If bitcoin will really become rare in our days now then the price of it will surely be increase. It will be a lot of higher than the original price of it. Also, another one bitcoin will be indemand for possesing it and mining it. And many people will be heads over heels for bitcoin because of it rareness.
the reduced supply of bitcoin can indeed affect prices to be more expensive, but the activities of people in the market will always exchange the bitcoin they have with cash and vice versa, buying and selling activities will increase so that market price movements are very influential by demand and supply on the market .