[bluefirebrand]

> If there are a million households who need a housing unit, need it so they're not on the street, but there are five million housing units in the area, housing will still be very cheap

This is only true if enough of those five million housing units are competing to get filled

If a single person or company owns all five million housing units, they can set the exact same, arbitrarily high price for all of those houses. Then it's a problem for the people who need houses: take it or leave it

[AnthonyMouse]

But your scenario is rarely if ever the case. Especially when referring to new housing, because landlords and construction companies are typically different entities, so when the new construction is complete it goes for sale into the market and anybody has the opportunity to buy it.

Meanwhile buying up an unbounded amount of newly constructed housing only to leave it idle would be extremely unprofitable, because they would have to be paying the construction companies the existing market rate (i.e. the monopoly price) to keep someone else from getting it, but then couldn't rent it out and recover any of the money because that would increase supply and lower prices (or, to put it another way, no further renters can afford the monopoly price so their choice is a lower price or an empty unit).