It's whatever maximum renters are willing to pay, combined with whatever minimum property owners are willing to accept and the availability of alternatives.

Applying a cost increase across the board, in a way where everyone knows it was across the board, will reset the market floor. If California (just as an example) can out and said "There will be a flat $200/month tax on all home rentals" you can be damn sure that every available property would align to +$200 over the course of a year or two.