IUC, DMU, and Redistribution: You Can\'t Get There From Here

Since some of the natives are getting restless about where all this IUC talk ends up, I figure it might help settle them down if I explain why I'm pretty sure the redistributive argument based on IUC+DMU is a nonsequitur. Brandon has already given a very important and sound objection, but his critique is external to the redistributive argument itself. I'm going to argue that even under very favourable assumptions, redistribution still makes no sense from a utilitarian standpoint.

For the purposes of the argument I will assume the following, roughly in order of increasing implausibility:

* Diminishing marginal utility holds robustly across the population, with relatively small variance around an average.
* Interpersonal subjective utility comparisons really are possible.
* Transaction costs of redistribution are zero, or close enough to zero to be neglected.
* Total wealth in the population is insensitive to the redistributive mechanism and will stay fairly static over time.

By the assumptions listed above, it appears to follow that expected[1] overall utility is maximized by redistributing wealth from the top to the bottom until everyone has an equal amount. But this only works if you consider "wealth" as monolithic good in abstracted isolation from everything else, and doesn't work so well when you actually try to model it slightly more realistically.

In our simple model, assume there are two goods -- liesure and money. People earn money through labour, which is isomorphic with giving up liesure. The same argument used in favour of egalitarian redistribution of money implies that everyone should be made to work the same amount of hours as well (calibrated to the population average), being that their DMU for leisure will also not vary too much around the average. Each individual will have a point at which they're indifferent between one more unit of leisure and one more unit of money, after which point they would normally stop working under free-market conditions. As stipulated, these points will vary between individuals, but not dramatically or systematically so.

But the fact people's utility curves will vary does matter. There will be many people whose DMU rate for income is higher than the average -- i.e. those who under free market circumstances would work less than the mandated work requirement, in exchange for accepting a lower income. Their loss in utility from having to work extra hours is, by definition, greater than the gain they get from extra income. On the other side, there will be many whose DMU rate for income is lower than the average, and who would therefore have worked longer than the requirement in exchange for a higher income. Their utility loss from the lower income is, by definition, greater than the gain from working less hours.

The upshot of all this being that everybody except those whose utility curves precisely match the population average is made worse off, and nobody is made better off. Removing the redistributive apparatus and allowing the resulting inequality would be a Pareto improvement. Consequently the "utilitarian" argument for income redistribution fails on its own terms. (Note also that the point generalizes to any system that applies a one-size-fits-all rule to a population that exhibits variance -- it need not be an egalitarian rule.)

Whoo. Okay, I'm sure there are obections that can be made to that, but it sure was fun!

fn1. I say "expected" because we aren't assuming away the knowledge problem of knowing everyone's individual utility curves, and thus have to make due with a statistical average. Even I'm not willing to indulge excursions quite that far into la-la-land.

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On a tangential note, is

On a tangential note, is there a name (e.g., Pareto or Kaldor-Hicks) for the sort of efficiency that can allegedly be achieved through redistribution?

Without whipping out a

Without whipping out a pencil and paper and doing the calculations, I can't be sure you're wrong. But something sounds fishy here. We have two proposals: A (redistribute income from rich to poor) and B (redistribute labor effort from those work a lot to those who a little). On your assumptions, A would increase total utility under ceteris paribus conditions. And you claim that, for similar reasons, B would also increase total utility under ceteris paribus conditions. But, you say, if we implemented both A and B, the net effect would be negative. Now, there are some functional forms that can produce that kind of result, but they usually involve some funky cross-partial derivatives, which I think would be hard to justify here.

But I'll admit I'm not quite sure where your logic goes wrong. Maybe I will whip out that paper and pencil.

Exactly what MIchael said.

Exactly what MIchael said. Matt is ignoring the fact that, through skill or luck, some people might make more money then others. Throw one Bill Gates in there, and the whole analysis goes out the door, right?

The entire logic behind "DMU => redistribution" is that if different people have different levels of wealth, then DMU implies it is a gain to redistribute. You have left out the different levels of wealth.

What's wrong with

What's wrong with redistributing from the very rich to the lowest paid workers who are already working the average number of hours or above? Won't that increase net utility?

More comprehensively: for

More comprehensively: for every given existing level of work/leisure why not redistribute wealth from the rich to the poor? Redistribute from the rich to the poor among all people working 0 hours a week, do the same for all those working 5 hours a week, likewise 10, 20, 40, 60, 80, or 100 any other number of hours of work a week.

Doesn't that redistribution increase net utility in your model?

If I understand John T.

If I understand John T. Kennedy's second comment, he seems to be making a fifth assumption, one not stated by Matt McIntosh. The assumption: There is a "social utility (or welfare) function"; that is, utility (if it could be measured for individuals) can and must be summed over all individuals. In other words, if X takes money from Y and the utility gained by X is greater (in absolute value) of the utility lost by Y, that's all right. Well, it's all right for those who believe in "social utility" or "cosmic consciousness." All who do, raise your hands.

I think Matt is making a

I think Matt is making a different unstated assumption, which appears necessary to his argument. Assumption: everyone makes roughly the same wages per unit labor.

Or, more likely, he's making a different, less clearly implausible assumption, which after much economic [choose: hand-waving|analysis] he believes produces equivalent consequences.

I'm voting for hand-waving personally, but I'm willing to be convinced otherwise. There's another explicit assumption that looks straw mannish. Only hard core marxists argue for "from:abilities::to:needs" anymore. No serious welfare state proposal is designed to equalize everyone's income.

My own US-birth, above average intelligence, education, middle-class privilege, personal ambition etc. have brought me to place where I can get people to pay me much more for a unit of my labor than the average person in the US, and at least an order of magnitude more than the world average. 10-20% of my earning power is not that much skin off my nose if it makes the world a better place and keeps some people from starving in the streets.

Come up with a way to do that effectively and efficiently and I might even sign on to letting the government do it (though I'd prefer to see it done voluntarily through NGOs and personal charity). Go for the marxist throat, and I'll be manning the barricades right along with the Randians.

My gut feel is that the utility case against redistribution rests on one of two significant problems: 1) redistribution's effect on net total wealth, and 2) the dis-utility of coercion.

Both effects are obviously (in hindsight anyway) extreme in the fundamental marxist vision, hence the utter failure. OTOH, it's very hard to compare fairly something like the current US or a modern welfare reform proposal to the laissez-faire state.

I think it's safe to say that any welfare state which doesn't explicitly seek to minize those effects is very likely to hurt far more than it helps.

It follows directly from

It follows directly from Matt's assumptions alone that that the redistributions I described in that second comment result in an increase in net utility.

We don't need to consider social utility per se, he's saying the rich generally value a dollar less than the poor. It follows in Matt's model that a forced transfer from the rich to the poor increases utility - the poor benefit from the transfer more than the rich suffer. Matt offered an argument that he thought cast that conclusion in doubt for utilitarianism but I sidestepped his argument by slightly modifying the structure of the transfer. Utilitarianism still holds forced transfers of wealth to result in a net gain under his model.

JTK, At first glance it

At first glance it might increase utility to shift money from rich to poor within classes. I don't think it takes into account the effect the shift will have itself. Doesn't real income effect how much work vs. leasure they will desire? Isn't the transfer a form of income or an impact on real income? Don't different people have different slopes to their graphs? Also their graphs may not be straight lines. If you redistribute money from one person who works 40 hours a week to someone else who makes less but works 40 you effect both of their desires regarding work. Not only may they move in different directions ending up in different hourly classes but they could also shift by different amounts due to slope ending up in different classes even if moving in the same direction.

Brian, Say you and Bill


Say you and Bill Gates work the same number of hours a week. By Matt's assumptions you will value $100,000 far more than Gates will. If we force Gates to turn over $100,000 to you you'll benefit far more than he suffers regardless of what assumptions you want to make about how this will alter your (and his) desire for leisure vs. work. It's not credible to say this is in doubt under Matt's assumptions.

JTK, You're right. I was


You're right. I was thinking of how this would play out and his last assumption didn't register. He assumed there would be no effects on total utility. Which pretty much screws his proof because there will be no shifting of working hours.

That last assumption is semi-contradictory with the idea that people are going to be able to make tradeoffs between work and leasure. In order for redistribution not to effect production that means that everyone will have to keep working the same hours. Thus, there really is no opportunity within the system for people to work less or more should their incomes be changed by the redistribution.

If we disregard the last assumption so as to allow for Matt's proof to have meaning and do assume the total output might change then your proof that his fails still holds. However, in the iterative case of your method you'd want to prevent people from watching Bill Gates and trying to work the exact same hours as him.

That is, to prevent production from falling, you should probably say that we distribute evenly over everyones first hour of work, second hour of work, third hour. I think that makes it better by removing this perverse incentive. Gates may not take to the idea of all his income being given away and switch to more and more leasure dragging everyone with him. It also gives people an incentive to work longer if redistribution is done per hour.

If the fourth assumption was not there then you get into incentives to avoid the tax. If you assume a prexisting non-redistributive system then it is likely that Gates has a huge pile of cash he can live off of. In which case if he really hated the fact that I was leeching off him he could stop working. If the system is in place from the start there really is no way for Gates to become rich in the first place. He'll never have more resources than even the lowlyest janitor who happens to work the same number of hours. Without the capital accumulation his income would not shoot up.

Which leads me to bring up another thing. Bill Gates income is invested in capital goods to a much larger extent than mine and with better business acumen. He is getting utility out of making jobs for other people whereas I get more of my utility from consumer goods. I might spend the extra money on luxury consumer goods. That is, he may have a much higher savings rate than me. So his utility will result in an increased production of utility for other people. Give that $100,000 to me and I may squander it on drugs while he may generate two jobs.