Should everyone crowd into New York and San Francisco?

A recent piece from the excellent Conor Sen has attracted some disputation.  The main claim is that building restrictions aren’t as bad as they might at first seem.  If you keep people out of Manhattan they move to Atlanta, and that produces synergies too:

Here in Atlanta, as in the rest of the Sun Belt, job migration is the driving force of the economy. Corporate relocations and expansions are celebrated here the way billion-dollar tech startups are celebrated in Silicon Valley. The “New South” would not have developed were it not for people looking to flee the crowded and expensive cities of the Northeast.

…Housing constraints in some cities accelerate economic development in emerging parts of the country. They decrease economic inequality between metro areas and lead to economic interdependence that drives civil rights. And they offer some promise to ease the pain of waning communities in the Rust Belt, Appalachia and beyond. A country where the vast majority of talented people move to one or two cities might be an economist’s idea of utopia, but a nightmare to those of us concerned about equality of economic opportunity.

Analytically, the first question is whether the biggest cities would attract too many people in the absence of building restrictions.  To answer that, you have to balance crowding costs vs. synergy benefits.  It can be said that average social returns to living in cities will equalize, even if marginal social returns do not.  Cross-city migration equates the average returns, even in the presence of externalities, just as in the classic “two roads” problem.  If one road is going faster than the other, people will switch, although the “final driver” still is not taking his entire social impact into account.

Note that if urban synergies are constant across scale, equality of the average across two cities will in turn imply equality of the marginal, and an efficient allocation of population across the larger and smaller cities will result.  Building restrictions won’t change that, although they do shift where the equalization margin will be at.

(Building restrictions also may mean NYC space is used inefficiently, even if the distribution of population across cities is more or less optimal.  Building restrictions are not identical to urban entry fees, but rather they shift space allocations at various margins of construction, though to potential movers their “entry fee” aspect may seem most important.  These marginal distortions may interact with the “entry fee” aspects of building restrictions in various ways, muddying the analysis.  Complicated!)

Now maybe synergies aren’t constant across urban scale, but suddenly the costs of building restrictions in Manhattan look lower.  They are defined by the differences in synergies across scale, which may not be such a huge number.  Furthermore synergies might be more important for the Atlantas than for the Manhattan, in which case the building restrictions in Manhattan could be welfare-improving.

(Note that if a city or region has really big firms, the chances that interpersonal synergies will be internalized into initial wage offers will be higher.  And there is a time horizon issue.  Circa the 1920s, Los Angeles synergies may have appeared much lower than those for NYC, but it probably ended up better for the nation as a whole that the racist “entry fee” for movie-making in NYC led to the creation of Hollywood on the West Coast.  Similarly, was it not also a good thing that NYC blew its chances of being the center of the American venture capital market?  If Peter Thiel were here, and communing with Kenneth Arrow, he might see too many risk-averse, conformist entrants into New York and look for a remedy, just as New York was itself once a respite from an overcrowded, restrictionist, religiously conforming Europe.)

OK, that’s scale but what about congestion costs?  They do seem to go up in a non-linear manner with scale, and that lowers the costs of building restrictions in Manhattan.  Manhattan is more likely to be too crowded than is Atlanta, as a first-order approximation.  Of course differential endowments across regions can complicate this, for instance NYC has better mass transit.

Now, to push this all one step further, is Peoria just a smaller Atlanta?  Does it too have synergy benefits?  (Or can we say that too many people stay in Peoria and too few go to NYC + Atlanta?)  Don’t we observe the very largest synergy benefits at small scales, namely going from households of one to two, two to three, etc.?  Might Peoria have the highest synergy gains of them all?  At least in utility terms if not in dollar terms?  Or do we need an ongoing risk of “Peoria brain drain” to induce Peoria residents to acquire the skills that they may or may not end up taking out of Peoria?

In any case, worth a ponder.