Taxes: Maybe I'm Just Stupid

Economic treatment of taxation is always a murky pond. Actually, it's more like a cess pool. I can appreciate the dazzling mental gymnastics of hard-core economics as well as anyone. In fact, I can appreciate them better than most. But I have always had a hard time digesting the disgustingly dishonest way people discuss tax rates and taxation in general.

Lies, Damned Lies, And Percentage Of Disposable Income
One classic example of what I'm talking about is how many people refer to cigarette taxes and lottery/gaming taxes as regressive taxes. The underlying assumption here is that, in the United States, cigarettes and lottery tickets are purchased mostly by people in the lower income brackets. These people (by definition) have less disposable income (i.e. "spending money") than the rest of us. So if a rich guy and a poor guy both buy a pack of Marlboro Reds, the rich guy spends a tiny fraction of his income, whereas the poor guy spends a potentially significant amount of his paycheck. As a percentage of disposable income, the poor guy pays more taxes.

In other words, let:

Y = disposable income
$6 = the price of a pack of cigarettes
T = the value of the tax, relative to disposable income

then, obviously when Y = $20,000, T = 0.03%, whereas when Y = $1,000,000, T = 0.0006%.

It should be clear that 0.03 > 0.0006 and, by this rationale, it has been said that cigarette taxes "disproportionately" affect poor people.

What's wrong with this picture? If you're a stickler for mathematical precision, you will have noticed that T does not actually correspond to the tax on cigarettes at all. What I have done is calculated the price of cigarettes as a percentage of disposable income. See what I did there? We're not actually discussing tax "fairness" here. All we're doing is employing elementary arithmetic to fixed values in an attempt to make it look as though somebody is fairing worse than somebody else.

How Milk Prices Punish The Clean-And-Sober
We could, in theory, go through the same exercise assuming a particular tax rate, and the result would be equivalent. But I wanted to highlight something important: For any static value, that value will be a higher percentage of a low number than of a high number.

I can do that with anything. See, watch...

Y = personal budget set aside for cocaine consumption
$3 = approximate price of milk
T = the percentage of milk as a % of Y

Then, someone who spends $300,000 per year on cocaine faces a value of T = 0.001%, whereas a person who gives $3 spare change to a hobo, not realizing that the hobo is going to use it to buy crack faces a value of T = 100% ! Clearly, United States milk prices disproportionately favor cocaine addicts! I cry foul!

Actually, It's Marginal Rates That Matter
Eventually, the economists chime in. They declare that "only marginal tax rates matter" because "people respond to incentives." The underlying argument here goes something like this...

Suppose you make $30,000/year, which puts you in the middle of a hypothetical $25,000 - $34,999 tax bracket at, say, 30% income taxes. One day, your boss offers you a special project at work that comes with a $2000 bonus. You have the time and resources to do it, so you say, "Sure!" You make an additional $2000 that year, and your final gross income comes to $32,000. Your tax bracket remains the same. You pay 30%, or $9600.

Now suppose your coworker has been working a bit longer than you have, and she makes $34,000 per year. Your boss makes her the same offer. But the additional income would bring her up to $36,000 annually, placing her in a new tax bracket of 35%. Her after-tax income would potentially be $23,400, whereas if she doesn't take the $2000 project, it will be $23,800. She actually makes more money if she does not take an additional $2000.

This example serves to illustrate the importance of marginal tax rates, even though I have cooked-up some hyperbolic numbers. And the example makes things quite obvious: marginal tax rates are very important to people who are making decisions about whether to make more money. Sometimes you walk away with more money if you earn less total income. It's counter-intuitive, but it's absolutely true.

The problem I have is that when people claim that it's only marginal tax rates that matter, they are being unbelievably foolish. Even if your own income never changed, your total tax rate would matter a great deal to you. It matters that the government levees an income tax of X%. That means your take-home pay is reduced by X%, despite the fact that your employer is willing to offer you exactly X% more for the work that you do.

It matters that you're not getting your X%. You earn that money by working, but the government takes a slice. While your marginal tax rate may impact some of the decisions you make, your total tax rate still matters.

People are so accustomed to politicized language in tax rate issues that they can't really even think about taxes rationally anymore. If everyone's tax rates go down, somebody argues that one segment benefited unfairly "as a percentage of" something or other. And the same if everyone's taxes rise. If the bureaucrats plan a special tax that hits you particularly hard, the behavioral economists are quick to point out that it doesn't really matter because, after all, we're not talking about your marginal tax rate, we're just talking about your total tax rate.

And so on and so forth. But what is the purpose of all this, except to confuse people? Why does ever tax rate discussion devolve into clever games of arithmetic? Why does the burden of a tax increase change depending on what percentage of what other aspect of your life someone bothers to place in the denominator of the expression?

How asinine can this get? A tax increase is a tax increase, for heaven's sake.


  1. LOL@your cocaine example. Never thought of it that way.

    But I think the careful way to clean up that sort of claim is to speak of marginal utility and forget about 'disposable' income. Taking $X as cigarette from a rich person means taking far less Utility (whatever that means) from than than when the same tax takes $X from a poor person.

    Now this is, in large part, *because* the poor person has far less disposable income. But I do think it avoids your 'cocaine' criticism.

    As for the example of 30% becoming 35%, I think that's wrong, and it's been a pet peeve of lots of lefty commentators: your second person would still pay 30% tax on the first $999 of the $2000 bonus, and then 35%on the remaining $1001. The $2000 bonus would still net her more money overall.

    There is an issue with benefits/deductions phasing out in a retarded way which can indeed sometimes lead to weird marginal 'cliffs', but it's just not a property of the income tax rate schedule itself.

    1. If you look at utility instead of income, then you run into the problem of the non-cardinality of utility. You can't really compare indifference curves between individuals.

      I admit the math in my marginal tax rate example is intended more to serve as an example for the concept, not to be an airtight case. There are better examples out there, I just wanted to touch on what the idea is, so that I could go one to say, "But still - total tax rates are important." The point is, it's not *solely* marginal rates that matter.

      But yeah.

    2. True, utility technically can't be compared across individuals. That doesn't stop people (esp the left) from trying. More to the point here though, without trying to pin things down further it's just not that controversial to suggest that $X has more utility to a poor person than to a wealthy person, for cigarette-tax-like values of X.

    3. IMHO, while you're not the first person to suggest that a dollar is worth more to a poor man than to a rich man, that is actually a bit of a controversial claim. My view is closer to Robert Murphy's here: