Comments on: The Big Answers, Part II

By: The Top Ten at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics

Thu, 31 Dec 2009 16:20:52 +0000

[...] In sixth and third places, we have the two posts where I presented the questions from the honors exam I administered at Oberlin College: The Honors Class, Part I and The Honors Class, Part II. The notable followups, of course, were the posts that revealed the answers: The Big Answers, Part I and The Big Answers, Part II. [...]

By: Steve Landsburg

Steve Landsburg — Sun, 27 Dec 2009 17:03:30 +0000

Ryan: All of your points are excellent, and I mention them all in the classroom when I teach this stuff (except for the observed heterogeneity of discount rates, which I’ll make a point of adding to the lecture next time). Please do continue to take up time and space around here.

By: ryan yin

ryan yin — Sun, 27 Dec 2009 16:31:48 +0000

Dr. Landsburg,

That’s a fair argument, but it seems to me rather different (in that it is more reasonable!) than the standard approach in the optimal taxation literature. For instance, Saez (2001) specifically defines preferences over consumption and income, a bad, so that preferences are necessarily heterogenous (given heterogeneity in how easy it is to earn income).

It also seems to me that there really is a fair bit of heterogeneity of preferences, especially when we add a time element (discount rates vary quite a bit, I think), so I don’t see how to apply the “behind the veil” approach in actual taxation. It also seems to me that the veil motivates taxation, it must be that people know where and when they are born even behind the veil or the primary issue would be redistribution across borders and savings policy. But I may be taking up more than my fair share of time and space here.

By: Steve Landsburg

Steve Landsburg — Sat, 26 Dec 2009 17:28:43 +0000

Ryan: If they have different utility functions, then I can’t see any justification for adding their utilities. First, as you point out, it would be meaningless to do this, since the functions are only defined up to an affine transformation. Second, even if it were meaningful, I can’t see what the justification would be.

What I tell my students is this: a) This whole procedure is predicated on the belief that, at least in the initial “behind the veil” state, everyone shares the same utility function, b) it is empirically the case that, at least to a very rough approximation, we do pretty much all seem to have pretty similar utility functions in the sense that we all seem to have coefficients of risk aversion that lie within a reasonably narrow range, and c) one might be able to use b) to get past the obstacle of a), but there are a lot of other obstacles, both practical and philosophical, along the way.

By: ryan yin

ryan yin — Sat, 26 Dec 2009 15:10:06 +0000

Dr. Landsburg,
At first I wasn’t imagining any particular experiment — just trying to maximize the sum of two utility functions. But I would say that I’m imagining her being uncertain not only about which productivity she’s born with, but which utility function she’s born with as well. (If we don’t allow for this type of uncertainty, how do we allow for the case where they actually have different preferences as well — e.g., different labor vs. consumption tradeoffs or a different Euler equation?)

By: Steve Landsburg

Steve Landsburg — Fri, 25 Dec 2009 05:18:44 +0000

Bennett: You *can* say that. The question asked for arguments in both directions; here I gave an example of one important argument I’d hoped to see in any good answer. There are lots of other arguments that could appear in a good answer also.

By: Bennett Haselton

Bennett Haselton — Fri, 25 Dec 2009 04:47:07 +0000

The given answer to Q10 is clever but it seems like it’s countered by an identical argument in the other direction.

You’re saying that when we find out the siblings are twins, their upbringings are now more similar than we previously thought, and since they still made opposite decisions about college, their genes must be more different than we had previously thought.

And therefore, (a) “Their genes are more different than we had thought, so in that respect the siblings are less similar than we had previously believed, so our results are less reliable.”

But why couldn’t you say equally in the other direction: (b) “Their upbringings are more similar than we had thought, so in that respect the siblings are more similar than we had previously believed, therefore our results are even more reliable.”

There could be a purely logical reason why (a) outweighs (b), but I’m not seeing it yet.

By: Steve Landsburg

Steve Landsburg — Thu, 24 Dec 2009 22:34:53 +0000

Ryan: I am not sure what experiment you’re envisioning. I am imagining that Eve knows her preferences but does not know whether she will have Eve’s consumption/labor or Adam’s consumption/labor. Likewise for Adam. We can apply any affine transformation you want to Eve’s utility function, and it won’t change her preferred tax rate. Likewise for Adam.

By: ryan yin

ryan yin — Thu, 24 Dec 2009 22:24:40 +0000

Dr. Landsburg,
You’re right as long as I apply the same transformation to both utility functions (which is to say, as long as I assume they have the same utility function). But there’s no reason I have to do that; since each of those transformations describes the same preferences, I could use one utility function to describe her preferences and another to describe his. This would in fact change which distribution (first best or second best) maximizes the sum of utilities.

By: Steve Landsburg

Steve Landsburg — Thu, 24 Dec 2009 03:27:24 +0000

Roger Schlafly: I see your point, though I think there are a lot of ways you could argue this. One twin went to college and the other didn’t; therefore we know they’re very different; nevertheless they’re earning the same wage. So maybe that means education made up for the big difference.