A Modest Sandwich Tax: the Economics of Deterring Self-harm

You are the Czar.  You have the power to unilaterally make policy. You want people to stop eating sub sandwiches. The average cost of a sandwich is $7. You propose to impose a $1 tax on sandwiches, dust off your hands, and say, “Problem solved.” A trusted adviser points out that this is a relatively small price increase, and will probably only cause a small reduction in sandwich consumption. You scowl, cup your chin, and say, “Point taken.” Then you impose a $7 tax on each sandwich. Your trusted adviser points out that this will have a more substantial effect, but at the cost of doing more harm to the remaining sandwich users. Some will continue to use sandwiches just as before, but now they are being squeezed with the tax. It does no good to ramp up the tax. You will have fewer sandwich eaters, but each paying a much higher cost for their sandwich habit. “What,” your adviser asks, “is the problem you’re trying to solve anyway? Quantify it. Are these sandwich-abusers doing self-harm to the tune of $2 per sandwich? $5 per sandwich?” You think it’s big. Comparable to the dollar-price. Say it’s $7-per-sandwich, because of gluten and obesity-related issues. With self-harm being this large, surely that justifies your sandwich tax? Your adviser points out that, no, a larger value here implies that it will be even harder to deter sandwich users. If they are really paying $14 per sandwich already ($7 in cash plus $7 worth of self-harm, appropriately quantified and converted to dollars), then the $7 sandwich tax is only a 50% price increase. And once again, ramping up the tax harms the remaining users even if it “helps” those who quit. You at first think your adviser is playing some having-it-both-ways trick, but then you realize that there really is a fundamental trade-off. A smaller tax will deter fewer sandwich eaters but be less harmful to the remaining sandwich eaters. A bigger tax will deter more sandwich eaters but be more harmful to the remaining sandwich eaters. (A final thought occurs. Maybe the Czar, even in his infinite wisdom, is mistaken about the hazards of gluten and the causes of obesity?)

You now observe a more serious problem. Some people seem to enjoy bonking themselves on the head with a mallet. Not like a fatal blow with a hard metal hammer, but a mild, dizzying shot with a padded weapon. It's part of some kind of game, the appeal of which you fail to understand. You insist on putting a stop to this at once with a severe penalty. Anyone who indulges in self-bonking will be punished with a stiff fine and a brief stay in jail. But your trusted adviser reminds you of your previous conversation about discouraging sandwich eating. “Convert the penalty to mallet-bonks. What would you say it amounts to?” You think about it and say that the penalty amounts to perhaps a single mild mallet-bonk. Your adviser points out that the penalty effectively doubles the price of self-bonking (assuming an implausible 100% chance of detection and conviction). You probably deter about half of them, but the remaining half suffer twice the harm. On average, you haven’t helped this group at all. (It could be much worse than this if the elasticity of demand for mallet-bonking is low; doubling the price reduces bonking by less than 50%. So with >50% of previous users paying double the cost, your penalty has made this population worse off as a whole. If demand elasticity is high, that could make your penalty look better. But it’s kind of implausible to think that people doing serious self-harm have highly elastic demand.) Once again, you suspect some kind of having-it-both-ways casuistry on the part of your adviser. I shouldn't try to deter mild self-harm, and now I shouldn't try to deter serious self-harm? But after a while you convince yourself that the degree of self-harm is irrelevant to your adviser's point. If someone is indulging much more severe forms of self-harm, they are effectively "willing to pay" much more for those habits. Deterring them will require a stiffer penalty. And once again the stiffer penalty doesn't "help." For every person that you deter from self-harm, there is another person whose harm you have doubled. And with inelastic demand it's actually worse than this. More like, for every person that you deter from self-harm, there is another person whose harm you have tripled. 

I explore this argument more generally in a previous post. There isn't a way to square this circle without adding in some weird, stilted assumption. Preventing vice-related self-harm by penalizing vices just doesn't work. Maybe people are far more sensitive to the legal penalty than the other costs (even when these things are of similar magnitude)? Maybe, but why would that be true? Maybe there are costs to third parties? ("Externalities" in the language of economics.) Sure, but there are bound to be externalities due to prohibition as well. Besides, most of the so-called externalities due to vices (particularly drugs and alcohol) are already internalized. A more elegant and direct approach is to target the externalities themselves. For example, issue stiffer penalties for property crimes and intoxicated driving in particular, not for intoxication in general. At any rate, we shouldn't fool ourselves into thinking we're helping people who indulge in dangerous hobbies by compelling (some of) them to quit. If any of this was too glib (and I think this final paragraph has given me away), this argument has serious implications for drug prohibition. A tax on harmful vices wouldn't be quite as bad as a legal penalty (police harassment/arrest/jailing), but in either case the people who indulge those vices are hurt more than they are helped. Perhaps education or mandatory licensing would at least help people figure out if their risk-taking is rational. But once people make up their minds to hurt themselves, it seems pointless and cruel to pile on.