"Who would build the roads in Libertopia?" I see criticism of libertarians all the time over this question. I would like to present a variety of solutions to this problem that don't require the use of force (taxes).
The first question is simply, "Why not let the government handle roads through tax funds?" The first reason is that taxes are theft. The second reason is that anything the government does inherently costs more than when people pay for their own services. This is because people like to save money while government officials don't. Government administrators have no economic incentive for cutting costs or coming up with an innovative solution. They get their budgets handed down to them and they expect the budget to increase every few years. If they don't spend all the money in the budget, they might get a little sign on their desk the says, "atta boy" and then they lose the funding next year. Capitalism is more efficient because it rewards competence rather than punishing it. If you as an employee of this company find a way to cut costs and improve services than your company will make more money and you will get a raise. See more about why capitalism is better than socialism in my upcoming post on the topic. The bottom line is, total road costs will be lower if the government stays out of the way, and it gives people more freedom to choose how much of their money they want to spend on roads.
Okay, how do we get the government out of the road business? Cities and counties cut road construction, maintenance, and repair from their budgets and return the money to the taxpayers. Rezone lots in residential neighborhoods so that homeowners' property lines include the portion of the road in front of their house. Some homeowners will pool their resources into an association to pay for maintenance. Homeowners can decide how well they want to maintain the road, and at what cost. Instead of your vote being 1 out of 10,000 we can increase the power of your vote to 1 out of 5-10 (however many houses are in your neighborhoods homeowners association).
What about larger roads that aren't in residential neighborhoods? Medium sized roads in cities can continue to be publicly owned. Elected officials can manage road maintenance projects and repairs that are funded voluntarily through crowd-funding. Roads that see heavy traffic will easily be paid for by the citizens who use the road and care about it. This gives people the choice to decide on their own terms if they want to pay for that road for the quoted price. People simply won't fund roads that are too expensive or not needed. And if people in the area really want that new bypass connecting one side of the city to the other than they can crowd-fund it.
How about interstates? Large major roads such as interstates and highways can be funded through tolls. People that drive on the roads can pay for them. The government can lease the roads to private companies who will charge tolls for a profit. The lease will expire periodically and new leasers can compete for the lucrative right to tolling fees at the cost of minimum maintenance levels set out in the contract. The toll roads that I've driven on are usually maintained better than non-toll roads. Most of them have electronic methods of payment where drivers don't need to stop. And someday, private companies might come up with something better than roads such as the hyperloop.
Will this ever happen? It is much easier to socialize a service than to privatize it because people underestimate the productivity of the private sector and feel that socialism keeps them safe. Let me illustrate this with a ridiculous hypothetical example; let's say the government socialized the production of socks. Everybody goes to the dmv-like store and waits in a very long line to buy socks. Libertarians come along and advocate the complete privatization of sock production. People will be scared of a sock shortage and they will ask, "But who will make our socks if the government doesn't do it?" Does anybody think that this is realistic? No this isn't realistic, and the same logic applies to roads.
Tolls, homeowners associations, and crowd-funding could all help to replace mandatory taxes and pay for roads. Roads would be paid for voluntarily instead of by force and at gunpoint. We will all pay less as competition drives down the cost of roads, and innovators in industry will come up with new means of transportation that are better than roads. This is the place that I want to live someday.