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CMI,
roads
Armies probably wouldn't be produced in an AC society, mainly because they aren't much good at creating anything but death and destruction, goods not in high demand. That's not to say money wouldn't be spent on defense, necessarily.
On monopolies and mergers...
any monopoly that forms in the absence of government intervention can't be hurting consumers...because the only way to get a monopoly in such a situation is to offer the highest quality product at the lowest possible price. So there's no reason to stop such a thing, as it is counterproductive. The same holds with mergers.
Criminal defense will be a lot cheaper in the absence of government-enforced supply restrictions, i.e. the bar.
Court system will probably work primarily through private arbitration. Arbitrators will compete on reliability and quality decisions. People/companies known to ignore the decisions of reputable arbitrators will go out of business because no one will deal with them. Such a system already exist when dealing with international companies...even without one overarching court system they still manage to resolve disputes. Dispute resolution is a service like anything else and can be provided by the free market.
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Thats the only way monopolies form? What about proprietary information and capital requirements in investment intensive industries?
Eg. AT&Ts (near) monopoly grew primarily out of the capital requirements for stringing wires all over the world, and would have been broken without government intervention by satellite and cellular technologies which were more efficient than duplicating the wired infrastructure.
Simplistic, yes, but not as simplistic as the claim that that monopolies only grow out of quality/price comparisons.