Today’s puzzle is specifically for the econo-geeks. Less geeky fare will follow in the near future.
Two of the main lessons that our undergraduates typically take away from their introductory classes are these:
- To minimize distortions, all goods should be taxed at the same rate.
- To minimize distortions, inelastically demanded goods should be taxed most heavily.
What is the correct response to this pair of apparently contradictory lessons?
- Economics is large. It contains multitudes. Get over it.
- Nobody ever said that all goods should be taxed at the same rate. The right lesson is that goods should be taxed in such a way that their prices all rise by the same ratio. That’s not the same thing, because different taxes are passed on to consumers in different proportions. So maybe that’s somehow consistent with the elasticity rule.
- Both of these “lessons” are based on maximizing consumer welfare. Maybe if we account for the producers, somehow everything will magically make sense again.
The right answer, alas, is “none of the above”. A is a non-starter. As for B and C, let’s assume that all supply curves are horizontal, in which case all taxes are passed on to consumers (which dispenses with B) and producers earn no surplus in any event (which dispenses with C).
So how about this?
- My Principles teacher never said anything about setting tax rates so that all prices rise by the same ratio! You’re just making that up!
Alas, what’s going on here is that your Principles teacher either didn’t cover indifference curves or didn’t have time to cover all of their cool applications. It is in fact true that to minimize distortions (at least among consumption choices, which, in view of our assumption about horizontal supply curves is all that matters here), all goods should be taxed in such a way that their after-tax prices rise in the same proportion. In other words, if we’re deciding between a “blue tax plan” that raises the price of eggs by 6% and the price of wine by 4%, and a “red tax plan” that raises both prices by the same amount, and if the rates are calibrated so that both plans raise the same amount of revenue for the government, then the representative consumer prefers the red tax plan. The usual argument is via indifference curves and hence doesn’t always make it into the Principles courses, but if you study economics long enough, you’ll run into it eventually.
Let’s try again:
- Hey, wait a minute! Your indifference curve diagram assumes I can only tax consumption goods. Shouldn’t I also have the option of taxing labor and/or leisure?
You’re right. The indifference curve diagram takes income as exogenous. If you’ve got to earn your income, then we should include leisure as another good. Go ahead and do that if you like, or just continue to assume exogenous incomes. Like options A, B, C and D, this is still a blind alley.
So what’s the right answer? It took me a little time to settle this in my own mind. (The question first popped into my head back when there was still a race for the Republican presidential nomination and I was trying to figure out if there was any way you could possibly justify Rick Santorum’s manifestly insane call for preferential taxes on manufactured goods.) Once I’d understood it, I Googled around a little and was surprised to find nothing on the Web that clearly addressed and resolved this little puzzle. So I thought I’d invite my readers to tackle it and see if their answers coincide with mine.
Please don’t post spoilers in the comments if you’re an expert in tax policy and have understood all of this forever, but all others are welcome. More than one very bright econ prof has tripped over this.