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No, Bitcoin isn't like heroin, cocaine or speed. If banned price would go down to almost nothing, probably in the hundreds of dollars, not in the thousand's like today. People would not flock to it, they would in fact avoid it.
What I mean by that is, the prices will go up because even if illegal, the people will want to get a piece of bitcoin and the people that are going to sell it will definitely be marking up the prices which will in turn artificially pumping up the prices., if the demand increases then the prices will go up, even if there is a lot of bitcoin in supply. Banning bitcoin would not mean that the prices will go down, its not like everyone will suddenly sell their coins because it is prohibited to even own one. You should learn the economics of illegal drugs as to why they have high(no pun intended) prices because that is what is going to happen when they ban altogether bitcoin. The best solution is to take care of the demand first, don't fight the wave instead go with the wave, apply regulations that are quid pro quo for both parties.