty price insensitive and work because that’s what they do– you could cut their income by hundreds of thousands of dollars and they would still work just as hard. They might grumble more, but they’d still make the next movie if they liked the script. They’d still produce their Fox news shows etc. There’s more to jobs for these people than just money. Paris Hilton (according to interviews) doesn’t even know what her income is– she has accountants to take care of that for her. She’s just able to buy what she wants when she wants it. Add to that, we already proved that we were not on the wrong side of the Laffer curve. We don’t know where that tipping point is, but we are nowhere near it. Yes, there is a tax rate that disincentivizes work, but we haven’t found it yet. (Deliberately left the Laffer curve discussion out of the article because I don’t want to attract all the Koch brothers crackpots. It is a separate but related issue.)

      Yes, exemptions etc. are skewed to favor people with good accountants. They will sneak back into the tax code no matter what. Taxes can be used to encourage behavior we like (giving to charity) and discourage behavior we dislike (cigarette taxes).

      What Warren Buffet is talking about is how if you don’t get any earned income and live off stock dividends, your tax rate is only 15% no matter how much money you make. He thinks dividends should be taxed at earned income rates.

    • Carolyn Says:

      I think the negative tax/innovation correlation is largely a myth. Progressives taxes usually mean that there is a decent safety-net in place for people to take risks and be innovative. Not having to worry about how you’ll pay for health care or education should Plan A fail, makes it a lot easier to pursue Plan A.

      This is an interesting take:
      ‘Rates of start-up creation here [in Norway] are among the highest in the developed world, and Norway has more entrepreneurs per capita than the United States, according to the latest report by the Global Entrepreneurship Monitor, a Boston-based research consortium. A 2010 study released by the U.S. Small Business Administration reported a similar result: Although America remains near the top of the world in terms of entrepreneurial aspirations — that is, the percentage of people who want to start new things—in terms of actual start-up activity, our country has fallen behind not just Norway but also Canada, Denmark, and Switzerland.’

      • nicoleandmaggie Says:

        There is a tax rate at which innovation will be shut off (think, 110% for example– you pay 10% plus everything you make if you come up with something). But we’re not there. Those rates are probably somewhere between 50 and 100%, and may vary considerably by person (and accountant) at the upper levels.

      • Kellen Says:

        I think Norway does a good job of reducing the risks to people wanting a start up. Need to support your family? You get a year? 2 years? paid leave after having a child. It’s not so scary to quit your job to start a new business when you know if you have a child, your spouse can get paid leave to care for them, you’ll have health insurance for the whole family, and probably other benefits that I don’t even know about.

  2. Cloud Says:

    I remember learning this stuff even in my relatively mediocre high school (in a very conservative place). I am having a hard time remembering that not everyone got that chance. Or not everyone remembers it.

    For me, the biggest problem with the “its not fair” argument against progressive taxes is that wealthy people are benefiting from a lot of the things that their taxes pay for: the social order that keeps people from storming their gates and stealing their stuff. The good roads that make it easy to move the stuff they sell around. Etc., etc. You could even argue that they get more benefit from these things than a poor person with nothing worth stealing and no car in which to drive the roads.

    Also, the people who argue most loudly at me that government shouldn’t take more of their money are generally not wealthy enough to have this discussion matter.

  3. Linda Says:

    Thank you for this! It’s such a clear explanation. I’m going to have to save this link for sure!

    I’ve often been puzzled by the argument that higher income tax rates act as disincentives for people to work hard or increase their income. If I earn an extra $1,000, even if I pay 50% in taxes I’m still earning more money than I would have if I didn’t take that chance or put in that extra time, etc. I guess this argument comes up because corporations pick up and move due to tax issues, so there is a thought that if taxes get increased on individuals there will be a similar repercussion.

    I think the excerpt that Carolyn posted points to a much bigger issue that stifles innovation, productivity, and entrepreneurship in this country: the issue of benefits like health care from a source other than an employer. I envy Jacq from Single Mom, Rich Mom who is able to work as a contractor when she wants and take off extended time. I could do that, too, although I have a lot of concern over securing adequate health care coverage. Jacq lives in Canada and can get decent health coverage through her government. Entering the health care market as an individual is pretty overwhelming and can be very expensive.

    • Cloud Says:

      I agree on the health care point- I personally know several people who are NOT going out on their own and starting businesses because they need health coverage for their families. Buying coverage independently is quite expensive for most people, and darn near impossible for people with certain pre-existing issues. The lack of discussion of this was one of the things that puzzled/angered me most during the health care debate here in the US.

      • nicoleandmaggie Says:

        We have a post on that… it’s the one about used cars. I’ll have to dig it up.

        There is a Ginormous literature on it… the term is, “job lock”

      • bogart Says:

        Seconding (or thirding) that. It astounds me that anyone could believe the US can foster innovation given how risky/difficult/impossible it is not to work for “the man.”

      • nicoleandmaggie Says:

        You can do it so long as your spouse works for “the man” (there’s papers on that too).

      • Cloud Says:

        Ah, but if your spouse works for the man but has little job security, you’re going to want a big buffer before you take the leap, because COBRA only lasts so long (and isn’t cheap).

        And if your day care expense is almost as big as your mortgage, then you can’t take the leap unless you save up a lot of money or bootstrap yourself to a place where you’re replacing enough income to keep the family solvent.

        I’ll bet there is literature on both of those scenarios, too, right?

        All of this makes me wonder about all this talk about job creation, when no one in government seems to be connecting the dots to some of the things that keep people from taking the leap into entrepreneurship. Says the woman who harbors dreams of going out on her own, but can’t see how to do it until the kids are at least in school….

      • nicoleandmaggie Says:

        Very true.

        We may start talking about those things again. I know Historiann gets upset when people talk about history cycling, but with the 99% protests in DC, I wouldn’t be surprised if people start focusing on daycare and other progressive issues that folks were pushing for back in the 60s and 70s.

        There’s not actually as big a literature on the effects of daycare on mom’s work as there ought to be. Huge literature on the effects of daycare on kids (resolution: high quality daycare good for low SES kids, low quality daycare bad for everybody), but not so big on mom’s work. Even though it’s been a big policy issue since the 1950s.

      • bogart Says:

        I am weirdly privileged in this regard because my DH’s pension includes (purchaseable, but at “reasonable” rates by US standards — at least for now; every state budget crisis invokes threatening rumblings) not only group coverage for him but also for me and our dependent(s). Ad infinitum, i.e., under current rules, I could have (purchase) it now and keep it (as long as I pay the premiums) until I keel over and DS until he’s adult, even if DH keels over. I do think that I have to stay married to the guy, though, so there’s always a catch ;). I am not using this, but it’s one more thing I keep in the back of my mind in terms of Efunds and such. In the contemporary US (sadly), it’s a pretty amazing thing.

  4. Foscavista Says:

    This is is a serious discussion, but I am fixated on “zubwats.” So, let’s change famous song titles/lyrics to incorporate this newly-minted currency!

    1. Brother, can you spare a zubwat?
    2. She works hard for the zubwats.
    3. Zubwats, zubwats, zubwats
    4. I’m your private dancer, dancer for zubwats, any old music will do.
    5. Only boys who save their zubwats make my rainy day.
    6. I got my mind on my zubwats, and my zubwats on my mind.
    7. Zubwats. Zubwats change everything.
    8. Zubwats make the world go around, the world go around.
    9. Keep your hoochie and the bank accounts. Cause boy, I bring home the zubwats now.
    10. If I had a million zubwats, I’d be rich.

  5. Comrade PhysioProf Says:

    The idea that people stop trying to make more money if the highest marginal tax rate is too high is absolutely f*cken absurd. Once you have hundreds of millions of dollars, there is simply no way to even spend more money that over your lifetime. But people still do everything they can to earn even more, billions and billions. If this marginal utility concept had any meaning, than hundred million and billionaires would just stop trying to earn any more money, because at that level, additional money has absolutely *zero* utility. You can’t even spend it. Yet they keep trying. Insane greedy billionaire f*ckes like the Koch’s spend their every waking moment trying to make sure that they don’t only have X billion dollars, but X.9 billion dollars. It can’t be because they expect some marginal additional utility from the extra 0.9 billion. Rather, it’s because human beings are competitive motherf*ckers who will die to “beat” other people.

    • nicoleandmaggie Says:

      Money isn’t the only thing in people’s utility functions. Like we said in a previous comment, many people at these high income levels are working for a reason besides just money. Fame, power, because they love basketball etc.

      What marginal utility is saying is that at some point it isn’t the extra dollar earned that’s driving folks. It has to be the extra billion dollars. Or something else. Marginal utility doesn’t become completely flat, and it never slopes down (you can always give money away) it just means that you need more of it to get the same effect you got with less of it when you were poor.

  6. Carnival of Personal Finance #333 | Sustainable Personal Finance Says:

    […] but I like the site, so I included it.TaxesNicole from Nicole and Maggie: Grumpy Rumblings presents Marginal tax rates: why they make sense, and says, “Professors Nicole and Maggie explain how diminishing marginal utility means that […]

  7. Kingston Says:

    “Job lock” — who knew there was a name for it? I really love this blog and your consistently valuable comments over at Get Rich Slowly. Please keep the good information coming.

  8. The Laundry Lady Says:

    Since the concern seems to be the fairness of tax rates perhaps the issue shouldn’t be an income tax at all, but rather a consumption tax. (Not that I ever expect any tax to truly disappear realistically). In many states food and clothing are already exempt from sales tax (and if they aren’t, they probably should be), so that protects some of the basic necessities of life from taxation, thus protecting lower income families. That way people have more direct control over their taxation (in that the more you consume, the more you pay in taxes). Generally speaking, the wealthy are far higher consumers than the poor, and if either group wants to keep more or less of their money they consume accordingly. This also “rewards” savings, so to speak, and Americans love their stuff so I don’t see a real risk of tanking the economy by adding a tax that might theoretically discourage spending. Payroll deductions of income tax are confusing to many people because they don’t really ever see that money (out of site, out of mind). I think opinions would be quite different if we had to pay a monthly or annual tax bill. (Ask anyone who pays quarterly taxes about that feeling). This would also simplify the system. No deductions, no accountants needed, you get taxed based on what you purchase and consume. This would eliminate the advantage to those who can afford to higher good accountants to find them obscure deductions. That being said, obviously accountants would still be necessary because of all the other kinds of taxes that exist, particularly for businesses. (In the interests of full disclosure, I grew up in a upper middle class family and while I always imagined that my husband’s income made us lower middle class, apparently the government does not. We are considered low income and could probably qualify for limited assistance if we chose to apply. But since we manage to live simply and pay our bills I prefer to leave that money in the over burdened system for those who are deeply struggling since as low-income single mothers, the unemployed etc. I’m definitely not criticizing those who rely on those government services; I’m just explaining my own decision.) While I personally hate the idea of paying a 20%+ sales tax on non-necessities, I prefer that to the 15 or 20% coming out of every paycheck. Yeah, I get some of it back at the end of the year, but I’d rather be putting it to work during the year for things we need (like paying off student loan debt, increasing our monthly grocery budget and making sure my growing toddler has shoes that fit) than waiting for the big check at the end of the year.

    • nicoleandmaggie Says:

      A consumption tax is much worse in terms of fairness based on utility than even a flat-tax would be. The poor spend almost all (100%) of their income on basic necessities, the rich spend much less in terms of percent of their income. So a consumption tax is much more regressive than an income tax. The rich will pay a smaller percent of their income in consumption taxes than the poor, even though the rich get less disutility from each dollar of tax. Yes, the rich will spend more dollars, but that’s only because they have more dollars to spend, it is exactly the same argument with the flat tax, but even worse in terms of marginal utility differences.

      Additionally, empirically consumption taxes more directly decrease spending than income taxes do– people who can spend less when the sticker cost is higher. So it hurts people most who have the least discretion and dampens the economy.

      And it would be a heck of a lot more than 20% sales tax to make up differences in income tax. Remember that most lower levels of government are already at ~8% sales tax to fund their spending.

  9. chacha1 Says:

    nicoleandmaggie, I would love to see what you have to say about the taxes we pay for “entitlements.” Because even people too broke to owe income taxes pay for Social Security and Medicare. (And Social Security + Medicare + defense eat up, what, 70% of all federal spending?) And are the rates for Social Security and Medicare not flat? Which makes them regressive, but maybe that is more “fair” since maybe broke people rely more heavily on these programs compared to rich people?

    I am one of those outliers who thinks Americans get a ton of value for their tax dollars, marginal rates should go up for those with incomes in the six figures, and capital gains should be taxed like wage income. Call me crazy. Our household income is around $150K and we pay a LOT of income tax. I don’t think we pay too much.

    On a tangent, DH is happily self-employed mostly because I am not. I work for The Man, who makes it possible for us to get almost-affordable health insurance. I think marginal tax rates have MUCH less of a squelching effect on innovation or entrepreneurship (not necessarily the same thing) than fear of our insanely inefficient disease-care system. Oh but I could rant all day. :-)

    • nicoleandmaggie Says:

      We actually have a post on entitlements already. No comments allowed though. Let me see if I can dig it up.

      Social Security is actually incredibly progressive. It is a secret redistribution program– poor folks get more out as a percent of what they put in than high income folks. Most people don’t know that though.

      I’m not 100% sure about the progressiveness of Medicare… the amount paid in should vary by income but the benefits are the same for everybody and because SES is correlated with health, low SES folks will use Medicare more intensively, but they’ll also die younger and use it for fewer years. Medicaid is available to make things more progressive. People who are on both are called dual-eligibles.

  10. Haig-Simmons Taxes: Is the tax system unfair to paid labor? « Grumpy rumblings of the untenured Says:

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  13. nicoleandmaggie Says:

    To readers coming in from political fora, I should also note that everybody does get taxed the same percentile on the first $X of income (or all married couples and all single people do anyway, and actually if you want to be technical because of deductions like the mortgage deduction, higher income itemizers may actually pay less!)… that’s because of how marginal tax brackets work. It’s fair! I’m sure that single McDonald’s mom would be happy to pay the 28% or 35% amount on the last dollar earned if it meant she were earning in the 28% or 35% bracket! I know I sure would be.

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