Here's how Mankiw's argument goes: Utilitarians want to use taxation to push incomes towards equality, because of the diminishing marginal utility of money. (Mankiw is right that we utilitarians generally like this -- extra money does much more for a poor person's happiness than a rich person's, so moving money down the income scale by progressive taxation will generate more happiness, and that's what utilitarians are all about.) However, insofar as income levels are correlated with effort, this sort of taxation will have negative effects on people's effort, and you don't want that because people expending less effort results in the creation of less awesome. So if you can find something that's correlated with income, but which is disconnected from effort, you have a reason to tax it. And it turns out that height is like that. So on a utilitarian view, height should be taxed. But taxing height? That's crazy! And in the view of one of the authors, this is a reductio ad absurdum of utilitarianism.
I was struck with the weirdness of a height tax the first time I heard about it. But I was also quite struck by these numbers from early in Mankiw and Weinzierl's paper:
Judge and Cable (2004) report that “an individual who is 72 in. tall could be expected to earn $5,525 [in 2002 dollars] more per year than someone who is 65 in. tall, even after controlling for gender, weight, and age.” Persico, Postlewaite, and Silverman (2004) find similar results and report that "among adult white men in the United States, every additional inch of height as an adult is associated with a 1.8 percent increase in wages." Case and Paxson (2006) write that "For both men and women...an additional inch of height [is] associated with a one to two percent increase in earnings."Updating the Judge and Cable result to 2009 money, the difference between being 5'5" and 6 feet adds up to $6,568 per year, even with the gender, weight, and age controls in place. One study explains this in terms of beneficial self-esteem effects coming from being the tall kid in adolescence, while another explains it in terms of childhood nutrition that affects a bunch of useful abilities like cognitive ability that actually cause the salary difference. Either way, taxing height would seem like a good idea to a utilitarian social planner. Taxing height wouldn't reduce anyone's effort, and unless parents decided to feed their children less to make them shorter or something ridiculous like that it wouldn't reduce total productive capacity in any significant way.
Even if height ends up being correlated with something particularly useful like cognitive ability, explaining both of these things in terms of childhood nutrition starts making a height tax look benign. Let's run an argument kinda like one Rawls uses in A Theory of Justice. Does any one child deserve to be fed and cared for better than another child? Of course not! All children equally deserve good nutrition and care from their parents. If the differences between the rich and poor come from the fact that the rich were well-fed as children while the poor were ill-fed, we have no reason to leave income levels where they are. "You deserve to make less money than him, because of differences resulting from how you were fed poorly as a child while he was fed well" is just madness.
Some people might want to push this argument further and say that we have positive reasons to undo differences that come from factors like childhood nutrition. Being a utilitarian, I'm not quite going to go there. But I'm going to ride the Rawlsian point far enough to say that there's no reason to maintain these income disparities. When you think about how much extra money tall people make, and the causes of the salary differences, the reasons for opposing a height tax lose their force. The Rawlsian point undercuts our anti-height-tax intuitions, so we have no reason to oppose a height tax. And then it's time for utilitarian considerations regarding the diminishing marginal utility of money to do the positive work, and push us to a height tax.
(Lots of people are probably freaked out by a height tax because we're generally freaked out when the government treats people differently because of uncontrollable bodily attributes like skin color and gender. It's interesting to look at affirmative action policies in this light. It's definitely wrong for the government to entrench unfair systems by treating different bodies differently. But is it okay for the government to treat different bodies differently to overturn unfair systems? Well, people disagree. But make no mistake -- when you look at the empirical data, that's what a height tax would be doing, and there's at least some support for that sort of thing.)
In the end, I'm unimpressed by the height tax argument against utilitarianism. Sure, height taxes are counterintuitive before you think about the relevant empirical data. But I feel like the content of Mankiw and Weinzierl's study undermines the anti-utilitarian punchline.
And it's not that utilitarianism is the most intuitive ethical theory. There's plenty of places where it looks counterintuitive -- 90% of people go against it in the fat man version of the trolley problem. One of the papers I'm presenting in my current tour around the country is on how to defend utilitarianism despite its counterintuitiveness. But if Mankiw was trying to throw a counterexample at utilitarianism, well, it's among the easier ones to outsmart.