The Central Business District is the contiguous, high-density commercial core of a metropolitan area — the zone where land values, employment density, transit convergence, and building height all peak simultaneously.
It is not simply “downtown.” A CBD is the specific zone where a city’s land-rent surface reaches its global maximum, and where the marginal productivity of the next foot of building height still exceeds its marginal cost. Operationally we delimit it as the polygon enclosing the top quintile of (employment density + assessed land value + transit accessibility), trimmed at the contour where commercial Floor-Area Ratio drops below roughly 5.
Five forces, roughly in historical sequence, explain why CBDs push upward rather than outward.
Alonso 1964; Muth 1969; Mills 1972. In equilibrium, firms that gain the most from a central location outbid those that gain less. Office firms (finance, legal, advertising) extract more value per square foot than retail, which outbids light manufacturing, which outbids residential. The bid-rent curve at the center slopes so steeply that the only way for the highest-paying tenants to afford their preferred location is to share the parcel — vertically. Verticality is the bid-rent curve made physical.
Marshall 1890; Jacobs 1969; Glaeser 1992, 2010. Density raises productivity: knowledge spillovers, deeper labor pools, shared specialized suppliers. The Marshall–Arrow–Romer model (within-industry spillover) and Jacobs’s cross-industry serendipity both reward proximity. Output per worker rises measurably with employment density, with an estimated elasticity of roughly 0.04–0.08 per doubling. That premium pays the rent that justifies the vertical building.
Otis 1853, Bessemer steel 1856, Chicago & New York 1880s. Vertical push only became feasible after two innovations: the safety elevator made the top floors rentable, and the steel frame freed the wall from load-bearing duty. Before 1880, building tall meant Romanesque masonry pyramids — the Monadnock Building’s six-foot-thick base walls being the canonical example. After, the height ceiling shifts from technological to economic.
NYC 1916, Chicago 1923, modern FAR regimes. Maximum FAR and height limits cap the curve irrespective of demand. Tokyo, Hong Kong, and Manhattan have demand for far more vertical space than Paris, London, or Washington DC, but only the first three permit FAR greater than 12. The variance in skyline shape across global CBDs is more a story about land-use law than about land prices.
Sassen 1991; Castells 1996. After 1970 the CBD becomes specialized as a command-and-control node for finance, advanced producer services, and corporate headquarters. This shifts vertical demand from quantity (more offices) to quality (signature towers, prestige addresses) and gives rise to the “trophy tower” phenomenon — skyscrapers as both productive space and brand asset.
The Cities tab assembles, per metropolitan area, the variables this model treats as right-hand-side: scale (population, metro GDP), demand from high-bid tenants (sector_finance, sector_technology, sector_government), agglomeration access (public_transit_score, walkability_score), and the policy ceiling (cbd_avg_far, max_allowed_far). The dependent variable is vertical stock (num_skyscrapers, num_buildings_over_10_stories, buildings_over_500ft) and its intensity (vertical_density). Cities that have the demand but lack the FAR (Washington DC, Paris) should appear as outliers below the predicted line; cities with FAR but lacking demand should sit above. The page is built so that pattern is visible to the eye.