Question for Libertarians on payment for services

I have a hard time wrapping my head around Libertarian ideas, but I am curious about something. I admit that my last question seem pretty silly, but I think it’s the only way I can understand how things would work.

If we had a Libertarian government, do I understand correctly that each person would only pay for services that we use? For example, if I didn’t want police or fire protection, I could choose not to pay for those services?

If not, how would the system work?

If so, if there weren’t enough residents of a city or town who wanted to pay for a particular service, say police, fire, school, or whatever, and it caused the cost to be too high for the remaining residents, either causing an undue financial burden, or, having to shut down the service, how would this problem be resolved?

Not all libertarians agree on these things. Like liberals and conservatives, libertarians (whether or not they are members of the Libertarian Party) often disagree among themselves.

The mainstream libertarian position would probably be that the purpose of government is to protect the lives, liberty, and property of its citizens, and that police and fire protection are therefore among the legitimate functions of government. The argument is stronger with respect to police. Police aren’t always summoned on behalf of a specific “customer”; they spend much of their time patrolling and responding to emergencies. When the state arrests and prosecutes a criminal, it does so not just on behalf of the victim, but on behalf of the entire society which has an interest in maintaining law and order.

Fire protection is more debatable; one can imagine contracting with private fire companies who respond to calls on behalf of their paying customers. (I believe this is the norm in some rural areas.) The problem is that fires have a habit of spreading, especially in densely populated areas, so that one person’s refusal to pay for service could jeapordize an entire neighborhood. So again, I think that even most libertarians accept municipal fire departments in urban areas.