City Observatory proprietor and Strong Towns columnist Joe Cortright comes to grips with the bid-rent curve, recognizing that "affordable housing" is misleading in the presence of "the tradeoff between cheap rents and costly transportation."  In its simplest form, the tradeoff manifests itself in rents (or mortgages).  In a monocentric city, a renter ought be indifferent between locating near the jobs and paying little for transportation, or locating at a distance, which means the rent on a comparable apartment will be lower in proportion to the transportation costs.  That might provide little comfort to people stuck in traffic.  Here's Mr Cortright.  "If you have to drive everywhere, and drive further for every trip, what you save in rent or mortgage payments, can be more than eaten up in car payments, gasoline purchases, and time wasted traveling."

In equilibrium, no, but to the extent that cars become more costly (thanks, fuel efficiency standards and crashworthiness standards) and the roads become more congested, the value of living closer to work goes up.  Thus do we get the rising rents in city centers.

The arbitrage principle is still at work.
It turns out that the value of accessibility gets priced in to the cost of walkable, well-located housing; and conversely, rental and for-sale housing that’s located at a distance from everything is priced at a discount to the market.

What this means as a practical matter that you can’t judge whether an individual household’s living situation is affordable just by looking at whether they spend less than 30 percent of their income directly on housing.
It gets more complicated if people are also judging locations on the basis of school quality or distance from noxious facilities such as rail yards or factories, or contemplating the incidence of crime.  In isolation, though, the price of house plus transportation tends toward an equilibrium in which the marginal renter or buyer is indifferent as to location.

That broad pattern is evident in the consumer expenditure reports your tax dollars pay to provide.
What’s interesting to note here, is how, within each quartile, households that spend less on housing end up spending a great deal more on transportation.  Conversely, households that spend a larger fraction of their income on housing spend, on average much less on transportation. For example, households in the second quartile who spend less than 30 percent of their income on housing spend 12.6 percent of their income on transportation. That falls to less than 10 percent for those who are somewhat cost burdened, and less than 5 percent for those who are severely cost burdened. This pattern across income groups is consistent with the idea of a tradeoff between cheaper rents and higher transportation costs.
Exactly as the theory of locational arbitrage would suggest. Thus, the normative conclusion Mr Cortright reaches might be too strong.
The practical implication is that we shouldn’t be talking about housing affordability in isolation. We should really be talking about “affordable living” rather than “affordable housing.” If your rent is low, but you have to spend a disproportionately large share of your income on transportation, then your living situation isn’t affordable.
The economist in me bridles at the use of "disproportionate." Relative prices matter, and what looks "proportionate" under one set of relative prices will appear "disproportionate" under a different set.  It gets more complicated if what people are doing is buying relatively inexpensive houses a long way from work in response to some combination of historically cheap gasoline and perceived better schools.  Oh, and you can capitalize the test scores in house prices.

In a subsequent article, Mr Cortright touches, indirectly, on the role of supply restrictions in generating steep rent gradients.
Last week, the Wall Street Journal reported on suburbs growing faster than cities. The article, “American suburbs swell again as a new generation escapes the city,” looks at Census data showing that some of the nation’s fastest growing cities are sunbelt suburbs."
There are a number of possible explanations for that phenomenon, and, again, locational arbitrage is in play.  Consider "High and rising rents & home prices in urban centers show demand is outstripping supply. Higher relative prices for city homes versus suburban ones is the most powerful pieces of evidence of consumer preference for cities." No, it's just your plain old bid-rent curve, and perhaps what we're seeing is the inconvenience of expressway congestion and the capacity constraints on Commuter Rail changing the incentives.  The townhouse (I don't want to complicate things further comparing large and small houses) a half hour commute away looks like a good deal; it has to get a lot cheaper relative to its central city counterpart when that commute becomes an hour.  It doesn't matter whether the city price goes up or the outskirt price goes down, and preferences can stay the same.

The policy problem might be too many regulatory constraints, such as zoning and parking minima.
The unrequited demand for urban living indicated by high rents and home prices, and the complaints about having to move to suburbs to afford homes signals that policy needs to respond by creating more housing in cities. When we finally make it as easy to build new housing in cities as we do in suburbs—for example, by allowing missing middle housing to be built—we’ll see urban population grow more rapidly.
Perhaps so, although mandating the construction of those missing-middle houses might not work so well. An advocate for building more roads might see in that "unrequited demand" those high urban rents being an artifact of expensive or slow transportation, rather than some desire to cluster with like-minded hipster.  I suspect, though, that simpler policies favoring experimentation with a variety of housing types will do more to fill that missing middle than any comprehensive policy from some Committee of Wise Experts.  I have seen that movie, and it was a flop.

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