Let's say the price of a bitcoin is US$33,000, and all the miners mine it or not mine it if their electricity kWh price is too high, and it is at an equilibrium that it is somewhat profitable and worthwhile for the miners to mine bitcoin.
Then in year 2024 May, when the rewards changes from 6.25 bitcoins to 3.125, and if the price of a bitcoin stays at $33,000, then it become unprofitable for many miners, and they would stop the mining, and for all the miners to still keep on mining, they would think that the price of one bitcoin is more like $66,000 as before. So would the perceived price of a bitcoin double every time the reward becomes half?
Or would the price just stay low, but just that all of a sudden, a portion of the miners would stop, but when it becomes easier to "win" the block every 10 minutes, some miners will join again, until it reaches an equilibrium around this lower price? But it seems many miners would think, it is so difficult to mine and be profitable, and therefore they are not selling their bitcoins at $33,000 but would demand a higher price.