Author Archive for Steve Landsburg

In the Matter of Todd Akin

Published
by
Steve Landsburg
on August 21, 2012
in Current Events and Politics
. 191 Comments

So there I was, putting together a long post on the fabric of the Universe, when Todd Akin came along and seemed to demand at least some brief commentary. A few remarks on that, and I’ll get back to the rest of the Universe in a day or two:

1) The exact quote, in response to a question about pregnancies resulting from rape, is: ““It seems to me, from what I understand from doctors, that’s really rare. If it’s a legitimate rape, the female body has ways to try to shut that whole thing down. But let’s assume that maybe that didn’t work or something: I think there should be some punishment, but the punishment ought to be of the rapist, and not attacking the child.”

2) It seems to me, from what I understand from news sources, that the female body does not in fact have ways of recognizing rape and preventing conception. I have absolutely no expertise in this matter; therefore my understanding might be wrong. Nevertheless, I’m happy to pass that understanding along.

3) It also seems to me that the phrase “from what I understand from doctors” says, in effect, “I am not an expert, so this might be wrong, but here’s what I’ve heard”. It is not unreasonable for people to make statements like this. In fact, I did it myself, just one paragraph back.

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Aaagh!

Published
by
Steve Landsburg
on August 15, 2012
in Back of the Envelope, Economics, Finance and Personal
. 76 Comments

I am buying a house, and am therefore faced with the choice between a 15 year mortgage at 2.875% and a 30 year mortgage at 3.49% (as of a couple of days ago; those rates have probably changed a little by now).

The main advantage of the 15 year mortgage is that it comes with a lower interest rate and, because I’m making larger monthly payments, it keeps my money out of the stock market, which is good if the market tanks. The main advantage of the 30 year mortgage is that it allows me to keep more money in the stock market for a much longer time, which is good if the market does well.

How should I weigh those factors? Economics tells me that I will solve this problem by forecasting the return on equities over each of the next 30 years, and computing, on the basis of my forecast, which mortgage will leave me richer in the long run. No, that’s not quite right. Actually, economics tells me that I’ll make many forecasts, assign each one a probability, and thereby compute two probability distributions for my future net worth and then choose the distribution I prefer.

Now let’s get serious.

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Enough Already!

Published
by
Steve Landsburg
on August 14, 2012
in Economics, Empirical Puzzles and Musings
. 70 Comments

Today’s email brings a gripe from Mark Skousen, the irrepressible impresario behind FreedomFest, who could have avoided this problem by being born in the old Soviet Union:

I was in the large Stop & Shop grocery store here in New York to buy some items, including a new tube of toothpaste. I like Colgate, but I can never seem to get the same toothpaste product.

Now I know why. Guess how many different types and sizes of toothpaste Colgate sells?

Ready?

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World’s Best Dad

Published
by
Steve Landsburg
on August 9, 2012
in Cool Stuff and Miscellaneous
. 8 Comments

Proof positive that I am not the world’s best dad:

Just to be clear, that is not me in the video; it is somebody who is clearly a much better father than I ever was! Original YouTube version is here.

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The Greatest Story Ever Told

Published
by
Steve Landsburg
on August 7, 2012
in Economics, Events, History and Self-Promotion
. 12 Comments

I gave a series of four talks last week at Cato University; only the first of them was broadcast by C-SPAN, and you can watch it here. (The title was “The Greatest Story Ever Told”, meaning the story of economic growth.)

Much of this material will look familiar to those who have watched other videos recently posted in this space, but I think it comes together a little better in this one. The remaining lectures contained more in the way of new material, and I’m hoping to be able to post at least some video excerpts in the near future.

There were a lot of fabulous talks at this event by such luminaries as Tom Palmer (here and here) and the extraordinary Robert McDonald, who held the audience in thrall with his gripping three-part series on the history of the American revolution (not, unfortunately, online, even in part).

If you missed it, there’s always next year!

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Paging Diogenes

Published
by
Steve Landsburg
on August 6, 2012
in Current Events, Economics, Technology and Truthseeking
. 43 Comments

Chapter 8 of The Big Questions is called “Diogenes’s Nightmare” and argues that: 1) In a world of honest truthseekers, there would be no disagreements about matters of fact; 2) In the world we inhabit, disagreements about matters of fact are ubiquitious; therefore 3) in the world we inhabit, there must be precious few honest truthseekers.

If you’re looking to ferret out one of those rare creatures, your best candidate might be a man who argues with eloquence and passion against subsidies for the industry where he makes his living. Meet David Bergeron.

David is the founder and president of Sundanzer, which supplies solar powered refrigerators worldwide, based on technology developed by David under contract to NASA. He also really really really understands why subsidizing solar technology is a terrible idea. And when I met him last week, he impressed me so much that I invited him to make a rare guest post here at The Big Questions. So without further ado:

Solar Subsidies: Misdirecting Industry and Consumers

A Guest Post

by

David Bergeron


In a recent Economist on-line debate, the affirmative motion “This house believes that subsidizing renewable energy is a good way to wean the world off fossil fuels” was surprisingly defeated.

In his closing remarks, the moderator softened his strident opposition to the negative case, even admitting that “subsidizing renewable energy, is wasteful and perhaps inadequate to address climate-change concerns.”

Beyond the Climate Debate

The debate, indeed, reopened the question whether anthropogenic greenhouse-gas forcing was a serious planetary environmental concern. But such focus short-changed what I think is the more important question for the Economist. Not only are the renewable-energy subsidies (such as for solar) wasteful and potentially insufficient, they are outright diabolical if indeed there is a looming environmental crisis.

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The Numbers Racket

Published
by
Steve Landsburg
on July 30, 2012
in Uncategorized
. 52 Comments

If you’re the sort of person who reads economics blogs, you’ve probably heard that the median US worker has enjoyed hardly any income gain over the past few decades. Here are the numbers behind the noise (all corrected for inflation):

A mere 3% increase over 25 years does indeed look pretty grim. And note that the year 2005 is pre-crash, so what we’re seeing is not an artifact of the recession.

Now let’s look a little deeper and ask which demographic groups account for all this stagnation. White men? Nope, their median income is up 15%. Nonwhite men? Up 16%. White women? Up 75%. Non-white women? Up 62%. That’s everybody:

What gives? How can the median income shoot up in every demographic sector while the overall median remains nearly unchanged?

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Uncle Ezra’s Crazy Housing Plan

Published
by
Steve Landsburg
on July 26, 2012
in Bad Reasoning, Current Events and Economics
. 25 Comments

Ezra Klein at the Washington Post offers a way out of the current mess:

Tomorrow morning, Bernanke could walk in front of a camera and announce that the Federal Reserve intends to begin buying huge numbers of mortgage-backed securities with the simple intention of bringing the interest rate on a 30-year mortgage down to about 2.5 percent and holding it there for one year, and one year only.

The message would be clear: If you have any intention of ever buying a house, the next 12 months is the time to do it. This is Uncle Ben’s Crazy Housing Sale, and you’d be crazy to miss it.

Now, financial markets are not my specialty, and maybe Klein has thought about this more deeply than I have, but there seems to be a little flaw in this plan.

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Faces of Evil

Published
by
Steve Landsburg
on July 25, 2012
in Current Events
. 22 Comments

On the left, James Holmes, who shot over 70 people and killed at least 12 in an Aurora, Colorado movie theater.

On the right, Torrence Brown, who was present in the theater (though not injured) and is reportedly preparing lawsuits against:

  • The theater
  • Holmes’s doctors (for “prescribing medication”)
  • Warner Brothers (because the movie that Torrence Brown elected to watch, and that James Holmes had never seen, was “too violent”)

Of course the scale of evil tips sharply to the left. But there’s plenty of evil to go around.

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Mitt Romney vs. Joe Paterno

Published
by
Steve Landsburg
on July 24, 2012
in Current Events and Economics
. 70 Comments

What do Mitt Romney and Joe Paterno have in common? They both devoted substantial fractions of their careers to promoting wasteful competition — Romney at the Olympics, and Paterno at the Penn State football program. How do Mitt Romney and Joe Paterno differ? Romney, unlike Paterno, devote a substantial fraction of his career to promoting healthy competition at Bain Capital.

To understand what’s wasteful about Penn State football, think about what life will be like now that the program’s been eviscerated. The overall quality of college football will decrease — but not by much. Any titles Penn State might have won, someone else will win instead, and the games leading up to those titles will be almost as fun to watch. But Penn State has reaped enormous rewards over the decades in exchange for its relatively small contribution to the quality of college football — and has plowed a substantial fraction of those rewards back into the program in order to maintain the flow of revenue. In short, Penn State football has sucked up a lot of resources while providing relatively little in return.

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Late Night Thoughts on Determinism

Published
by
Steve Landsburg
on July 23, 2012
in Musings and Philosophy
. 38 Comments

Last week, we had some discussion of free will, which prompted some comments about determinism. I’m not convinced that determinism has all that much to do with free will one way or the other, but since the topic’s been raised, here are a few bullet points, jotted down late at night, which I hope will still make sense in the morning.

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The Wrong Tool for the Job

Published
by
Steve Landsburg
on July 19, 2012
in Bad Reasoning, Economics and Paul Krugman
. 43 Comments

Paul Krugman, defending the IS-LM (a/k/a “old Keynesian”) model of the macroeconomy as a non-rigorous but useful “scratchpad”, misses the point by a mile:

It’s a simplified model that more or less gets at what you think are the essentials of an issue, and is easy to work with, so you can use it to reach quick first-pass judgments about policy or whatever.

………

But IS-LM isn’t the prime example of a scratchpad. What is?

The answer is, supply and demand.

It is not easy to derive supply and demand curves for an individual good from general equilibrium with rational consumers blah blah. And it’s definitely not easy to justify consumer and producer surplus as measures of welfare. And there have always been some purists who condemn any use of the S and D curves we all grew up with, the use of triangles to measure welfare loss, and all that.

But for the most part nobody pays attention. The supply-and-demand framework is so convenient, while pretty much getting at what you want to get at, that it’s what almost everyone uses to get a first-pass analysis of economic issues.

Okay, look. Supply and demand (and, especially, triangles of welfare loss, etc) are not entirely rigorous, but they’re good useful simplifications that actually give useful (though approximate) answers to important policy questions. Sort of like Ohm’s Law for electrical circuits.

But IS-LM is not like that at all, because IS-LM does not even address the key policy questions in macroecomics. IS-LM can tell you, perhaps, how to fight a recession, but it can’t tell you whether the recession is worth fighting — not even loosely, because the model contains no individual utility functions and no social welfare function. It therefore does not allow you even to formulate the question of whether a given policy is worth its costs, because it provides no framework for weighing costs against benefits.

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Free to Choose

Published
by
Steve Landsburg
on July 18, 2012
in Philosophy
. 92 Comments

The subject of free will came up earlier this week, and I notice that Sam Harris has a new book on the subject, which I have not yet read. Some of you have asked for me to elaborate on my remarks on this subject in The Big Questions. Here are a few bullet points:

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The Long Now

Published
by
Steve Landsburg
on July 16, 2012
in Musings, Oddities, Philosophy and Self-Promotion
. 24 Comments

Here is a link to my piece in today’s issue of Time.com; and here’s the executive summary:

Deep inside a West Texas mountain, engineers are building a clock designed to click for 10,000 years. Amazon.com’s Jeff Bezos has sunk $43 million into this project and that’s just a start. What’s the purpose? “To foster long-term thinking and responsibility in the framework of the next 10,000 years”, say the organizers.

Now thinking and responsibility are two different things, but it’s hard to see how this project is likely to encourage either. Re thinking: The question of what we owe to future generations is subtle and difficult and requires close attention to difficult arguments; it’s hard to see how a ticking clock will do to foster that kind of effort. And as for responsiblity — if responsibility means making a better life for our distant descendants, then Bezos’s $43 million would almost surely be better spent on lobbying for lower capital taxes. Whether the goal is thinking or responsibility, a giant clock seems like a giant waste of time.

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Charting the Tax Plans

Published
by
Steve Landsburg
on July 16, 2012
in Back of the Envelope, Bad Reasoning, Current Events, Paul Krugman, Policy and Politics
. 48 Comments

Ezra Klein, quoted with approval by Paul Krugman, offers this chart of how the Obama and Romney tax proposals will change rates for taxpayers in various quintiles:

What we’re supposed to infer, according to Krugman, is that

we have an election in which one candidate is proposing a redistribution from the top … downward, mainly to lower-income workers, while the other is proposing a large redistribution from the poor and the middle class to the top.

But no such thing is remotely true. What we actually have is an election in which both candidates are proposing massive redistributions from the top downward, one slightly less so than the other. You’d never know this from looking at Klein’s chart because it illustrates changes in rates, whereas what actually matters is the rates themselves. It makes no sense to ask whether any particular group ought to be paying more or less without reference to how much they’re already paying.

Indeed, this is a classic example of what I once called the “Grandfather Fallacy” — by focusing on changes instead of absolutes, Klein’s chart conceals any existing inequities and hence treats them as “grandfathered in”.

Fortunately, Greg Mankiw has provided the numbers that allow us to make the requisite correction. Here, according to Mankiw, are the current tax burdens on various income groups (counting transfers as negative taxes, as of course one should):

Bottom quintile: -301 percent
Second quintile: -42 percent
Middle quintile: -5 percent
Fourth quintile: 10 percent
Highest quintile: 22 percent

Top one percent: 28 percent

That “-301 percent” means, for example, that a typical family in the bottom quintile receives $3.01 in net transfers for every $1 that it earns.

By adding these numbers to the numbers in Klein’s graph, we can construct a picture that actually depicts something interesting, namely the projected tax burdens for each group. It looks like this (the vertical axis represents percentage of income):

Note, for example, that, contrary to the impression you might have gotten from Klein’s and Krugman’s posts, both plans place the highest percentage burden on the top 1%, and both plans place a negative burden on the middle quintile — though Obama’s does both of these things to an ever-so-slightly greater extent than Romney’s does. There’s room for disagreement about which plan is fairer, but no room, I think, for disagreement about which chart is relevant.

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Chain Reaction

Published
by
Steve Landsburg
on July 12, 2012
in Anecdotes, History, Math, Oddities, Religion and Statistics
. 38 Comments

If you study economics, or statistics, or chemistry, or mathematical biology, or thermodynamics, you’re sure to encounter the notion of a Markov chain — a random process whose future depends probabilistically on the present, but not on the past. If you travel through New York City, randomly turning left or right at each corner, then you’re following a Markov process, because the probability that you’ll end up at Carnegie Hall depends on where you are now, not on how you got there.

But even if you work with Markov processes every day, you’re probably unaware of their origins in a dispute about free will, Christianity, and the Law of Large Numbers.

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Goodnight to the Street Sweepers, Night Watchmen, Flame Keepers…

Published
by
Steve Landsburg
on July 11, 2012
in Music
. 6 Comments

More great music, a propos of nothing in particular:

(YouTube version here.)

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Disposable Thumbs

Published
by
Steve Landsburg
on July 10, 2012
in Fluff
. 26 Comments

The average economist would sacrifice 1.02 years of life to avoid losing a thumb, or .77 years of life to get a paper published in the American Economic Review. An AER publication, then, is worth about 3/4 of a thumb.

We learn this from a study by three economists who sent out 1300 questionnaires, all to economists who had recently published in one of six major journals. They received 85 responses. Of these, 7 were discarded because they claimed to value their thumbs more than their entire hands, or their hands more than their entire arms, and another four were discarded because they indicated they were willing to sacrifice life-years for the privilege of losing a body part. The remaining 74 respondents valued their body parts as follows:

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China Doll

Published
by
Steve Landsburg
on July 9, 2012
in Romance
. 39 Comments

China has one of the highest male-female sex ratios in the world; as I discuss in Chapter 17 of The Armchair Economist, that means women can afford to be picky. Here (as reported in the May 14 issue of The New Yorker) are the requirements listed by a female graduate student seeking a mate on the Chinese equivalent of match.com:

  • Never married
  • Masters degree or more
  • Not from Wuhan
  • No rural I.D. card
  • No only children
  • No smokers
  • No alcoholics
  • No gamblers
  • Taller than one hundred and seventy-two centimeters
  • More than a year of dating before marriage
  • Sporty
  • Parents who are still together
  • Annual salary over fifty thousand yuan
  • Between twenty-six and thirty-two years of age
  • Willing to guarantee eating at least four dinners at home per week
  • At least two ex-girlfriends but no more than four
  • No Virgos, no Capricorns.

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Tuesday Puzzle

Published
by
Steve Landsburg
on July 3, 2012
in Math and Puzzles
. 28 Comments

There’s an old puzzle popular among a certain type of schoolchildren that challenges the solver to write as many positive integers as possible using exactly four 4’s, together with some set of mathematical operations. (As is often the case with school children, the exact rules tend to get negotiated in real time as the puzzle is being solved.) Some examples are:

But when I became a man, I put away childish things. So here’s the grown-up version of the problem, which I got from Mel Hochster over 20 years ago, and still don’t know how to solve:

This being a grown-up problem, the rules are carefully specified:

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New Math

Published
by
Steve Landsburg
on July 2, 2012
in Miscellaneous
. 24 Comments

It was obvious the police department was running an investigation that paralleled mine, the two interesecting at more than one point.

—Sue Grafton, V is for Vengeance

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A Naive Question

Published
by
Steve Landsburg
on June 29, 2012
in Current Events and Law
. 92 Comments

Can someone help me understand this?

1) The Constitution, as amended, gives the federal government the right to levy taxes uniformly across the states, and also to tax income.

2) The federal gasoline tax is neither levied uniformly across states nor is it a tax on income. Thus it must be justified under something other than the explicit taxing powers set forth in the Constitution.

3) I’ve always sort of presumed that the missing justification is provided by the Commerce Clause.

4) In other words, the right to levy a gasoline tax seems to be dependent on the Commerce Clause.

5) By the same reasoning, the right to levy a tax on not-having-health-insurance would seem to be dependent on the Commerce Clause.

6) But John Roberts says explicitly that the Commerce Clause can not be used to justify a tax on not-having-health-insurance.

7) How, then, can a tax on not-having-health insurance possibly be constitutional? It’s not levied uniformly across states, it’s not a tax on income, and we have the Chief Justice’s word that it can’t be justified by the Commerce Clause. Whence, then, the constitutional authority to levy such a tax?

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Post Mortem

Published
by
Steve Landsburg
on June 28, 2012
in Current Events
. 49 Comments

So the individual mandate is Constitutional because it’s a tax.

I wonder if the Chief Justice forgot that all tax legislation must originate in the House of Representatives. There’s that pesky Constitution again.

Hat tip to Jim Kahn for this.

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Edited to add: The really striking thing about this ruling is that someone could use the exact same reasoning to decide that Social Security is constitutional. This is what’s known as a reductio ad absurdum.

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Public Service Announcement

Published
by
Steve Landsburg
on June 28, 2012
in Blogging
. 30 Comments

I’ve been traveling and hence not blogging much the past several days. I’d intended to post something for today, but since I don’t know what’s going to happen at 10AM, and since that’s likely to be the only thing anybody wants to talk about today, I think I’ll hold off. I’ll be back soon though!

Meanwhile, once 10AM has come and gone, feel free to use this space for (thoughtful!) discussion of the Supreme Court decision, whatever it may be.

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Thursday Solution

Published
by
Steve Landsburg
on June 21, 2012
in Economics and Puzzles
. 39 Comments

Last week, I challenged readers to reconcile two apparently contradictory statements, both of which are frequently made in economics textbooks:

  • To minimize distortions, all goods should be taxed equally.
  • To minimize distortions, inelastically demanded goods should be taxed more heavily. (This is sometimes called the Ramsey rule, after Frank Ramsey, who plays a major role in the final chapter of The Big Questions).

I’ll give you the answer in a minute. The executive summary is that a) “Inelastically demanded goods should be taxed more heavily” is true only in very special circumstances; in general a much more complicated formula is needed, b) When all goods can be taxed, that complicated formula does in fact tell you to tax them all equally, and c) a lot of textbooks give incredibly misleading accounts of all this.

The more detailed answer follows; if you prefer a more mathematical account, click here. To keep things manageable, I’ve assumed all supply curves are perfectly elastic.

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Immigration Followup

Published
by
Steve Landsburg
on June 20, 2012
in Current Events and Policy
. 150 Comments

I’m a little frazzled this week, so I haven’t caught up with all the comments on Monday’s
post on immigration, but I know there’s been some discussion about the actual costs and benefits of admitting unskilled immigrants. I thought I’d supply some numbers that might inform that discussion; all of this is lifted from Chapter 20 of The Big Questions.

When an unskilled Mexican immigrant arrives in the United States, his wages typically rise from about $2 a hour to $9 an hour — call it a $7 an hour gain. He also bids down the wages of American workers by (and this is a high-end estimate from the labor economics literature) about $.00000003 per hour; multiply that by a hundred million American workers and you’ve got a collective $3 an hour loss.

Now there seems to be something like a consensus that it’s okay for US policies to benefit US citizens at the expense of Mexicans, but there also seems to be something like a consensus that there’s a limit to that; we would not want, for example, to allow Americans to hunt Mexicans for sport. So when we consider turning someone away at the border, one good question is: Are we willing to do $7 worth of harm to a Mexican in order to confer $3 worth of benefits on American workers?

Note that the potential Mexican immigrant is typically much poorer than those American workers, and that it’s not uncommonly argued that we should care more about the poor than about the rich. If you weight that $7 loss to the Mexican and that $3 gain to the Americans accordingly (i.e. assuming logarithmic utility, which is a quite conservative assumption — that is, one that biases the result in the anti-immigration direction), you discover exclusion hurts the Mexican about five times as much as it helps the Americans.

So, at least if you buy into that way of thinking (which pervades a lot of the policy literature) then exclusion is justified only if you “count” a Mexican as less than one-fifth of an American. That’s a pretty extreme position. It’s not as extreme as hunting Mexicans for sport, but it’s still pretty extreme.

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And Everyone Who Supports Vaccinations is Motivated by a Desire to Stab People….

Published
by
Steve Landsburg
on June 19, 2012
in Bad Reasoning
. 27 Comments

In an apparent case of libertarianism run amok, two cognitive scientists and one economist have declared (in effect) that proponents of income redistribution are always and everywhere motivated by exactly the same psychopathic impulses that lead people to scratch other people’s cars, break streetlamps, and engage in other forms of senseless destruction.

That’s not a conclusion; it’s their starting assumption. Then they do an experiment in which some subjects choose to engage in a mild form of income redistribution — and conclude that psychopathic behavior is frighteningly widespread.

Now I too am generally skeptical of the impulse to redistribute other people’s income, but even I concede that redistribution is rarely entirely senseless and pretty much never entirely destructive. In particular, the experimenters consider a case where money has just been redistributed and subjects are given the opportunity to (partly or fully) reverse that redistribution. Those who exercise that opportunity are labeled “destructive”. So apparently, in order to avoid the “destructive” label, you must passively accept any arbitrary redistributions imposed by authority figures without ever feeling any impulse to redistribute in the opposite direction.

In the experiment, each subject is initially awarded 1000 tokens. The paper is so poorly written that it’s hard to be sure, but I think these tokens are ultimately exchangeable for money; it’s mentioned that the average subject earns the equivalent of nine British pounds. One subject is then given the opportunity to destroy some of the other subject’s tokens, thereby returning some funds to the experimenters or to the taxpayers who are funding this experiment.

Rather shockingly (to me) only about 15.5% of the subjects exercised this option; given the presumption of public funding, I’d have hoped for a higher number. The experimenters, however, want to conclude that these 15.5% are the sorts who are likely to key your car.

This stuff is infuriatingly stupid. Even more distressingly, Robin Hanson, who is much much much too smart for this, seems to have fallen for it.

Continue reading ‘And Everyone Who Supports Vaccinations is Motivated by a Desire to Stab People….’

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Lest We Forget

Published
by
Steve Landsburg
on June 18, 2012
in Current Events and Policy
. 106 Comments

Thanks to an election-year conversion by the President of the United States, 800,000 young people born outside the country will now be spared the threat of deportation. That’s a good thing. But let’s not lose sight of the fact that the biggest victims of American immigration policy are not the ones we deport; they’re the ones who never got to come here in the first place.

The President defends his new policy as humane. Put aside the question of where his humanity has been for the past three and a half years and ask yourself what’s so humane about protecting the children of relatively rich “illegals” (that is, the ones who have had the opportunity to earn American wages) while we continue to bar the door to their desperately impoverished cousins.

Regarding the beneficiaries of this new policy, the President says that

These are young people who study in our schools, they play in our neighborhoods, they’re friends with our kids, they pledge allegiance to our flag …

Why is any of this relevant? When did visibility become a criterion for moral status?

This is indeed a time to celebrate and I don’t want to diminish that. But I do have two questions for the President:

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Thursday Riddle

Published
by
Steve Landsburg
on June 14, 2012
in Economics and Empirical Puzzles
. 64 Comments

Do any of you guys know anything about economics? Because I have a question I can’t answer and I’m hoping you can help me.

In many real estate markets (including the one where I’m currently shopping), the agent’s commission is equal to a fixed percentage of the sale price. (Typically it’s 6%, though this is split evenly between the buyer’s and seller’s agents, each of whom gives a cut to their respective agencies, so either agent’s take-home is more on the order of 2%).

This means that if you sell a million-dollar house, you earn TEN TIMES the commission of your identical twin who sold a hundred-thousand-dollar house, though I doubt very much that you did ten times the work or bore ten times the expense.

Now, plenty of hundred-thousand-dollar houses are being sold, which means that plenty of agents are settling for the relatively dinky commissions. Question: Why are those agents not attempting to steal some of the high-end business by offering to accept a smaller percentage? After all, 1% of a million is still a lot more than 2% of a hundred thousand.

You might say that the agencies collude to restrain them — but what stops a rogue agency from busting the cartel?

All too many times in my life, I’ve noticed some apparently anomalous behavior which I’ve challenged myself and/or others to explain with the tools of game theory, axiomatic bargaining theory, and the theory of markets — only to discover that the true explanation is “It’s required by law”. (Of course one can always step a little further back and try using economics to explain the advent of the law.) But I don’t think that’s the case here. (I’m prepared to be wrong about this, though.)

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Tuesday Solution

Published
by
Steve Landsburg
on June 12, 2012
in Puzzles
. 33 Comments

Remember the bullet problem from two weeks ago? If not, I’ll give you a few moments to refresh your memory.

Okay. Are we ready?

I am pretty well convinced that 16 bags suffice, as argued by Mike H, Jeffrey, Brian, and Jacopo, and generalized by Categories+Sheaves.

The explanation I liked best was Jeffrey’s. Let me try to illustrate it. (Warning: There’s no way, I think, to make this instantly clear. It will take a little work to understand it. Only you can assess the opportunity cost of your own time!)

The gray rectangle is the room you’re in.

The blue dot is you. The red dot is the shooter.

With mirrors on all the walls, you’ll perceive yourself as standing in an infinite grid. The graph shows 16 of the grid rectangles, but the pattern continues forever in every direction.

You’re standing at some point (a,b). The shooter is at some point (p,q). You’ll see copies of that shooter at every point with coordinates (2m ± p, 2n ± q) where m and n range over all integers. Sixteen of those infinitely many points are shown in the picture.

Continue reading ‘Tuesday Solution’

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