Sunday, February 26, 2006

Could I Pass 8th Grade Math?

Yes, it turns out. As would Kieran Healy and PZ Myers. But I passed in my standard half-assed fashion getting 9/10 correct. I would, however, cry foul. The quiz claims I got #2 wrong: Is "-7" an integer, whole number, prime number or irrational? I said it was a whole number, but it is also obviously an integer. Given that whole number is a rather vague concept with many definitions that is used only in 8th grade algebra (Wikipedia says it is either all integers, non-negative integers, or positive integers), I'm going to claim victory (in actuality you talk only of integers and their subsets, not whole numbers, but I thought that maybe since whole numbers and integers were both possibilities they had non-standard definitions in this context).

At Crooked Timber there is a weak debate about whether or not "-7" is a prime number. People are getting all caught up trying to divide things by "1" and itself, but the relevant fact about primes is that they provide a unique factorization of any positive integer. If you had both positive and negative primes, then you would not have such a unique factorization (though prime means something slightly different in ring theory, 'cause the important idea is dividing, and not factoring).

Wednesday, February 22, 2006

Industrial Policy

In and among other activities, I spent the weekend reading about industrial policy and strategic trade policy (the other major activity was understanding Krugman's very excellent 1981 article, "Intraindustry Specialization and the Gains from Trade"). What's really quite funny about reading these articles from the mid-1980s is how of the moment they are. Interest in strategic trade policy arose from the academic end because there happened to be some nice advances in academic modelling that let you think about market imperfections and international trade. While all that is well and good, an academic fashion does not a policy argument create. And the wide-spread interest in the policy implications of that research came about only because this was the 1980s and we all feared the spectre of Japan, and wondered how we would ever keep up with their marvelous economy, fueled by the genius of the MITI bureaucrats. The issue bubbled along into the first Clinton Administration, with Paul Krugman (a major player in the academic end of it) saying the theory had little practical significance and getting pissed off at Laura Tyson et al. And then....the second half of the 1990s came, and productivity took off in the US and it was apparent that Japan was stagnant. You don't hear much mention of strategic trade policy or industrial policy anymore, now do you?

And for good reason, I'd say. At least in the academic formulations, strategic trade theory is one of those odd theoretical curiosities that arise all the time in international trade, but which you'd be insane to base policy around (has any country tried to stop growth in the good they export in an industry in which they are dominant on the grounds of immiserizing growth? Don't think so.). It turns out that strategic trade policy in its pure form relies upon knowing precisely what the pay-offs of a game are, and also knowing which game your oponent is playing. For you have to subsidize your domestic oligopolist by enough to make them gain either greater market share than, or force out, a foreign competitor. And the simple confusion between the game being a prisonner's dilemma, or it being an oligopolist thing with either Bertrand or Cournot competition can cause you to subsidize by too much, or worse, too little (for then you gain nothing at all for your money).

Because the implicit world model that advocates of strategic trade policy have going for them is a very queer one. It seems odd to suppose that any one industry is so so beneficial to the country that the country must must have it (for, at best, that is what strategic trade theory will get you: one industry here or there). Any given industry is probably pretty dispensable. What matters a hell of a lot more is the agglomeration of businesses hanging around. Because that is where new jobs and ideas and growth will come from. Not any one industry, but the possibility of creating more. And that comes from all sorts of marvelous other government policies that, to list, would make me sound remarkably conservative. To advocate an industrial policy is to claim that we need to help businesses. And yet to do so by advocating creating all kinds of additional distortions is just odd.

Friday, February 17, 2006

Hating on algebra

Richard Cohen sets off a vast string of comments by going on an anti-algebra screed. His basic premise, that algebra doesn't help you think straight, is defensible insofar as logical thinking is required in most any discipline and so you can learn it well by taking another discipline seriously. Yet to see logic stripped down is certainly clarifying. And algebra is not only about logic, but also about having a sense of quantities and how they fit together. This is basic to being an informed citizen and consumer of goods and information (not that I read the Post, but I'd never ever trust any commentary from Cohen on any economic topic ever again). People who claim that they've done fine in life without any mathematical knowledge are certainly not lying, but a bit of quantificational reasoning adds a richness to your understanding of the world that can only help.

Kevin Drum says that algebra is boring but it lets you do calculus, which is beautiful. I'd say that knowledge of algebra lets you do abstract algebra, which is possibly even more beautiful (though in a very different way). He also wonders if he'd trade knowledge of calculus for a working knowledge of French. Given that I can get by in French and have taken advantage of that to spend time in France and Senegal, and that I'm a math major and so sort of know calculus, I'd say that a) they aren't strictly comparable and that b) the kinds of experiences I've had based on French could be loosely approximated in English (say, England and the Gambia)*, but that knowledge of math has opened up whole areas of study -- economics, which I've taken advantage of, and, say, physics, which I haven't -- that wouldn't have been available without math knowledge. So if I had to choose just one, I'd take the math. Though I'm quite content to know both.

*Obviously the beauty of, say, Provence is unparalleled, but I could go to Provence and not speak French. The unique experience of speaking French is interacting with people with very different perspectives, something that you can come close to by finding English-speaking people from far away places (though by speaking english their perspective is closer to yours, but...).

Wednesday, February 15, 2006

Why do we enjoy things?

Seen (or a close approximation to) in a New York cafe (along with the actual Chelsea Clinton):
"We've raised prices 10%, we hope this won't affect your enjoyment of the cafe."
The straight neo-classical view is that this sentence is non-sensical: I'm eating the same cake so I'll derive the same amount of utility from it, whatever the price. A piece of cake is a piece of cake and its utility is constant. The only difference a change in price will make is that I'll go to the cafe less, or order less stuff while I'm there; my budget constraint has shifted inwards, but the utility from a fixed kind of cake remains constant.

Everyone I've given this reasoning to has violently disagreed: a $4 piece of cake identical in all other respects to a $4.40 piece of cake does not taste the same. Not only will you consume less cake over time, but your enjoyment of a given piece of cake will be decreased. People either take this as a general indictment of my attempts at economic cleverness, or else as a reason to embrace a "behavioralist" interpretation of the feeling. But what mechanism does the latter imply (for my cleverness is unimpeachable)?

One way to think about the experience of eating the cake is in a Stiglitz-like way: a consequence of the dependence of quality on prices (following the title of his 1987 JEL article). Price is a signal of quality and not scarcity. By paying more, you expect a higher quality piece of cake. Because your expectations are not met and it is a $4 quality piece of cake -- and not a $4.40 quality piece of cake -- you are disappointed. Your expecations are not met and so the utility from eating that cake is less if you have to pay more.

The other proposed mechanism is that somehow you feel cheated, ripped off, or taken advantage of. I cannot, however, articulate a coherent argument for that position (given that you aren't obliged to go to the coffee shop and purchase cake).

So I come to the quite banal point that our enjoyment of an event is quite dependent on our expectations of our enjoyment of that event (or, to put it in statistics talk, our prior matters).