Friday, 6 May 2011

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.