[dragonwriter]

The administrative cost imposed by private insurance on administration is not the cost spent by private insurance on administration. The biggest share of it is the administrative cost imposed on providers for dealing with private insurance (there is also a cost, in terms of coordination of benefits, imposed on public insurers). Your analysis, unlike the source I cited, entirely ignores administrative costs imposed by the private insurance system on actors other than the private insurers themselves, which misses the bulk of the costs associated with the private insurance system we have.