15 November, 2007

Soak the Tall: A Lesson in Optimal Taxation

Greg Mankiw suggests that it may be a good idea to tax people based on height. That's right, by the inch.

Why are *most* taxes bad? Because they distort people's decisions from the social optimum. It is sort of tricky to nail down exactly what this distortion is. Don't ever listen to an economist that tells you income taxes are bad because they discourage work. Discouraging work isn't bad in and of itself. it is bad only insofar as it people's decisions are distorted.

Consider this very very stylized example. You have $100 to invest in either railroads or steamboats. You know the exact return from each project. Invest $100 in railroads and receive $200 in one year. Invest $100 in steamboats and receive $250 in one year. However, the government has decided to tax the return (revenue minus costs) from steamboats at a 50% tax rate. So you earn $100 from project A and only $75 from project B. Thus, you choose to invest in project A and earn $100.

But is this the best social outcome? Under this tax scheme, the government earns $0 in tax dollars and you earn $100. What if the government instead taxed you a lump-sum amount? An amount that is not affected by the decision you make. Suppose they tax you $50 no matter what decision you make. Then you earn $50 from project A and $100 from project B. You choose project B. In this outcome, the government earns $50 in taxes and you still earn $100. This is summarized in the following table.

Tax SchemeReturn on SteamboatsReturn on RailroadsProfitTaxes
50% Steamboat Tax$100$75$100$0
$50 Lump Sum Tax$50$100$100$50

The idea is that the government should let each person make the best decision they can and then tax away. By altering the individual's incentives they make poorer decisions that "reduce the size of the pie". The problem is that it is simply not possible for the government to collect a lump-sum tax. The U.S. government would have to tax each person $8,000, which many people simply couldn't afford. Moreover, there would be no room for redistribution.

Some taxes can get close to a lump-sum tax. For example, taxing things that people are unlikely to change their consumption of--like tobacco or AIDS drugs. However, taxing the latter may not be in good taste. Another such tax is height. (Almost) no decision you can make will change your height. Thus, it does not distort decisions. Moreover, height is highly correlated with income, so a lot of costless redistribution can be achieved by taking from the tall and giving to the short.

Mankiw goes on to discuss various reasons why we are averse to the height tax despite the fact that it accords with our analysis.

(That was a lot more pedagogical that I thought it would be.)


Elliot said...

Well, you did call it a "lesson." And income level is highly correlated with height? Bizarre.

Anyway, very interesting. I guess one (one being a non-economist) does assume that all taxes distort choices by changing the incentive structure, and if one wants Gov. revenue you just have to deal with that.

But I don't understand why instituting a lump sum tax would be so difficult - why not (for I'm sure there are reasons that will be quite self-evident once you point them out) a simple, progressive lump-sum tax? 10,000-30,000 bracket pays $2,000 a year on up to 100,000-250,000 bracket pays whatever, $10,000 a year. An optimal amount so that it is still more beneficial to make 150,000 than 90,000 and people have an incentive to increase their incomes.

Elliot said...

Wait...I guess that would be the income tax. Ha ha.

spencer said...

Yes. Also, such a tax would be highly regressive.