The US government takes 5.62 trillion in local, state, and federal taxes from people each year, and when it unilaterally increases those prices people must pay up, renounce citizenship, or be thrown in jail at gunpoint.

Where's the cost/benefit analysis to show that those services you tout (infrastructure, etc.) are actually provided efficiently? For those cases where private examples exist alongside (FedEx/UPS/email vs. Postal Office; SpaceShipOne/SpaceX vs. NASA; Google self-driving cars vs. California train-to-nowhere; Coursera/Udacity/Khan vs. Dept. of Ed) the comparison is not flattering.

I see this mistake in economic thinking over and over again when it comes to public vs private and it's getting to be rather dull. You need to do a much deeper dive into economics or step back from making these types of statements. Much of the most "efficient" government spending is spending that the private sector would not take on because it is "inefficient" in the narrower definition of a corporation. FedEX/UPS would be much smaller companies if they'd had to rely on private corporations to builds roads and highways. The Internet would never have reached the same critical mass as private telephone companies (dial up) would never have bothered wiring huge swaths of this country where houses or farms are miles apart. UPS and FedEx (sensibly) cherry pick the richest segments of delivery as the Postal Service has to cover the non profitable segments. SpaceX would not be able to launch if it wasn't for government funded space infrastructure initiatives.

IF a market is such that it can be serviced by the private sector efficently that's always the better choice. In many cases here the government, if it was in it already, will remove itself over time (USPS is going through this now on a massive scale) But there are multiple examples over the course of time where only something like a national government can rationalize the investment in infrastructure that results in dramatic improvements down the road (Eisenhower's Federal Highways, Massive Power projects, Telecommunications)

Your factual claim that infrastructure would not exist without the government is actually not true; look at the history of private roads/turnpikes and rail in the US and Britain:

http://eh.net/encyclopedia/article/klein.majewski.turnpikes

> Private road building came and went in waves throughout the nineteenth century and across the country, with between 2,500 and 3,200 companies successfully financing, building, and operating their toll road.

"Your factual claim that infrastructure would not exist without the government". Your desire to reduce this to black and white statements tells me you're only interested in convincing yourself you're right. "private telephone companies (dial up) would never have bothered wiring huge swaths of this country where houses or farms are miles apart." It's not too hard to deduce from my statement that private telephone companies would have wired parts of the country where homes were very close together and they could therefore reasonably price their services and capture a profit. And roads would be built to the most populous towns and cities where there would be enough traffic to create tolls low enough that people would adopt the roads.

Again, government investment in infrastructure makes a lot of sense, and happens, when the economics do not make sense for a private company.

  spending that the private sector would not take on... 
  The Internet would never...private telephone companies 
  (dial up) would never...SpaceX would not...only something 
  like a national government

Note your continual use of "only" and "never". You made this a black and white question. I'll freely admit that the government can build infrastructure; you should admit that history shows that independent individuals can as well. Then the question returns to the relative cost-efficiency of each provider, which was my original point. And that's an empirical question: could these services be rendered for less than $5.62 trillion in taxes per year?

The relevant question is not “could” they be rendered for less than $5.62 trillion, but “would” they be. From what I have observed, privatization of infrastructure does not typically result in cost savings; corporate profits soak up whatever was previously “government waste”.

I'm aware of the large libertarian chunk of HN and have nothing against libertarians.

But api made no references or comments about the efficiency of government services; he merely stated that companies use government services.

Not to be rude, but it seems like you are looking to start a political debate where there isn't one (and a conversation that has been had over and over again in HN threads).