Lots and lots of examples of savings through contracting out benefit programs, and not just to JP Morgan (they just happen to be the ones to hate at the moment):
Even liberals agree that this is a better way of doing things, even if they have to do so in a backhanded manner:
Guess what happened in the '90s. That's right: food stamps moved to EBT cards administered by private companies instead of paper coupons issued by the federal government.Administrative costs for the food stamp program are at the lowest they've been since the 1990s.
This is just a start. There are plenty more. And even if there weren't, it's a no-brainer: private administration is, almost without exception, vastly less expensive that the federal government doing something.