Suppose we have a group of similar people. One of them has to do some unpleasant or dangerous job, defending the border against the Blefuscudians, say. Has to be one person, they can’t rotate. So what is the welfare-maximizing way to allocate this bad job? Have a draft where someone is picked by lot and compelled to do it, or offer enough extra pay for it that someone volunteers? You’d think that standard micro would say the market solution is best. But — well, here’s Nick:
The volunteer army is fair ex post. The one who volunteers gets the same level of utility as the other nine. … The lottery is unfair ex post, because they all get the same consumption but one has a nastier job. That’s obvious. What is not obvious, until you think about it, is that … the lottery gives higher expected utility. That’s the result of Theodore Bergstrom’s minor classic “Soldiers of Fortune” paper.
The intuition is straightforward. Think about the problem from the Utilitarian perspective, of maximising the sum of the ten utilities. This requires equalising the marginal utility of consumption for all ten men. … The volunteer army gives the soldier higher consumption, and so lower marginal utility of consumption, so does not maximise total utility. ….
If we assume, as may be reasonable, that taking the job reduces the marginal utility of consumption, that strengthens the advantages of the lottery over the volunteer army. It also means they would actually prefer a lottery where the soldier has lower consumption than those who stays home. The loser pays the winners, as well as risking his life, in the most efficient lottery.
It’s a clever argument. You need to pay someone extra to do a crap job. (Never mind that those sorts of compensating differentials are a lot more common in theory than in the real world, where the crappiest jobs are also usually the worst paid. We’re thinking like economists here.) But each dollar of consumption contributes less to our happiness than the last one. So implementing the fair outcome leaves everyone with lower expected utility than just telling the draftee to suck it up.
Of course, this point has broader applications. I’d be shocked if some version of it hasn’t been deployed as part of an anti-Rawlsian case against social insurance. Nick uses it to talk about CEO pay. That’s the direction I want to go in, too.
We all know why Bill Gates and Warren Buffett and Carlos Slim Helu are so rich, right? It’s because they sit on top of a vast machine for transforming human lives into commodities market income is equal to marginal product, and Buffet and Gates and Slim and everybody named Walton are just so damn productive. We have to pay them what they’re worth or they won’t produce all this valuable stuff that no one else can. Right?
The problem is, even if the monstrously rich really were just as monstrously productive, that wouldn’t make them utility monsters. Even if you think that the distribution of income is determined by the distribution of ability, there’s no reason to think that people’s ability to produce and their ability to derive enjoyment from consumption coincide. Indeed, to the extent that being super productive means having less leisure, and means developing your capacity for engineering or order-giving rather than for plucking the hour and the day virtuously and well, they might well be distributed inversely. But even if Paul Allen really does get an ecstasy from taking one of his jets to his helicopter to his boat off the coast of Southern France that we plebes, with our puny so-called vacations [1], can’t even imagine, the declining marginal utility of consumption is still going to catch up with him eventually. Two private jets may be better than one, but surely they’re not twice as good.
And that, if you believe the marginal product story, is a problem. The most successful wealth-creators will eventually reach a point where they may be as productive as ever, but it’s no longer worth their while to keep working. Look at Bill Gates. Can you blame him for retiring? He couldn’t spend the money he’s got in ten lifetimes, he can’t even give it away. But if you believe his salary up til now has reflected his contribution to the social product, his retirement is a catastrophe for the rest of us. Atlas may not shrug, but he yawns.
Wealth blunts the effects of incentives. So we want the very productive to have lots of income, but very little wealth. They should want to work 12 hour days to earn more, but they shouldn’t be tempted to cut their hours back to spend what they already earned. It seems like an insoluble problem, closely related to Suresh’s superstar doctor problem, which liberalism has no good answer to. [2]
But that’s where we come to Harry Bergeron. It’s perfectly possible for superstar doctors to have both a very high income and very low wealth. All that’s required is that they start in a very deep hole.
If we really believed that the justification for income disparities is to maintain incentives for the productive, we’d adopt a version of the Bergeron plan. We’d have tests early in life to assess people’s innate abilities, and the better they scored, the bigger the bill we’d stick them with. If it’s important that “he who does not work, neither shall he eat,” [3] it’s most important for those who have the greatest capacity to work. Keep Bill Gates hungry, and he might have spent another 20 years extracting rents from network externalities creating value for Microsoft’s shareholders and customers.
There’s no shortage of people to tell you that it might seem unfair that Paul Allen has two private jets in a world where kids in Kinshasa eat only every two days, but that in the long run the tough love of proper incentives will make more pie for everyone. Many of those people would go on to say that the reason Paul Allen needs to be encouraged so strenuously is because of his innate cognitive abilities. But very few of those people, I think, would feel anything but moral outrage at the idea that if people with Allen’s cognitive capacities could be identified at an early age, they should be stuck with a very big bill and promised a visit from very big bailiffs if they ever missed a payment. And yet the logic is exactly the same.
Of course I’m not endorsing this idea; I don’t think the rich, by and large, have any special cognitive capacities so I’m happy just to expropriate them; we don’t have to work them until they drop. (People who do believe that income inequality is driven by marginal productivity don’t have such an easy out.)
But it’s funny, isn’t it: As a society we seem to be adopting something a bit like the Bergeron Solution. People who are very productive, at least as measured by their expected salaries, do begin their lives, or at least their careers, with a very big bill. Which ensures that they’ll be reliable creators of value for society, where value is measured, as always, in dollars. God forbid that someone who could be doctor or lawyer should decide to write novels or raise children or spend their days surfing. Of course one doesn’t want to buy into some naive functionalism, not to say conspiracy theory. I’m not saying that the increase in student debt happened in order that people who might otherwise have been tempted into projects of self-valorization would continue to devote their lives to the valorization of capital instead. But, well, I’m not not saying that.
[1] What, you think that “family” you’re always going on about could provide a hundredth the utility Paul Allen gets from his yacht?
[2] That post from Suresh is where I learned about utility monsters.
[3] I couldn’t be bothered to google it, but wasn’t it Newt’s line back in the day, before Michele Bachman picked it up?
