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> How many are the examples when the federal government was more efficient (as in effect per unit money) than a commercial company?

Here is the thing: commercial companies have incentive to stay efficient as long as there is viable competition from a public agency, which provides a baseline in terms of cost and quality.

As soon as public agencies are out of the picture, then there is little incentive for private companies in staying lean and efficient: Why deliver what you promised when you can go over-budget? The threat that an expensive project will be left unfinished gives you leverage to ask and approve excess costs. Why compete with other companies when you can collude with them and laugh together on your way to the bank?