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For the housing market, I think the answer is that we have both structural and cyclical unemployment. Best I can tell, we absorb about 1.5 to 1.6 million newly completed housing units a year. In 2006 we peaked at almost 2 million. We're currently at 800K. Part of the difference between the 2 million and the 800K is going to come back once the recession is over (and we consume the excess inventory.) That looks to me like cyclical unemployment. Another part of that difference won't be coming back - it generated the over supply of housing units. That portion looks to me like structural unemployment. Those folks are going to have to find something else to do (along with their brethren in related industries.)
I think I may have found some good topics about differential equations. You should be able to find many at Askdiana.net