# To divide by income or not to divide by income: that is the question

When I point out that price discrimination has largely spared poor people from public college price increases (as is true), I occasionally find people telling me I need to divide by income. That is, instead of just looking at the dollar amount each income group is paying, I should take that dollar amount and divide it by their income. I am not adverse to dividing things by income, but I do wonder when it is and isn’t appropriate.

In some sense, it is always fine to do something like that. As long as people know what’s going on, then it’s fine: they can interpret it how they see fit. But the question then is when should you interpret it as having any particular meaning? I don’t have an answer to this question, but I’d like to see other people chime in. What follows are just things to consider.

First, on the college question, it deserves pointing out that even when you divide by income, it is the case that college has become more affordable in the last 15 years for the poorest quarter of kids. Whereas attending public college took up 48% of the parental income of poor kids in 1992, it only took up 44% of that income in 2007. So, for poor kids at least, looks like things are improving and headed in the right direction! Yay!

Second, do we selectively apply this divide-by-income style of analysis or apply it to everything? So for instance, if you divide college prices by income, it is certainly the case that they make up a higher percentage of the income of poor kids than rich kids. But that’s true of all other prices as well. Actually, it is more true of other prices because other prices don’t usually have steep income-based discounts like college prices do. So you can graph college prices of each quartile divided by the income of each quartile and it will show regressivity. But if you graphed twix prices of each quartile divided by income, it would be way more regressive. Same with milk prices, car prices, twinkie prices, chicken prices, cereal prices, newspaper prices, prices for the Jacobin magazine, and so on.

So what does that really mean at the end of the day except that poor people are poor and rich people are rich? I don’t really know. It seems to me that what’s significant about college is that relative to most prices that are the same for everyone, poor people get a break on college.

Third, should we employ divide-by-income methodology for subsidy payments as well, or just prices? For instance, suppose I had a plan to give everyone who makes \$10k/yr an extra \$1000. And then everyone who made \$20k/yr would get an extra \$1999, \$30k/yr an extra \$2998, \$40k/yr an extra \$3997, and so on. To my eyes, this looks like a really bad policy. Once you get out to someone making \$1 million dollars, you are giving them somewhere just below \$100k! The rich are scoring out big time on this. But wait, if you divide all of these cash grants by income, you would see that it is a progressive policy! Measured as a percentage of income, the poorest get the biggest boost, the rich the smallest boost, and so on. By the way, this is effectively what would happen if you subsidized college all the way to free. The rich kids would get the most out of it (relative to the status quo) and the poor the least, measured in dollar terms. But measured as percentage of income, the figures would reverse, and show the poor getting the most. Shrug.

Again, I ask, what sense are we supposed to make of all of this ultimately? When is this method supposed to be used and when is it not? To the untrained eye, it appears that the answer is: do it selectively when it’s necessary to make out a point that the data doesn’t otherwise support. Though I may just be cynical.