Thursday, February 25, 2016

Demand Response to Vice Prohibition

I’ve made the point before (here and here) that drug prohibition is a losing battle. In order to deter drug use, you have to raise the cost faced by the consumer of drugs. In this post I want to make a simple scaling argument. My conclusion will be that the costs of prohibition most likely scale faster than the benefits.

Supposedly drug users irrationally harm themselves with their nasty habits, so we have to stop them. That’s a typical rationale for drug prohibition: People don’t fully account for the cost of their vices, so it would be good to stop them from indulging. But then these supposedly irrational drug users are presumed to respond rationally to legal sanctions. It’s akin to believing, “People don’t respond rationally to the [pharmacological] risks of drug use, but they do respond rationally to the [legal] risks of drug use.” Say the sentence without the words in square brackets to see the obvious contradiction. Maybe we can be more precise than this hand-waving.

Let’s suppose a potential drug consumer faces a price “X”. This X is the full economic cost to the user. It factors in the money paid to obtain the drugs, the time spent acquiring and using them, the potential health risks of using, the potential shame and social sanctions if his use is discovered, potential harassment by police, jailing, prison, etc. You can express X in any units. “Dollars” would be the most obvious: monetize the time value and the health and legal risks and roll it all up into a clean dollar figure. Or you can express it in “man-hours of labor,” or “% risk of completely ruining your life,” or “expected years (or months or days or hours) spent in misery.” It doesn’t matter for our purposes. I’m not going to try to estimate what this cost is, or even specify which drug I’m talking about. What matters is that you have this price called X, and to get you to stop using drugs I have to increase X. This is how drug prohibition works.

How strongly do you react when I raise X? Maybe there is a simple inverse relationship, whereby if I increase X by some factor Z, rates of drug use drop by a factor of 1/Z. So, for example, if I double the cost, I cut the amount of drug use in half. Taking that example, we have half as many users, but they are all paying twice the cost! It’s a wash! (By the way, I am leaving out *many* of the other costs of drug prohibition.) The chart below shows what this relationship looks like (simple inverse-relationship chart here). It is impossible to achieve “success” in this world. Hammer the users as hard as you like. The total cost will stay flat. This is a losing game, especially when you factor in the cost of waging a drug war.

(The “quantity consumed” is in arbitrary units. It doesn’t matter whether “5” means “5 metric tons per year” or “5 million users,” and again it doesn’t matter what drug I’m talking about or what the real-world value is. I’m simply making a scaling argument here, so the actual values don’t matter. These are *not* supply-and-demand curves from economics 101, which traditionally cross and tell you the market price and quantity supplied. Although the “Quantity Consumed” curve *is* actually a demand curve. If it’s confusing that I’m recycling the y-axis for three different kinds of values, don’t get hung up on it. My point is to show how total costs scale up with the price faced by the user.)

But maybe there’s reason for hope! Maybe it’s not a 1/Z relationship, but more like a 1/Z^2 or a 1/Z^10 relationship between price and total use. If this is the case, we do added harm to the remaining users, but those remaining users drop off quickly. Quickly enough that the total cost falls. Anything with a 1/Z^(anything greater than 1.0) relationship will show this falling cost pattern. The chart below shows what a 1/Z^1.5 relationship looks like.

Success! The cost falls when you hammer drug users with harsher penalties. (Once again I’m ignoring a whole host of other relevant costs.)

Is the above scenario reasonable? Not really. It assumes that drug demand is fairly elastic. “Demand elasticity” is usually expressed as a (% change in demand) / (% change in price). If you increase the price by 1% and demand falls by 2%, the elasticity is 2.0 (demand is fairly elastic). If you increase the price by 1% and demand falls by 0.5%, the elasticity is 0.5 (demand is fairly inelastic). Very roughly, inelastic demand means people are willing to pay quite a bit more to keep buying the product; elastic demand means that people buy quite a bit less when the price rises significantly.
Demand for drugs is actually quite *inelastic*. You can raise the price by a lot and you get a small demand response. Measured elasticities for common addictive substances (tobacco, alcohol, heroin, cocaine) are typically in the -0.3 range. So the relationship between cost and quantity probably follows more like a 1/Z^0.5 (anyway, 1/Z^(something-between-0-and-1) relationship, probably closer to 0 than 1). A 1/Z^0.5 relationship gives you a picture like the following:

The total cost *increases* as you increase X. There are fewer users, but they each face a much greater cost. Doubling the price doesn’t quite cut the using population in half, so you have *more than* half as many users each facing twice the cost. Here prohibition is clearly a losing game. It does you no good to hammer the users with stiffer sanctions because the costs scale up *faster* than the benefits.

Quite a lot is left out of this analysis. Harm to third parties is ignored, but then many of the costs of *prohibition* (as opposed to the costs imposed by the users themselves) are born by third parties. It’s not at all clear that accounting for the costs to third parties swings the analysis in favor of prohibition. Indeed, including those costs would most likely strengthen the case *against* prohibition. Also consider that many of those “costs to third parties” involve behaviors that are already sanctioned. Economic crimes to acquire drug money, pharmacologically induced violence (which despite a few scare stories is grotesquely exaggerated by the popular media), child neglect, and driving under the influence are already criminalized. If the goal is to deter these behaviors, we should crack down on them specifically. It makes no sense to focus our law enforcement resources on a behavior that kinda sorta sometimes leads to these other social problems. Address those problems directly if they are problems worth solving. If someone wants to do a more thorough accounting of these third-party costs, I’d love to see it. But please don’t dismiss my argument because I left out this consideration.

I want to clarify that my above argument does *not* apply to all crimes, but it does apply to all crimes in which the criminal harms primarily himself.  The prohibition approach makes the following deal with such “criminal”: “I’m going to harm you if you indulge in self-harming behavior X.” The vice-criminal already faces an implicit tax on the vice, in that such a vice has intrinsic harms. ("Vice-criminal" contains a wonderful double-meaning; a vice-criminal is not really a criminal, in the same way that the vice president is not really the president.) A real criminal is someone who primarily harms a third party, but whose crime imposes minimal cost/risk to himself. Sanctioning a crime raises the price from something negligible to something large. Sanctioning a vice raises the price from “already substantial” to “somewhat more substantial.” If you’re trying to deter a vice with inelastic demand, it’s hard to gain any ground. We should approach vices with “harm reduction,” not a prohibition approach. I don’t’ doubt that there are real harms associated with many vices.  These are costs to be managed, not problems to be “solved.”

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