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Monday, December 07, 2009

Why Declining Marginal Utility Matters

Before any more about declining marginal utility, let me explain why the assumption of declining marginal utility matters so much to tax policy.  (This post will, I hope, begin to reply to some of the comments on an earlier post, which asked me to explain why I was talking about individual utilities at all.)

One popular approach to distributive justice within the tax legal academy is welfarism.  (Sometimes this commitment is explicit, sometimes not.)  In a welfarist approach, redistribution is desirable only if it increases overall social welfare.  

Thus there are two steps to the welfarist analysis: a welfarist first determines individuals’ utilities, and, second, to arrive at overall social welfare, the welfarist aggregates those individual utilities in some way.  (My earlier post described a sort of step zero: before all this utility determining and aggregating, a welfarist has to figure out what she means by "utility.") 

Step 1 (determining individual utility) and Step 2 (aggregating those utilities) are very different.  Utility is a fact about the world.  Once utility is defined, people have a certain level of utility, whether that level can be measured or not.  So Step 1 is descriptive

But while individual utilities are a fact about the world, how the welfarist chooses to aggregate these utilities--his "social welfare function"--is a judgment.  Thus Step 2 is normative.  For example, a utilitarian approach weights each individual’s utility equally and adds up individual utilities to arrive at overall social welfare.  A completely egalitarian social welfare function requires complete equality of welfare.  A moderately egalitarian social welfare function weights the utility of the less-well-off more than the utility of the more-well-off.  Tax legal scholarship sometimes explicitly adopts or assumes a utilitarian social welfare function, but more often does not specify a social welfare function.

If we assume that all individuals have the same utility curve (yes, I know that is a huge assumption--but it's also a very common one in the literature, so bear with me!), declining marginal utility means that even a welfarist who gives no explicit weight to equality will support redistributive taxation that transfers money from the rich to the poor (or the more-well-off to the less-well-off).  The reasoning is simple: ignoring transaction costs, the dollar will “do more good” in the hands of the poor person than in the hands of the rich person.  If Rich (who is rich) and Penny (who has only pennies) have the same utility curve, and that curve has declining marginal utility, taking $100,000 from Rich and giving it to Penny increases overall utility, because getting $100,000 increases Penny’s utility more than losing $100,000 reduces Rich’s. In other words, declining marginal utility can, assuming that all individuals have the same utility function, justify redistributive taxation.

Posted by Sarah Lawsky on December 7, 2009 at 10:15 AM in Tax | Permalink

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Comments

I'm looking forward to the whole paper. Especially if it comes with all the chocolate-chip cookies you've decided are no longer yummy.

In the meanwhile, my nit would be to claim that evaluation of the social welfare function is both normative, as you describe, and also descriptive. The SWF can incorporate popular normative preferences for fair distributions, which means that we have to measure who is a Rawlsian, who a utilitarian, and then figure out how they perceive their criteria are being met (and decide whether to count mistaken impressions -- the revenge of the normatists). (Normatist: (n) 1. Someone who wants to use norms to measure stuff. 2. (arch.) People who prefer the larger of the two Cheers barflies.)

Posted by: BDG | Dec 7, 2009 9:01:28 PM

Well, then, the solution to the tax policy question is simple: measure every person's individual utility curve, and determine what tax policy places every person at the highest possible point on their utility curve.

Unless, oh dear - what happens if different policies place different people at different places? What if there's no "one, true way?" No one tax cut to rule them all?

Okay, so maybe my sarcasm is misplaced, but I figure if there was a particular answer, that The Google would have found it by now. I mean, it's the smartest thing in the universe, right?

Okay, I'll stop talking about that which I do not know.

Posted by: Matthew Reid Krell | Dec 7, 2009 11:55:36 AM

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