regulating rents is inherently tied to new housing, because there aren't enough units. The problem of only luxury apts being built wouldn't be solved because the housing regs make it unprofitable to build anything else & capitalism rules the day (ugh).
regarding EXISTING stuff, a capped rent will result in lower quality maintenance, lower quality replacement parts, and less of both.
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@woozle in NYC we've seen landlords simply refuse to rent apartments that are rent controlled and take it as a tax loss (oversimplified). There are some immoral but very logical financial reasons they do this.
Tiny Apts WOULD be a great option, but that brings us back to housing codes. Ex. NYC requires every bedroom to have a window so that you can escape in a fire. This prevents empty office buildings from being converted because every floor's center ends up filled with empty space
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