Since the total number of bitcoin is fixed, so the value of bitcoin will keep grow, and it's price will keep grow also. So will there a price cap for bitcoin?
Yes Op, I believe that as the demand will keep on increasing day after day so shall the market value of Bitcoin keep on increasing. But remember that Bitcoin market value Will get to height where its value will remain stable and then , other altcoins will start getting more acceptance world over and that will create a strong competition among them.
We still haven't seen even 1% of the world using BTC yet. Once that happens the market cap will have to be really high. If we get to 10% of the entire world has or uses bitcoin the price will have to be worth millions each.
It will be the single biggest event in the world(cyrptocurrency) that turns people into millionaires.