Sprawl and Land-Use Controls

Week 4 · Why market cities can spread out too far

Read: Brueckner, Chapter 4; Eid et al. (2008).

The model

Cities grow outward because, at the edge, land is worth more to a developer than to a farmer. That is efficient if prices reflect all costs and benefits. Brueckner identifies three market failures that make the market edge too far out:

  1. Unvalued open space. Farmland and woods at the fringe give nearby residents views, recreation, and habitat. The farmer’s rent \(r_A\) leaves this out, so land is converted too cheaply.
  2. Unpriced congestion. Drivers do not pay for the delay they impose on others (Traffic Congestion). Commuting feels cheaper than it really is, so people live too far out.
  3. Unpaid infrastructure costs. New subdivisions often pay the average cost of roads, pipes, and schools rather than the higher marginal cost of serving the fringe.

Market edge versus efficient edge

Take an open city where residents earn \(y\), enjoy consumption \(\bar{c}\) set by the outside option, and pay commuting cost \(t\) per mile. Urban land at distance \(x\) rents for \(r(x) = y - \bar{c} - t x\), and the market city stops where this falls to \(r_A\):

\[ \bar{x}_{\text{market}} = \frac{y - \bar{c} - r_A}{t}. \]

Now count the social costs: each mile of commuting also imposes a congestion cost \(e\) on others, and each lot of farmland has an open-space value \(v\). The efficient edge is where the social value of urban land equals the social value of farmland:

\[ \bar{x}_{\text{efficient}} = \frac{y - \bar{c} - r_A - v}{t + e}. \]

Both corrections pull the efficient edge inward. The gap is excess sprawl.

Fixing it

The best remedy targets the failure directly: a congestion toll for unpriced driving, an open-space or development tax (or public purchase of land) for lost open space, and impact fees for infrastructure. A blunter tool is an urban growth boundary, which caps the edge directly but does not distinguish among the reasons for sprawl.

Simulation

Show the simulation code 
xMarket = netY / tS
xEff = Math.max((netY - v) / (tS + e), 0)
excess = xMarket - xEff
area = r => Math.PI * r * r
xmaxS = xMarket * 1.2
rowsS = d3.range(0, xmaxS, xmaxS / 200)
Plot.plot({
  height: 340, marginLeft: 70,
  x: {label: "Distance from the CBD (miles) →", domain: [0, xmaxS]},
  y: {label: "↑ Value of land in urban use, above farm rent ($)", grid: true},
  color: {legend: true, domain: ["Private value (what developers see)", "Social value (counts congestion)", "Open-space value v"], range: ["#2b6cb0", "#881124", "#4a7c3a"]},
  marks: [
    Plot.ruleY([0]),
    Plot.line(rowsS, {x: d => d, y: d => netY - tS * d, stroke: () => "Private value (what developers see)", strokeWidth: 2}),
    Plot.line(rowsS, {x: d => d, y: d => netY - (tS + e) * d, stroke: () => "Social value (counts congestion)", strokeWidth: 2}),
    Plot.ruleY([v], {stroke: "#4a7c3a", strokeWidth: 2, strokeDasharray: "5,4"}),
    Plot.ruleX([xMarket], {stroke: "#2b6cb0", strokeOpacity: 0.5}),
    Plot.ruleX([xEff], {stroke: "#881124", strokeOpacity: 0.5}),
    Plot.text([{x: xMarket}], {x: "x", y: netY * 0.9, text: () => "market edge", textAnchor: "end", dx: -4}),
    Plot.text([{x: xEff}], {x: "x", y: netY * 0.8, text: () => "efficient edge", textAnchor: "end", dx: -4})
  ]
})

Things to try

  1. Set \(e = 0\) and \(v = 0\). Why do the two edges coincide? What does this say about sprawl when prices are right?
  2. Turn on only the congestion externality \(e\). How much does the efficient edge move in? Which policy fixes this failure?
  3. Turn on only the open-space value \(v\). Which policy fixes this one?
  4. Because land area grows with the square of the radius, a small excess in miles can mean a large excess in land. Find settings where excess sprawl is under one mile but more than a quarter of the city’s land should have stayed open.
  5. An urban growth boundary set at the efficient edge would stop the sprawl. What would it do to land rents inside the boundary, and who would gain?

What the evidence says

Critics of sprawl often point to health: people in sprawling neighborhoods drive more, walk less, and are heavier on average. Eid et al. (2008) ask whether sprawl causes weight gain or whether people who are already prone to it choose sprawling neighborhoods. Following the same individuals over time as they move between more and less sprawling places, they find no evidence that sprawl causes weight gain; the correlation reflects sorting. The lesson for policy: the case against sprawl rests on the market failures above, not on health.

Closer to home

  • Maine’s 1988 Growth Management Act encourages towns to plan for designated growth areas. Which of the three market failures does growth-area planning address?
  • Picture new subdivisions along the roads out of Lewiston–Auburn or Portland. Who pays for the new roads, school buses, and water lines?

Network lens: highways as spokes of a network

Sprawl follows the transportation network. Baum-Snow (2007) asks how much of postwar suburbanization was caused by the interstate highway system. Because highways were not built at random, he uses the 1947 national highway plan to predict where highway “rays” would run through central cities. He finds that each additional ray reduced central-city population by roughly 18 percent. In the model, a new highway is a lower \(t\) along one spoke of the network, and the city stretches out along it.

Did you know?

Oregon’s 1973 land-use law required its cities to draw urban growth boundaries, and the Portland, Oregon, metro area adopted its boundary in 1979. It remains the best-known growth boundary in the United States and a common case study in debates over whether boundaries raise housing prices.

Practice questions

  1. Name the three market failures that can cause excessive sprawl, and match each with a policy that targets it.
  2. Using a graph of land value against distance, show the market edge and the efficient edge when there is unpriced congestion.
  3. Explain the identification problem in studying sprawl and obesity, and how Eid et al. (2008) address it.

References

Baum-Snow, Nathaniel. 2007. “Did Highways Cause Suburbanization?” Quarterly Journal of Economics 122 (2): 775–805. https://doi.org/10.1162/qjec.122.2.775.
Eid, Jean, Henry G. Overman, Diego Puga, and Matthew A. Turner. 2008. “Fat City: Questioning the Relationship Between Urban Sprawl and Obesity.” Journal of Urban Economics 63 (2): 385–404. https://doi.org/10.1016/j.jue.2007.12.002.
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