Diminishing Marginal Utility is Not Universal

A while ago there was an article in Slate arguing (or, well, claiming to be arguing, and then sort of backing away from arguing in its strongest form) that one shouldn't work less to spend more time with one's family, even if one (rather sensibly) prefers spending time with one's family to working. The argument basically depends on the concept of diminishing marginal utility, namely the concept that, as you do more of a thing, the gains from the last little extra bit of it you do go down steadily. It's a basic principle of economics that one should do various things until their marginal utilities are equalized; if the marginal utilities of different things aren't equal, you should take away the last unit of the thing with the lower marginal utility and replace it with a unit of a thing with a higher marginal utility, and you'll get higher overall utility. The argument of the Slate column is that one should adjust one's work and leisure until the marginal utilities of the last hour worked and the last hour spent with your family are the same. I guess it's kind of tough to argue with that claim itself, though as I suggested above it's a far cry from "don't spend more time with your family." People might currently be over-consuming work, i.e. working until the marginal utility (all things considered) of the last hour worked is substantially lower than that of the last hour of leisure spent with their families, in which case they should work less and play more. Or it might be the reverse: arguments from marginal utility don't help us distinguish.

My point in this post is more to argue about the idea that one can always count on a declining marginal utility of all things. This ties in with a thought I had a while ago about why the marginal utility of money income is so clearly declining. As best I can tell, the primary or perhaps exclusive reason why this is true (and it's very well established that it is true, and it's a very good argument for redistributive policies) is the fundamental economics concept that individuals are rationally self-interested. The way this works is that, when the universe hands you a dollar of income, of course you use that dollar in the way that has the highest marginal utility possible. You'd be irrational not to. (And yeah, it's rarely plausible to conceive of this process in single-dollar increments; whatever.) But then, when the universe hands you your second dollar of income, you'll still use it in the highest-marginal-utility fashion, but you won't be able to get the same utility on that dollar as you got on the first one. Why? Because you've already done the thing that gets you the highest return for one of your income dollars. You can't do it again. The low-hanging fruit has been plucked, and can't be plucked again. This argument can be extended ad infinitum for a formal economic proof that, if individuals are rational in the usual way we assume them to be in conventional microeconomics, the marginal utility of income must be declining. No rational person could ever get a higher marginal utility out of their Nth dollar of income than they got out of any one of dollars 1, 2, 3, ... N-1, because they would've been irrational not to spend one of their earlier dollars on the thing they eventually spent their Nth dollar on.*

But does this argument always work? I think that it rather plainly does not. The key point in the case of income is our ability to go after the low-hanging fruit, but that won't apply in all cases. Some activities might have marginal utilities that are drawn from independent identical probability distributions, i.e. each time we do them we'll have the same odds of having a very high marginal utility, a medium marginal utility, a very low one, etc. Is that utterly implausible? I don't think so. Consider, for instance, my serious hobby of playing golf. Each time I go out on the course, I might play very well or I might play very badly. Now, it's not quite fair to say that the probabilities of each are IID for each round. There are factors that affect how I play on a given day, but over the long run they mostly even out and we can treat them as part of the probability distribution itself. So there's no particular reason why I must get more out of my tenth round of golf this summer than out of my sixteenth, or why I must get more out of the difference between a two-round week and a three-round week than out of the difference between a five-round week and a six-round week. I think a lot of things have this property, that we cannot in any particularly effective way target the highest-marginal-utility parts of an activity, and, if I'm right about that, we should not necessarily expect the law of diminishing marginal utility to apply to anywhere near every activity. In fact, in some cases we may get an increasing marginal utility. In the golf example, the more I play the better I get (ceteris paribus), so the more I'll get out of each additional round. In other contexts there might be threshold effects, where I achieve some particular utility bonus only upon reaching a certain level of consumption of an activity; in that case, marginal utility has a spike around the threshold.

None of this negates the basic point that one should balance marginal utilities, or the inference drawn from it that life typically demands a balance of activities. In part, though, this comes from the existence of budget constraints, which force us to trade our leisure, i.e. time we spend doing whatever we think will produce the greatest amount of pleasure, for our sustenance, i.e. the material necessities of life, by working for pay. It might be the case, for instance, that the marginal utility of work qua work is always quite low, much lower than the marginal utility of spending time with your family even out to infinity, but that the bundling of work with income means that the combined marginal utility of (work + income) will be higher than the marginal utility of leisure until we reach the point at which the marginal utility of income starts to decline. In any event, we should not necessarily expect the marginal utility of leisure spent with one's family to decline much at all, since it is not immediately obvious to me that there is a great deal of ability in this area to target the low-hanging fruit. The details, of course, probably vary from personal circumstance to personal circumstance, but one cannot simply assume that marginal utility diminishes because it does so for common economic goods, like income or apples.


*Actually, there may be significant threshold effects with income, as there most definitely are in the world of production, where we call them economies of scale. This gets back to the point about how one neither receives nor spends one's income in continuous dollar-sized portions. In particular on the spending side, having 99% of the ability to buy Good X or Service Y has 0 utility, but if you get that extra 1% you're good to go.