It costs any government at least twice as much to do something as it costs anyone else.
David Friedman is usually much more careful in his formulations: I doubt he really means "anyone else." But you get the gist. The Wikipedia article on The Machinery of Freedom states about Friedman's Law, "empirical research is still inconclusive." That's correct literally. But most of the data I know of support it when you take into account the deadweight loss (DWL) from taxes. Remember that if the government does it, it likely taxes people to do so.
Robert P. O'Quinn, in a study done for the Joint Economic Committee (a study I can't track down on the web), found that if all federal tax rates (excise taxes, personal income taxes, payroll taxes, corporate taxes, etc.) were raised by a small amount, the deadweight loss would be about 33 cents per dollar raised.
So if the apparent cost of having government do something is just 50% more than the cost for the private sector, there you have it. If x is the cost to the private sector, 1.5 x is the cost to the government. But taking into account DWL, the cost to the government is 1.5x*1.33 = 2x. QED.
Does it cost the government 50% more, not taking account of DWL? The studies I've seen say so. Check for example, data that Steven E. Rhoads references (in The Economist's View of the World) on garbage collection and claims processing where government provision costs anywhere from 43% more to 100% more.
Question: what are other cost comparisons between government and private that you know of and what are their findings?
Update: I forgot to give a Hat Tip to Charley Hooper. He was the one who, in a discussion last week, put the standard cost difference together with the deadweight loss.