The county doesn't have a "rainy day fund". Jason Thompson said so.
Using the same track of thinking as "Why Should City Taxpayers", the county also budgets funds for the city, such as:
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 a "rainy day fund" for debris removal.
If you were twice as smart as you are now, you'd be absolutely stupid.
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