This is a complex issue. if you add apartments for the same number of citizens prizes should go down, but that's hardly the nature of the system we are working with here.
If you have a busy highway and add more lanes will traffic jams go down?
But this can happen with certain products, including housing, by driving new demand. Imagine your street has a great fruit store that caters to locals and is a bit busy but reasonably priced.
Three other fruit stores see the demand and open up, offering slightly different fruit and other higher margin products like pies and smoothies. People start coming from all over the city for fruit, and tourists come to try local fruit they can't get at home.
Now you have four busy fruit stores, and they gradually raise prices and focus on higher margin items instead of everyday fruits and veg.
This happens all the time with bars and restaurants, too, as a neighborhood gets trendy. And it can happen with housing, because upscale housing brings rich people to the neighborhood, which makes other rich people feel more at home, even in less fancy housing.
If you have a busy highway and add more lanes will traffic jams go down?
This is a complex issue.
https://usa.streetsblog.org/2017/06/21/the-science-is-clear-...
https://en.wikipedia.org/wiki/Induced_demand