Are misconceptions worse if they're about facts or concepts?

In a post on Marginal Revolution called "Economic Misconceptions," Alex Tabarrok says:

Students typically come to an economics class with many misconceptions, not just random errors but systematic biases.

He gives several examples from a 2009 study by a macroeconomics professor who surveyed his students. For instance:

When asked about profits as a percentage of sales the median student guessed 30% (actual rate, closer to 4%).

In each example, the "misconception" is a guess about a specific fact, which is always in the form of a percentage. But I wonder if this is such a good way to tell whether someone has "misconceptions" about economics. The implication is that we should be good at estimating percentages on the spot.

But why would you think the human mind was well-equipped to do that? Maybe economics professors have some misconceptions about how people think or how they should think.

I notice that all the questions asked of the students (at least the ones given in the blog post), the correct answer was either a tiny or huge percentage. For instance, in the example I quoted, the correct answer is tiny — 4% — and in another question, the correct answer is huge — 248% (in case you're wondering, that's the increase in American incomes since 1950).

By contrast, the median wrong answers the students gave were 35%, 30%, 11%, and 25%.

The students might not have had any fundamental misconceptions about how the world works — maybe people are just bad at guessing percentages. So they gravitate toward mid-range ones like 25%, 30%, 35% because they feel like these are relatively safe guesses. They really have no idea, but they don't want to be too far off.

I've also seen polls asking what percentage of Americans are Jewish. I can't find these now, but I remember the answers being around 25% or 30%. The correct answer is between 1% and 2%.

But again, does this represent a serious problem that should be corrected? Anyone who needs to know the actual statistic can easily look it up. Beyond that, is it so bad if people intuitively imagine a given minority group as making up a much larger chunk of the population than it actually does?

I'm more convinced by this New York Times column by Robert H. Frank, which focuses not on people's success or failure at guessing statistics but on their understanding or misunderstanding of basic concepts. And Frank targeted not just economics students but economics professors:

Consider, for example, the cost-benefit principle, which says that an action should be taken only if its benefit is at least as great as its cost. Although this principle sounds disarmingly simple, many people fail to apply it correctly because they do not understand what constitutes a relevant cost. For instance, the true economic cost of attending a concert -- its ''opportunity cost'' -- includes not just the explicit cost of the ticket but also the implicit value of other opportunities that must be forgone to attend the concert.

Virtually all economists consider opportunity cost a central concept. Yet a recent study by Paul J. Ferraro and Laura O. Taylor of Georgia State University suggests that most professional economists may not really understand it. At the 2005 annual meetings of the American Economic Association, the researchers asked almost 200 professional economists to answer this question:

''You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton? (a) $0, (b) $10, (c) $40, or (d) $50.''

The opportunity cost of seeing Clapton is the total value of everything you must sacrifice to attend his concert -- namely, the value to you of attending the Dylan concert. That value is $10 -- the difference between the $50 that seeing his concert would be worth to you and the $40 you would have to pay for a ticket. So the unambiguously correct answer to the question is $10. Yet only 21.6 percent of the professional economists surveyed chose that answer, a smaller percentage than if they had chosen randomly.

Some economists who answered incorrectly complained that if people could apply the cost-benefit principle, it did not really matter if they knew the precise definition of opportunity cost. So the researchers asked another group of economists to answer an alternative version of the question in which the last sentence was revised to read this way: ''What is the smallest amount that seeing Clapton would have to be worth to you to make his concert the better choice?'' Again, the correct answer is $10, and although this time a larger percentage got it right, a solid majority still chose incorrectly.

When they posed their original question to a large group of college students, the researchers found that exposure to introductory economics instruction was strikingly counterproductive. Among those who had taken a course in economics, only 7.4 percent answered correctly, compared with 17.2 percent of those who had never taken one.

Teaching students how to weigh costs and benefits intelligently should be one of the most important goals of introductory economics courses. The opportunity cost of trying to teach our students an encyclopedic list of technical topics, it seems, has been failure to achieve that goal.