This has been dramatically demonstrated in Berkeley, where I live. We have added tons of 0- and 1-bedroom apartments recently. These are very expensive, $3000/mo+. This building boom has caused the price of rent-regulated older apartments to plunge. What had been renting for $2252/mo in November 2018 is now renting for $1688/mo in November 2023. That is a significant increase in affordability of studio and 1-bedroom apartment, effected by building newer, expensive ones.
Edited to add sources:
The discussion is too long for me to recapitulate here, but all of my data in various forms and some visualizations are available here:
https://observablehq.com/@jwb/berkeley-rent-board-data
Also in random tweets such as:
https://twitter.com/Jeffinatorator/status/172890293692602402...
I believe these are visible to non-account holders.