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Katerina Valtcheva
Professor Charles Becker
Econ 345
March 3, 2013
For this technical presentation I have chosen Jan Brueckner’s paper from 2007 titled
“Urban growth boundaries: An effective second-best remedy for unpriced 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, unpriced 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 makes heir result so divergent from previous findings is their
assumptions that the city has dispersed employment, where trips within the city are
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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 CobbDouglass 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
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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
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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 unpriced 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.
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References:
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.