26 Oct 2011

## Yet Another Quick Note on Tax Theory

OK in the comments on previous posts it is clear that a lot of readers didn’t get the point I was making originally, that there is a legitimate sense in which an income tax hurts individuals more than a comparable consumption tax. So let me take another stab at it. (It should go without saying that this analysis doesn’t mean I’m “for” a consumption tax, especially since–in practice–we’d end up with both an income and consumption tax.)

First, let me point out that it’s not true that you can gauge the harm of a tax by simply looking at how much revenue the government derives from it. Some people thought, “If, by construction, we’re comparing a consumption tax to an income tax that keeps government revenue constant, then aren’t they equally harmful?” But no, that’s not right. At an income tax rate of 100%, the government wouldn’t take in any revenue, but it would devastate the economy as all transactions went into the black market and many activities simply disappeared. At an income tax rate of 0%, the government wouldn’t take in any revenue either. I didn’t just prove that those two outcomes are equivalent, as far as taxpayers are concerned.

Second and more to the point: In general, if the government is going to extract \$x from you as a taxpayer, you don’t want them putting additional constraints on how you finance the blow. If you owe the government \$x per year, the best thing (from your POV) is a head tax; the government says, “Do what you want with your income and spending decisions, but you owe us \$x or else we kill you” (or whatever).

Now suppose instead, the government said, “Over the course of the year, keep track of how much money you spend on food. We will keep y% of those dollars, before they reach the grocer.” The government then picks y% so that, after you adjust to the new situation, they end up taking \$x total from you each year.

Assuming such a y exists, so that you end up in a new equilibrium, spending enough on food so that \$x still goes to the government, then you are probably worse off than before. (For sure you would be, if you were the only person this happened to. Then food prices would be basically the same, and you’d bear the full brunt of the food tax.) Because of the y% tax, on the margin food is now pricier to you (compared to other things) than it was before. So in addition to taking \$x from you, the government has pushed you artificially out of buying as much food as you would have, even in the alternate scenario where you were down \$x. You could always match your spending decisions that you implement when the government imposes no constraints, but you probably won’t since they probably have you spending too much on food.

If it’s still not clicking, try flipping it. Suppose the government were going to give you \$12,000 in cash, or a \$12,000 voucher that had to be spent on food from the grocery store and that couldn’t be transferred to another party. You would clearly prefer the cash, because you could always spend it all on grocery store food if you wanted. But, you could use it on other things too.

So if you generally get the above logic, then realize that’s what’s going on with an income vs. consumption tax. A consumption tax is worse than a head tax; the former artificially penalizes using labor and other productive factors to earn an income, rather than “consuming” them through leisure or idleness (which is not taxed as “consumption”).

But, an income tax is even worse than a consumption tax. Not only does an income tax ding you when you sell your labor or rent out your productive factors for money, but then if you want to spend it on future consumption (as opposed to present consumption), it dings you again, because the vehicle you use is to invest it (in a bond, share of stock, etc.) and then the income tax hits you when you earn interest, dividends, or capital gains in the future period.

Just as the food tax in our above example made food artificially expensive, so too does an income tax make future consumption artificially more expensive relative to present consumption. So if the percentages are designed by construction to extract the same total revenue, then an income tax is worse than a consumption tax in the sense that it pulls out the same \$\$ but also puts another artificial restriction on your behavior.

#### 8 Responses to “Yet Another Quick Note on Tax Theory”

1. EB says:

Why do you continue to rag on Wenzel?

Seriously, how does one subscribe to the comments for a particular thread?

• Bob Murphy says:

Are you making a joke about Wenzel? I can’t tell. Anyway, I’m not responding to Wenzel, I’m responding to new comments on my last post that have arisen in the last 24 hours.

I don’t know about subscribing to comments, sorry. When I am rolling in cashflow I’ll pay someone to professionally run this thing.

• Joseph Fetz says:

Bob, I think that he is actually misconstruing this as an attack on Wenzel. At least, that is what it looks like from here. It obviously isn’t.

2. Chris Pacia says:

Bob,

Doesn’t a consumption tax also hit you when you earn interest, dividends, and capital gains? After all one doesn’t earn interest to roll it over for perpetuity — it’s eventually cashed out for consumption. Does this not lower the return in a similar way as the income tax?

If I invest \$1,000 and grow it (income tax-free) to \$2,500, but have to pay a %20 consumption tax, this necessarily reduces my return to \$2,000. Is this any different than if I had been paying an income tax on my dividends each year? Under a revenue-neutral income tax, wouldn’t I still have roughly \$2,000 to consume at the end of the period? I’m not sure I see how a consumption tax is a benefit over an income tax.

• Bob Murphy says:

Chris, I can’t come up with an example right now (not enough time). But I claim that you are missing something. If the government adjusts the percentages so that even after the person optimizes (in light of the fixed tax), the government collects the same revenue, then the person’s preferences would rank his consumption stream under the income tax regime as less desirable than the consumption stream he chooses under the consumption tax regime.

What you’re missing in your calculation is the “double tax” aspect of it. First assume there’s no tax, and the interest rate is 100%. So I earn my income from selling labor, and then I can buy apples that are \$2 right now, or are effectively \$1 right now if I buy a “future apple.” So I allocate my income between present and future apples.

If the government now comes in and levies an x% tax on consumption in all periods, then it’s true, I effectively have x% less income. But the tradeoff between present and future apples is the same. Apples in the present are \$2(1+x%) while apples in the future are, right now, \$1(1+x%).

This isn’t what happens when the government imposes an x% income tax levied on all income earned per period. The reason is that if I actually want to consume a “future apple,” I don’t spend \$1 today to buy a claim. I.e. I’m not actually “consuming” it today.

Rather, I take the \$1 and buy a bond, that yields \$1 in interest over the year. Then I buy a \$2 apple next year with it and consume that apple then.

Since the income tax will hit me on that \$1 in interest next year, it means I will have less than \$2. So I will need to invest more than \$1 in period 1 to eat the future apple.

So we see that back in period 1, after I get my labor income and the government takes its x% cut (with an income tax), I can now spend \$2 on an apple today, or I have to spend more than \$1 to get an apple delivered next period. Thus the government is not only making me poorer, but it is making future apples artificially expensive.

So if the percentages are adjusted such that the government extracts the same revenue from me under either tax, then the hit to my overall income is the same; the taxes are equivalent on that score. But the income tax also makes future apples become costlier in terms of present apples, which makes me deviate from what would have been my optimal present/future allocation.

I understand I’m not really giving you a bulletproof argument. I could do it with a formal neoclassical model with utility functions, but I think a lot of people would say, “I don’t trust math. You must be from Chicago.”

You can do it with a geometric approach too.

I don’t think it is an artifact of math assumptions, I think it is a general principle. The reason it’s hard to see it is that we are always saying after people adjust, the government has levied such a high tax rate that they are still paying in the target revenue. So that might be the part of the argument that is throwing some people.

• Bob Murphy says:

This might help: Don’t think of it as a 20% consumption tax versus a 20% income tax, because they wouldn’t raise the same revenue. Even if the worker works the same # of hours, he ends up saving less under the income tax, so his lifetime income is lower. Hence, a 20% income tax wouldn’t raise the same revenue from him, as the 20% consumption tax. Since the guy is going to save less (and thus earn less interest income), maybe the government has to impose a 23% income tax to raise the same lifetime revenue from his, as it would get from a 20% consumption tax.

And then to take the principle further, suppose that either the 20% consumption tax or the 23% income tax would let the government extract \$10,000 per year from this guy. If instead it imposed a \$10,000 head tax, then the guy’s consumption would probably end up higher than under the consumption tax regime. This is because the marginal incentive to work for money (instead of using those hours as leisure) would go up, since consumption isn’t being taxed on the margin anymore. (After you pay the flat \$10,000, you’re free.)

So when mainstream economists say that a head tax is better than a consumption tax is better than an income tax, they mean “if you allow the government to fiddle with the parameters under each regime, so that even after individuals adapt to the new regime, the government is taking the same amount of total tax revenue.”

Rothbard and others have raised some good objections to this approach; he’s got an essay today at LRC. I’m just trying to be clear on what the standard mainstream analysis is.

3. Papi says:

I agree with your main point on the double-ding, but I do take issue with the claim that an unavoidable tax (head tax) is preferred to an avoidable tax. I think that’s Chicago creeping into your brain, since Chicagoans hate elastic taxes as distortionary.

I would prefer an avoidable tax. Like coupons you have the choice of paying money or paying with effort or consumption changes. And remember choices are welfare-enhancing.

• Bob Murphy says:

Papi, I probably should have done a better job of specifying what we are holding constant when we say “head tax is better than consumption tax is better than income tax.” Usually with these things (and here you and Rothbard can object with good reason) we mean, “Adjusting the percentages so that the total revenue collected is the same.” So if the head tax is \$1000, or the government keeps jacking up the sales tax until it gets you to cough up \$1000, even after you adapt, then you are worse off in scenario #2.

To make it ridiculous, suppose I said, “In Scenario #1, I hit you with a feather. In Scenario #2, I let you choose whether I hit you with a bat or a golf club. Which scenario do you prefer?” It would be rather incomplete for you to say, “Choices are welfare enhancing, so I choose Scenario #2.”