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Austria and Switzerland are the two I'm most familiar with. Vienna is one of the most affordable cities in the world, in terms of rental costs.
Can see how supply could be reduced by it in terms of fewer developers thinking it's financially viable to build apartments, but that's a problem to be solved...not a reason to not do it.
As somebody mentioned upthread... it'd need to be accompanied by empowered housing associations and social housing projects. Clearly the current situation of developers building luxury flats with one or two"affordable units" couldn't continue.
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The pinkos are clutching handbags about the tax breaks for landlords in Vienna.
https://www.tandfonline.com/doi/full/10.1080/02673037.2020.1806992Which brings up the problem with rental property... Who finances the construction and management?
Where? My understanding is that it leads to a shortage of rental property which blocks new tenants, and a disinclination to improve current property.
Krugman..
https://www.nytimes.com/2000/06/07/opinion/reckonings-a-rent-affair.html
Edit to add.. a gloss
https://www.governing.com/gov-institute/voices/col-rent-control-bad-idea-making-comeback.html