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.

Totes stolen from http://mrski-apecon-2008.wikispaces.com/Sun%27s+Page

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.