Optimal tax theory - contraception edition

Tyler points to some data on the price elasticity of demand for the Pill as contraception among college-aged American women. A price increase from $5-$10 per month to $30-$50 per month resulted in a 2 - 4 percent drop in use of the Pill. The paper says the price increase was "more than three-fold". If a 300% increase in the price of the Pill results in a 3% drop in demand, that's about the lowest price elasticity of demand I've ever seen - around 0.01.

Oh, the fun tax theory exam questions that could flow from this! Recall that the naive interpretation of Ramsey tax theory says that you want to tax more heavily those goods that are inelastic in demand: that way, deadweight costs are lower. But the more accurate interpretation of Ramsey (here too) is that you want to tax more heavily those goods that are complements to untaxed leisure in a world in which we can't tax leisure directly. Further, we have Pigovean reasons for taxing public bads and subsidizing public goods.

So, is the Pill a complement to leisure or to labour? Tyler points to some evidence from the paper's abstract:

Women who lack insurance and have sex infrequently appear to substitute toward emergency contraception; uninsured women who are frequent sex participants appear to substitute toward non-prescription forms of birth control. Additionally, we find small but significant decreases in frequency of intercourse and the number of sex partners, suggesting that some women may be substituting away from sexual behavior in general.

If intercourse is leisure rather than investment in work-related social capital, then we might have some Ramsey argument for taxing contraception. But it's not immediately clear in which direction any Pigovean argument might run. Neither is it even immediately clear in which direction any long-run Ramsey argument might run if you think through some general equilibrium arguments about sex, positional goods, and hypergamy; easy to imagine how it could go either way.

There's at least a short essay exam question in there on tax theory for anybody who's lecturing tax in public economics next year; it's a nice one where there are lots of clearly wrong answers but also many potentially right answers so long as the argument is reasonable.

Happy Valentine's Day!

Elasticity and taxes

Tyler points to Matt Rognlie:

A famous result in public finance, the Atkinson-Stiglitz theorem on the optimality of direct taxation, captures this intuition in a striking way. Atkinson and Stiglitz show that if the utility function is weakly separable between consumption of various goods and labor (intuitively, the amount you work has nothing to do with your consumption choices, except insofar as working more gives you more money to spend), then no consumption taxes are needed to attain the optimum. You don’t levy higher taxes on gas than soy milk because soy milk has a higher elasticity; you just determine the optimal tax schedule on income and then stay away.

Matt then uses this to argue against petrol taxes as being particularly efficient: petrol demand is relatively inelastic, so some folks reckon it ought be taxed more heavily for revenue reasons. I agree with Matt's conclusion, but for different reasons.

I'm sure Seamus will correct me if I have this wrong (in his usual very polite "I think you meant to say" kind of way), but I thought the implication of Atkinson-Stiglitz was that when consumption of various goods is more strongly a complement of leisure than of work (weak separability from labour fails), taxation of commodities strongly complementary to leisure may become optimal. We can't tax leisure directly and so people choose too much of it relative to an ideal; taxes on complements to leisure become a second best. I'd be very surprised if petrol were a stronger complement to leisure than to labour. And so the Ramsey-style case for petrol taxes fails.

Hoisted from the comments: Ramsey pricing and alcohol

Seamus reminds us that Ramsey pricing does not necessarily recommend taxing inelastic goods; rather, it recommends, because of the existence of untaxed leisure, that optimal taxes will vary with goods' cross-price elasticity with leisure. Goods complementary to leisure draw a higher optimal tax than goods complementary to labour. Seamus's interpretation of Ramsey follows, I belive, Corlett and Hague's classic rendition.

The Tax Working Group's paper on "Other Base Broadening Ideas" takes an alternative interpretation of Ramsey

Ramsey taxation

The Ramsey theory of taxation recommends higher tax rates on goods with the most inelastic demand as a means of raising revenue in the most efficient way possible. This is based on the assumption that taxes on goods with inelastic consumer demand would have small distortions relative to goods with more elastic consumer demand, and therefore lower dead weight costs.

The McLeod review found that in the New Zealand context, where tobacco and beer are thought to have the most inelastic tax bases, while the demand for wine and spirits are more elastic, it was not possible to justify the then levels of excises and duties on Ramsey taxation grounds.
p.28

Note that "not possible to justify" means "the excise tax should be cut substantially or eliminated", not "too low".

The Tax Working Group uses the standard undergrad textbook formulation of the Ramsey Rule (see Hindriks and Myles, for example). The result holds under assumptions of infinite supply elasticity (because otherwise deadweight losses to consumers are only part of the welfare effects); if there are cross-price effects between taxed goods, things also get much more complicated - Ramsey then doesn't reduce to the inverse-elasticity rule. And if there are cross-price effects between taxed goods and leisure, then we get the Corlett and Hague result.

So, is alcohol a greater complement to leisure than are other goods, and in particular is it a greater complement to leisure than to labour? Tough call. Lots of business lunches are facilitated by alcohol, and there is decent evidence that drinkers earn more than never-drinkers, partially due to complementarity between drinking and business activity. But neither forms of the Ramsey rule particularly suggest increasing the alcohol excise tax, and the McLeod review firmly opposed it.