Over at the New York Times, Paul Krugman and Casey Mulligan have been having a debate. Mulligan says that seasonal variation in teen employment shows that labor supply, not labor demand, is behind high unemployment. Krugman responds that since firms make employment decisions way ahead of time, we can still see teens get hired in the summer based on prior commitments.
I have a different potential explanation for the pattern. First (in a shameless plug for the University of Michigan) I will link to this 2007 AER paper by Robert Barsky, Christopher House, and Miles Kimball. The paper is a two-sector New Keynesian sticky-price model of the economy. The sectors are the durable goods sector and the nondurable goods sector. Business cycles are driven by demand shocks, which act through sticky prices.
The key result of the model is that business cycles are entirely caused by demand shocks to the durable goods sector. It's not that hard to explain the intuition. Since durable goods (buildings, vehicles, machines) last a long time, it's very easy for firms and consumers to change the timing of their purchases of durable goods; if prices are too high, just wait to buy (and if everyone does this, it's a recession). But nondurable goods are things we need a constant stream of (think food, gas, electricity). We can't delay our purchases of those, so we smooth our consumption of them, buying about the same amount in recessions and booms.
This effect would explain why teens get hired in the summer even when full-time workers can't find a job. The reason is that teens work almost exclusively in the nondurables sector - food preparation, hospitality, grocery stores, etc. Since nondurables demand holds up in a recession, you'd expect to see the normal seasonal employment pattern hold up for teens. But there can still be a deficiency in demand for durables sector employment, which is why full-time workers can't find jobs.
(Side note: this two-sector model also gives a good reason for using core inflation, not headline inflation, as a barometer of business cycles, since things like food and energy are nondurables.)
Anyway, I think this two-sector model resolves the "Mulligan puzzle" in a fairly simple manner. A two-sector explanation would allow the seasonal pattern of teen employment to persist even over a very long period of low demand. No labor supply shocks are needed.