I think the price may increase after each change of reward per block, but the price will always depend on the number of people and companies that will trade with btc.
Upon further change in the value of the rewards for a block used in 2020, the number of mined bitcoins will fall to 864 each day and the rewards for the block will be split.
In 2024, with another reduction, it will be 432 per day. Sometime around the year 2032 will be mined for almost 99% of all Bitcoins. If bitcoin legalizing worldwide, the price could go up rocket manner.