Here is a simple math problem: A bat and ball cost $1.10. The bat costs a dollar more than the ball. How much does the ball cost?

Thousands have taken the test and most answered incorrectly. More than 80% of university students gave the wrong answer. Ivy Leaguers did a little better. Still, more than 50% answered incorrectly.

Nobel Prize winner in economics Daniel Kahneman, professor emeritus of psychology at Princeton, presents this problem in his book Thinking, Fast and Slow. He explains that part of the reason for the wrong answer is that “many people are overconfident, prone to place too much faith in their intuition. They apparently find cognitive effort at least mildly unpleasant and avoid it as much as possible.”

The wrong answer to the bat and ball question is quick and stress free. Kahneman calls this way of thinking System 1. Most often System 1 serves us well enough. It is useful for routine, mundane matters. How could we get through the day except by making quick decisions about a thousand, mostly trivial matters? We survive because we can quickly process millions of bits of information that our brains take in and make sense out of them so that we can successfully negotiate the world around us.

But not everything we encounter is susceptible to quick thinking. Getting the right answer to the bat and ball question required something else. Kahneman says that our brains also have what he calls System 2 thinking. When we use it, we often get better answers to mathematical, statistical or other complex problems. But since System 1 thinking is fast and requires little effort, it usually trumps System 2 thinking, even when it should take a back seat. So we may wind up feeling that we are right when, in fact, more effort reveals that our intuition failed us.

Fast, unreflective thinking works where events are repetitive and predictable, as is most of what we encounter daily. It doesn’t work so well, though, when problems are novel, complex or abstract.

Health care is an issue that requires Systems 2 thinking but often falls prey to Systems 1. “Health care costs pose a daunting problem. As we saw in the bat and ball problem, it isn’t easy to think straight about numbers. So when we hear that health care costs are rising faster than the rate of inflation and will in a century have gone from 15% of the average person’s income to 62%. That seems unreasonable and unsustainable. The commonplace conclusion is that we can’t continue to afford this and, therefore, cuts need to be made.

But this conclusion may be wrong, according to William J. Baumol, an NYU economist, in his new book, The Hidden Cost Disease: Why Computers Get Cheaper and Health Care Doesn’t. “Although costs of personal services [such as health care and education] appear to be out of control, they are actually falling in terms of the labor time required to earn enough to pay for them,” Baumol writes. There are few technological advances that can reduce labor costs in these areas because machines can’t replace people while in other areas technological innovations replace labor costs and the cost of the machines themselves become cheaper with additional innovations. Think about the cost of computers, for example.

So health care occupies a greater percentage of the average person’s income in part because others things have become cheaper.

Baumol makes an interesting argument. It isn’t an easy one to follow. And he may be wrong on the facts. But the concept is a valid one. It requires System 2 thinking to grasp what he is getting at. This means that if we want to insure that our grandchildren won’t be deprived of services that add to the quality of their lives, we had better understand the true nature of the problem that we face.

Hard choices about health care will have to be made. But let’s at least acknowledge that solutions that rest on sound bites and appeal to people’s emotions may not give us the best results. In this case, they may give us disastrous results that will be paid for by our grandchildren.

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