[charliea0]

Well demand rising is an abstraction for relative balance between buyers and sellers of a good.

Say there’s one free apartment in NYC and two marginal buyers submit bids: Alice and Bob. If Alice offers $1000/month and Bob offers $1200/month, then Bob gets the lease. The marginal rent is $1200.

If another apartment is built then Alice leases it and the marginal rent is $1000. Similarly, if a new buyer Charlie enters the market and bids $1500 then $1500 is the marginal rent.

The number of people with apartments depends only on the number of apartments built. Which buyers get apartments depends on their relative ability to pay. The price depends on what the marginal apartment-buyer will pay. That is the lowest amount offered that still gets an apartment.