Against Drug Prohibition

There are numerous posts on this blog that argue against drug prohibition. Here I am trying to gather the concepts from those scattered posts into one long-ish piece. Having read everything I can find about this topic, I have found the arguments for drug legalization to be overwhelming. Indeed, I have had trouble finding a serious argument in favor of drug prohibition ("serious" by my own not-exactly-strict standards). Basic economic theory provides a powerful case that drug prohibition will fail. Theory aside, our actual experience with drug prohibition has been an unmitigated disaster.

"Basic economics?" you say. "Make something more expensive and people will do less of it, right? Prohibition should work according to basic econ." I think this is the starting point for most people who favor prohibition. What it misses is the cost imposed on the people who continue to use and the people who stop using. Of course, you can deter a few marginal drug users by increasing the cost of drug use, say by imposing legal penalties on use or driving up the market price with supply-side interdiction. But such a policy is only "working" in the narrowest possible sense. To "work" in the sense of passing a cost-benefit test, someone has to tally up the harm done by the policy and seriously compare it to the supposed benefit. One cannot simply claim some deterrence has been achieved (no matter how minuscule) and claim victory.

An important insight here is that "prohibition" doesn't mean "you can't do it anymore." It is more realistic and more useful for analysis to think of prohibition as raising the cost of certain behaviors. These behaviors, namely drug use/production/transportation/sale, still happen. It's just that the users/producers/mules/dealers incur a higher cost. Obviously these things are still worth doing under a prohibition regime. It's important to keep track of exactly how much higher the cost is, who is paying it, and how much society as a whole benefits. When people continue to engage in the prohibited behaviors at a higher cost (as compared to the cost if the behavior were legal), it's possible that this "higher cost paid" swamps the supposed benefit from whatever deterrence it achieves, making the policy as a whole a net loser. As we'll see, when the prohibited behavior has inelastic demand, which almost certainly describes drug use, it becomes overwhelmingly likely that the costs of prohibition exceed the benefits.

There are two major rationales for drug prohibition: paternalism and externalities. The "paternalism" line of reasoning is that drug users are irrational and simply don't know what's best for themselves. They don't appropriately factor in the harm caused by their drug use, the thinking goes, so there is a role for government in discouraging their drug use. Under the "externalities" argument, drug users cause harm to innocent third parties who have no say in the drug user's choice. Drug users themselves may or may not be rational, but their choice to use drugs benefits them at the cost of society at large. They do things like go on a public rampage or drive intoxicated. Society has a legitimate interest in deterring these behaviors, even if we reject the paternalistic idea that we should protect people from themselves.

In addition to these, there are also some less-than-serious rationales for drug prohibition. "Drug use is just wrong" or some variation of that theme comes to mind. It's hard to take such assertions seriously. I'd be on equal footing if I asserted "No it isn't." We'd be equally matched in a standoff without ever having discussed any material facts or presenting any actual arguments. Is coffee "just wrong"? How about legal drugs like alcohol and tobacco? If illegal drug use is wrong because it's inherently wrong to break the law, doesn't legalizing drugs solve this particular problem? Someone who dips their toe into this line of argument quickly finds himself arguing that the wrong-ness of a drug depends on the pharmacological consequences or the social acceptance of the drug, which are empirical questions. And once you admit that something is an empirical question, you've completely neutered the "just plain wrong" line of reasoning. If you're mistaken about the pharmacology of various drugs and the related social harms (which I believe are routinely grotesquely exaggerated), then you're likely to be mistaken about the "just wrong"-ness of those drugs.

There are of course other rationales. You could come up with a longer list, depending on how thinly you slice them. But most are some subset of the paternalism and externalities arguments.

Against Paternalism

It is almost impossible to make drug prohibition "work" for the users themselves. When government threatens that it will fine, harass, imprison, and beat people if they use drugs, they are not doing these people any favors, even granting that they manage to deter some proportion of them from using.

To see why, you have to think clearly about how much you are raising the cost of drug use, and realize that the continuing users continue to pay that cost. You can think about the amount of drugs consumed being some function of the total price. Now, it doesn't matter that users "pay" in multiple ways for their habit: part of the price of drug use is literally the money that chances hands, part of the cost is time and effort spent finding a dealer, plus the pharmacological risks of harm, the risk of legal penalties, social stigma, opportunity cost for the time spent intoxicated, etc. These things are all different and would be measured in different "units," but you could (for the sake of analysis) collapse it down to some dollar figure, or some "total risk of mortality", or "years spent incarcerated," or a portfolio of several kinds of costs. Let's imaging coming to some agreement on the "exchange rates" between these different kinds of costs and put them all on one scale, and let's convert everything into dollars. (This is just a simplification. My argument does not depend on actually doing this, nor does it hinge on agreeing on the various exchange rates.) We can create a function, a curve that tells us how much people will buy at a given price. Economists call these functions "demand curves." See here for a pretty thorough treatment in a previous post.

Suppose there are N total users if the price under legalization is $X. Imagine that drug prohibition doubles the cost to $2X. Demand follows some kind of inverse function of the price. So, for example, doubling the price reduces the number of users to half, and quadrupling the price reduces the number of users to 1/4. Under this demand function, drug prohibition is a wash from the point of view of the drug users. Increasing the cost to kX dollars reduces the number of users to N/k. You always get a total cost of $NX. Ramping up prohibition doesn't avoid social costs; it just means that you have fewer users paying a much greater cost. It's a wash from the point of view of the users, but probably a net loss when you factor in the cost paid by society to enforce prohibition (unless we assume the externalities are implausibly large).

It's probably worse than this, because demand for drugs is relatively inelastic. That means users are relatively unresponsive to price changes. It takes a large increase in price to achieve a modest decrease in demand. In the previous paragraph I was using a f(k) = 1/k type of curve, which describes a demand curve that's neither elastic nor inelastic. This curve gets you something like a ~1% increase in price causes a ~1% decrease in demand. Very inelastic demand means it takes more like a 3% or 10% increase in price to get a 1% reduction in quantity demanded.  Demand for drugs probably looks more like f(k) = 1/sqrt(k). Quadrupling the price will get you half as many users, but each is paying four times the cost. There is a net loss for the users themselves, and once again probably a net loss to society as a whole (factoring in enforcement and other costs). The total cost (to users) actually rises as we increase the penalty for drug use. Hammering users harder doesn't produce a Drug Free America. It just means that we needlessly penalize a shrinking but increasingly desperate population of addicts.

The chart below is a graphical demonstration of what's happening. Moving to the right we see increasing drug costs, reflecting stricter enforcement. The quantity consumed (red) decreases while the cost per user (blue) increases. Multiplying these quantities gets you the total cost "paid" by drug users, the green line, which increases as drug enforcement gets stricter.

(The three curves are on different scales with different units, but that doesn't matter. The result that the total cost to users rises as the penalties for drug use increases. These aren't the intersecting supply-and-demand curves that you see in Econ 101, although the red curve actually is a demand curve.)

I have seen attempts to measure the elasticity of demand for various drugs. I've seen ranges of estimates in the 0.1-0.3 range for heroin, perhaps a bit more elastic (0.3-0.7 range) for cocaine. I don't know how much to trust these empirical estimates, so I won't dwell on them. But it makes intuitive sense that people who compulsively use addictive drugs, or who pay a very large opportunity cost to indulge them, probably have inelastic demand.

It's worth keeping in mind that the analysis above is totally sanitized to remove any trace of human misery. The ways that prohibition increase the price of drugs include throwing people in jail, SWAT-raiding the residences of suspected dealers (often terrorizing their families), subjecting users to dangerous black-market supplies of substances that aren't inherently dangerous, depriving families of a parent or earner, and so on. Abstraction is useful, but it's also useful to step away from the abstraction for a moment and remember we are capable of making moral judgments, too.

The drug user isn't literally a logic-machine, crunching the numbers and converting "probability of incarceration" into dollars in some great decision-making calculus. But s/he's surely doing some approximate version of this. If you suppose s/he is doing no such thing, then it's worth pondering how the legal penalties imposed on drug use are supposed to affect the behavior of drug users. It's fine to claim that people are to some degree irrational, but to dismiss any and all response to incentives is to admit that prohibition is futile. I think it is special pleading to claim that drug users are highly responsive to legal penalties while they are at the same time immune to considerations of the other kinds of costs.

Against the Externalities Rationale

A more plausible rationale for drug prohibition is that drug users cause "externalities." They operate a vehicle while dangerously intoxicated. They engage in irrational, violent behavior while under the influence. They commit property crimes to finance their addictions. And so on. I have a long post here discussing this rationale and explaining why it's probably wrong.

For one thing, the externalities supposedly attributable to drug users are grossly exaggerated. These socially destructive behaviors do occur for sure, but they are so rare that it becomes almost implausible to blame the drugs themselves for the behavior. Since there are overwhelmingly more drug users who are not engaging in these kinds of anti-social behaviors, a more plausible story is that poor impulse control causes those behaviors, or perhaps poor impulse control exacerbated by a drug habit.

For another thing, the anti-social behaviors blamed on drug use are already illegal. They are already penalized, and the drug user is already factoring these risks into the decision to use or not use. As I said in my previous post on this topic:

Assuming the penalties for these crimes have been appropriately set, drug-induced criminal behavior is *not* an externality. The potential drug user already faces the threat of a penalty, and moderates their drug use accordingly. It is the same as a potential CO2 emitter facing a perfect carbon tax while choosing how much to emit. The external cost is already internalized, so it ceases to be an externality. That’s not to say there is no harm. When the air is polluted or there is an unnecessary death or beating, somebody surely is harmed. It's just that the polluter (or criminal) pays the social cost of the harm. Suppose we had an appropriately high carbon tax, and suppose drug use induced people toward excessive CO2 emissions. We wouldn’t consider it an “externality” problem or a drug problem. We might adjust the size of the tax to address the problem directly, which is probably what we should do for drug-induced crime.

 If the problem is that people actually don’t understand the causal link, that “crack will turn you into a murderer/thief/assailant with an X/Y/Z% probability”, then the solution is some kind of ad campaign with credible information about these risks. The solution is not a blanket criminalization of drug use.  The potential user with accurate information will grind through the logic: “This habit will turn me into a criminal with probability X, which will almost surely land me in prison for Y years…”(No, he won’t literally do this, but will do so in an approximate fashion.) In this sense drug-induced criminal behavior is already criminalized and the penalty is already built into the cost of doing drugs. It’s already part of the price the user faces. If you object that drug users don’t have the foresight to consider the cost to himself of his future criminal behavior, then you should seriously doubt the entire enterprise of drug prohibition in the first place!  Come up with whatever assumptions you prefer about drug users, their degree of rationality, their behavior, their response to costs, etc.; these assumptions have to be consistent. They can’t contradict each other, which (I think) is what some very confused, very sloppy drug warriors have done. You don’t get to assume that drug users miscalculate the pharmacological risks of drug use but correctly estimate the legal risks. Either their talents for risk-estimation are well-calibrated, or they are not.

Perhaps the large social harms from drug use are due to things that aren’t criminalized. Things like neglect of one’s family or career are either not criminalized or are under-policed. If anyone is proposing we criminalize these behaviors, please suggest a proposal that makes sense, one that doesn’t further destroy the family. Clearly throwing a borderline negligent parent into prison has some harmful ramifications for his/her children, and throwing the same parent in prison on a drug charge has the same effect. If we’re not going to criminalize Behavior A, it makes little sense to criminalize Behavior B which (again tenuously) causes Behavior A.

It turns out that my analogy to an appropriately set pollution tax is a little bit off. In the case of a tax on an externality, society as a whole is compensated for the harm done. A tax serves the dual purposes of compensating the polluted and deterring the polluter. You still get some pollution, but the harm is compensated. In the case of a drug-induced murder or other crime, society at large does not collect the value of the penalty imposed on the criminal. So taking as a given the notion of "drug-induced crimes", the externality is not as fully internalized as it is in the case of a pollution tax. This concept will be important in the discussion below.

If the goal is to deter anti-social behaviors, the appropriate policy is to directly penalize those behaviors. If the penalty for theft and other property crimes is too low, increase it. If the penalty for intoxicated driving isn't sufficient, either increase the severity of the penalty (unlikely to work in my opinion) or increase the probability of being caught (much likelier to work). It would be incredibly inefficient and unfair to target the dozens of drug users who aren't bothering anybody just to deter the one who is. Given the extreme heterogeneity in people's drug habits, labeling a drug as "the cause" of someone's problematic behavior is dubious at best.

It's also worth pointing out that many "drug related" externalities are actually the product of prohibition, not an effect of the drug's intrinsic pharmacology. Intravenous drug use is probably a function of the high market price of heroin and cocaine. The communicable diseases (HIV, hepatitis, etc.) common in communities IV drug user would never have happened if people had access to cheaper drugs, and in fact these diseases dropped off dramatically when needle exchanges started to operate in many cities. (Bear in mind that these needle exchanges were officially illegal, but were tolerated once it was overwhelmingly evident that they were helping.) Likewise, most "drug violence" is actually violence related to the illegal drug market. You just don't see this kind of violence in the market for alcohol...outside of the 1920s when it was actually illegal. If we're going to have an honest accounting of "drug-related externalities," let's put some of the blame on prohibition.

A Tax Beats a Ban

Putting aside all of the above about the "paternalism" and "externalities" stories. Suppose there is a rational reason to deter drug use. Even admitting this, there are better policy responses than prohibition. You can simply place a punitive tax on drug use. The basic intuition here is that in the case of a tax, society collects the value of the punishment imposed on drug users. In the event of a ban (entailing legal penalties like jail time), the cost imposed on drug users is a dead-weight loss to society. You can harass, jail, or flog drug users. But unless the punishers are exceptionally gleeful sadists, nobody benefits from the harm imposed on users.

We'll start with a little bit of basic econ. Don't worry if you get lost in the following discussion; I will try to restate the point clearly in plain English at the end. The formalism isn't necessary to "prove" anything; rather it is intended to discipline our thinking and show critics that their criticisms are being accounted for. The figure below shows intersecting supply (red) and demand (black) curves. The upward-sloping red line, the supply curve, captures the idea that as the price increases, suppliers will want to produce more to sell at the higher price. The downward-sloping black line, the demand curve, captures the idea that as the price increases, buyers will buy less (discussed at length above). Ultimately, suppliers and buyers will agree to a given price and quantity, where the curves intersect. Quantity Q will be sold at price P. If too much is produced, suppliers would have to sell the excess at a loss. If too little is produced, unmet demand will lead to high market prices and encourage more production. There are reasonable debates about whether this model perfectly captures the realities of a market economy. But surely something like this equilibrium is going on. There are forces pushing the price to P and the quantity to Q, and any deviation from this equilibrium will induce market forces to nudge us back to point (Q,P).

The above chart assumes no externalities, no costs to third parties. But now we can suppose that drug use causes significant externalities. Now there is a divergence between the "marginal private benefit" (felt by the users) and the "marginal social benefit" (felt by society at large). Drug users consume too much because they aren't factoring in the costs to others. Effectively society is "subsidizing" the habits of drug users by putting up with all of their anti-social behavior, without being compensated for it. That looks something like this:

The solid black line is the demand curve faced by drug users. The dotted black line is the demand curve for society as a whole. The difference between the two captures the notion that users are "free riding" on everyone else. Users are consuming the higher quantity Q_act, while the optimum for society as a whole is Q_opt. (By the way, MSC is "marginal social cost", MPB is "marginal private benefit", and MSB is "marginal social benefit". The private benefit is higher than the social benefit because the users aren't factoring the costs to third parties into their decisions.)

What's needed here is some kind of policy device that forces drug users to feel the social costs of their actions. A tax or legal penalty will lower the solid black line, ideally until it overlaps the dotted black line.

This lowers the amount of drug use from Q_act (from the previous figure) to Q_opt. If this seems convoluted, it's not. Everyone who favors drug prohibition is following some version of this logic: penalize a behavior and you get less of it.

If we're trying to shift the demand curve, a tax is strictly superior to a ban. We can divide these intersecting supply and demand curves into several areas, each of which has a specific interpretation.

In the untaxed/unpenalized world, the MSC curve intersects with the MPB curve (around Quantity =11 and Price = 10, the point of area E in yellow). A+B+C+E represents the consumers' and producers' surpluses. The producers earn a profit above and beyond their production costs, because otherwise they wouldn't bother to produce anything. The consumer values the goods and services at some value above and beyond what they pay for them, otherwise they wouldn't bother to buy anything. Thus we get the "double 'Thank you'" in market exchanges, in which the consumer values the goods more than the money and the producer values the money more than the goods. Unfortunately, there's more going on here. Society at large is subsidizing users and dealers. Areas C and E represent a transfer from society to drug users and producers, not a surplus for society as a whole. Area D is a dead-weight loss. It is the amount by which the cost of production exceeds the social value of the thing being produced. So areas C and E are a transfer (a wash for society as a whole), A and B are true surplus, and D is a loss. The total surplus is A + B - D

Now suppose we impose legal penalties. The marginal private benefit (MPB line) is lowered to overlap with the marginal social benefit (MSB line). The supply and demand curves intersect right around Quantity = 9, Price = 7.5, where the points of triangles A and B meet. Drug users still enjoy a consumer surplus of A, and producers a surplus of B. We've eliminated the dead-weight loss of D, and the transfer represented by triangle E doesn't happen. Area C  now represents a cost that is paid by drug users and producers, but which does not get paid to anyone. A legal penalty is equivalent to imposing a tax on drug users and then throwing away the revenue. The total surplus is now A + B - C. This might or might not be better than A + B - D from the no-tax-no-penalty world discussed in the above paragraph; it depends on the relative sizes of C and D. But we can do better.

Now suppose we impose a tax on drug use, rather than a legal penalty like harassment, imprisonment or flogging. Once again, we lower the MPB line so that it overlaps with MSB line, and again we intersect at the point Quantity = 9, Price = 7.5. Drug users and producers still enjoy the surplus of A+B. Area C is not a pure loss as it is in the "penalty" regime; it is a transfer. Tax revenue is collected and is not thrown away. Areas D and E disappear from this calculus, because drug use has been reduced to the socially optimal level. So we end up with a surplus of A + B. This is strictly better than A + B - C or A + B - D.

Strictly speaking, a tax beats a ban.

Anticipating some objections to this line of reasoning. One is that a tax "just isn't severe enough." Imprisoning someone is pretty harsh, while paying a surcharge at the pharmacy doesn't seem so bad. Of course this objection would be nonsense. The tax can be arbitrarily severe. Doubling the price doesn't seem to do the trick? Okay, then quadruple, or sextuple, or octuple the price.

Another objection is that prohibition is of an entirely different character than a tax. To purchase an illegal substance, you need to find a dealer, which may require a categorical decision about your lifestyle. On the other hand, a tax just means you shell out more money. That's fine. In addition to a tax, we can impose "user licensing." In addition to paying a surcharge that increases the market price of drugs, users must pass an onerous licensing process. Once again, this is a continuously and arbitrarily adjustable lever with which we can increase the cost of drug use. If the half-day drug safety seminar isn't sufficient, make it a week-long boot camp. The graduate can purchase pharmaceutical-grade heroin. But they have to show they've learned proper hygiene and safety, things like "don't mix with other drugs" and "how to clean your works". User licensing might actually manage to meaningfully inform some drug users of the risks, something that current policy has utterly failed to do. And with a clean, legal supply, there will be far fewer accidental overdose deaths.

Importantly, taxes and user licensing are "high probability" deterrents. The chance of getting caught, much less serving any actual time, is pretty slim for a typical user or even a typical dealer. This deterrent might be sufficient for a typical "risk averse" individual. But the personality type that is attracted to potentially addictive drugs is probably not risk averse. These people are probably risk neutral or even risk-seeking. They obviously enjoy a certain kind of thrill. Deterrence is more effective when the probability of punishment is high, particularly for risk-neutral and risk-seeking personalities. Ramping up the severity of the penalty quickly bumps into diminishing returns. For a given "expected punishment" equal to the severity of the penalty times the probability of getting caught, we're better off trying to raise the probability of getting caught than in ramping up the penalty. (Citation needed. I don't know a lot about this, but have heard criminologist Mark Kleiman say this. Megan McArdle also discusses this at length in her book The Upside of Down, and Alex Tabarrok has made this point repeatedly at Marginal Revolution. I'm trusting that the impression they gave me on this point is correct.)  In a tax-and-licensure regime, essentially 100% of drug users get hit with the deterrent. In a prohibition regime, only a fraction of offenders actually get punished. It's almost like our prohibition regime was meant to target middle-class, bourgeois-values kinds of people, the kind of people who you don't much need to worry about developing a dangerous drug habit. And it fails for lower-class individuals, who probably know people with criminal records, can easily find a drug hookup without accidentally asking a cop, and who don't blush at a small chance of a bad outcome, possibly because they have less to lose. Prohibition is poorly targeted to the kinds of people we want to deter. (Of course I'm not saying that anyone is immune from drug addiction because of their socioeconomic class; I'm merely pointing out that socioeconomic class is a risk factor and that there are policy implications for knowing this.)

It's worth considering the consequences of setting the tax or licensing requirements too high. Make the penalties and restrictions on legal use too high and we will simply drive people back to the black market.

The Black Market

A possible objection to the tax-and-license regime is that drug users might avoid the taxes and licensure requirement by buying on the black market. If we just get a black market again, then legalization would be a failure, right?

I think this objection is probably wrong. For one thing, you'd likely have the majority of the drug supply coming from the legal supply chain, unless the taxes were implausibly high. For example, most people buy alcohol from legal grocery and liquor stores, even though a relatively small amount of alcohol is illicit moonshine and home-brewed beer. People can get around the (onerous) taxes and regulations on alcohol, but most don't. For another thing, even if there is a black market operating alongside the legal market, it's likely that the black market would be diverting from the relatively clean and safe legal supply chain. It wouldn't be a clone of the current black market, where people are cooking up who-knows-what in dirty home labs. There is a black market for cigarettes in states that have set their cigarette taxes too high, but mostly this involves smuggling in cigarettes that are legally produced in other states. People aren't growing clandestine tobacco crops or manufacturing super-concentrated synthetic nicotine in secret labs. They are diverting from an existing, legal, (relatively) safe supply chain.

Again, the legalization regime has a clear benefit over the prohibition regime. If policymakers decide that the black market is too big, they have a continuously adjustable lever to tone it down: they can lower the tax or licensure requirements. If doing this means too many new drug users, they can ramp it back up and decide to just live with the black market problem. There is a classic trade-off here. A legalization regime would at least allow us to be honest about the nature of the trade-off and give us more tools to pick where we want to be on the trade-off curve. Prohibition doesn't give us a continuously adjustable lever in the same sense. Sure, you can ramp the penalty up or down, from a year in prison to two years in prison, or anywhere in between, or anywhere outside of that range for that matter. But prohibition ensures that the entire trade is dominated by the black market. The shift to "100% black market" that we get under prohibition is categorical, not adjustable. You fundamentally cannot adjust this without legalizing the market.

Supply Interdiction

The above analysis mostly talks about targeting drug users themselves with jail time or punitive taxes. But the harshest punishments and most enforcement resources fall on suppliers. Illegal drug production usually triggers severe mandatory minimum sentences, measured in years or decades of incarceration. Transporting or merely possessing large amounts of drugs usually triggers similar penalties. The above analysis still applies. Supply interdiction doesn't mean that drugs disappear from the marketplace. It simply means that the market price is higher than it would otherwise be. We can think of supply interdiction as just another means of raising the price faced by the drug user, similar to a tax or a penalty faced directly by the user. Or you can redo the above analysis by shifting both the supply curve and the demand curve. The basic result does not change. (The supply curve will shift leftward to reflect the fact that suppliers will produce less at any given price. The intersection with the demand curve will occur at a higher price and lower quantity, which are the predictable effects of banning something.)

In this article by Benjamin Powell at the Library of Economics and Liberty, there is an excellent explanation of what happens when you try to shift the supply curve for a good with very inelastic demand. See the figure here in the middle of the page. Note the very small reduction in the quantity of drugs consumed compared to the extremely large increase in price. This isn't some trick of drawing the axes on different scales. It is an inevitable consequence of inelastic demand. As Powell explains, hammering drug suppliers harder actually increases their revenue:

The main effect of a supply-side drug war is a large increase in the price of drugs. Revenues of drug dealers equal the price of the drugs times the quantity sold. Because the drug war increases price more than it decreases quantity, the remaining drug dealers have more revenue as a result of the drug war. In the above figure, the drug war costs suppliers the revenue in the blue box, but suppliers gain the revenue in the larger red box. They can use this increased revenue to buy better technology to smuggle drugs into the United States, to buy more and better weapons to fight law enforcement, or to corrupt more judges and police officers.

Of course revenue isn't profit, but this should still be a worrying result for anyone who is pro-drug war.

At his blog The Big Questions, Steven Landsburg explains here and here why it's futile to deter suppliers with penalties. He presents an little economic formalism to explain what happens when you try to prohibit something.

Gary Becker Made Similar Arguments

In a paper titled The Economic Theory of Illegal Goods: The Case of Drugs by Gary Becker, Kevin Murphy, and Paul Grossman, the authors make essentially the same argument I make above. They use more formalism but come to similar conclusions. They also make many other points I haven't touched on. So I'm pretty sure I'm basically on the right track, even if I might have goofed on a detail here or there. I wrote about it at some length here. Basic common-sense economics gets you to the conclusion that drug prohibition is overwhelmingly likely to fail, and some guys who are smarter and more thorough than me got to this conclusion well before I did. I recommend reading the whole paper, or if you don't have time for that my post summarizing it (both linked to above). Some excerpts:

Optimal public expenditures on apprehension and conviction of illegal suppliers obviously depend on the extent of the difference between the social and private value of consumption of illegal goods, but they also depend crucially on the elasticity of demand for these goods. In particular, when demand is inelastic, it does not pay to enforce any prohibition unless the social value is negative and not merely less than the private value.

... 

We show that a monetary tax on a legal good could cause a greater reduction in output and increase in price than would optimal enforcement, even recognizing that producers may want to go underground to try to avoid a monetary tax. This means that fighting a war on drugs by legalizing drug use and taxing consumption may be more effective than continuing to prohibit the legal use of drugs.

…when demand for drugs is inelastic, total resources spent by drug traffickers will increase as the war increases in severity, and consumption falls. With inelastic demand, resources are actually drawn into the drug business as enforcement reduces drug consumption.

I found the following passage absolutely stunning:

The conclusion that with positive marginal social willingness to pay-no matter how small-inelastic demand, and punishment to traffickers, the optimal social decision would be to leave the free market output unchanged does not assume the government is inefficient, or that enforcement of these taxes is costly. Indeed, the conclusion holds in the case we just discussed where governments are assumed to catch violators easily and with no cost to themselves, but costs to traffickers…The optimal social decision is clearly then to do nothing, even if consumption imposes significant external costs on others.

They aren't stacking the deck by making some weird libertarian assumption about inefficient government or massive negative side effects (assumptions which accurately describe the actual real-world war on drugs). And yet they reach the conclusion that drug prohibition almost certainly isn't worth pursuing. There's more. They relax the "inelastic demand" assumption and still find the verdict to be quite firmly against prohibition:

Even if demand is elastic, it may not be socially optimal to reduced output if consumption of the good has positive marginal social value…[some technical details, elasticity conditions, etc.]… It takes very low social values of consumption, or very high demand elasticities, to justify intervention, even with negligible enforcement costs.

…when demand is inelastic, total production costs rise as consumption falls, and enforcement costs rise more rapidly. With inelastic demand, a war to reduce consumption would be justified only when marginal social value is very negative. Even then, such a war will absorb a lot of resources.

Using more formalism than I do above, they also discover the solution of a tax beating a ban:

Our analysis shows, moreover, that using a monetary tax to discourage legal drug production could reduce drug consumption by more than even an efficient war on drugs. The market price of legal drugs with a monetary excise tax could be greater than the price induced by an optimal war on drugs, even when producers could ignore the monetary tax and consider producing in the underground economy…With these assumptions, the level of consumption that maximizes social welfare would be smaller if drugs were legalized and taxed optimally instead of the present policy of trying to enforce a ban on drugs.

There are a lot of other details to that one could discuss here. Several large volumes could be written on how drug policing corrupts political institutions and the police, in a few countries leading to a failed state. Or one could discuss the knock-on effects of incarcerating large fractions of prime-age males in inner city communities and the absolute havoc this wreaks on traditional life cycles and social norms. A related point, volumes could be written about the systemic racial disparities, which are real and have real effects whether they are intentional or not, whether they are motivated by explicit racism or not. Or we could discuss at length how drug policing degrades trust between police and the communities they serve even when they show up to perform a legitimate policing function, like solving a property crime or a murder. Or someone could write several long papers about how black markets encourage violence because they don't have legal means of resolving disputes, and that this violence is a significant fraction of the total violence in our society (at least in the United States; Jeffrey Miron and Paul Goldstein have done some excellent work on this subject). Someone could write a book about how the war on drugs eviscerated our constitutional rights by constantly carving out "drug war exceptions" to the Bill of Rights (Radly Balko's Rise of the Warrior Cop does exactly this). All of these are very important and deserve a serious treatment. What is surprising is that we reach a strong verdict of "drug prohibition fails" without ever considering these very serious problems. Some basic economic reasoning counter-indicates drug prohibition, without even diving into these other topics.