Pretty easy.... start with healthcare. The US has a private system with the highest per capita costs in the world and sketchy outcomes. Most to all 1st world systems (not just some) that are government systems are
remarkably more cost effective.
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Healthcare is an example of the private sector doing it far less effectively than public sector...
But, that actually is not the point. There are some functions that are government functions that should not be sold to the highest bidder. Often the profit motive conflicts with the public interest. For one, its not a good idea to allow a public servant, a judge, not the highest paid profession, to be a gate keeper for the success of a private business. Bad things can happen.... and do.
http://www.debatepolitics.com/break...end-use-private-prisons-4.html#post1066219853
National defense, police, criminal justice, code/regulation enforcement, tax collection, the public lands are some of the things best left in the public domain, for a variety of reasons, but the principal reason to reduce the chance for corruption.