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?
No, there is a limit to the amount of money in the world so even if we are talking about really big numbers there is still a limit, also when bitcoin reaches a high enough market cap and the economic system is in ruins the prices will be determined in bitcoin and its price on fiat will be irrelevant.