I live in the County, I pay more for trash pickup than you do, and they don't offer recycling.
My taxes help pay for schools within the city limits, 911 services (also used by city residents), food banks within the city, charitable organizations within the city, and cultural resources (various museums within city limits), etc., etc., etc. For a complete list, go to page 17 of the Adopted 2011-2012 New Hanover County budget.
If county taxpayers didn't "contribute" to all these city organizations and services, there would be enough money to budget for debris removal.
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