Drug Prohibition or Drug Taxation?

Intro to Supply and Demand Curves

I’ll formalize the economics of drug prohibition in this post. First a review of some concepts (or an intro if you’ve never taken any economics).

With price on the y-axis and quantity on the x-axis, there is a downward-sloping demand curve and an upward sloping supply curve. The slope of the demand curve indicates that people become satiated as they consume more and more; this is true for *any* kind of good or service. The very first few “units” are worth quite a lot; imagine the most devoted uber-fans at the very front of the line, who will derive the greatest enjoyment from the first few units produced. As more is consumed, desires are satisfied, and at some point additional units made available for consumption bring negligible pleasure to the consumers. The upward-sloping supply curve represents the costs of production, which should increase as more is produced. For the first few units, you can use the very most productive fields (for a product that is farmed) or the most productive machinery or the most skilled and dedicated workers. As those factors of production get employed, producers start reaching for less productive means, and at some point it becomes too costly to employ any more resources in production.

These curves intersect at a point that marks the market price and the quantity produced, the y and x coordinates respectively. The area between the supply curve and the price line represents the “producer’s surplus” and the area between the price line and the demand curve represents the “consumer’s surplus.” Both areas summed together represent the “social benefit” of that particular good. People can and do argue about whether this is a valid approach to judging social welfare, but it’s a good starting point for analysis. The only alternative is inane blather. Let’s at least start with some formalism. (MSC = Marginal social cost, MSB = Marginal social benefit)

Considering Costs to Third Parties

When discussing something like drug use or pollution, there are potential harms to third parties (“externalities” in econospeak) that need to be considered. The idea here is that someone who uses illegal drugs doesn’t bear the full cost of his actions. In this case there is a private benefit and a social benefit. The social benefit is *lower* than the private benefit for any given quantity of drug use. This is bad, because it causes people to consume more than the socially optimal amount. The quantity consumed will be at the intersection of the private benefit and social cost curve, when we’d like it to be at the intersection of the *social* cost and *social* benefit curve.

If you are a paternalist, meaning you like the idea of protecting people from themselves, this analysis is still the right approach. You can think of a person as having multiple “selves.” One such self really wants to use drugs and thinks the costs are worth the benefits, and the other self thinks the first guy is nuts and would rather not be injured by him. The divergence between the social benefit and the private benefit can represent this self-harm, or it can strictly speaking represent the costs imposed on third parties, or it can be some combination. I will use the same graphs in any case.

If everyone is free to choose whatever level of drug use they please, assuming there are significant externalities from drug use, there will be too much of it. So presumably government policy can curb this excess use. There are two ways to do this. I can tax you, or I can beat you. I’ll call these options the “tax” and “prohibition” regimes. In either case, the private benefit curve drops. If consuming drugs comes with a beating or a hefty tax, it becomes less pleasant to consume for any given quantity, so this shifts the demand curve down. Ideally, you would set the tax or the severity of the bludgeoning *just right* to push the private cost curve to perfectly overlap the social cost curve. (Of course, prohibition doesn’t involve literal beatings…usually. I’m using “beating” as short-hand for all the other nasty things we do to people who use illegal drugs, such as imprisonment, social shaming, harassment, removal of children, and, yes, the occasional beating.)

Another approach is to shift the supply curve, which is the effect of targeting drug suppliers. Supply-side policies actually represent the bulk of drug control efforts, at least in the US. But I'm not going to treat them in this post. I'm rather taking the supply curve as a given and asking what happens when you target the demand side. 

Social Welfare Consequences of Drug Policy

We can determine the welfare consequences of different policy responses by drawing areas on the supply and demand curves. (“Welfare” means something like “total summed benefit to society.” It has nothing to do with the word's more colloquial meaning, being programs that help the poor or transfer payment programs. Incidentally, those programs can and should also be treated with an analysis like this one.) The chart below shows the social cost curve (the supply curve) and the private and social benefit curves (the demand curves). Triangles A and B are the consumer’s surplus and the producer’s surplus, as described above, for the scenario when drug consumption is at the social optimum. The quadrilateral C represents a “transfer”; drug users benefit from consuming more, and producers benefit from the higher price, but their gains are society’s loss. Without getting into a theological discussion of whose interests and benefits should count, let’s just call C a “wash” for now. Triangle D represents the true social cost of drug use. (Keep in mind this formalism works for any externality; the graph would look the same if I were examining air pollution.) Triangle D is the area between the marginal social cost curve and the marginal social benefit curve, integrated over the range that separates the social optimum and the private optimum. In the case of *no* drug policy, the total social welfare is equal to A + B + C – C – D. The C cancels, so I’m left with A + B – D.

If I *tax* drug use, and if it’s an optimal tax that moves the private benefit curve down to the social benefit curve, then I end up with something like the very first graph in this post. Consumption drops, and so does the price. C disappears for both the consumers and the producers of drugs, so they lose out on this benefit, but society collects C worth of taxes. The “losses” to users and producers of drugs are society’s “gain.” And the deadweight loss in triangle D goes away. So we end up with a total social welfare of A + B. In this imaginary scenario, society is better off by an amount D. (We should keep in mind that setting the optimal tax is *not* so easy, and in fact many drugs that are relatively harmless have been given a bad name by an overzealous media and an over-credulous society. So it’s worth thinking about the harm done in a scenario where the social and private benefits are *actually* the same, but the public believes they diverge. In that case you would punish a perfectly harmless hobby, and you’d end up with a net loss of social welfare. This surely describes what’s happening for at least some illegal substances. That might be a good exercise for a future post.)

A prohibition regime, on the other hand, has nastier welfare implications. We still shift the private benefit curve down to overlap social benefit curve, but in this case no tax is collected. The full area of C is lost, and this loss does not become “society’s” gain. Unless the agents we employ to harass drug users are particularly gleeful sadists, the harm imposed on drug users doesn’t get offset by a corresponding benefit to some other party. It is simply lost. The deadweight loss D is also gone, but the cost of eliminating it is unnecessarily high. Total social welfare in this scenario is A + B – C. If the area in C is actually greater than D (which depends on the exact shape of the supply and demand curves), then it’s possible that prohibition is better than *no* drug policy. But it’s strictly worse than a tax. 

This approach might seem odd for a number of reasons. Should we really consider the benefits to drug producers and drug consumers in our welfare calculation? Shouldn’t the social optimum quantity be *zero*, at least for certain drugs? To the first question, I’d say we’re comparing *different* regimes, so the total social welfare doesn’t matter. What matters is the difference between, say, laissez-faire and prohibition (a difference represented by C – D), or between prohibition and taxation (represented by C). Likewise, if I say, “The welfare transfer C from society to drug consumers and producers is immoral. I’m not going to count it as a benefit in my social welfare calculation.” That’s fine. In this case the welfare difference between taxation and prohibition is *still* C, because you still have in one case a tax that is collected and in another a punishment that is not “collected” by anybody.  

Edit 2/29/2016: I believe I made a minor goof above. Area C should be split into two sections. Split it by drawing  a vertical line upward from the price-quantity intersection point (at roughly (8,7.5) on my graph) to the MPB (solid black line). One section, a parallelogram, is a transfer (under a tax policy) or a pure loss (under a prohibition policy). The other section, a triangle, is a loss of consumer and producer surplus. I'll show what this looks like in a later post. I think this is a relatively minor correction.

To the second question, chart where the social optimum is *zero* drug use looks like the chart below. There’s no “A” or “B”. Of course in this case, it doesn’t actually matter whether you drive the private benefit curve down to the private benefit curve with a tax or a punishment. No tax will be collected nor will any punishment *actually* be imposed if consumption is literally zero. But such implausible scenarios aren’t terribly interesting. 

Other Considerations

There are other practical and moral considerations here. I’m not pretending that this approach to cost-benefit analysis “solves” the problem and tells us the ideal policy regime. As a practical matter, it’s actually quite difficult to deter drug use. Demand for drugs is quite inelastic (discussed here). Users will pay very high prices, so it’s difficult to deter them with either a tax or a penalty. If you believe the estimates for the number of heroin users from the SAMHSA surveys, and if you believe the CDC’s estimates for the number of heroin overdoses, you get something like a 1.5 – 2.5% mortality rate *per year* for heroin users, just from overdoses. (Depending on which year you look at.) This is huge. When economists and actuaries monetize the risk of death, they get values in the range of $50,000 to $120,000 for a 1% chance of death. Basically, these are the sums people will pay to avoid a 1% chance of death. So heroin under the current regime faces a very heavy implicit penalty, and we still have just shy of a half million users in this country. You’d have to resort to inhuman levels of cruelty (err…more so) to deter heroin use any further. If you look at drug use surveys that span several decades, you see up and down movements of usage rates that have nothing to do with official policy. So it’s pretty hard to claim we’ve achieved a significant level of deterrence. The deterrent effect of drug prohibition is surely real, but it’s more like a rounding error than a driving force.

There are moral considerations, too, and these are very important. But this post is already long. I won’t delve into theology right now. I’ll just say that there are no moral trump cards. There are still trade-offs, even if they are moral trade-offs. If we have more cocaine users under laissez-faire drug policy, but we have more gang members murdering each other under prohibition, we might consider both of these costs to be on a higher moral plane than mere monetary considerations. Maybe we consider cocaine use and murder “just evil” and refuse to monetize them, and we stoutly refuse to compare them to the frivolous pleasure reaped by drug users. But this still presents a trade-off to be managed.