One common argument against building new urban housing is that cities are geographically constrained by their natural and political boundaries, and thus can never build enough housing to bring prices down. This claim rests on a variety of false assumptions.
The first false assumption is that the amount of land in a city limits the amount of housing in that city. If you assume that every bit of residential land must be occupied by single-family houses on 1/5 of an acre on land, I suppose this assumption makes sense. But in reality, you can always put more people on a block of land. Where today you have big houses, tomorrow you could have small houses. Where today you have small houses, tomorrow you could have small apartment buildings. Where today you have small apartment buildings, tomorrow you could have large apartment buildings. Even in midtown Manhattan, where I live, there are lots to two-to-four story buildings that could be knocked down and replaced with larger buildings. If Manhattan had the density of Mongkok (a popular Hong Kong neighborhood with 340,000 people per square mile), it could accommodate almost 7 million people- about 80 percent of the city of New York’s population.* And if Manhattan had enough housing to accommodate Mongkok-type densities, a whole lot of housing units (either outer borough units or older Manhattan units) would become vacant, causing rents to plunge.
The second assumption is that a city’s built-up core is its entire housing market. But this is wrong, because Manhattan landlords compete not just with each other, but with landlords in the outer boroughs and the suburbs. So if enough housing units were, for example, built in New Jersey, demand for housing in Manhattan would eventually decrease.
*A common counteragument is that demolishing and rebuilding housing is expensive. This argument fails tor two reasons. First, the differences between high-cost cities and low-cost cities have far more to do with land costs than with construction costs. For example, metro San Francisco’s construction costs per housing unit are only 1.7 times higher than those of Atlanta, but its metro land costs are more than fifteen times higher (data here).