There is no reason to think there is enourh room for everyone who wants to like in San Francisco, and statistics prove they heve not been building much. Mean while in other states we find areas of demand where housing is not expensive. Where I live you can rent one bedroom apartments for under $1000, mohe in won't be until spring as the building is still under construction. The owners are planning on starting the next building when this is done. That is what allosing building does.

The only way they can maintain one is through legal force. Zoning laws are almost entirely that force; they're a way to establish a cartel of homeowners.

They can withhold supply, and that might have an effect on market prices.

It applies more to things like retired people living by themselves in a 3 bedroom house.

Though if they can't withhold supply, how are those cartels supposed to hold up prices, then?

(Except that they can prevent construction of new units through zoning.)

OPEC does that via production cuts. Or rather tries to do that.

Housing activists in Melbourne have been campaigning about that for years now

I did not believe that was true until I stumbled on it happening. A rich lawyer, a salary far too big to spend, so they collected (empty) houses. They did not care about cash flow

A tax on empty houses in areas with accommodation shortage at worse cannot hurt and at best could free up a lot of accommodation

It would be better to say that rents are lower in rural areas because there is either more supply or lower median salary.