If your goal is to decrease costs, the amount of supply needed may be surprising of latent / induced demand is very large. If NYC cost 1/4th the price to live there it would probably triple in population, so you'd need 40 million new units to get the costs down that much, and the price of the penthouse looking at central park would probably increase even if mean and median costs go down a lot. If a city is at the equilibrium point where supply meets demand, more housing may only keep prices flat for a large amount of new housing.
If your goal is to decrease costs, the amount of supply needed may be surprising of latent / induced demand is very large. If NYC cost 1/4th the price to live there it would probably triple in population, so you'd need 40 million new units to get the costs down that much, and the price of the penthouse looking at central park would probably increase even if mean and median costs go down a lot. If a city is at the equilibrium point where supply meets demand, more housing may only keep prices flat for a large amount of new housing.