Thursday, April 21, 2011

Local nonsatiation and the "man who can't be taxed"





















Some people I've talked to are of the opinion that I've been too harsh on Steven Landsburg. They say that I've been too harsh because:

A) Landsburg wasn't talking about current consumption being constant, he was talking about consumption from now until the end of time being constant.

B) Landsburg was assuming full employment (i.e. no wasted resources), so consumption from now until the end of time is in fact fixed, since it must then equal income from now until the end of time.

Yes. If by "consumption" Landsburg means "the present value of (infinite) lifetime consumption", and if he is assuming full employment, then Reasons 1 and 4 from my previous blog post do not apply (and Reason 2 is nitpicky). So was too quick to label Landsburg's idea "nonsense" and hit him with the Bat Boy picture?

The thing is, even granting the aforementioned assumptions, Landsburg is still clearly wrong. And the reason is not hard to see.

The reason is something called Local Nonsatiation. It is a basic axiom (assumption) of economic theory. It means that you're never 100% satisfied. And if you're never 100% satisfied, then any additional dollar you get will increase your utility, because you will use it to buy some of what you want. Conversely, any dollar that I take away from you will shrink your utility, because that is a dollar that you would have otherwise used to buy something you wanted.

In Landsburg's example, the rich and idle Mr. Kendrick consumes essentially zero; hence, confiscating his bank account does not hurt him in any way. This statement clearly violates Local Nonsatiation. By confiscating Kendrick's bank account, the government has reduced Kendrick's choice set. The set of possibilities open to Kendrick is now smaller. Hence, by Local Nonsatiation, Kendrick's lifetime utility must go down

Why does Kendrick's utility go down? Perhaps he wanted to leave his wealth to his heirs. Perhaps he planned to consume more someday. Perhaps his wealth was a safety cushion that made him feel secure. Who knows! The point is: as long as Local Nonsatiation applies, you're always worse off with less wealth. It really is that simple.

Landsburg compares Kendrick to a dead man, since he consumes nothing. But there is a big difference between the ascetic and the dead. That difference is called the future. A live Kendrick may have very little current-period consumption, but he has the option to consume more, or give away his wealth, in the future. You cannot take options away from a dead man, but you can take them away from an ascetic.

Now, you may ask: OK, but why should we assume that Local Nonsatiation holds? What if someone really could be completely, utterly satisfied with what he has - not just today, but forever? 

Fine. Maybe Kendrick is a bodhisattva, and has reached his bliss point. He violates Local Nonsatiation. BUT, if you take away Local Nonsatiation, then Landsburg's case completely falls apart, for a different (and yet still obvious) reason.

Central to Landsburg's case is the statement that "taxes must impose a burden on someone." But that is only true if Local Nonsatiation holds. If people can be perfectly satisfied with X amount of stuff, then taking any extra stuff away from them imposes no burden on them whatsoever, because they still have X. Taxing a man who is still at his bliss point after being taxed is like finding apples on the ground; it's a free lunch. If you don't understand that, you need to think harder!

Ever heard "There's no such thing as a free lunch"? Well, take away Local Nonsatiation, and that's no longer true. That's why economists pretty much always assume Local Nonsatiation!

So we arrive at a concise statement of Landsburg's error: The statements that "Taxation must impose a burden on someone" is logically inconsistent with the statement that "There exists a person who cannot be burdened by any tax."

All the brouhaha about full employment, interest rates, price levels, accounting identities, etc. is just a fun sideshow. The central point here is that Landsburg is making a case that is logically contradictory. In my opinion, the logical contradiction is immediately and clearly obvious. And that is why I called his case "nonsense."

But yes, of course Steve Landsburg is not insane. He's just wrong! We all say slightly insane things from time to time...


Update: Steven Landsburg responds in the comments:
The assumption throughout this exercise, as I believe I've made clear multiple times, is that Mr Kendrick is at what you call his bliss point...The other assumption is that people other than Mr Kendrick are not at their bliss points. (Mr Kendrick, as the article makes clear, is a very unusual person.) 
Well, that clears things up! It appears we have isolated the nub of the problem: Landsburg believes that taxation of a person who is at a bliss point must still impose a burden on someone, somewhere.

This is not correct. Suppose I have everything that I could ever possibly want (I am at my bliss point). I also have a chocolate bar, which I do not want. A man (the "government") comes and takes my chocolate bar and gives it to a third person, Ry, who enjoys eating the chocolate bar. My utility is not decreased, since I am still at my bliss point. Ry's utility has been increased, since he enjoyed the chocolate bar. No third party has been affected by this event. Hence, confiscation of my chocolate bar (taxation) has not imposed a burden on anyone, anywhere, at any time. The taxation was a Pareto Improvement.

From this simple and indisputable example we see that taxation of a person who is at his bliss point can be a Pareto Improvement, and hence need not impose a burden on anyone. This is why Landsburg's argument is a fallacy.

Update 2: Greg Mankiw chimes in. He thinks Landsburg is making an interesting point about tax incidence. Seems to forget that you can't actually do tax incidence - the traditional way, anyway - unless you have Local Nonsatiation, which Landsburg says he is chucking. Oh well.

Update 3: Niklas Blanchard with more reasons Landsburg is wrong.

14 comments:

  1. "The statements that "Taxation must impose a burden on someone" is logically inconsistent with the statement that "There exists a person who cannot be burdened by any tax.""

    I don't see these as logically inconsistent. Just because taxes always burden someone doesn't mean there couldn't be someone else who can't be burdened.

    Taxing a man who is at his "bliss point" is not a free lunch. I think Landsburg is just saying the lunch is paid for by someone other than the man accountants would say is being taxed.

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  2. The assumption throughout this exercise, as I believe I've made clear multiple times, is that Mr Kendrick is at what you call his bliss point. So much for the first part of your argument.

    The other assumption is that people other than Mr Kendrick are not at their bliss points. (Mr Kendrick, as the article makes clear, is a very unusual person.) So much for the second part of your argument.

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  3. Anonymous8:40 PM

    Noah,

    It seems to me that your argument only holds if Kendrick is satiated and continues to consume. Landsburg was assuming that through some kind of lending mechanism (he called it a "Bank") Kendrick stopped consuming at his satiation point and allowed others to consume. Thus the tax burden falls on them.

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  4. It's still nonsense because of both A) and B).

    A) From now until the end of time? Is the heat-death of the universe really relevant? Seriously, what does that have to do with anything that happens between now and the next time Kendrick parks a car, or even the end of his finite lifetime? Shouldn't we at least give a nod to matching maturities?

    B) Landsburg was assuming full employment. Now that is just funny, in a really sad kind of way.

    Cheers!
    JzB

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  5. Woohoo! Logic win and I get a chocolate bar from a rich person!

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  6. Anonymous11:51 PM

    Unfortunately, you still do not get it. Money is not equal to wealth!

    If Mr Kendrick has 100 apples, is satiated with 1 apple and lets the remaining 99 apples rot then taxing away 99 apples is a) pareto improving and b) is not a burden on anyone.
    This is not what this exercise is about. Mr Kendrick has 80 million dollars, and dollars would be taken away.

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  7. I believe I found another fallacy in Landsburg point. I'm not an economist by training or vocation, so please correct me if I get this wrong.

    Landsburg appears to assume that Mr. Kendrick's money appeared from nowhere. Someone, at some point, earned that money (or wealth, as it were). It represents the ability to purchase goods and services that Kendrick or his ancestors earned and locked away. Landsburg looks to me to treat the money Kenrick has in a bank/under his mattress/lining his grave as equivalent to seinorage; money the government acquires from somewhere but does not represent tangible wealth. In that case, spending it might reduce other consumption or be identifiable with a tax (Seinorage is considered a tax, no?). But since the two are not equivalent (someone made Mr. Kendrick's candy bar), redistributing that wealth can have a positive impact on the economy.

    Is this instinct anywhere near correct? Thanks for your analysis, Noah.

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  8. Anonymous10:54 AM

    This point seems to be solely that "The true incidence of a tax is not necessarily on the person who writes the check to pay the tax bill." This "point is pretty standard and hard to argue with."

    Read Mankiw's summary of this (repeated below) -- http://gregmankiw.blogspot.com/2011/04/people-talking-past-each-other.html

    I am regularly struck by how bloggers so often want to pick fights with other bloggers. Rather than giving others the benefit of the doubt, they often seem to interpret the writing of others in the worst possible light so they can then point out how foolish it is. As an example, see
    This Steve Landsburg post
    Followed by this Brad DeLong critique
    And this Paul Krugman critique
    And Steve's two replies.
    As far as I can tell, all Steve is saying is that the true incidence of a tax is not necessarily on the person who writes the check to pay the tax bill. He just made the point in a particularly dramatic way. At its heart, however, his point is pretty standard and hard to argue with.

    FYI, more interesting to me is this Landsburg post, where Steve argues that a rich person who wants to raise taxes on the rich should be voluntarily paying more right now. One example is the rich person who lives in very nice publicly-provided housing on Pennsylvania Avenue in Washington DC.

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  9. I read the comment thread of the last post "Dead Man Followup" of Landsburg. I note that Noah posted some comments and Landsburg choose to ignore them. So for me the issue is settled: Steven Landsburg is an arrogant ignorant.

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  10. I think we're all avoiding the elephant in the room here: Noah is assuming Bat Boy is insane just because he's odd-looking. Shame on you, Noah!

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  11. I think Landsberg's 'can't tax a dead man' is about the crowding out effect pure and simple. The incidence of the tax falls not on the guy getting his jollies parking cars (coz. there's no change in his behaviour) but on who ever was affected by the changes in prices brought about by the Govt. spending the money. What if the crowding out effect is zero (a general slump) or negative (i.e. the Govt's spending on Public goods or infrastructure or killing vampires allows everyone to have more of what they fancy at lower cost)?
    Well, one way Landsburg could argue that there is still a 100 % crowding out effect is by saying 'well, the Govt. is just one of a number of potential Govts. hovering in phase space, like 'Fringe' the T.V show, and just waiting to displace the Govt. in our reality. In that case there is still a crowding out effect so long as Govts. use tax revenue on economic goods. In other words, Landsburg is pointing to a sort of extreme path-dependence and graininess our normal economics refines away from.
    Indeed, the nagging quality of Landsburg's gedanken- the reason they get under one's skin- is this spooky Zen or Hassidic quality. It's like in the movie 'a serious man'- did the wife just kill a Rabbi or was it a dybbuk? But, what after all is the difference between a Holy Rabbi and an accursed dybbuk? These are questions fit to be posed to a 'serious man' precisely because they point beyond logic and merely verbal argumentation.
    Still the statement 'Taxation must impose a burden on someone' (even assuming we're operating on the p.p frontier) isn't true. There can be novel forms of economic goods created by the Govt at the very moment a tax is paid on them. Indeed, all economic activity, in their genealogy, originate in some sense in this hybrid manner.

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  12. Anonymous : "FYI, more interesting to me is this Landsburg post, where Steve argues that a rich person who wants to raise taxes on the rich should be voluntarily paying more right now. One example is the rich person who lives in very nice publicly-provided housing on Pennsylvania Avenue in Washington DC. "

    More proof that Landsburg is a fraud. Collective action problem, anybody?

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  13. Landsburg says:
    1) A tax imposes a burden.
    2) If a tax has no effect on a man’s lifestyle, then it imposes no burden on him.
    3) Therefore, if a tax has no effect on a man’s lifestyle, then it must impose a burden on someone else.

    A tax does not impose a “burden,” per se. A tax takes existing assets and transfers them to government ownership. This is commonly referred to as a “burden,” because we assume that anyone losing assets is burdened. We assume that taking assets from people makes them feel pain. The steps should read:

    1. A tax always makes someone lose ownership of the assets they own.

    2. Mr. Kendrick is insane, so he does not feel burdened by the tax.

    3. Therefore, although this is a burden-free tax, Mr. Kendrick still loses control of the assets he owns.

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  14. If I understand this post correctly, Steven Landsburg is not only an ignoramus in macroeconomics, but also in microeconomics.

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