Staying Out of the Corner
Tradeoffs, not solutions.
In economics, one of our favorite concepts is tradeoff. In a world of pervasive scarcity, every choice has a cost. Recognizing this fact about the human condition should lead us to see the world in terms of marginal benefits and costs. As we think about how to allocate our time and resources, we need to ask whether devoting the next unit of one those things toward a goal is really worth more than what will be given up.
Suppose you are a college student with an exam tomorrow morning and midnight is approaching: You are trying to decide whether or not to keep studying. The later it gets, the smaller will be the additions to your knowledge from each 15 minutes of studying (the “marginal benefits”) and the greater will be the value of the sleep you sacrifice (the “marginal cost”). At some point the cost of sleep forgone will exceed the gains from 15 more minutes of studying and you will close your book and go to bed.
What would likely not make sense is staying up all night to keep studying. You might be fooled into thinking this would be the best choice because, after all, you really want to do well on the exam. The smart student, however, recognizes that both studying and sleep are inputs for doing well and that just as it would be silly to sleep and not study, it would be equally irrational to study and not sleep.
Economists refer to doing all of one thing and none of another, oblivious to marginal costs and benefits, as a “corner solution.” (This name comes from the production possibilities frontier graph on which a “do one thing only” solution is indicated by the “corner” where the curve meets the relevant axis.)
Corner solutions are almost always bad ideas because we can usually do better by doing less of the one thing and reallocating our resources in some other way that will bring greater net benefits — that is, by making tradeoffs.
In the Earthquake’s Aftermath
We can see this principle in action as we think about the rebuilding in Japan after the recent earthquake and tsunami.
It would be tempting to say that new structures should be able to withstand a 9.0 earthquake, and perhaps a tsunami, so that we never see a repeat of such destruction. But when we bring the economic way of thinking to this question, we have to at least ask whether doing so would be a corner solution. In fact, it’s entirely possible that requiring that new buildings be able to withstand a 9.0 quake would actually kill more people than it would save.
Bringing buildings to that level of protection would require a great deal of resources. The marginal costs of increased earthquake protection are certainly above zero and perhaps rise dramatically as we get into the 8.0 or 9.0 range. It’s also the case that the marginal benefits of additional protection decline at some point, if only because the odds of an earthquake shrink quickly as we climb the Richter scale. So there is an optimal amount of earthquake protection where, to the chooser, the additional benefits are just equal to the additional costs — and it might well be below the level at which buildings could withstand a 9.0 quake.
Put differently: Rather than devote all those resources to protection from another extremely unlikely 9.0 quake, why not use them to do other things that might save more lives? For example, it’s possible that the resources required to upgrade buildings from 8.0-proof to 9.0-proof would be better used to buy mosquito netting against malaria in Africa, or to invest in AIDS research, or to help provide cleaner water around the world. Each of those uses of resources might well save more lives for the same cost than would the maximum earthquake-proofing of Japanese buildings.
Centralization versus Decentralization
The irony is that to the extent resources are allocated by a central authority spending other people’s money collected by force, marginal costs and benefits aren’t likely to be taken into account. In contrast, decentralized price-guided allocation through private property — and the responsibility that follows ownership — is far more likely to produce wiser decisions at the margin.
Do I know that more lives would be saved by not making the buildings safe from 9.0 quakes and using the resources elsewhere? No, I don’t. But I do know that, in Tom Sowell’s words, “There are no solutions, only tradeoffs.” What Sowell means, and the lesson I want to impart, is that the wise use of resources cannot eliminate all bad things in the world, so we need to ask whether the sacrifice at the margin isn’t greater than the gain. That question puts the economic way of thinking in the service of humanity and probably saves lives.
Comment by Steve Fritzinger on 24 March 2011:
Your point about marginal returns is especially relevant to earthquakes.
If you suffer an 8.9 quake which kills many people, requiring builders to build for an anticipated 9.0 seems to make sense. You’ve already been hit by a quake in the 8s and 9.0 is a nice round number.
But the Richter Scale is logarithmic, not linear. A 4.0 quake releases roughly 31 times more energy than a 3.0. That means the power of a quake roughly doubles for .2 increase in its Richter magnitude (That’s off the top of my head and the relationship between the energy released in a quake and the amount of damage it can cause is complicate. But the point stands).
The .1 between 8.9 and 9.0 is huge. Rebuilding Japan to withstand a 9.0 quake means rebuilding it to withstand a quake 50% stronger than the strongest quake in recorded history.
Comment by John on 24 March 2011:
I’m a bit disappointed. I think it’s clear that the situation in Japan doesn’t remotely resemble to static trade off presented in the graph. The choice in not merely one of trading off between goods on an existing production frontier but also a question of which frontier curve they want to be on.
Comment by Lynn on 24 March 2011:
Good article but a poor example. The goal of the engineers should not be to produce a reactor that can “withstand” a huge quake but one that will fail safely. That is different, easier and more economically beneficial given the costs of potential pollution.
Comment by Curt Doolittle on 24 March 2011:
Two comments above, together, provide insight:
RE: “The goal of the engineers should not be to produce a reactor that can “withstand” a huge quake but one that will fail safely.” @Lynn
RE: “The choice in not merely one of trading off between goods on an existing production frontier but also a question of which frontier curve they want to be on” @John.
Lead us to “Take great risks, but plan for failure.” This is Taleb’s recommendation for creating a safe and secure but evolutionary society in a nutshell.
Here in the pacific northwest, we largely build with sticks. They wobble nicely, and they’re cheap to repair. But stick-building doesn’t work with urban density. You have to ‘harden’ urban buildings if you want to make them taller. And harder and taller buildings are harder on humans when they collapse.
The deaths in japan were not from the quake. They were from the Tsunami, and then because of the lack of regulation on near-shore building, combined with the political fantasy of sea walls — which was a policy mistake no different from the engineered dikes of Louisiana’s Katrina.
Human beings often seek a discount on hostile land, and they take on risk in exchange. Better to leave that land a park, then occupy it at a temporary discount, which must then be paid for by others. It is the socialization of the costs of their risk that is the problem in any economic analysis.
Comment by Joker on 24 March 2011:
Horwitz: While a great article, as to be expected from you, the example is fairly poor. In comparison to how many buildings are on the Pacific coast of Japan, very few were destroyed by the earthquake itself. Curt Doolittle is correct in that virtually the destroyed buildings were the result of the tsunamis that came after the initial quake. And, if any one were to do the math and physics on the power of a 7-10 meter tsunami, they would see instantly it’s almost foolishness to even attempt to construct buildings to resist it, and that’s before factoring in costs of such buildings.
Comment by Michael Smith on 25 March 2011:
The above are all smart and relevant comments. I got smarter just reading them.
The tsunami caused at least 95% (probably more) of the deaths, and an even higher monetary percentage of the structural/infrastructure/land damage. What can stop that except the massive relocation of population and their things…by fiat decree!
However, I think that the 2011 Japan earthquake is a good example for the Horowitz’s point. There are two key variables in play in this “Trade Off” Corner Corner effect.
First: the frequency of 8.0 and greater earthquakes (granted that Japan is on a very active subduction zone (8.0 to 9.0 and greater events are going to be more frequent than say, in Los Angeles). Let’s say it’s -I don’t know- around 200 to 400 years, perhaps more.
Second: the rate of, naturally reoccurring rebuilding and upgrading of structures, and infrastructure, over 4 or 5 generations is perhaps a 75% replacement/upgrade rate or so. Double that; 100-150% new things, which will naturally be more and more 8.0+ resistant each cycle.
Seems to me that; as upgrades will reasonably happen gradually over time –just due to technological and material advances alone– the costs will be spread over time, approaching a negligible near term cost increase.
Therefore, all major public policy reactions will be a tradeoff between short term emotional peace of mind (the do something – disease) and at the cost of a huge amount of GDP resources. With no real long-term cost efficiency, a waste of resources will occur (unless money is unlimited in Japan – a trillion here a trillion there – who would notice?).
Real people, in a real economy, in the real present, and the near future…ultimately, the majority of the resources would be better off used elsewhere.
Comment by anon on 27 March 2011:
How is buying mosquito netting in Africa, or providing cleaner water around the world, relevant for the Japanese?
Comment by Stefan Stackhouse on 28 March 2011:
Information matters. Knowing that a location is vulnerable to an earthquate or a tsunami, and what the probabilities of various intensities of these might be, does make a big difference. In the absence of good information, people often tend to excessively discount their risks, especially the improbable “long tail” risks. This can result in suboptimal tradeoffs being made.
The problem, of course, is that our knowledge is seldom perfect. We don’t really know how frequent earthquakes or tsunamis of the magnitude that recently hit Japan happen. There actually is a probability – admittedly small – that it could happen again tomorrow. We also don’t know if that is the worst that could hit them. Could something even worse ever hit? We don’t know, but it might.
This same situation is faced almost everywhere, because there is no location on earth that is totally invulnerable from SOME sort of natural disaster.
That doesn’t mean moving all the way “into the corner”, if for no other reason than that there are also uncertainties on the other end of whatever tradeoff you are considering. It does mean, however, that a healthy dose of humble respect for our ignorance, and allowing an extra margin of safety to cover those unknowns, is in fact a quite rational and appropriate approach for these types of decisions.
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