Alex Tabarrok and Matthew Yglesias comment on “the marginal utility of money income.” I’ll have to write something longer about this some day, but for now let me just reiterate my current understanding that there is no such thing as a utility function. Rather than people arguing over the shape of the utility function, I hope they can move forward to thinking more directly about what people will do with their money.
From my earlier blog entry:
Like Dave Krantz, I’m down on the decision-theoretic concept of “utility” because it doesn’t really exist.
The utility function doesn’t exist
You cannot, in general, measure utility directly, and attempts to derive it based on preferences (based on the Neumann-Morgenstern theory) won’t always work either because:
1. Actual preferences aren’t necessarily coherent, meaning that there is no utility function that can produce all these preferences.
2. Preferences themselves don’t in general exist until you ask people (or, to be even more rigorous, place them in a decision setting).
So, yeah, utility theory is cool, but I don’t see utility as something that’s Platonically “out there” in the sense that I can talk about Joe’s utility function for money, or whatever.
Call it value, not utility
The above is commonplace (although perhaps not as well known as it should be). But my point here is something different, a point about terminology. I would prefer to follow the lead of some decision analysis books and switch from talking about “utility” to talking about “value.” To the extent the utility function has any meaning, it’s about preferences, or how you value things. I don’t think it’s about utility, or how useful things are. (Yes, I understand the idea of utility in social choice theory, where you’re talking about what’s useful to society in general, but even there I’d say you’re really talking about what society values, or what you value for society.)
Just play around with the words for a minute. Instead of “my utility function for money” or “my utility for a washer and a dryer, compared to my utility for two washers or two dryers” (to take a standard example of a nonadditive utility function) or “my utility for a Picasso or for an SUV,” try out “my value function for money” or “the value I assign to a washer and a dryer, compared to the value I assign to two washers or two dryers” or “the value I assign to a Picasso or to an SUV.” This terminology sounds much better to me.
P.S. See Dave’s comments here.
Also see the comment thread.