The iron law of prohibition is a term coined by
Richard Cowan in 1986 which posits that as law enforcement becomes more intense, the potency of prohibited substances increases.
Cowan put it this way: "the harder the enforcement, the harder the drugs."
This law is an application of the
Alchian–Allen effect;
Libertarian judge
Jim Gray calls the law the "cardinal rule of prohibition", and notes that is a powerful argument for the
legalization of drugs.
[ It is based on the premise that when drugs or alcohol are prohibited, they will be produced in black markets in more concentrated and powerful forms, because these more potent forms offer better efficiency in the business model—they take up less space in storage, less weight in transportation, and they sell for more money. Economist ]Mark Thornton
Mark Thornton (born June 7, 1960) is an American economist of the Austrian School. DiLorenzo, Thomas (2011-02-11My Associations with Liars, Bigots, and Murderers ''LewRockwell.com'' He has written on the topic of prohibition of drugs, the econo ...
writes that the iron law of prohibition undermines the argument in favor of prohibition, because the higher potency forms are less safe for the consumer.
Findings
Thornton published research showing that the potency of marijuana increased in response to higher enforcement budgets. He later expanded this research in his dissertation to include other illegal drugs and alcohol during Prohibition in the United States (1920–1933). The basic approach is based on the Alchian and Allen Theorem. This argument says that a fixed cost (e.g. transportation fee) added to the price of two varieties of the same product (e.g. high quality red apple and a low quality red apple) results in greater sales of the more expensive variety. When applied to rum-running, drug smuggling
The illegal drug trade or drug trafficking is a global black market dedicated to the cultivation, manufacture, distribution and sale of prohibited drugs. Most jurisdictions prohibit trade, except under license, of many types of drugs through ...
, and blockade running the more potent products become the sole focus of the suppliers. Thornton notes that the greatest added cost in illegal sales is the avoidance of detection.[ Thornton says that if drugs are legalized, then consumers will begin to wean themselves off the higher potency forms, for instance with ]cocaine
Cocaine (from , from , ultimately from Quechua: ''kúka'') is a central nervous system (CNS) stimulant mainly used recreationally for its euphoric effects. It is primarily obtained from the leaves of two Coca species native to South Ameri ...
users buying coca
Coca is any of the four cultivated plants in the family Erythroxylaceae, native to western South America. Coca is known worldwide for its psychoactive alkaloid, cocaine.
The plant is grown as a cash crop in the Argentine Northwest, Bolivia, ...
leaves, and heroin users switching to opium.
The popular shift from beer to wine to hard liquor during the US Prohibition era has a parallel in the narcotics trade in the late 20th century. Bulky opium was illegal, so refined heroin became more prevalent, albeit with significant risk from blood-borne disease because of injection by needle, and far greater risk of death from overdose. Marijuana was also found too bulky and troublesome to smuggle across borders, so smugglers turned to refined cocaine with its much higher potency and profit per pound. Cowan wrote in 1986 that crack cocaine was entirely a product of the prohibition of drugs.[ Clinical psychiatrist Michael J. Reznicek adds ]crystal meth
Methamphetamine (contracted from ) is a potent central nervous system (CNS) stimulant that is mainly used as a recreational drug and less commonly as a second-line treatment for attention deficit hyperactivity disorder and obesity. Methamphe ...
to this list. In the 2010s the iron law has been invoked to explain why heroin is displaced by fentanyl
Fentanyl, also spelled fentanil, is a very potent synthetic opioid used as a pain medication. Together with other drugs, fentanyl is used for anesthesia. It is also used illicitly as a recreational drug, sometimes mixed with heroin, cocain ...
and other, even stronger, synthetic opioids.
With underage drinking by teens in the U.S., one of the impacts of laws against possession of alcohol by minors is that teens tend to prefer distilled spirits, because they are easier to conceal than beer.
Derivation
Consider the situation where there are two substitute goods and , denoting the higher and lower quality goods with respective prices and , and where i.e. the higher quality good has a higher price. Each of these goods has a compensated demand curve (a demand curve which holds utility constant) of the form
where
with denoting the utility function of the consumer. Furthermore, we will also assume that income is held constant, as income effects are indeterminate in forecasting changes in demand.
Suppose that there is an associated cost that is added to each good due to transport costs. We want to know how the ratio of demand changes for the two goods based on . Taking the derivative with respect to yields
From our assumptions, we have that the total price for each item is . Therefore, we may compute to be
We may now rewrite () as
Finally, using the cross- elasticity of demand,
we arrive at the following expression of the derivative
Now, we want to show that , but seem to be stuck with elasticities that are indeterminate. However, Hicks' third law of demand gives us and . To see why this is, suppose that we take a more general version of the compensated demand function with goods and compensated demand curves , for .
For a homogeneous function of degree , defined as
Euler's homogeneous function theorem
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''d ...
states that
Compensated demand functions are homogeneous of degree 0, since multiplying all prices by a constant yields the same solution to the expenditure minimization problem
In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: "how much money do I need to reach a certain level of happiness?". This question comes in two parts. Given a consumer's utility function, pr ...
as the original prices. Thus,
Dividing by the stock yields
which establishes Hicks' third law of demand.
Using Hicks' law, () is rewritten as
Suppose for the sake of contradiction that . Then,
By initial assumption, our two goods are substitutes. As such, and , implying that
But, this contradicts the assumption that . Thus, we conclude that . This implies that as the transport costs increase, the higher quality good will become more prevalent than the lower quality good. In the drug-specific context, as costs associated with drug enforcement increase, the more potent drug will become more prevalent in the illegal drug market.
References
Further reading
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Economics laws
Prohibition
1986 in economics
Drug control law
Smuggling
Law and economics
Mathematical economics