The countervailing argument is that when you destroy an ethnic group, you also destroy a culture. Of course, that’s of little additional consequence if the primary aficionados of that culture are all among the dead. You could counter-argue (correctly) that we all benefit from being able to dabble in a wide variety of cultures, tasting their food, listening to their music, hearing their stories, assimilating their insights. And that might very well be a significant argument in a world where a series of genocides had reduced the world’s stock of cultural diversity far below its present level. But as the world stands today, I suspect that cultures are worth very little at the margin (that is, we could stand to lose any one culture without missing it very much). There’s only so much you can assimilate in a lifetime, and to a considerable extent, time spent in contact with one culture is time not spent in contact with another.

So I’m not sure why the adjective “genocidal” is so often taken to be pejorative. I’m also not sure there’s any point to condemning some mass murderers more fervently than others, but if we’re going to play that game then I’m inclined to count genocidal intent as a mitigating circumstance.

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Banks, by their nature, are susceptible to bank runs. Depositors panic and demand their money back, the bank doesn’t have enough cash on hand to meet all the demands, this generates even greater panic and even more demands, and pretty soon the bank is selling off assets at fire sale prices in a desperate attempt to placate the depositors. Back before Federal deposit insurance, this used to happen from time to time. According to Yale’s Professor Gary Gorton, author of Slapped By the Invisible Hand: The Panic of 2007, it happened again recently. The great crisis of the past few years was just another bank run, pure and simple.

The only difference is that this time the banks were non-traditional financial firms like Bear Stearns (as opposed to, say, the Bailey Building and Loan Association) and the depositors were large financial institutions like Fidelity (as opposed to the good citizens of Bedford Falls). Here (with a hat tip to Gorton) is how that non-traditional banking system worked: Suppose Fidelity is sitting on, oh, say, half a billion dollars in cash that it would like to deposit in an interest-bearing account someplace. So they open an account at Bear Stearns. Unfortunately half-billion dollar accounts at Bear Stearns (unlike your checking account at the Bank of America) are uninsured, which makes Fidelity a little nervous about turning over so much money in exchange for nothing more than a deposit slip. So Bear Stearns, along with the deposit slip, hands over a half billion dollars worth of collateral, in the form of bonds. Fidelity takes physical possession of these bonds, so that it’s covered if Bear Stearns goes bankrupt or absconds with the money. (Bankruptcy law allows Fidelity to keep the bonds if it’s holding them when Bear Stearns goes under.) When it’s ready to make a withdrawal, Fidelity returns the bonds and gets its cash back. This exchange of collateral is what’s called the repo market.

Now suppose that Fidelity starts to worry about the value of the collateral it’s holding—say because it’s not sure how many of those bonds are backed by hinky subprime mortgages. Sure, the bonds are worth half a billion now, but they might be worth only 400 million by tomorrow morning. They say to Bear Stearns: “Umm. We’re a little worried here. If you want to keep our deposit, we’ll be needing more collateral please”. But if several depositors say this at once, there’s not enough collateral to go around—so depositors start making withdrawals (or, equivalently, depositing less money per unit of collateral). And if you’ve ever seen It’s a Wonderful Life, you know what happens next.

Some of Professor Gorton’s conclusions:

• Bank runs are not driven by irrationality; they are perfectly rational responses to new information about banks’ solvency. Of course “rational” is not at all the same thing as “desirable”.
• It is wrong to say that the crisis was caused solely by the collapse of the subprime mortgage market. That market, by itself, is too small to cause a crisis of this magnitude. Besides, the timing is wrong. Subprime mortgages started going under in January, 2007, but the panic didn’t get underway until the following August. Gorton likens the subprime mortgage market to a small E. coli infection somewhere in the nation’s beef supply. The infection itself is only a small problem, but the ensuing panic can cause the entire beef industry to collapse.
• Where there are banks, there will be bank runs. Therefore this problem is structural; it’s not a one-time thing. On the other hand, imperfect as they are, banks are pretty much indispensable.

To this I would add the observation that fire sales are not unambiguously bad things; they are bad for the sellers but very good for the buyers. So toting up the losses to Bear Stearns and its ilk is a very poor way to measure the cost of this crisis. The real cost has been that with the collapse of the repo market, traditional banks had no place to sell off their loans, and therefore became quite reluctant to initiate new loans, making it difficult for businesses to maintain their operations. Without denying the reality of that cost, it’s worth remembering that it’s a relatively short-run phenomenon.

There is much more here and in Gorton’s book.

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Like everyone else I know, I am of course a longtime fan of the webcomic XKCD. But somehow it took me until last week to become aware of the frequently brilliant competitor Luke Surl, of which the above is a delectable example. What else out there am I missing?

Hat tip to Harry Brighouse of Crooked Timber.

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(To follow this, you’ll need to know a little bit about complex numbers, say at the level of Steven Strogatz’s recent blog post at the New York Times. Several of Professor Strogatz’s commenters lamented his omission of the Euler formula. This post is my attempt to fill that gap. You can also view this as my first annual pi day post, slightly belated because 3/14 was a Sunday this year.)

So. With imaginary interest, you deposit a dollar on January 1, and by the end of the year, it’s grown to 1+i dollars, represented by the “Dec. 31″ point on the following graph. It’s as if you’d started at the point 1 and traveled upward along the red line to your end-of-year destination.

If these accounts prove popular, competing banks will be forced to offer an even better deal— compound imaginary interest. Instead of waiting all year to collect your imaginary dollar, you collect half an imaginary dollar halfway through the year and then continue to earn interest on your new principal of (1+i/2) for the second six months.

You can see this in the next graph. You get your first interest payment on June 30, bringing you from the point 1 to the point (1+i/2) at the upper vertex of the shaded triangle. For the second six months, we have to treat that (1+i/2) the same way we treated your initial principal of 1. That means constructing a triangle similar to the shaded one, but using the blue line as the new base. The upper vertex of that triangle shows us how much you’ve got on December 31.

And of course it doesn’t stop there. Before long, another bank offers to compound your interest not twice a year, but four times. How much do you have at the end of the year? Four triangles reveal the answer:

Now take note of this: As you travel along the red lines, from your initial principal of 1 to your new principal balances on March 31, June 30, September 30 and December 31, it looks an awful lot like you’re traveling around a circle. When a new bank offers to compound your interest twelve times a year instead of four, there are going to be twelve much skinnier triangles and the red path around them is going to look even more like a circle.

So when a very competitive bank comes along to offer you imaginary interest compounded continuously, they’ll determine your end-of-year balance by going to the limit and drawing an honest-to-God circle, starting at the point 1, and traveling counter-clockwise a distance 1, like so:

(The December 31 endpoint happens to be at about .54 + .84 i . )

Of course, you might want to leave your money in this account for more than a year. As your interest continues to compound, you move farther around the circle. At the end of two years, you’ve traveled a distance 2, and at the end of three years, you’ve traveled a distance 3, like so:

And if you choose to leave your money in the account for, oh, say, about 3.14159 years, then you will travel a distance 3.14159 around the circle, landing at the point -1. (Remember that π, which is just about 3.14159, is the length of the top half of a circle of radius 1.)

Not a bad outcome from the bank’s point of view! You lend them a dollar for a year, and after 3.14159 years, you owe them a dollar! (Of course after another 3.14159 years, you’ll have traveled all the way around the bottom half of the circle and have your original dollar back again.)

Alright, that’s one way to calculate your bank balance after π years. But a faster way is to remember the formula for compound interest: If you deposit a dollar at an interest rate of r for time t, then your ultimate balance is e^{r t}. In this case, the interest rate is the imaginary number i and you’ve invested for time π, so your ultimate balance should be e^iπ.

The bottom line: Our first calculation says your balance is -1. Our second calcuation says your balance is e^iπ. But surely your balance is equal to your balance! Therefore:

Et voila.

Hat tip: The idea of using imaginary interest payments to explain Euler’s formula is inspired by David Mumford’s article on calculus reform.

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Unless Krugman or someone like him offers an irresistible target tomorrow, I’ll see you next on Monday. Thanks for visiting.

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You can watch the video interviews at BigThink, where, as always, I wish they would post transcripts; reading is faster than viewing and skimming is faster still. But if you’ve got the patience, some of these are fun.

What’s your (realistic or fanciful) scenario for the end of days?

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Suppose that year after year, you spend more than you earn. You are worried that you’ve become fiscally irresponsible. Which of the following is not a path back to fiscal sanity for your household?

1. Spend less.
2. Earn more.
3. Stop at the ATM more often so you’ll have more cash in your pocket.

Do we all understand why the answer is C? Good. Now let’s try another one.

Suppose that year after year, your government spends more than it collects in taxes. You are worried that it’s become fiscally irresponsible. Which of the following is not a path back to fiscal sanity for the government?

1. Spend less.
2. Collect more taxes.

The answer is not A. Spending less—at least spending less on things you don’t need—can certainly be a path back to fiscal sanity for a government just as it is for a household.

What about B—raising taxes? There seems to be this idea floating around that raising taxes is sort of like earning more income, and can therefore also be a path back to fiscal sanity. But that’s wrong. Raising taxes is not at all like earning more income; instead it’s very like visiting the ATM.

Here’s why: The government’s chief asset—in fact, pretty much its only asset—is its ability to tax people, now and in the future. The taxpayers are the government’s ATM. Make a withdrawal today, and there’s less available tomorrow.

Now the ability to tax is a pretty huge asset and the government has not (yet!) come close to depleting it. In that sense, there’s a lot of money in the bank. But no matter how much you’ve got in the bank, a policy of ever-increasing withdrawals is nothing at all like a decision to earn more income. (Besides, a lot of us have other uses in mind for that money.) It’s important to get the analogy right. And it’s clear from the op-ed pages that not everybody gets this.

There is this notion abroad that an extra billion in federal spending can be converted from “irresponsible” to “responsible” as long as it’s accompanied by an extra billion in tax hikes. That’s like saying a $500 haircut can be converted from “irresponsible” to “responsible” as long as you withdraw the $500 from your bank account.

So when the president appoints a commission on fiscal responsibility, as he did a couple of weeks ago, I find myself hoping that its members understand this simple point—and worrying that they don’t. Fiscal responsbility means spending less. Taxes have almost nothing to do with it.

Of course the problem with spending cuts is that there’s always someone opposed to them. The solution is to package a whole lot of cuts together so almost everyone has something to gain. Here, then, is an idea to get the commission started: Currently the Department of Agriculture steals from workers and business owners to give to farmers, the Department of Labor steals from farmers and business owners to give to workers, and the Department of Commerce steals from workers and farmers to give to business owners—with a lot of wealth falling through the cracks along the way. Eliminate all three departments and every American will lose one friend and two enemies. It’s the responsible thing to do.

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What interests me in all this is the promiscuous use of the adjectives “anti-gay” and “hypocritical”. The senator seems to be charged with three counts of anti-gayness, with hypocrisy as an aggravating circumstance. First, he opposes anti-discrimination laws. Second, he opposes gay marriage. Third, he opposes an official day of recognition for gay rights activist Harvey Milk.

Now let’s take these one at a time.

• I share the senator’s opposition to anti-discrimination laws. If that makes me anti-gay, you can also label me anti-black, anti-Jewish, anti-Republican and anti-economist, because I support your right to discriminate against those groups as well. I support your rights not to date economists, not to drink with economists, and not to hire economists. I do not believe that makes me anti-economist and I do not believe it makes me a hypocrite.

  Now you might or might not think that the analogy between gays and economists, or the analogy between dating and hiring, is seriously flawed. We’ve had that discussion in comments elsewhere on this blog, I don’t propose to repeat it here. Here I’m asking you only to accept that some people (me, for example) find these analogies compelling and therefore share the outed senator’s position on discrimination law without bearing any animus toward gays.

  Moreover, as far as I am aware, there is no known correlation between sexual orientation and susceptibility to argument by analogy. Therefore, a gay man who shares my position ought not be suspected of hypocrisy.

• Next, we have the issue of gay marriage. I am for gay marriage. I am for polyamorous marriage. I am for marriage between three gay men, two eunuchs and a bull dyke. I am for recognition and enforcement of pretty much any lifestyle contract that consenting adults want to enter into. But I also have dear friends who oppose gay marriage, and I am quite sure that their opposition is not motivated by animus toward gays.

  I have one friend, for example, who has proved himself over many years to be one of the world’s great celebrators of diversity, but who opposes gay marriage because he fears that gays, moreso than straights, will game the system by marrying or unmarrying as needed to secure tax advantages. Straights might do the same, but they will do it less because they’re more likely to be locked into marriages through childbearing. I happen to think this argument is completely nuts. (For the record, I think my friend is absolutely right that gays will game the system somewhat more than straights will, and that that’s a bad thing. I just think he’s absolutely nuts to put quite so much weight on it.) But everyone I know believes at least ten things that I think are completely nuts. I do not jump to the conclusion that they believe those things because they are hostile or angry or anti-this-group-or-that. I think they believe these things because they are mistaken. (Or even possibly because they’re right and I’m mistaken.) And I don’t see any reason why gay people can’t be as easily mistaken as straight people. So I don’t see any reason why gay people can’t, like my friend, consistently, honestly, and non-hypocritically, oppose gay marriage, even while lamenting the hardships a marriage ban imposes on themselves, their partners and their friends.

  Or take Megan McArdle (a/k/a Jane Galt), who I do not know personally, but who has moved me with a clearly heartfelt account of her reasons for equivocating on the marriage issue. I don’t share her equivocation, but regarding her motivations, I think it would be insanely uncharitable to take her at anything other than her word.

• As for the third issue, the Harvey Milk Appreciation Day, this is just, of course, a bit of silliness. There are all sorts of reasons someone might think the calendar is already too cluttered with Appreciation Days. I would not even vote for an Isaac Newton appreciation day, and whatever you might think of Harvey Milk, he surely did less for the world than Isaac Newton. Someone else might disagree. And again, I don’t see any reason why your sexual orientation should influence your opinion on this matter.

So I think it would be good if everyone lightened up on the accusations and on the schadenfreude. The twin tragedies here are that a man’s life has been upended and that we live in the sort of world where this kind of thing can upend your life.

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I can’t figure out her point. I am all for identifying problems and brainstorming about radical solutions, but I have no idea what problem Lowrey thinks she’s addressing.

The primary problem with representative democracy is that our representatives are captured by special interests. My senators plot to steal from you and your senators plot to steal from me, with a lot of collateral damage along the way. (And yes, you and your neighbors do constitute a special interest, as do I and mine.) The problem is exacerbated by the fact that my neighbors and I have a lot of interests in common, making it easier to steal on all our behalves at the same time. The solution is to make each senator’s constituency more diverse, not, as Lowrey proposes, less.

In my book More Sex is Safer Sex, I offered a few ideas along these lines, culled from the past few years of lunch table chat:

• Divide senatorial constituencies according to the alphabet, so that instead of a senator from Alaska and a senator from Wisconsin, we’ll have a senator for everyone whose last name begins with AA through AE. The point being that it’s easy to think up earmarks and pork barrel projects that will benefit the citizens of Alaska at everyone else’s expense, but not so easy to think up pork barrel projects that will benefit everyone whose last name happens to begin with Q.
• Give each voter two votes to cast in every senatorial election. You get one vote to cast in your own state and one to cast in the state of your choice.

  Again, this forces senators to answer to broader and more diverse constituencies, diluting the power of localized special interests.

• This one’s not in the book but should have been: Give each senator a personal budget so that once he;s voted for $X billion worth of spending, he’s not allowed to vote for any more spending until he gets re-elected. This pits his various sub-constituencies against each other, so that the New York Senator who lobbies for subsidies to New York City is sure to get a negative earful from upstate.

Am I serious? Of course I’m serious. I’m serious about the importance of identifying deep problems, calling attention to them, and thinking outside the box. That’s why I was thrilled recently to run Jamie Whyte’s guest post, proposing a novel and thought-provoking solution to another problem with democracy, namely: Voters with little impact on the outcome have little incentive to become well informed.

What are your best proposals for political reform—and what problem do they address?

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The Obama administration has its knickers all in a twist over rising health insurance premiums. As you wade through the rhetoric, here are a few things to keep in mind:

1. Greed does not cause rate hikes. I’m not sure why some premiums have shot up lately, but I’m quite sure that “greed” is not the answer. That’s because I’m quite sure that the insurance companies are no greedier today than they were a year ago. To explain a change in prices, you’ve got to point to something that’s changed. Greed is pretty much a constant.

   So what relevant factor has recently changed? The only plausible candidates are costs, including expected future costs due to health care “reform”. What costs, specifically? I wish I knew. Maybe some commenter does.

2. Greed, by itself, does not cause high prices either. In competitive markets, greed causes low prices as greedy companies struggle to steal each others’ customers.
3. Monopoly causes high prices. Monopoly power, like greed, can’t explain recent rate hikes because monopoly power in this market has not recently changed. But monopoly power, unlike greed, can explain permanently high prices. And there is considerable monopoly power in this market, partly because you’re not allowed to shop for insurance out of state and largely because your employer does your shopping for you. The Administration has shown almost no stomach for combatting this problem.

   Instead, their position is something very like this: “We can’t help ourselves from misusing our power to prop up this terrible monopoly, so give us the power to control it.” Kind of like the alcoholic who needs you to buy him a drink to steady his nerves before he drives home tonight. Don’t let him snow you.

4. Profits do not raise costs. The administration wants you to believe that we could lower the cost of insurance by limiting the profits of insurers. That’s bad economics, bad accounting and bad arithmetic.

   Imagine a hypothetical insurance company that forgoes profits in order to keep down premiums. That insurance company, just like any other, needs capital to operate—but it can’t attract investors, because it has nothing to attract them with. So where does the capital come from? It’s got to come from taxpayers—taxpayers who fork over money that could otherwise be earning income in retirement accounts. And that forgone income is a fullfledged cost.

   So yes, a publicly run insurance company could choose to earn $12 billion less in profit and return that saving to us in lower premiums—but only by taxing us enough and reducing our savings enough so we collectively earn $12 billion less in interest, dividends and capital gains.

   By analogy, that same public insurance company could hypothetically require 10,000 clerical workers to put in 40 hours a week at zero pay. Would that reduce the cost of insurance? Surely not. It would reduce the premiums, but not the cost. Instead, it shifts the cost to those 10,000 workers, who, I’m sure, would tell you quite forcefully that the cost to them is considerable.

   Capital and labor are costly. Those costs are quite literally unavoidable. They can be shifted around but they can’t be eliminated. Lowering wages does not lower costs; it just shifts them on to the backs of the conscripted workers. Lowering profits does not lower costs; it just shifts them on to the backs of the conscripted investors, for which read “taxpayers”.

   [These arguments apply to ordinary profits. If you think that profits in the insurance industry are excessive, then we're back to the issue of monopoly power, which is the only plausible source of consistently excessive profits. Keep in mind too that a single years' profits are the wrong way to measure excess; all industries have good years and bad years.]

5. Choices must be made. Adminstration spokesperson Robert Gibbs said the other day that you shouldn’t have to choose between having more health care and having more housing. Note well that when he says that’s a choice you shouldn’t have to make, what he means is that it’s a choice you shouldn’t get to make. He wants to make it for you.

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