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Urban growth boundaries: An effective second-best remedy for unpriced traffic congestion?

By Katerina Valtcheva  TP_Katerina


For this technical presentation I have chosen Jan Brueckner’s paper from 2007 titled “Urban growth boundaries: An effective second-best remedy for un-priced traffic congestion?” In this paper he explores the welfare gain from using UGB as a tool for reducing the distortions created by a first-best toll regime in a congested city and, specifically, un-priced traffic congestion. His paper is based on previous scholarly works, which have proven that appropriate urban growth boundaries (UGB) improve welfare: but what Brueckner is interested in his paper is quantifying this welfare gain. Brueckner’s findings show that UGB are not an effective substitute for a first-best toll regime, nor are they effective as a second-best method in a congested city. These findings are relevant for cities that satisfy the assumptions of the standard monocentric city model.

Brueckner uses Anas and Rhee’s 2006 paper “Curbing excess sprawl with congestion tolls and urban boundaries” as a starting point for his work. In their paper, the two economists numerically evaluate congestion tolls and UGB in a congested city. Their findings show something rather different than previous works on the subject. It turns out that when a city substantially differs from the standard monocentric model used by Brueckner, a toll regime is shown to increases welfare, while the use of UGB, in fact, reduces welfare. What make their result so divergent from previous findings are their assumptions that the city has dispersed employment, where trips within the city are explained by commuting as well as shopping, and “consumer location choices are influenced by random idiosyncratic preferences” (Brueckner 2007).

In his paper, Brueckner makes assumptions based on the standard framework used for a congested monocentric city. Some important assumptions utilized include Cobb-Douglass preferences of consumers over housing consumption and the radial symmetry of the city with a constant fraction of the land used for housing and the rest for radial roads. In addition, he follows a paper from 1985 by Pines and Sadka when he assumes that the city is fully closed with each resident receiving an equal fraction of the aggregate residential rent revenue, which allows him “to conduct a straightforward welfare analysis” (Brueckner 2007). He also assumes that the revenue from tolls is equally redistributed to consumers.

The author defines a number of equations, which express the number of residents that live beyond a certain distance from the central business district (CBD) (Fig. 1), the cost per mile of commuting at a certain distance (Fig. 2), the congestion toll per mile at this distance (Fig. 3), and the commuting cost from that distance (Fig. 4), respectively.


Figure 1


Figure 2


Figure 3


Figure 4

By differentiating the equations in figure 1 and figure 4, Brueckner obtains two relationships (Fig. 5).


Figure 5

The first one shows how, as the distance from CBD increases, the population that lives at a greater distance decreases at the same rate; the second relationship shows that as this same distance increases, so do commuting cost at a rate that equals the cost of direct commuting at that distance along with the cost of the toll. Finally, Brueckner shows that income must equal the sum of exogenous income, income from rent and the income from the toll. It is important to note that in Brueckner’s analysis the “density in any one location in the city depends on densities at all other locations” (Brueckner 2007) as in his model his city is congested. As an implication, instead of solving a set of static simultaneous equations, Brueckner uses an iterative procedure that relies on the equations shown on figure 5 to find the equilibrium of the system.

The results from the method previously described allow Bruecker to compare the welfare generated in a laissez-faire equilibrium, a toll-regime equilibrium, and an equilibrium under an optimal urban growth boundary. As he compares the equilibria generated under four cases of different parameters, he finds that UGBs fail to increase central density in congested cities. This failure to noticeably raise densities around centers of employment is the main reason Brueckner gives for the poor performance of the method. As this is unlikely to change even if a city has more than one such center, Brueckner believes that his findings will hold even if he did not use the monocentric city model in his study. This is one area where I see potential for further improvement of the paper and a strengthening of its implications via performance of numerical analysis for a city with multiple employment centers as well as performance of the same analysis when adding other features to the model. Proving that UGBs are not an effective method of reducing distortions caused by a first-toll regime regardless of the assumptions used to model a city would increase the scope of Brueckner’s findings.

Brueckner’s paper is important as it quantifies the results from previous papers and, thus, takes the knowledge about UGB a step further. Without it a city could have wasted time and resources setting a growth boundary in hope of reducing un-priced traffic congestion only to find out that despite the fact that UGBs generally increase welfare, they are ineffective when used for the previously mentioned purpose.


Brueckner, Jan K. “Urban growth boundaries: An effective second-best remedy for unpriced traffic congestion?.” Journal of Housing Economics 16.3 (2007): 263-273.

Anas, A., Rhee, H.-J., 2006. Curbing excess sprawl with congestion tolls and urban boundaries. Regional Science and Urban Economics 36, 510–541.


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