## Monthly Archive for September, 2011

### Happy Birthday

MathOverflow turns two years old this week — a milestone in the transformation of mathematical research into a massively collaborative endeavor. It’s happening on blogs, it’s happening on mailing lists, and it’s happening in a big way on MathOverlow, where mathematicians ask and answer the sorts of questions that might come up in the faculty lounge — if the faculty lounge were populated by hundreds of experts pooling their expertise.

If you’re interested in mathematics at the research level, MathOverflow is a place to learn something new and fascinating every single day. (If you are not doing mathematics at a research level, feel free to read but please don’t feel free to join the fray; questions at anything below about a second-year graduate level should be directed to MathStackExchange, another massively collaborative site aimed, roughly, at the college level — which reminds me that it’s not just mathematical research, but also mathematical education, that is being revolutionized before our eyes.)

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### D’oh!

Well, it took embarrassingly long for me to see this but there’s really a very simple resolution to the quandary I posted Monday. The key point is this:

In a flexible price world, anybody can supply money at a social cost of zero. In a fixed price world, only the government can.

To be more precise: I currently hold \$11. Suppose I agree to hold a twelfth. In a flexible-price world, I can get this dollar from the government (which prints it up at zero cost) or I can get it from my friend Jeeter, whereupon the price level adjusts and the rest of the world’s real balances (including Jeter’s) are restored to their original level. No social cost either way. In a fixed-price world, I can get this dollar from the government (which prints it up at zero cost) or I can get it from my friend Jeeter, whereupon prices don’t move and the rest of the world’s real balances are reduced. Zero social cost one way, positive social cost the other way.

### A Keynesian Quandary

Last week I blogged about my perplexity regarding the Keynesian notion of a liquidity trap.

In thinking about this harder, I’ve come to realize that a good part of my confusion has nothing to do with liquidity traps. It comes down to a very specific question about sticky-price models in general.

I expect this discussion will be interesting only to the most wonkish of my readers. The non-wonkish are invited to ask for clarifications, but please don’t jump in claiming to have “definitive” answers unless you’ve got a good grasp of the basics. I’d like to keep this discussion on track, and I’d like to learn something from it. Uninformed noise will be counterproductive.

For what it’s worth, I’ve discussed this offline, at considerable length, with several very good macroeconomists who eventually pronounced themselves as confused as I am. I really am hoping somebody with the right insight will pop up here and set us all straight.

### Neutrinos and Appomattox

Scientists at CERN have found apparent evidence that neutrinos can travel faster than light.

Suppose that tomorrow historians at Harvard find apparent evidence that the South won the American Civil War — not in some metaphorical “they accomplished their goals” sense, but in the literal sense that it was actually Grant who handed his sword to Lee at Appomatox and not the other way around.

Question: Of which conclusion would you be more skeptical?

Of course your answer might depend on exactly what this new “apparent evidence” consists of. So let me reword: As of this moment, which do you think is more likely — that neutrinos can travel faster than light, or that the South won the Civil War?

### Are These The Good Old Days?

I am not well versed in Keynesian business cycle theory. Therefore I have a very naive question for the Keynesian economists:

Why aren’t you thrilled with the current state of the economy?

Here’s why I ask: According to what I take to be an orthodox Keynesian view, we are now in a liquidity trap. (My question does not apply to Keynesians, new or old, who believe otherwise.) That means that people want to hold lots and lots of money instead of spending it. Cool! We can provide money at almost zero cost. So it should be easy to make people very happy. What’s the problem?

Of course, people are working less, but that makes perfectly good sense in a world where people prefer to consume less. Why spend all day on an assembly line churning out widgets that people prefer not to buy?

A quick and obvious answer is that the people who are choosing to accumulate money and the people who are out of work are not the same people. In other words, to put this in slightly more technical language, you can’t address this question in a so-called “representative agent model” — a model that abstracts from interpersonal differences.

Still: The theory, as I understand it, is that vast numbers of people are choosing to hold vast amounts of money. Since money can be produced costlessly, this ought to count as a very good thing — which should offset a lot of very bad things, no?

Whatever answer there is might vary from one Keynesian economist to another, so let me subdivide my question into two:

1. Why aren’t “old Keynesians” perfectly happy with the current state of the economy?
2. Why aren’t “new Keynesians” perfectly happy with the current state of the economy?

### A Tale Told By an Idiot

In sixth grade, I did not read My Side of the Mountain, though it was assigned for class. In eighth grade, I did not read Little Women and in ninth grade I did not read Great Expectations and The Good Earth. As I passed through high school, I worked my way through much of the western canon, not reading The Scarlet Letter, Bartleby the Scrivener, The Return of the Native, and dozens more. In eleventh grade, we were assigned two books by Steinbeck, two by Hemingway, two by Sinclair Lewis and two by William Faulkner. I did not read the Steinbeck, Hemingway or Lewis but for some long-forgotten reason I violated years of established tradition by tackling the Faulkner — specifically As I Lay Dying and The Sound and the Fury.

As I Lay Dying went down pretty easily, but I remember many nights struggling my way through The Sound and the Fury, Cliff notes at my side. It felt like scaling Everest, and the vistas at the top were worth the climb.

A couple of weeks ago, as part of my ongoing project to read great novels, I decided to revisit The Sound and the Fury, and I’m more than glad I did; I finally have an answer to give the next time I’m asked what one novel I’d bring to a desert island. But what I’m flabbergasted by is this: How did this book ever get assigned to high school students in the first place? I ask for at least two reasons:

### Survival of the Fittest

The Wall Street Journal reports that `daily deal’ sites like Groupon are dying fast, casualties of the expensive competition for new users. Groupon now spends about \$8 to lure one active user.

This looks like a good example of Darwinian competition yielding an inefficient outcome — as we should expect. (See Chapter 8 of my book The Armchair Economist for more on why Darwinian competition is nothing like market competition, and far more likely to yield bad outcomes.) Vast sums are being spent in an arms race with relatively little social value. Surely consumers benefit from all this competition, but it’s highly implausible that they benefit enough to justify such high expenditures. Even after the recent Great Winnowing, about 350 of these sites remain; surely consumers (none of whom have the time to visit 350 sites a day) would be almost equally well served by 50 sites, at about 1/7 the cost.

### Compassion Play

One thing I like about the study of economics is that it fosters compassion. When part of your job is to predict human behavior, you quickly learn the value of understanding other people’s problems. When the other part of your job is ferreting out the unseen global consequences of our choices, you’ve taken the first step toward caring about those consequences.

For example: Suppose a guy with no health insurance and no assets shows up at a hospital emergency room with an urgent life-threatening condition. Should you let him die? Ordinary compassion says no. The heightened compassion of the economist says, at the very least, maybe.

First, a policy of providing emergency health care to everyone is pretty much the same thing as a policy of providing emergency health insurance to everyone. It was specified here that this was a guy who didn’t want health insurance. So let’s recognize for starters that such a policy runs counter to — I am tempted to say runs roughshod over — the guy’s own revealed preference. It’s an odd sort of compassion that forces people to buy things they don’t want.

Now you might object that nobody’s forcing this guy to buy emergency health care; we’re trying to give him emergency health care. Not so fast. Here’s the first place where a little economic training goes to hone one’s sense of compassion: The emergency health insurance we’re foisting on this guy has a cost. We can spend that money on emergency rooms or we can spend it on a myriad of other things the guy might prefer. How is it compassionate to give him one thing when he prefers another?

This is particularly true if the guy happens to be very poor. Poor people have a lot of problems, and emergency health care is only one of them. They need better education, they need better transportation, and they need a little help buying groceries.

There is room for lots of debate and lots of disagreement about how much we as a society should be spending to help poor people. That’s not the issue here. The issue here is: Given that you’ve decided to spend an extra such-and-such many dollars a year helping poor people, why would you spend it in this particular way rather than one of the many other ways they could use it? For God’s sake, why not at least ask them if they’d rather have the cash?

### Cats, Dogs and Quantum Mechanics

The game of Cats and Dogs works like this: You and your teammate are placed in separate rooms and forbidden to communicate. You are each asked a randomly chosen question: Either “Do you like cats?” or “Do you like dogs?” (Each of your questions is determined by a separate fair coin flip.)

A little reflection should convince you that if you are allowed to meet with your partner and plot strategy before the game, then the best you can do is agree to always agree — say by both always answering “yes”. That way, you win 75% of the time, and there’s no way to do better. In particular, there’s nothing to be gained by randomizing your answers.

That, at least, is true, in a world governed by the laws of classical physics and probability theory. But in a world governed by the laws of quantum mechanics — which is to say, in the world we live in — you can in principle do better. Namely: You each carry with you one of a pair of entangled “quantum coins” (actually elementary particles, but I prefer to think of them as coins, since you’re going to use them as randomizing devices).

### Thursday Puzzle and More

Yesterday’s post on taxation generated a whole lot of comments that deserve responses; unfortunately I’m too swamped right now to respond. Worse yet, I’ll be out of town — and probably not blogging — for the next few days. Sometime next week, I’ll try to craft a new blogpost addressing much of what was said in those comments.

Meanwhile, here, courtesy of our frequent and invariably interesting commenter Mike H, is a puzzle to keep you busy while I’m gone:

### The Romney Plan

I have not read or even skimmed Mitt Romney’s 160-page economic plan; all I know is what I’ve seen in the headlines. So all of this is subject to revision. But:

### Moral Matters

The ever-insightful philosopher Peter Smith has a number of interesting things to say about abortion, but I found one of those things particularly striking — partly because I don’t recall ever having thought of it before, and partly because, in retrospect, I don’t see how I could have failed to think of it.

Namely: The argument is made that zygotes/embryoes/fetuses, even at a very early stage, have the full moral status of human beings. Yet if that were true, surely we’d want to divert a substantial portion of the medical research budget away from relatively minor scourges like, say, cancer, to the spontaneous abortions that take the lives of something like 30% of these full-fledged humans. In a typical year, there are about 8 million cancer deaths worldwide; the number of early-stage spontaneous abortions must be at least twice that.

In Smith’s words:

very few of us are worried by the fact that a very high proportion of conceptions quite spontaneously abort. We don’t campaign for medical research to reduce that rate (nor do opponents of abortion campaign for all women to take drugs to suppress natural early abortion). Compare: we do think it is a matter for moral concern that there are high levels of infant mortality in some countries, and campaign and give money to help reduce that rate.

Smith is struck by the fact that this attitude is very widespread; I am more struck by the fact that it seems to be very widespread even among those who characterize themselves as pro-life.

### Recap

Some commenters still seem confused about the locus of disagreement in this week’s back-and-forth with Paul Krugman. I post today not to beat a dead horse, but to clarify the issues for those who are interested in understanding them. Please keep any discussion both civil and on-topic. I’ve numbered the points below for easy reference.

### Krugman Followup

What I like about people in academics is that when we disagree, we actually care about figuring out who’s right — and therefore we have a tendency to reach consensus, though it can take a while.

Anybody who blogs often enough (very much not excluding yours truly) is occasionally going to post something that, at least as written if not as intended, is objectively plain flat out wrong. Paul Krugman did that a couple of days ago, I responded, he’s responded to my response, and at least 4/5 of our disagreement is now resolved. That’s exactly as it should be.

### Thursday Puzzle

Our frequent and reliably insightful commenter Jonathan Kariv sends along this neat puzzle:

Your enemy chooses 10 points on an infinite tabletop and gives you 10 coins of the same size (let’s say U.S. quarters). Can you always place the coins on the tabletop in such a way that all 10 points are covered, but no two coins overlap?