In Chapter 2 we considered probability models for the analysis of the consumption of drugs, both licit and illicit. Those models relate the decision to consume drugs to various socioeconomic factors such as age, sex, income, occupation, as well as to their price. Estimates of those models reveal the impact of changes in the determining factors on the probability of consuming the drug in question. Accordingly, that methodology deals with who does or does not consume drugs, but not how much is consumed; or in other words, the extensive margin of drug consumption is considered by the probability models rather than the intensive margin. The reason for this focus is that most data pertaining to drug consumption deal not with the actual quantity consumed; rather, they are typically surveys of participation, whereby respondents state “yes, I do consume marijuana” or “no, I do not”.

The distinction between (i) participation and (ii) how much is consumed is important for the interpretation of the price elasticity of the demand for drugs. The conventional price elasticity of demand answers the question: By how much would total consumption of the drug rise following a 1 per cent fall in its price? By contrast, probability models typically deal with a different question: By how much does the number of users of marijuana (or “participation”) rise following a 1 per cent fall in its price? The latter question relates to the participation elasticity, which is not the same as the conventional price elasticity. As the participation elasticity holds constant consumption per user, it ignores what happens to the consumption of pre-existing users when the price falls, thus understating the price sensitivity of total consumption.