Even better: a very high tax on the assessed unimproved land value of all privately owned land. This removes the ability to speculate on real estate entirely, which, if you think about it, maybe shouldn't be allowed in the first place, since it is the only good that has a truly fixed supply. This would cause real estate prices to plummet, then remain relatively stable. Obviously you couldn't just do it starting from nothing, but in the long run it would solve housing scarcity, as well as drastically reducing rent seeking behavior, without draconian measures or ending the free market.
This idea is called Georgism, and it's not new. It was also supported by several economists, including Milton Friedman.
also tie tax bracket to rent above a reasonable AMT like 10 percent at 1k, 20 percent at 2k, 35 percent at 3k, 60 percent at 4k, I mean different size rentals will have a different formula, just for examples sake.
This idea is called Georgism, and it's not new. It was also supported by several economists, including Milton Friedman.