Week 7 · Why the same demand boom raises prices in some cities and building in others
When more people want to live in a city, two things can happen: builders add homes, or prices rise. Which one wins depends on the price elasticity of housing supply, \(\varepsilon_S\): the percentage increase in the housing stock when prices rise 1 percent.
With constant-elasticity supply and demand, if demand rises by \(X\) percent (at every price, people want \(X\) percent more housing), the new equilibrium satisfies
\[ \%\Delta P \approx \frac{X}{\varepsilon_S + \varepsilon_D}, \qquad \%\Delta Q \approx \varepsilon_S \cdot \%\Delta P, \]
where \(\varepsilon_D\) is the (absolute) price elasticity of demand. When supply is elastic, the boom shows up mostly as new homes. When supply is inelastic, it shows up mostly as higher prices.
A useful test: compare home prices with the minimum profitable production cost, what it costs to build a home plus a normal profit and a modest amount of land. If prices sit far above that cost for years, something is preventing builders from adding homes, which economists often interpret as an implicit “regulatory tax.”
Prices and quantities start at 100 (index values). Increase demand and see how the outcome depends on supply elasticity.
P1 = 100 * Math.pow(1 + X / 100, 1 / (eS + eD))
Q1 = 100 * Math.pow(P1 / 100, eS)
Pgrid = d3.range(60, 200, 1)
Plot.plot({
height: 340, marginLeft: 50,
x: {label: "Housing quantity (index) →", domain: [60, 200]},
y: {label: "↑ Price (index)", domain: [60, 200], grid: true},
color: {legend: true, domain: ["Supply", "Demand before", "Demand after"], range: ["#2b6cb0", "#999", "#881124"]},
marks: [
Plot.line(Pgrid, {x: p => 100 * Math.pow(p / 100, eS), y: p => p, stroke: () => "Supply", strokeWidth: 2.5}),
Plot.line(Pgrid, {x: p => 100 * Math.pow(p / 100, -eD), y: p => p, stroke: () => "Demand before", strokeDasharray: "5,4"}),
Plot.line(Pgrid, {x: p => 100 * (1 + X / 100) * Math.pow(p / 100, -eD), y: p => p, stroke: () => "Demand after", strokeWidth: 2.5}),
Plot.dot([{q: 100, p: 100}, {q: Q1, p: P1}], {x: "q", y: "p", r: 5, fill: "black"})
]
})Geography and regulation together. Saiz (2010) measures how much land within reach of each U.S. metro area’s center is lost to water and steep slopes, using satellite and elevation data. Metros with more unbuildable land have less elastic housing supply, and those same metros also tend to have stricter land-use regulation. Supply elasticity, in turn, shapes whether demand growth shows up as price growth or as new homes.
Prices far above building costs. Glaeser and Gyourko (2018) compare home prices with the minimum profitable production cost. In most of the United States, prices are close to that cost. In a set of high-demand, mostly coastal metros, they are far above it, which points to regulation rather than construction costs as the main reason housing is expensive there. They also argue that restrictions in productive cities keep workers out of the places where they would earn the most.
A city’s housing market is not an island. Commuting networks tie Portland to South Portland, Westbrook, Scarborough, and towns farther out, and tie Lewiston–Auburn to Portland and Augusta. When building is constrained in the center, demand spills along the commuting links into surrounding towns, raising prices there and lengthening commutes. Mapping commuting flows (for example, from Census commuting data) shows which towns are part of the same housing market and where new housing would relieve the most pressure.
The idea that land-use regulation acts like a tax on new housing goes back decades, but Glaeser and Gyourko’s comparison of prices with construction costs made it measurable for every metro area, and it now shapes debates over zoning reform across the country.