# Landsburg s New Puzzles.

Can You Outsmart an Economist? 100+ Puzzles to Train Your Brain

By Steven Landsburg

288 pp.; Mariner, 2018

Steven Landsburg teaches at the University of Rochester, where he ponders the "big questions" and writes terrific, accessible books on economics. His latest is Can You Outsmart an Economist? and it continues this tradition. To Landsburg, "Economics is, first and foremost, a collection of intellectual tools for seeing beyond the obvious." "If this book has a moral," he professes, "it is this: think beyond the obvious."

The book offers a number of puzzles involving economics, probability and statistics, and more. They range from easy to difficult. Consider this easy one:
```   Suppose the government imposes a
price ceiling on wheat, so that instead
of selling at the current price of, say \$4
per bushel, nobody is allowed to charge
more than \$3 a bushel. What happens
```

Don't be fooled into thinking that wheat will be more abundant. Those who are fooled will conclude that the price of bread will fall. A student of economics knows that price ceilings cause shortages. Wheat will become scarcer, the supply of bread will decrease, and the price of bread will rise. Puzzle solved.

Now consider a more difficult puzzle:
```   My wife and I each drive exactly the
same number of miles every day and
would continue to do so even if we upgraded
our vehicles. Now, which would save more
gas--replacing my wife's 12-mile-pergallon
SUV with a 15-mile-per-gallon
SUV, or replacing my 30-mile-per-gallon
car with a 40-mile-per-gallon car?
```

The trap here is to think that replacing the car is a better idea because getting another 10 mpg beats getting another 3 mpg with the SUV. Or that replacing the car is better because 40 mpg is 33% more than 30, whereas 15 mpg with the new SUV is only 25% more than 12. To the contrary, Landsburg explains, "the SUV uses so much gas to begin with that a little added efficiency goes a long way." Replacing the car would reduce the Landsburgs' fuel consumption by 7%, but replacing the SUV would reduce it by 14%. Landsburg later adds that the assumption that he and his wife wouldn't change their driving habits despite the vehicle change is an "arbitrary (and probably quite unrealistic) assumption." It would be realistic to assume that after replacing the SUV with one that gets better gas mileage, his wife will drive more. As a result, they wouldn't get the 14% reduction in fuel consumption.

Better solutions to puzzles anticipate changes in behavior. Landsburg follows up the fuel efficiency puzzle with one about child safety:
```   Infants traveling on airplanes are currently
permitted to ride in their parents'
laps. Every five years, approximately
two of those infants die from injuries
sustained during turbulence. If a new
rule required each infant to be strapped
into a separate seat, how many infant
lives could be saved?
```

Reckoning that the regulation would save two babies per five years fails to anticipate changes in behavior. Landsburg asks:
```   Under the new rule, how many families
would choose to drive rather than pay
for an extra airline seat? How many of
those families would be involved in car
accidents? How many of those car accidents
would result in infant fatalities?
```

He reports that economists who tackled those questions found that "for every two infant lives saved in the air, there would be about seven infant lives lost on the roads." The effect of a regulation requiring infants to have their own airplane seats would therefore be a net loss of five babies' lives.

Many solutions require a calculation. Take "The Gender Gap." "Alice" observes that women earn 77% of what men earn. "Bob" is skeptical of this because it suggests that employers are leaving money on the table; for example, if a manager is paying a man \$10 an hour to generate \$11 of revenue per hour, he could substitute a woman for the man, pay her \$7.70 per hour, and increase his profit from \$1 to \$3.30 per hour.

Landsburg supposes that half the labor force is women. Firms pay two-thirds of their revenue to workers. Of the other third, they pay half to bondholders and half to stockholders. "To a very rough approximation," he continues, "the total value of the bond market and the total value of the stock market are equal." Given those assumptions, Landsburg calculates that by substituting women for men in the workplace and paying them 77% as much, managers would increase profits by 42%. Without doubting that some employers may be oblivious to increasing profits this way, Landsburg argues that a 42% increase in profits is so "huge" that its "widespread" existence must be "implausible." Confident that gender discrimination does not explain why women earn 77% of what men earn, Landsburg speculates as to what else might account for the gap.

This reviewer wants to question a few of the author's "rough but reasonable" assumptions. If the labor force consists of more men than women, won't it become increasingly difficult to substitute lower-paid women for higher-paid men? In order to measure the gain to stockholders, is the relevant comparison between "the total value of the bond market" and "the total value of the stock market," or the market for all corporate liabilities including bank loans and the stock market? If the latter, and corporate balance sheets show more debt than equity, will substituting women for men be even more profitable? By questioning these assumptions, I am not arguing that they are unacceptable; I am merely trying to test my understanding and join the fun of solving the puzzle.

Exploiting irrationality / Economists conventionally assume that individuals are rational. On one level, this means that if an individual prefers apple pie to blueberry pie, and blueberry pie to cherry pie, he'll prefer apple to cherry. Landsburg introduces Sidney Morgenbesser, who ordered apple among those three flavors. When the waitress mentions that she actually has no blueberry pie on-hand, Morgenbesser changes his mind and picks cherry. That's not only funny; it's irrational.

Landsburg writes, "You're irrational if your preferences allow me to bleed you dry." He would offer Morgenbesser the apple, blueberry, and cherry pie, and Morgenbesser would pick apple. Landsburg would then say there really was no blueberry, prompting Morgenbesser to pick cherry. Landsburg agrees so long as Morgenbesser pays a nominal charge for the switch. Landsburg would then announce that blueberry is back on the menu. Now Morgenbesser selects apple and is willing to pay another nominal amount to get it. Landsburg would then continue to remove and replace the blueberry pie, pumping money out of Morgenbesser and proving that Morgenbesser is irrational.

Buyers of the book can take Landsburg's quiz that evaluates how rational they are. Most questions, by themselves, do not reveal whether an individual is rational. Answers to pairs of questions, however, can reveal inconsistencies that suggest the quiz taker is irrational. One question asks how much the reader would give up to avoid playing Russian roulette with two bullets in a pistol with six chambers. The next question would note that the six-shooter now holds four bullets and ask how much the reader would pay to remove one of those bullets. Although I thought carefully about my answers, my score was mediocre. If I lose my job as an economics professor, maybe I'll look for work as a "performance artist."

Many puzzles involve probability and statistics. For instance, Landsburg enjoys demonstrating what is known as Simpson's paradox, a phenomenon in probability and statistics in which a trend appears in several different groups of data but disappears or reverses when the groups are combined. In perhaps the best-known real-world example of this paradox, in the 1970s lawyers sued the University of California, Berkeley on grounds of sex discrimination in admissions. Their evidence was that graduate programs admitted 46% of male applicants versus 30% of female applicants. Landsburg presents a table showing the numbers of men and women that applied to each of six departments, as well as the numbers accepted. Half the departments admitted more women than men. Four of six departments accepted a greater percentage of women than men. How did a smaller share of all women get accepted overall? Landsburg explains, "Women were being disproportionately rejected because women were disproportionately applying to the most selective departments." Using the numbers Landsburg provides, 72% of female applicants applied to the three departments with the lowest acceptance rates for women. Meanwhile, 34% of male applicants applied to the three departments with the lowest acceptance rates for men. "The moral," the author warns, "is to beware of aggregate statistics."

Albert and the dinosaurs / There are some puzzles I can solve without peeking at the solution. There are many I was unable to solve, though I could understand the solution once I read it. Some have solutions beyond my understanding.

One of the most challenging puzzles is "Albert and the Dinosaurs." Albert is trying to drive home from work without being attacked by dinosaurs. Apparently, he does survive the attacks, but he'd prefer to avoid them, as much as possible. To avoid them, he must go straight at the first intersection and right at the second. What makes this a puzzle is that "Albert is extremely absent-minded" and does not recognize either intersection. The author anticipates in the introduction that "you might be tempted to ask: 'But what has this got to do with economics?"' His response is that economics is "anything to do with thinking beyond the obvious." Albert will need to do that in order to avoid the dinosaurs as much as he can.

Landsburg explains that, given Albert's absent-mindedness, his optimal course of action "is to flip a fair coin at each intersection, with the faces labeled 'straight' and 'right.'" On any day, there are three possible outcomes.

* The coin shows right at the first intersection with probability 0.5, and Albert is attacked by a dinosaur.

* The coin shows straight at the first intersection and straight at the second intersection with probability 0.5 X 0.5 = 0.25, and Albert is attacked by a dinosaur.

* The coin shows straight at the first intersection and right at the second with probability 0.5 x 0.5 = 0.25, and Albert makes it home unmolested.

But this is only scratching the surface because Albert cannot recall at which intersection he is. The first question is: "What's the probability that Albert is approaching First Street?" Imagine what happens day after day. Each day Albert arrives at the first intersection. Half the days he makes it to the second intersection. So over the course of say, 100 days, he arrives at the first intersection 100 times and arrives at the second approximately 50 times. Thus, on these 150 times when he's arriving at an intersection, two-thirds of the times (100 + 150) it's the first intersection. Does this change the probability that Albert gets home? Landsburg shows how it might and adds that "it depends on exactly how we interpret the word probability." The discussion becomes very complicated thereafter.

Readers who demand more relevance of Albert and the Dinosaurs to economics will probably not be satisfied. Landsburg leaves whatever applications there are to the imagination. The puzzle serves to show the extensive amount of thinking one can do beyond the obvious.

Conclusion / The author delivers on his intention to show the reader a good time. Landsburg's enthusiasm for solving puzzles is contagious. He introduces puzzles he has known since his childhood as well as some that perplex full-time thinkers. One should expect a few humbling experiences.

The author also delivers on his intention to squeeze in some intellectual edification. There are "morals" galore. Unfortunately, one puzzle the author doesn't grapple with is why citizens who wouldn't challenge say, a scientist, nevertheless expound uninformed on economic affairs.

PHIL R. MURRAY is a professor of economics at Webber International University.