Resolving a Cocaine Paradox with Derived Demand

Earlier this year, Tom Wainwright appeared on Russ Robert's EconTalk to discuss his new book, Narco-nomics. This book is about the economics of the drug trade. During their conversation, Wainwright described how governments in countries like Colombia eradicate millions of acres of coca leaf crop every year as part of the "war on drugs." The idea behind this policy is that by making coca more expensive, we will also make cocaine more expensive since it is the drug's key ingredient. However, to the chagrin of policy makers, the price of cocaine has not risen much (if at all).

Wainwright's explanation for this seeming paradox is that 1) the price of coca represents a small portion of the price of cocaine (less than 1%), and 2) drug cartels have market power that allows them to negotiate lower prices with coca leaf growers. These both sound like good reasons to me, but I think Wainwright maybe forgetting one other reason that output prices might not be rising along with input prices. Specifically, Roberts and Wainwright carry on their conversation as if the price of all other inputs into cocaine production stayed the same in the face of coca eradication. But why should we expect that?

Coca seems to have no substitutes in the production of cocaine. So all other inputs should be complements in the production process. That means an increase in the price of coca will lead cocaine producers to use less coca and less of all other inputs. As cocaine producers purchase less of these other inputs, the price of these other inputs will fall to clear their respective markets. As a result, the price of coca goes up, the price of other inputs goes down, and the price cocaine will increase by less than the price of coca (possibly much less if the supply of other inputs is very price inelastic).

Since the "other inputs" used in cocaine products beside coca leaf include the violent aspects of the drug trade, I wonder if this analysis implies that those services would be in less demand? If so, maybe coca eradication at least makes trafficking less violent? I kind of doubt it, but it is something to think about.

Anyways, if you want to think about this some more, you can do so more formally using the derived demand model that I explored in my last post. Here's a quick visual representation of the analysis above using the derived demand model. For simplicity, I drew this assuming you need 1 unit of coca and 1 unit of "other services" to make 1 unit of cocaine. As you can see, the price of coca goes up, the price of other inputs goes down, and the price of cocaine goes up by less than the price of coca.