Economists have twisted themselves in knots trying to explain why housing prices in cities like San Francisco and Boston are so high. One theory says that the cities have better amenities. Another says that moving to these cities makes workers more productive (presumably because of the higher quality of their colleagues) so people will pay more to live there.

Lately, though, three economists from Philadelphia and New York have been pushing a completely different argument, which is a version of the old riddle about what happens when an irresistible force meets an immovable object.

The irresistible force, in their telling, is rapidly rising incomes in the top tier of the U.S. population. Their immovable object is the supply of buildable land in "superstar cities," which are mainly along the coasts where there isn't much room to grow.

Simply put, a certain percentage of rich Americans would like to live for whatever reason in, say, San Francisco. But at some point, there's no more room to build there. So the arrivistes have to pay a premium to move in. Prices go up. The number of rich Americans keeps going up and the number of houses in San Francisco doesn't. So the rich newcomers are pushed out by even richer newer-comers. And before you know it, people are paying millions of dollars for houses that would go for $150,000 in Rochester. (Pictured is a house you won't find in Rochester. It's a Spanish-style home in San Francisco on the cliffs above China Beach, going for $23.5 million, offered by Alain Pinel, Realtors.)

What goes for San Francisco goes for other superstar cities such as Los Angeles, Boston, New York, and Seattle, say the authors: Joseph Gyourko and Todd Sinai of the University of Pennsylvania's Wharton School and Christopher Mayer of Columbia University's Graduate School of Business.

The authors sum it up this way: "Living in a superstar city is like owning a scarce luxury good."

Their theory implies that the price gap between superstar cities and the rest could get even bigger in coming years if incomes of rich Americans continue to rise and the supply of houses in the cities remains fixed. The U.S. population will simply re-sort itself again, with the richest supplanting the slightly less rich from their homes along Superstar Boulevard.

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