What price to charge?

1. higher - gouging, profiteering, monopolistic rents

2. same - collusion, price fixing

3. lower - unfair competition, predatory pricing

All are illegal!

I'm fairly certain none of those things are illegal. You've just incompletely specified the problem and are consequently reaching the wrong conclusion. It's true that all of those things _can_ be illegal, just like moving your hand or your foot can be illegal if you do so with sufficient force against a person, and not moving your hand or foot can be illegal if you, say, are stopping police from enforcing the law. But that doesn't mean "moving my hands" and "not moving my hands" are crimes.

Charging higher prices as a monopoly is not in itself illegal. Other conditions have to be true.

Collusion and price fixing require you to conspire.

Charging lower than someone else while being a monopoly is not illegal either. The FTC has a little page for this: https://www.ftc.gov/tips-advice/competition-guidance/guide-a...

None is illegal if you don't have a monopoly.

So if you do have a monopoly, what is the legal price to charge?

The monopoly is what is illegal, not the price you charge.

It's not illegal to have a monopoly. It's illegal to exploit it in certain ways.

This is mostly a distinction without a difference in practice. Exploit it in certain ways and your monopoly gets broken apart- thus illegal. See ATT/ Ma Bell

It's a very practical distinction since you can avoid exploiting it in certain ways and thus not get into any trouble at all. Violator monopolies do not exert predatory pricing, etc, by accident.

Very good point.