Inequality, Recessions, and Broken Windows

One problem with standard models of recessions is that they present all 'agents' as being identical.  The economy would have less problems if that were true.  Indeed, the broken window fallacy really is a fallacy if there is high inequality.  For example, suppose that 90% of the population is living paycheck-to-paycheck and is already spending as much as they can.  In this case, a recession is caused by the 10% of the population that is rich enough to be able to cut back on spending.  In most recessions a lot of this group owns businesses and they dramatically reduce investment which is the most volatile component of GDP and most responsible for recessions.
This relates to the so-called broken-window fallacy.  If you break a window in each person's home, then 90% of the homes still will not increase expenditures.  They will simply buy less of something else to be able to fix the window.  Fridrich Bastiat thought that broken windows could not increase aggregate demand because he thought that everyone is already spending all that they can every day.  In this case, the broken window is effective with the 10% of households that are rich enough to have savings (and directly or indirectly own businesses) to spend more money than they otherwise would.  It certainly would not work to increase expenditures of the poor who are already spending all they can.
Similarly, in the Capitol Hill Baby Sitting Coop example, one way to cause a recession is if 10% of the homes are hoarders who end up with all of the scrip (money).  Then 90% of the households cannot spend money even though they want to and the economy grinds to a halt.  The only way to eliminate this problem would be if the poor get more money.  This could happen if the rich spend down their savings rapidly, but sometimes the factor that causes them to accumulate savings in the first place could prevent them from dissaving (spending).