Competition would be at an all-time high, prices would be at an all-time low, innovation would drastically accelerate due to the Government no longer impeding it. Everyone would do what's in their own self-interest, and with Government no longer attempting to monopolize gun ownership, attempting to initiate force against anyone would be significantly higher in risk, especially due to better purchasing power, since people would stop exchanging in the US Dollar.
Anything the Government does that there's a demand for would be provided by private businesses and paid for voluntarily. Road Pirates/Police would be completely replaced by self defense and Private Security, which is cheaper and more effective than Road Pirates/Police, who take 15 minutes on average to arrive, and don't even work for us.
If this doesn't answer your question, maybe you should ask more specific things, since this question is incredibly broad.
And how long do you think it would take other countries like Russia or China to drop two or three hundred thousands troops in the US to restore order and goverment. That would happen probably just before Russia marched through Europe since NATO would collapse without US support.
I guess it would take until China's fascist leaders shove their heads so far up their ass that they think an armed America, with no Gun Restrictions, would just lay down and let them. The capability of organizing does not disappear with Government, restraint does. All those guns, all that technology, and all of those people don't just evaporate, the evil force preventing us from defending ourselves does. If China is so willing and ready to send "three-hundred thousand" people to their deaths, I suppose that's their decision. Of course, that's the assumption that there would even be a fight, since people wouldn't be fighting the Government anymore, if they show up and attempt to take over America, they'd have no way to force us all to comply, since technology would continue to exist that allows us to trade around the Government. They'd be straight wasting their time.
I suppose the funniest part of this anti-thought you're exhibiting would be that you believe there's any one singular thing to be fighting against, for them. If the US Government collapses, it won't be from violent revolution, it'll be from innovations which prevent them from continuing to interfere in our ability to freely exchange. With the creation of things like Crypto Currency and 3D printers, their ability to interfere is already disappearing. If they attempt to initiate force against the new free society, they'd just be encouraging the 327-million people living here to defend themselves. No army in the world outnumbers the general populace, the only thing which allows them to maintain control is the illusion of authority.
I find it hard to believe that citizens armed with shotguns, rifles, and pistols would be any match for a professional army with tanks, backed up with air power and artillery. China would be in this country in a blink of an eye just to get our petroleum.
This country like a number of other nations were formed for mutual defense. We've added a lot of stuff besides defense but defense is the basic reason for the nation and the government. Without the government to focus all divergent interest into defending the nation, the country would fall to a foreign power in no time at all.
The basic problem with anarchy is that the whole is stronger than all the parts because the parts will not act in unison to meet a global problem. The only way you can get all parts working together to accomplish a goal is with a centralize power which can make it happen. Thus we are back to some kind of goverment.