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Friday, December 04, 2009

Declining Marginal What?

Yesterday I described some intuitive support for declining marginal utility.  But commenter freight train demands that I back up:  "What is the definition of marginal utility?" he asks.

Is...[utility] measured across the desire or across the fulfillment of the desire? What's the measure of that "worth?" ....Is [it] measured by what someone wants - ie, thinks will result from an additional dollar - or what they actually get from that additional dollar?

I agree: I cheated.  We can't figure out whether the marginal utility of income declines until we know what utility is.  After the jump, I expand upon and ultimately avoid the question.

Freight Train "I demand that you define your terms and defend your
fundamental assumptions, or I will RUN YOU THE HELL OVER."

Some people take the position laid out by GJELBlogger in the comments to my previous post and say that utility (or well-being) is equivalent to happiness (also sometimes referred to as "subjective well-being").  This is an older view that has recently been revived in the legal academy and elsewhere

Most economists and many law professors equate well-being with preference satisfaction, whether actual preferences or “laundered” preferences (that is, preferences for things that informed, rational individuals acting only out of self-interest would prefer).

Still others believe welfare to consist in the satisfaction of certain “capacities,” or objective goods.

I'm not going to take a position on the definition of utility, at least for this series of posts, but freight train is right that this matters tremendously for lots of reasons.  Some of the supposedly relevant studies that I'll discuss in a subsequent post are of only limited importance if you take the view that, say, utility is equivalent to preference-satisfaction.

And then freight train takes it to the next level:

[S]hould tax policy be based on what individuals want most? A poor person may feel the lack of a loaf of bread, while a rich person may feel the lack of a private jet, but does that mean that redistributive tax policy needs to respect both desires equally?

So freight train is challenging this whole way of thinking about tax policy: why focus on maximizing utility, he asks, instead of on, say, fairness?  There is a lot to say on this topic, but for this series of posts I will just say that much current tax legal scholarship focuses on maximizing utility.  Thus, whether you agree with that approach or not, you (by which I mean, of course, me) might want to grapple with the key assumptions that often accompany it.  And one of those assumptions is that income has declining marginal utility.

Image credit: Hunter-Desportes, Freight train (1975) (Flickr.com); used under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 Generic License.

Posted by Sarah Lawsky on December 4, 2009 at 05:08 PM in Tax | Permalink


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Typos galore in the last comment. I do, in fact, know basic grammar.

Posted by: Michael Risch | Dec 5, 2009 11:05:39 AM

"So freight train is challenging this whole way of thinking about tax policy: why focus on maximizing utility, he asks, instead of on, say, fairness?"

I would add that I'm not sure that freighttrain's comment need be such a challenge to thinking about things. Sure, the rich person might really, really, really want that plane, but when deprived of food for a week, they would really really really want some bread first. In other words, utility is a function of substitution of preferences, and you have to look at wealth effects on utility. Since utility differs for every person, the implications of freight train's question is whether we should maximize utility based on the sum of individual preferences given their subjective wealth, or whether we should maximize utility based on some objective baseline of wealth. I think that any rational tax policy has to have some form of objectivity built in (not necessarily Rawl's maximin, but something), or else the policy would always be to tax everyone to near death and give all the money to the person who has an unbridled love of pennies, since those are incredibly cheap to provide.

This is why I ask about Arrow's impossibility theorem - so long as people have different ordered preferences, there is arguably know way to maximize social welfare by comparing goods. I think that's why most economists substitute money for utility - with the idea that people can buy what makes them happiest). If that substitution is true, then there must be a decreasing marginal utility to income at the extremes - I'm not willing to accept that the starving person who needs a loaf of bread to survive could ever have less social welfare gain from a $2 meal than the rich person who spends $100,000 on jewelry. Of course, in the middle there may be some variation - perhaps it's not a constantly decreasing function.

Posted by: Michael Risch | Dec 5, 2009 11:03:28 AM

Another complicating factor is that we don't typically think of policy as an individualized utility function (social welfare is the important thing, right?). If so, then the heroin addict (with increasing marginal utility) and everyone else (decreasing or zero marginal utility) combine to make a downward sloping demand curve.

This is true even for bread v. planes. Sure, rich people might have a higher comparative utility for planes v. bread, but if you are viewing bread and planes as the relevant substitutes, the amount of societal first dollars spent on bread will be higher. Indeed, this holds true even on an individual level. If you said to the $1m net worth individual - you can buy a plane for $1m, but you can't eat, OR you can buy bread for $1, and you have $999,999 to buy things other than planes, I am betting that 100% of them will spend that first dollar on bread. It's the reason why all rich people don't starve to death. Furthermore, the value of the second plane, third plane, fourth plane, etc. will also be decreasing.

In other words, while I think the different definitions of utility are interesting theoretically, in reality they definition doesn't change the simple fact that in general the more of something you have, the less value the next one will have to you.

Side question: how does Arrow's Impossibility Theorem tie into all of this?

Posted by: Michael Risch | Dec 5, 2009 7:17:48 AM

Yeah, I never know how to deal with the capabilities approach. It might be a welfarist approach, but it certainly might not be. But that's beside the point--your "railroad as declining and marginal utility" comment is clearly what we should all take away from this particular thread. Really, really nice.

Posted by: Sarah Lawsky | Dec 4, 2009 8:28:31 PM

I'm a bit disappointed. I thought you were going to suggest that railroads were a declining, marginal, utility.

As for welfare and capabilities, at least in his most recent book Sen seems to suggest that welfare isn't defined in terms of capability satisfaction, but welfare (or well-being) is one thing and capabilities are another, and we just lump both of them (and a lot of other stuff) together in our social choice functions. How that's supposed to work isn't very clear to me at all, and unfortunately Sen doesn't much help us, at least in his new book. (This is a bit crude as a description of Sen's view, at least in his new book, but close enough for a blog comment, I think.)

Posted by: Matt | Dec 4, 2009 8:15:28 PM

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