Higher rents inflate asset prices, but higher asset prices also inflate rents because buying becomes too expensive and rents can safely grow because people who can't buy must rent.
Direction of causality goes both ways. It's positive feedback loop that's barely contrained by any reality. That's why it seems to run away towards infinity despite only small changes in supply and demand.
There's no good solution to your example because there's simply too few properties. Some people will become homeless. The same number in each scenario. It hard to tell how much total rent will be transferred in each scenario because competition for rentals is harder in second one but 0.5N properties have zero rent.
This economic reasoning doesn't make sense to me. If a buyer can't buy because an investor priced them out, they'll become a renter (+1 demand), and that property will become a rental property (+1 supply). These things cancel out. You still haven't explained the imbalance (lack of rental properties versus number of renters) that causes rents to go up.
However, the other poster brought up vacancies, which is a good point. That does give a plausible way that investors can cause rents to go up. But rents are going up even in places where vacancy rates are decreasing, so it's not the full picture.
If you proposed a large vacancy tax as a way to remove this contribution to increasing rents, I'd support that. But the other stuff should not contribute to reducing rents, and it won't be close to a complete solution. Rents should remain high until you build. FWIW, I actually do support all your other proposals too, because reducing prices is good, I just don't think it will solve the rental crisis.
There's inefficiency when property becomes a rental. As you noticed vacancy is one factor. There's also the rent itself that's aimed at extracting value from the person that needs a limited resource more than the investor.
Vacancy tax would be great but it's way harder to track vacancy than ownership. And it wouldn't help with the rent. Money would still flow through this channel from people who get their income mainly from work to those who get their income mainly from capital. And there are so many channels through which this process happens that if we could limit this one a bit it would be something.
Hoarding limited resorce that everybody needs is one of the societally worst things somebody can do with money. We'd be better off if that money was redirected to literally almost anything else.
Direction of causality goes both ways. It's positive feedback loop that's barely contrained by any reality. That's why it seems to run away towards infinity despite only small changes in supply and demand.
There's no good solution to your example because there's simply too few properties. Some people will become homeless. The same number in each scenario. It hard to tell how much total rent will be transferred in each scenario because competition for rentals is harder in second one but 0.5N properties have zero rent.