Affordability and Density Part 2

Some further thoughts on my last post and the pushback I got in the comments.

The key point is that it all depends on the shape of the demand curve.  Picture a typical supply and demand chart, in which the quantity demanded (on the x axis) decreases with price (on the y axis) so that the demand curve is downward-sloping.  Meanwhile the quantity supplied increases with the price, so that the supply curve is upward-sloping.  The actual price and quantity are determined by the point at which the lines cross.

So far so good.  An increase in supply will reduce prices or increase quantity or both.  But if we want to know more about the consequences of shifting the supply curve, we need to know the shape of the demand curve.  If it is steeply downward sloping, then an increase (rightward shift) in the supply curve will result in a sharp drop in prices and a small increase in consumption.  If the demand curve is nearly flat, on the other hand, an increase in supply will result in only a small drop in price but a large increase in consumption.

Implicit in the "induced demand" or "latent demand" view of highways is that the demand curve for road capacity is nearly flat.  (To be clear:  in this way of thinking about things, the "price" of driving on a road is not a dollar cost but rather the time it takes to get from point A to point B.  The supply curve, meanwhile, is simply a vertical line that is determined by whoever controls infrastructure spending.  I am ignoring toll roads for now, because toll roads generally aren't subject to "induced demand," at least not if the tolls are high enough.)  This isn't always true—I've read that the highways in Detroit are never congested anymore, which suggests that at some point road capacity can outstrip demand—but it is probably true-ish in cases where planners are considering adding roads to address congestion.

Now maybe the demand curve for housing in cities is steeper, in which case a supply increase can result in a significant price reduction.  When I have more time I'll write another post about city size.  But for now I'll just note that the demand curve for housing in a given city is probably flatter in the long run than it is in the short run.  It may even be upward-sloping in the very long run.  In other words, in the short run people's locational decisions are very "sticky."  If you live in Cleveland, then probably you have a lot of friends in Cleveland.  You work or go to school in Cleveland.  You know your way around Cleveland.  Moving to New York isn't something you would do lightly, even if rents in New York were as cheap as rents in Cleveland (which they are not).  Of course people do move from city to city, but they probably don't do it in response to small or short-term shifts in housing costs.

But that's in the short run.  In the long run, there are large flows of people into and out of cities.  The death rate in Detroit is high, but probably not high enough to explain why its population has fallen from 1.8 million in 1950 to 714,000 in 2010.  People in New York City have always been fond of sex, but probably not fond enough to explain why its population rose from 3.44 million in 1900 to 4.77 million in 1910, to 5.62 million in 1920, and to 6.93 million in 1930.

The reason these migration flows matter is that they imply that population can be highly responsive to changes in housing prices.  And that, in turn, implies that in the long term, the demand for housing in a given city may be essentially flat.  As people are choosing between Cleveland and New York City, a high percentage may choose New York City if rents are the same in both cities.  And that may be as true when New York has 12 million people as when it has 8 million.  It may even be truer, since what is attractive about New York City involves proximity to a lot of other people.

Anyway, as I said, some of my analysis is going to have to wait for another post.  I just wanted to point out that the real debate here is about the shape of demand curves, and there are reasons to think that in the long run the demand curve for housing in a given city might be flat or flattish.  I'll finish by pointing out that this all started with this tweet:

Is there ANYWHERE in the world where hyperdensity has been followed by lower housing costs? https://t.co/uDe9DUzNks @lloydalter @felixsalmon

— John Massengale (@jmassengale) June 30, 2016

Yglesias's answer was "Tokyo."  But then he followed up with a tweet stating that affordability should be measured by density.  So New York City is vastly more affordable than Houston or Cleveland, San Francisco is more affordable than Kansas City, and so forth.  There's a sense in which that's not wrong!  It really does make a tremendous amount of sense to build housing where people want to live.  It allows more people to "afford" living in cities that offer good jobs, or good governance, or whatever.  It just feels like a bait-and-switch to use the term "affordability" to mean "density" and not "low prices."  If you promise affordability, and what you deliver is endlessly upward-spiraling rents, people are going to be disappointed.  It seems better to me to use terms that mean what they sound like.