Visualizing sprawl in American cities

Published February 1, 2023

How can we visualize sprawl? Bid rent theory is a one option for understanding how land prices are distributed in cities. Developed by William Alonso in 1960, bid rent theory is based on the idea that land nearer to the city center is more desirable for retail businesses due to the larger number of proximate customers. Likewise, residents are willing to pay more for greater access to business services. The amount land users are willing to pay is known as bid rent.

Bid rent theory explains why areas closer to the center city are more dense, as higher land prices encourage the construction of taller buildings and the adoption of smaller living spaces. When plotting prices against distance from the city center, you would expect a negative curve where land prices decrease as distance from the city center increases.

Since Alonso proposed the theory, however, the rise of cars as American's primary mode of transportation has radically altered the distribution of land prices in cities. Cars greatly increase the viable commuting radius of a city, decreasing land prices in the city center and increasing prices in the suburbs.

Compare, for instance, the bid rent curves for the Atlanta, a younger and notably car-centric city, and Chicago, an older city with a wider range of transportation methods.

Chicago conforms to bid rent theory, exhibiting a negative decline as distance from the city center increases. In contrast, Atlanta's bid rent curve is practically flat.

While there are many factors that influence price and density distributions in cities (zoning, redlining, and natural features to name a few), bid rent curves are nonetheless a fun way to think about land use and price distribution in cities.

I calculated and visualized bid rent curves for the 100 largest metro areas in the United States. A key consideration when calculating bid rent curves is determining the center of a city, of which there is no clear consensus. Following the advice of Matthew Holian, I used coordinates geocoded by Wilson and colleagues (2012), who based city centers off the location of each city's city hall. You can find my full code and documentation on Github.

Take a look below.