UPDATE BELOW: OMG. Even economist Paul Krugman screwed up on this one.

A Facebook friend provided a link to the following article from 2009 by John Carney and Vincent Fernando. It’s titled “French: The Most Productive People In The World.” Carney and Fernando have unintentionally provided a “teaching moment” about marginals versus averages.

Here’s one of the key paragraphs:

France has $36,500 GDP/Capita and works 1,453 hours per year. This equates to a GDP/Capita/Hour of $25.10. Americans, on the other hand, have $44,150 GDP/Capita but work 1,792 hours per year. Thus Americans only achieve $24.60 of GDP/Capita/Hour.

Carney and Fernando argue that the French have figured something out that we harder working Americans have not. They write:

The real message here is that the French are likely some of the most productive people in the entire world.

They’re right that the French people who are working are some of the most productive people in the world. But that doesn’t mean that the French have something to teach us.

Here’s what’s going on. The French minimum wage in 2009 was 8.71 Euros per hour. At the exchange rate then of $1.33 to the Euro, that translates to $11.58 an hour. That means that people in France whose value of marginal product was less than $11.58 an hour did not have jobs. So who was left? Only those whose value of marginal product was above $11.58 an hour. That’s how the average wage in France could be so high. The French government lopped off a large portion of the population, the least-productive portion.

In the United States, we could do the same. Have the government raise the minimum wage to, say, $12 or $13 an hour and that would lop off the least-productive workers. Then the average wage of the remaining workers would be higher, in fact much higher than the average in France. But, of course, those people who previously worked and now don’t would be worse off. Our GDP per working American would be higher but our GDP per American would be lower.

UPDATE: Berry College economics professor Frank Stephenson, one of my favorite letter writers to the Wall Street Journal, e-mailed me with a link to a very similar post he wrote on this same issue in 2005. Guess whom he was criticizing.