The economic logic behind a public [health insurance] plan springs from these information and selection problems. Private health-insurance companies are currently spending a fortune in a negative-sum game by which they try to make other private companies and not themselves actually pay for treating sick people. A public plan run by bureaucrats would not face those incentives, and would not waste money in that way. A public plan would, however, have its own inefficiencies: it would be run by bureaucrats, and would waste money in other ways.
Which set of inefficiencies would be greatest? We don’t know. The argument for a public plan is that we should be like the mongoose Rikki-Tikki-Tavi, whose motto is: “run and find out.” We should set up a public plan, let it compete with the privates, and see if it can provide care people like more cheaply than the private insurance companies. Friedrich Hayek would approve: the idea is to use the market as an institutional discovery mechanism.
Hayek’s argument for subjecting government services to private competition is actually explicit and has a far more multidimensional rationale than Brad DeLong imagines, and can be found in Hayek’s Law, Legislation and Liberty. I recommend the book to your attention, Brad.