This is not how it works. Just because the mining reward will shrink, it doesn't ensure price increase. If the miners can't pay their bills, they simply shut down their business. Block reward shrinking means pretty much hash rate decline on the long term.
When Bitcoin network hash rate shrinks a lot because miners shut down their rigs, Bitcoin blocks will need more time to be found and Bitcoin network will need more difficulty epochs to adjust. Slowly if there is hashrate, new blocks will be found, quick or slow and after a few weeks or months, network hash rate will be good enough for lower network hash rate to work normally.