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You conveniently left out the part where many large corporate landlords collude by using software like RealPage to enable widescale price fixing.

As do small landlords. they can only do this because supply is so constrained.

In your first case they increase rent as a group and have 80+% occupancy.

In your second case they increase rent and people are forced into having roommates.

that is also assuming the demand is atomic when that isn't necessarily the case. A lot of that pooled demand can come from singular sources. in other words, not all demand is created equal