Thursday, November 15, 2007

Moral Hazard Fundamentalism Redux

I posted somewhat infelicitously (or even more infelicitously than usual!) a while back on this topic . I have a neat example to make my point, now.

Imagine a society where everyone has the same opportunities for producing income. Working with high effort, they make $144 with probability 2/3 and $0 with probability 1/3. Working with low effort - slacking- they have equal probability of making $144 or $0. Utility is the square root of income, minus 1/2 if they work hard, or minus 0 if they slack off. People maximize expected utility. In one society - let's call it the ownership society - the state is a night watchman state and does no redistribution. Everyone works hard in this society, since this gives utility of 2/3(12) -1/2 = 6.5, while slacking gives utility of 1/2(12) = 6. Another society - let's call it Slackerland - practices complete egalitarianism, redistributing all income. Of course, with incentives dulled, everyone slacks off in Slackerland - the bums! If they are large enough in number, each will enjoy a certain income of $72 (compared to an average income of $96 in THE OWNERSHIP SOCIETY, the wonder of the world, where incentives are as sharp as tacks and moral hazard dare not appear). But oh my, the Slackers enjoy utility of of 8.48, the square root of 72 - more than the 6.5 utils the citizens of the ownership society enjoy*!

Moral hazard fundamentalists ignore the fact that moral hazard is often an inescapable byproduct of doing something good, namely spreading risk. The welfare state dulls incentives: therefore it is bad. Bad welfare state! Get down!

*I am assuming that private income insurance is unavailable - due to adverse selection (I'd need, obviously, to heterogenize my people and their opportunities and the numbers in my example would be the averages.)

2 comments:

kevin quinn said...

Whoops: the denizens of the ownership society get 7.5 - not 6.5 - utils. Still less, NB, than the slackers get.

YouNotSneaky! said...

This is true as far as the example goes. But I think that as soon as you allow folks a continuous choice of effort then this result can be "killed" - provided that it's optimal to supply a above-the-minimum level of effort in the "night watchmen only" society, then the "night watchmen only" society will wind up with a higher level of utility than the "gov provided social insurance" society.
Though it's probably sensitive to how exactly it's set up (what functional forms etc).