The regulation is single family zoning. Zoning makes it impossible to stack high rise apartment buildings in the areas that people want to live in.

People want to live in those areas because of the lower density. Remove that and they become much less desirable.

Of course demand is elastic.

Do you think, people will migrate to a city with an unaffordable housing (unaffordable for them)?

Unless you are living in North Korea, the competition is also there.

No, it is inelastic:

- inelastic means the demand is more or less independet of the price; you can't "just stop renting & living" if prices are going up, your options to bypass are highly limited -> therefore its called >inelastic<

You can "just stop renting" and move somewhere else.

Housing demand is less elastic than, let's say, potato demand, but it's not "absolutely inelastic" as you have said.

Good transit and road infrastructure also both make demand more elastic because the choice of where you can live without changing jobs expands.

In MBA101-bobos world this is true in theroy, in practice its not. (let me guess: You do not have children, yet, right?)

Thats always the biggest difference:

In theory, there is no difference between practive and theory - but in practice, there is ;-)