Sticky demand

Miriam Weeks (aka Belle Knox) has an op-ed at Time about rising college tuition, subsidies, and the high implicit marginal tax rates the means-tested subsidy regime implies for students like herself who have relatively high earnings during college. But rather than focus on her (quite reasonable) argument about the abuses of an industry in which I am objectively a member of the exploitative class, let’s change the subject to exegesis of a tangential sentence about another industry:
“Demand for education, kind of like demand for porn, is pretty inelastic.”

This glib remark strikes me as highly dubious but also typical of libertarians, which I understand to be Ms. Weeks’ political perspective. Just as when liberals say something (say, health care not directly related to communicable diseases) is a “public good” they don’t really mean that it is non-rivalrous and non-excludbale, but only that they think the state ought to pay for it. Likewise when libertarians say something (and in particular a vice) is demand inelastic they don’t actually mean that quantity demanded doesn’t respond to changes in price, but only that they don’t want the state to regulate it. (Conversely, libertarians tend to play up elasticity with regards to taxes that they don’t like).

But let’s unpack what it would mean for porn demand to be inelastic. First, we can consider short-run elasticity. Elasticity is largely a function of substitutability and purchasing porn has good substitutes (starting with rewatching previously purchased porn) and so should be elastic. Moreover, demand for vices tends to follow a zero-inflated count distribution which means much of the total demand is concentrated among the heaviest users and which in turn means that you have to worry about income effects imposing a hard constraint as heavy users simply run out of money and therefore their demand is relatively elastic in terms of purchasing power even if their desire is unsatiated.

Moreover, we can take a long-run view. In the long-run as people shift to new margins very few things are inelastic. For instance gasoline is famously inelastic in the short run but this isn’t really true in the long run as we saw when the price of gasoline rose in 2006 and 2007 it led to a decrease in demand for exurban housing and SUVs and so the price of gasoline was less inelastic in the long-run than in the short-run. For vices we have the rational addiction model that suggests that even if demand is inelastic in the short-run (ie, addicts gotta get their fix) it is elastic in the long-run as price hikes motivate current users to quit and/or potential new users to refrain from starting. That is, if porn becomes expensive we should expect to see some current consumers learn to rely on their imaginations and new potential users fail to have sufficient exposure to be captured and conversely if porn becomes cheap we should expect to see more people develop the habit of frequently consuming it.

And putting aside theory, it’s something of an empirical question since first VHS and then the internet radically reduced the price of pornography (especially if one includes “transport” costs of hassle, shame, etc). I am highly skeptical that this decrease in the total price has led to no more consumption, as we would expect if demand were perfectly inelastic. That is, if demand for porn were perfectly inelastic this would imply no greater consumption today than in 1995 or 1985 or 1975 and this strains credulity.

The reason this matters is that if demand for vices is in fact elastic, or even just imperfectly inelastic (like gasoline), then it matters what the total price (including transport) is. This in turn means that decriminalizing vices is not a free lunch of just giving up enforcement costs (and evasion of enforcement) but you’ve also got to face the facts of increased demand.