Subject of the paper: The paper should answer the questions as directed. The books will be provided to you. The cases which are asked in the list of questions are included in the textbooks I will send to you.
List of Questions (follow directions presented)
PART A: Answer any 5 of the questions A.1 – A.8. Do not answer additional questions. This part is worth 15% of the exam.
Briefly define and give a specific example of:
A.1. Scale economies in connection with urban economics (i.e., related to land use, housing, or firm location)
A.2. Pecuniary agglomeration economies
A.3. Technological agglomeration economies
A.4. Retail agglomeration economies
A.6. ceteris paribus assumption
A.7. A numeraire good
A.8. An efficient allocation of resources
PART B: Answer any 3 of the questions B.1 – B.7. Do not answer additional questions. This part is worth 30% of the exam.
B.1. Derive (using graphical or algebraic methods) the housing-price curve in the standard [textbook] case.
B.2. What conclusions about the shape of the housing price curve, the slope of the housing price curve, and total expenditures on housing (total rent) are supported by the Simple Urban Model?
B.3. Explain how the edge of the city is determined in the Simple Urban Model.
B.4. What is the effect of a higher t (marginal cost of commuting) on the allocation of land to housing and farming in Brueckner’s Simple Urban Model?
B.5. What is the effect of a higher t (marginal cost of commuting) on the price of housing in Brueckner’s Simple Urban Model?
B.6. Why do the poor reside closer to the CBD in Brueckner’s Simple Urban Model?
B.7. Contrast land-weighted density with population-weighted density. What causes a difference between the density measures? Which measure is more accurate? Why?
PART C: Answer only 1 of the questions C.1 – C.2. Do not answer additional questions. This part is worth 55% of the exam.
C.1. According to Glaeser & Gyourko, “How Should Housing Affordability Be Measured?”
C.2. What caused the decline of his birthplace, Newark, NJ, and other East-Coast cities, according to Richard Florida? What defined the economy of these cities? What ethnic groups comprised these cities? What changes in ethnic composition has ensued because of gentrification? What causes “gentrification” according to Florida?
What, according to Florida, are the five dimensions of the New Urban Crisis? Explain why these dimensions are important, according to Florida.
Resources (will provide the pdfs once I accept the tutor):
Jan K. Brueckner (B), Lectures on Urban Economics, MIT Press (2011) ISBN: 978-0-262-01636
Richard Florida (F), The New Urban Crisis: How Our Cities Are Increasing Inequality, Deepening Segregation, and Failing the Middle Class and What We Can Do About It, Basic Books (2018) ISBN: 978-1541644120
Edward Glaeser and Joseph Gyourko, Rethinking Federal Housing Policy: How to Make Housing Plentiful and Affordable, AEI Press (December 16, 2008) ISBN-13: 978-0844742731 (PDF: http://www.aei.org/wp-content/uploads/2014/03/-rethinking-federal-housing-policy_101542221914.pdf)
Lectures on Urban Economics
Lectures on Urban Economics
Jan K. Brueckner
The MIT Press
© 2011 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic
or mechanical means (including photocopying, recording, or information storage and
retrieval) without permission in writing from the publisher.
For information on special quantity discounts, email firstname.lastname@example.org.
Set in Palatino by Toppan Best-set Premedia Limited. Printed and bound in the United
States of America.
Library of Congress Cataloging-in-Publication Data
Brueckner, Jan K.
Lectures on urban economics / Jan K. Brueckner.
Includes bibliographical references and index.
ISBN 978-0-262-01636-0 (pbk. : alk. paper)
1. Urban economics. I. Title.
Why Cities Exist 1
Scale Economies 2
Agglomeration Economies 5
Transport Costs and Firm Location 10
The Interaction of Scale Economies and Transportation Costs in the
Formation of Cities 16
Retail Agglomeration and the Economics of Shopping Centers 18
Analyzing Urban Spatial Structure
Basic Assumptions 25
Commuting Cost 26
Consumer Analysis 27
Analysis of Housing Production 33
Population Density 39
Intercity Predictions 42
Modiﬁcations of the Urban Model 51
A City with Two Income Groups 51
Commuting by Freeway 56
Adding Employment Outside the CBD 57
Durable Housing Capital 61
Cities in Developing Countries 65
Urban Sprawl and Land-Use Controls 69
Empirical Evidence on the Spatial Sizes of Cities 70
Market Failures and Urban Sprawl 73
Behavioral Impacts of Urban Sprawl 80
Using Land-Use Controls to Attack Urban Sprawl 80
Other Types of Land-Use Controls 84
Congestion Costs 92
The Demand for Freeway Use 95
Trafﬁc Allocations: Equilibrium and Social Optimum
Congestion Tolls 104
Choice of Freeway Capacity 110
Application to Airport Congestion 112
Housing Demand and Tenure Choice 115
Housing Demand: The Traditional and Hedonic Approaches
The User Costs of Housing 119
Tenure Choice 124
Down-Payment Requirements, Tenure Choice, and
Mortgage Default 130
Property Abuse and Tenure Choice 133
Rent Control 137
Housing-Subsidy Programs 145
Homelessness and Policies to Correct It
Local Public Goods and Services
The Socially Optimal Level of a Public Good 161
Majority Voting and Voting with One’s Feet 163
Public-Good Congestion and Jurisdiction Sizes 174
Capitalization and Property-Value Maximization 179
Tax and Welfare Competition 183
Pollution from a Single Factory and Governmental Remedies 188
Bargaining as a Path to the Social Optimum: The Coase Theorem 196
Cap-and-Trade Systems 200
Evidence on Air Pollution and Property Values 204
The Economic Theory of Crime 208
Additional Aspects of the Theory 215
How to Divide a Police Force Between Rich and Poor
10.5 Summary 229
Urban Quality-of-Life Measurement
Theory: The Roback Model 233
Measuring Urban Quality of Life 241
Additional Issues 244
This book offers a rigorous but nontechnical treatment of major topics
in urban economics. The book is directed toward several potential
audiences. It could be used as a main textbook, or possibly a supplementary book, in an undergraduate or master ’s-level urban economics
course. It could be used as background reading in a PhD-level course
in which students would also read technical journal articles. It could
also be read by economists or researchers in other ﬁelds seeking to
learn what urban economics is about.
To make the book accessible to a broad group of readers, the analysis
is mostly diagrammatic. A few chapters make use of some simple formulas and a bit of algebra, but calculus is almost absent. Even though
the treatment is nontechnical, the analysis of urban topics attempts to
rely on rigorous economic reasoning. The orientation is conceptual,
with each chapter presenting and analyzing economic models that are
relevant to the issue at hand. In contrast to the cursory theoretical
development often found in undergraduate textbooks, the various
chapters offer thorough and exhaustive treatments of the relevant
models, with the goal of exposing the logic of economic reasoning and
teaching urban economics at the same time. Because of its conceptual
orientation, the book contains very little purely descriptive or factual
material of the kind usually found in textbooks. Instructors wishing to
expose students to such material could supplement the book with other
readings. Some topics not associated with sharply deﬁned models,
such as urban poverty, receive no coverage.
Exercises are presented at the back of the book, for possible use
when it is employed as an undergraduate text. They develop numerical
examples based on the models presented in the chapters. Footnotes
throughout the chapters point to exercises that are relevant to the
In view of the nature of the book, the list of references is not particularly extensive. No attempt is made to provide exhaustive citations of
the literature on each topic. Instead, one or two representative citations
might be given as part of the discussion of standard material that is
well accepted among urban economists. However, when a speciﬁc idea
advanced by a particular author is discussed, the appropriate citation
is included. Although the citations are not exhaustive, readers seeking
more exposure to a topic can always ﬁnd references to the literature in
the works that are cited.
Since the book has grown out of my own research on a variety of
topics in urban economics, the references include an unavoidably large
number of my own papers. Other researchers should recognize that
this pattern does not reﬂect an opinion about relative contributions to
the ﬁeld. Again reﬂecting my own interests within urban economics,
the book contains less material on the New Economic Geography, an
area of active research in the ﬁeld since the early 1990s, than would a
book written by an NEG researcher. The material relevant to NEG is
conﬁned to chapter 1.
The book’s suitability as a text for an undergraduate course in urban
economics, or for a series of such courses, would depend on the length
of the course(s). All the chapters can be covered in the undergraduate
urban sequence at UC Irvine, which runs for two quarters of 10 weeks
each. In a semester-length course of 15 weeks, some of the chapters
would have to be dropped, and only about half of the book could be
covered in single-quarter course.
This book has grown out of 30 years of teaching urban economics
to undergraduates and PhD students, and I’m grateful to all my students for the opportunity to reﬁne my views on the subject. As for
assistance with the book itself, I’m indebted to Nilopa Shah, one of my
PhD students at UC Irvine, for her expert work in preparing the ﬁgures.
I also thank various reviewers for helpful suggestions that improved
the book in many places.
Why Cities Exist
In most countries, the population is highly concentrated in a spatial
sense. For example, cities occupy only about 2 percent of the land area
of the United States, with the rest vacant or inhabited at very low
population densities. Even in countries that lack America’s wide-open
spaces, spatial concentration of the population can be substantial, with
much of the land vacant. This chapter identiﬁes some forces that lead
to the spatial concentration of population. Thus, it identiﬁes forces that
help to explain the existence of cities.
Depending on their orientation, different social scientists would
point to different explanations for the existence of cities. A military
historian, for example, might say that, unless populations are concentrated in cities (perhaps contained within high walls), defense against
attack would be difﬁcult. A sociologist might point out that people
like to interact socially, and that they must be spatially concentrated
in cities in order to do so. In contrast, economic explanations for
the existence of cities focus on jobs and the location of employment.
Economists argue that certain economic forces cause employment
to be concentrated in space. Concentrations of jobs lead to concentrations of residences as people locate near their worksites. The result
is a city.
The two main forces identiﬁed by economists that lead to spatial
concentration of jobs are scale economies and agglomeration economies. With scale economies, also known as “economies of scale” or
“increasing returns to scale,” business enterprises become more efﬁcient at large scales of operation, producing more output per unit of
input than at smaller scales. Scale economies thus favor the formation
of large enterprises. Since scale economies apply to a single business
establishment (say, a factory), they favor the creation of large factories,
and thus they favor spatial concentrations of employment.1
Whereas scale economies operate within a ﬁrm, without regard to
the external environment, agglomeration economies are external to a
ﬁrm. Agglomeration economies capture the beneﬁts enjoyed by a ﬁrm
when it locates amid other business enterprises. These beneﬁts include
potential savings in input costs, which may be lower when many ﬁrms
are present, as well as productivity gains. A productivity effect arises
because inputs (particularly labor) may be more productive when a
ﬁrm locates amid other business enterprises rather than in an isolated
spot. The mechanisms underlying these effects will be explained later
in the chapter.
Transportation costs also inﬂuence where a ﬁrm locates, and they
can lead to, or reinforce, spatial concentration of jobs. This chapter
explains several different ways in which transportation costs affect the
formation of cities. The last section explores a special kind of agglomeration force: the kind that causes the clustering of retail establishments
and the creation of shopping malls.
The role of scale economies in the formation of cities can be illustrated
with a simple example. Consider an island economy that produces only
one good: woven baskets. The baskets are exported, and sold to buyers
outside the island. The inputs to the basket-weaving process are labor
and reeds. With reeds growing everywhere on the island, the basketweaving factories and their workers can locate anywhere without
losing access to the raw-material input.
The basket-weaving production process exhibits scale economies.
Output per worker is higher when a basket-weaving factory has many
workers than when it has only a few. The reason is the common one
underlying scale economies: division of labor. When a factory has
many workers, each can efﬁciently focus on a single task in the production process, rather than carrying out all the steps himself. One worker
can gather the reeds, another can prepare the reeds for weaving, yet
another can do the actual weaving, and still another can prepare the
ﬁnished baskets for shipment.
1. When used with “scale” or “agglomeration,” the word “economies” means “savings”
Why Cities Exist
Slope = QB /LB
Slope = QA /LA
The production function for the basket-weaving process is plotted
in ﬁgure 1.1. The factory’s output, Q, is represented on the vertical axis,
and the number of workers, L, on the horizontal axis. Since the reed
input is available as needed, it does not have to be shown separately
in the diagram. Because the curve shows basket output increasing at
an increasing rate as L rises, scale economies are present in basket
weaving. This fact can be veriﬁed by considering output per worker,
which is measured by the slope of a line connecting the origin to a point
on the production function. For example, the lower line segment in the
ﬁgure (call it A) has a slope of QA/LA, equal to the rise (QA) along the
line divided by the run (LA). The higher line segment (call it B), which
corresponds to a factory with more workers (LB as opposed to LA), has
slope QB/LB, equal to output per worker in the larger factory. Since line
B is steeper than line A, output per worker is higher in the larger
factory, a consequence of a ﬁner division of labor.
Using this information, consider the organization of basket weaving
on the island economy. If 100 workers are available, the question is how
these workers should be grouped into factories. Consider two possibilities: the formation of one large 100-worker factory and the formation
of 100 single-worker factories (involving “backyard” production of
baskets). The natural decision criterion is the island’s total output of
baskets, with the preferred arrangement yielding the highest output.
Basket output of the island economy.
(b × c)
(a × b × c)
100 × 1α
1 × 100β
The answer should be clear: given the greater efﬁciency of workers in
large factories, the 100-worker factory will produce more output than
the collection of 100 backyard factories.
But it is useful to verify this conclusion in a more systematic fashion.
Let α be output per worker in a factory of size 1, equal to the slope of
a line like A in ﬁgure 1.1 with LA = 1. Let β be output per worker in a
factory of size 100, equal to the slope of a line like B with LB = 100. From
the ﬁgure, it is clear that β > α. Now consider table 1.1.
The island economy’s total output of baskets equals (number of
factories) × (workers per factory) × (output per worker). Table 1.1
shows that this output expression is largest with one large factory. It
equals 100β, which is larger than the total output of 100α from the collection of backyard factories, given β > α.
Since the island economy gains by having one large basket factory,
the economy would presumably be pushed toward this arrangement, either by market forces or by central planning (if it is a command
economy). But once one large factory has been formed, the basket
workers will live near it, which will lead to the formation of a city.
This story is highly stylized, but it captures the essential link between
scale economies and city formation, which will also be present in more
complicated and realistic settings. But something is missing from the
story. It can explain the formation of “company towns,” but it cannot
explain how truly large urban agglomerations arise.
To see this point, consider a more realistic example in which the
production process is automobile assembly. This process clearly exhibits scale economies, since assembly plants tend to be large, typically
employing 2,000 workers or more. Thus, an assembly plant will lead to
a spatial concentration of employment, and these auto workers (and
their families) will in turn attract other establishments designed to serve
their personal needs—grocery stores, gas stations, doctor ’s ofﬁces, and
Why Cities Exist
so on. The result will be a “company town” with the auto plant at its
center. But how large will this town be? In the absence of any other large
employer, its population may be limited in size, say to 25,000. The
upshot is that, while scale economies by themselves can generate a city,
it will not be as large as, say, Chicago or Houston. In order to generate
such a metropolis, many ﬁrms must locate together in close proximity.
For this outcome to occur, agglomeration economies must be present.
Agglomeration economies can be either pecuniary or technological.
Pecuniary agglomeration economies lead to a reduction in the cost of
a ﬁrm’s inputs without affecting the productivity of the inputs. Technological agglomeration economies raise the productivity of the inputs
without lowering their cost. Simply stated, pecuniary economies
make some inputs cheaper in large cities than in small ones, while
technological economies make inputs more productive in large cities
than in small ones.
1.3.1 Pecuniary agglomeration economies
The labor market offers examples of pecuniary agglomeration economies. Consider a big city, with a large concentration of jobs and thus a
large labor market, where many workers offer their labor services to
employers. Suppose a ﬁrm is trying to hire a specialized type of worker,
with skills that are rare among the working population. With its large
labor market, a few such workers might reside in a big city, and one
presumably could be hired with a modest advertising effort and modest
interviewing costs. However, the labor market of a small city probably
would contain no workers of the desired type. This absence would
force the employer to conduct a more costly search in other cities, and
to bring job candidates from afar for interviewing. The ﬁrm might also
have to pay relocation costs for a hired worker, adding to its already
high hiring costs. Thus, by locating in a big city, a ﬁrm may lower its
cost of hiring specialized labor. The existing employment concentration
in the big city thus attracts even more jobs as ﬁrms locate there to
reduce their hiring costs. The big city then becomes even bigger as a
result of this agglomeration effect.
Locating in a big city could also reduce the cost of inputs supplied
by other ﬁrms (as opposed to labor inputs supplied by individual
workers). For example, the large market for commercial security
services in a big city would support many suppliers of security guards.
These suppliers would compete among one another, driving down
prices and thus lowering the cost of security services used in protecting
ofﬁce buildings or factories. Big-city competition could also reduce the
prices of other business services—legal and advertising services, commercial cleaning and groundskeeping, and so on. The same effect could
also arise in the context of locally supplied physical inputs, such as ball
bearings for a production process or food inputs for the company cafeteria, where competition among big-city suppliers would reduce input
costs. As in the case of hiring costs, the job concentration in a big city
is self-reinforcing: once jobs become concentrated, even more ﬁrms will
want to locate in the big city to take advantage of the lower input costs
In some cases, a small-town location might mean that a particular
business service is entirely unavailable locally, just like the specialized
worker discussed above. For example, a ﬁrm might require specialized legal services (help with an antitrust issue, for example), and
there might be no local law ﬁrm with such expertise. The ﬁrm would
then have to pay high-priced lawyers to travel to its headquarters
from their big-city ofﬁces, or else would have to develop the required
expertise “in house” at high cost. In this case, higher input costs
arise from the sheer local unavailability of the service in the small
city rather than from the low degree of competition among local
Firms also purchase transportation services, which are used in shipping output to the market and in shipping inputs to the production
site. A ﬁrm can reduce its output shipping costs by locating near its
market, and it can reduce its input shipping costs by locating near its
suppliers. A big city, with its many households, is a likely market for
output, and it may also host many of a ﬁrm’s input suppliers. In this
situation, the ﬁrm can minimize its shipping costs for both output and
inputs by also locating in the big city. Note that the resulting pecuniary
agglomeration beneﬁt is slightly different from those discussed above.
Instead of facing a lower unit price of transportation services in the big
city (a lower cost per ton-mile), the ﬁrm beneﬁts from being able to
purchase less of these services because of its proximity to the market
and to suppliers.2
2. Paying high-priced big-city lawyers to travel to a ﬁrm’s small-city location ﬁts into
this scenario. The ﬁrm is transporting its legal input, an outcome that could be avoided
by locating in the big city.
Why Cities Exist
Another observation is that this scenario “stacks the deck” in favor
of the transportation-cost argument for a big-city location. Suppose
instead that input suppliers are in a different location, while the market
is still in the big city. Then, locating there will save on output shipping
costs, but the inputs will have to come from afar. In this case, the location with the lowest total transport cost may not be in the big city, so
that transport-related agglomeration economies may not be operative.
This case is discussed in detail later in the chapter.
1.3.2 Technological agglomeration economies
Technological agglomeration economies arise when a ﬁrm’s inputs are
more productive if it locates in a big city, amid a large concentration of
employment, than if it locates in a small city. To understand how such
an effect can arise, suppose that a high-technology ﬁrm spends substantial sums on research and development. This spending leads to
new technologies and products, which the ﬁrm can then patent, allowing it to earn revenue from licensing its discoveries. Suppose for simplicity that the ﬁrm’s output is measured by the number of patents it
generates per year, and that the only input is labor, measured by the
number of engineers the ﬁrm employs.
The production function is plotted in ﬁgure 1.2, with the output
(patents) again on the vertical axis and the input (engineers) on the
Technological agglomeration economies.
horizontal axis. The ﬁgure shows that research and development exhibits scale economies, although this feature isn’t crucial to the story. The
ﬁgure also shows two different production functions, which apply in
different situations. The lower curve is relevant when the ﬁrm locates
in a small city where few other high-tech ﬁrms are present. The upper
curve is relevant when the ﬁrm locates in a big city amid a large
number of other high-tech ﬁrms. The greater height of the upper curve
indicates that the ﬁrm produces more patents, for any given number
of engineers, when it locates in a big city. Thus, engineers are more
productive, generating more patentable ideas, in the big city.
This beneﬁcial effect could be a result of “knowledge spillovers”
across high-tech ﬁrms, which are a type of externality. While engineers
within a given ﬁrm collaborate intensively in producing patentable
ideas, spillovers arise when contact between engineers in different ﬁrms
also stimulates this productive process. For example, engineers from
different high-tech ﬁrms might socialize together, sharing a pitcher of
beer at a Friday “happy hour.” Although the engineers wouldn’t want
to divulge their company’s particular secrets, the happy-hour discussion might cover more general ideas, and it might get the engineers
thinking in new directions. At work the following week, this stimulation may start a process that eventually leads to patents that wouldn’t
have been generated otherwise. Thus, the engineers end up being more
productive because the large high-tech employment concentration
allows them to interact with peers doing similar work in other
Although a big city is likely to have a concentration of high-tech
employment, allowing knowledge spillovers to occur, some big cities
may not have many high-tech ﬁrms. Thus, the big city/small city distinction may be less relevant for knowledge spillovers than it was for
pecuniary agglomeration economies. Instead, what may matter is the
extent of the city’s employment concentration in the industry in which
such spillovers occur. If a small or medium-size city happens to have
a big employment concentration in the relevant industry, it will offer
strong technological agglomeration economies for industry ﬁrms
despite its limited size.
Might some kinds of knowledge spillovers occur across different
industries, so that a city where many different industries are represented is also is capable of generating technological agglomeration
economies? For example, might knowledge spillovers arise between
manufacturers of medical equipment and producers of computer soft-
Why Cities Exist
ware? This type of linkage seems possible, and to the extent that it
exists, the overall employment level in a city (rather than employment
in a ﬁrm’s own industry) might be the source of technological agglomeration economies. City size may then capture the extent of such economies, as in the case of pecuniary agglomeration economies.
As will be discussed further below, empirical research on agglomeration effects sometimes ﬁnds evidence of such a link between and
worker productivity and total employment (and thus city size). “Urbanization economies” is a name sometimes given to this effect. But the
empirical evidence for a link between productivity and own-industry
employment in a city is much stronger (this effect is referred to as
“localization economies”). Thus, technological agglomeration economies appear to operate more strongly within industries than across
In addition to knowledge spillovers, several other channels for such
an agglomeration effect can be envisioned. When a city’s employment
in a particular industry is large, the existence of a large labor pool
makes replacement of workers easy. As a result, unproductive workers
can be ﬁred with little disruption to the ﬁrm, since they can be immediately replaced. Recognizing this possibility, employees will work
hard, achieving higher productivity than in an environment in which
shirking on the job is harder to punish with dismissal.
The large labor pool also gives employers a broad range of choice
in hiring decisions, which may make it harder for any individual to
secure a ﬁrst job in the industry. Workers may then have an incentive
to improve their credentials via additional education and training, and
these efforts would lead to higher productivity. Thus, the existence of
a large labor pool may raise productivity for workers trying to get a
job as well as for those worried about losing one.
A third channel could arise through the phenomenon of “keeping
up with the Joneses.” In a city with high employment in a particular
industry, workers may be likely to socialize with employees working
for other ﬁrms in their industry, as was noted above. In addition to
making comparisons within their own ﬁrm, workers may then judge
their achievements against those of friends in other ﬁrms. This comparison may spur harder work as employees try to “look good” in the
eyes of a broader social set. Thus, in addition to being driven by knowledge spillovers, the higher worker productivity associated with technological agglomeration economies could arise from these three other
A vast empirical literature tests for the existence of agglomeration
economies. For a survey, see Rosenthal and Strange 2004. Early work
investigated the connection between worker productivity and both
own-industry and total employment in a city (see Henderson 1986,
2003). As was noted earlier, such studies often ﬁnd evidence of an
own-industry effect for knowledge-intensive industries, in which spillovers are likely to occur, without ﬁnding much evidence of a totalemployment effect. Another empirical approach relates worker
productivity to employment density in a city (Ciccone and Hall 1996).
Yet another approach links the birth of new ﬁrms to own-industry
employment, on the belief that business startups are more likely to
occur in areas offering agglomeration economies (Rosenthal and
Strange 2003). A similar approach relates employment growth to ownindustry employment and other agglomeration factors (Glaeser et al.
1992). Other research focuses more explicitly on knowledge spillovers
by considering patent activity. A patent application must cite earlier
related patents, and some work shows that cited patents tend to be
from the same city as the patent application, indicating local knowledge spillovers (Jaffe, Trajtenberg, and Henderson 1993). Other research
relates the level of patenting activity to a city’s employment density
(Carlino, Chatterjee, and Hunt 2007). This literature offers an overwhelming body of evidence showing the existence of agglomeration
economies, mostly of the technological type.
Transport Costs and Firm Location
As was seen above, transportation-cost savings can be viewed as a type
of pecuniary agglomeration effect, which may draw ﬁrms to a large
city when both its market and suppliers are located there. However,
when the market and suppliers are far apart, the ﬁrm’s location decision is less clear. To analyze this case, consider a situation in which a
ﬁrm sells its output to a single market, presumably located in a city,
and acquires its input from a single location distant from the market.
Viewing the input as a raw material, let the input source be referred to
as the “mine.” Moreover, suppose that the mine and the market are
connected by a road that can be used for shipments (see ﬁgure 1.3), and
that the ﬁrm’s factory can be located anywhere along this road, including at the market or at the mine. The mine and the market are D miles
Why Cities Exist
Mine versus market.
Shipping costs exhibit “economies of distance” in the sense that the
cost per mile of shipping a ton of material declines with the distance
shipped. Figure 1.4 illustrates such a relationship, with the vertical axis
representing cost per ton and the horizontal axis representing shipping
distance (denoted by k). The ﬁgure shows shipping cost as having two
components. The ﬁrst is “terminal cost,” which must be incurred
regardless of shipping distance. This is the cost of loading the shipment
onto a truck or a train, and it is represented by the vertical intercept of
the line. The second component is variable cost, which equals the
product of the ﬁxed incremental cost per mile (equal to the slope of
the line) and the distance shipped. Variable cost is thus the height
of the line above its intercept. The presence of economies of distance
can be seen by drawing a line between the origin and a point on the
curve. The slope of this line is equal to cost per mile (analogous to
output per worker in ﬁgure 1.1). As shipping distance increases, this
line becomes ﬂatter, indicating a decline in cost per mile. The reason
for this decline is that the ﬁxed terminal cost is spread over more miles
as distance increases.3
For the current analysis, it is convenient to use a somewhat less
realistic transport-cost curve that has zero terminal costs but still exhibits economies of distance. Figure 1.5 shows two such curves, with
economies of distance following from their concavity (which reﬂects
declining variable cost). The lower curve represents the cost per ton of
shipping the output different distances. To understand the upper curve,
suppose that the production process entails reﬁning raw materials,
with production of the reﬁned output requiring that a portion of the
input be removed and discarded. Then, to produce a ton of output, the
reﬁning factory requires more than a ton of input. The upper curve
represents the cost of shipping this amount of input various distances.
In other words, the curve represents the cost of shipping enough input
to produce a ton of output.
Cost for enough
input to produce
a ton of output
Cost for a
ton of output
D – k0
Input and output shipping.
3. A diagram like ﬁgure 1.4 can be used to illustrate transport mode choice between truck
and train. Relative to trains, trucks have low terminal cost (they can be driven directly
to a shipment pick-up point), but they have high variable cost, using more fuel and labor
per ton shipped than trains. Therefore, the truck line in a diagram like ﬁgure 1.4 would
start below the train line and eventually rise above it. As a result, a shipper choosing the
cheapest mode would select truck for a short-distance shipment and train for a longdistance shipment.
Why Cities Exist
The fact that the unreﬁned input and the reﬁned output are
qualitatively similar (both being, in effect, dirt) is convenient. This
similarity means that the cost of shipping a ton of input or output
a given distance will be the same, which ensures that the input shipping cost curve in ﬁgure 1.5 (which pertains to more than a ton) will
Things are more complicated if inputs and outputs are qualitatively
different. In the baking of bread, for example, the ﬂour input is compact
but the output of ﬁnished loaves is very bulky, so that a ton of output
is more costly to ship than a ton of input. Figure 1.5 would have to be
modiﬁed to ﬁt this case.
The information in ﬁgure 1.5 can be used to compute the best location for the factory. If the factory has a contract to deliver a ﬁxed
amount of output to the market, its goal is to minimize the total shipping cost per ton of delivered output. This total includes both the cost
of shipping the output and the cost of shipping the input, with the
latter cost pertaining to enough input to make a ton of output.
Suppose the factory is located k0 miles from the market. Then the
output must be shipped k0 miles and the input must be shipped D – k0
miles (recall that D is the distance between the mine and the market).
The output shipping cost (per ton) is represented in ﬁgure 1.5 by h, and
the input shipping cost (per ton of output produced) by g. The total
shipping cost per ton of output at location k0 is then h + g. To ﬁnd the
best location, this calculation procedure must be repeated for all k0
values between 0 and D, with the location yielding the lowest total cost
chosen. The required steps are cumbersome, however, and the answer
is, so far, unclear.
The answer can be seen immediately, however, if ﬁgure 1.5 is redrawn
as ﬁgure 1.6. This new ﬁgure has two origins, one at 0 and the other at
distance D, and the input shipping curve is drawn backward, starting
at the D origin. Now, total shipping cost (per ton of output) at location
k0 is equal to the height of output curve at that point plus the height of
the input curve at the same point, which equals the cost of shipping
the input D – k0 miles. Therefore, shipping cost per ton of output is
equal to the vertical sum of the two curves at any point, and the resulting curve is the upper hump-shaped one in ﬁgure 1.6. By inspection,
it is easy to see the cheapest location. It is an endpoint location, with
the factory located at the mine. All other locations, including the market
and points between the mine and market, result in higher total shipping costs.
The mine is the best location because the production process is a
“weight-losing” process. In other words, more than a ton of input is
transformed into a ton of output. In this case, it doesn’t make sense to
ship the input at all, since some of the material will be discarded in the
reﬁning process. Only the output should be shipped.
This appealingly simple rationale partially obscures the logic of the
solution. The logic has two components. First, because of economies of
distance, it isn’t economical to ship both the input and the output. In
this case, two intermediate-distance shipments would occur, failing to
exploit the lower cost per mile of longer shipments. Thus, either the
output should be shipped the entire mine–market distance of D miles
or the input should be shipped the entire distance. The best choice is
the one that is cheaper, and, given the weight-losing nature of the production process, shipping the output all the way costs less. This argument shows that economies of distance, omitted from the partial
explanation above, are crucial to the solution.4
4. If transport costs instead exhibited diseconomies of distance (with the curves convex),
then intermediate-distance shipments would be desirable, and the best location would
be an intermediate point between the mine and market. This result, which can be seen
by redrawing ﬁgure 1.6 for the diseconomies case, shows that weight loss in production
isn’t sufﬁcient for a mine location to be best.
Why Cities Exist
Suppose the production process is, instead, weight gaining. An
example would be Coca-Cola bottling, in which syrup (evidently
produced under secret conditions near the company’s headquarters
in Atlanta) is combined with water to produce the ﬁnished product.
In this weight-gaining case, the heights of the input and output
curves in ﬁgure 1.5 are reversed, as are the heights in ﬁgure 1.6. The
hump-shaped curve in ﬁgure 1.6 then reaches its low point at
the market rather than at the mine, making the market the best
location for the factory (in this case, the bottling plant). The outcome
is natural since it would make little sense to ship ﬁnished Coca-Cola
long distances when its main component (water) is available
In reality, the bottling of soft drinks is indeed a “market-oriented”
production process, with bottling plants located in many cities across
the United States. The theory says that weight-gaining production processes should all share this feature, while weight-losing processes
should be oriented to the mine (or the input). This simple model,
however, omits many elements of reality, including the existence of
multiple markets and multiple input sites for a given ﬁrm, as well as
“bulk” differences between inputs and outputs, which (as explained
above) complicate the picture.6 Nevertheless, the model shows that
transport costs will affect where ﬁrms locate and thus will inﬂuence
the formation of cities.
In the simple case analyzed, this inﬂuence can be delineated. The
market (presumably a big city) will attract weight-gaining production
processes as ﬁrms seek to minimize transport costs. Therefore, the city’s
existing concentration of jobs and people will attract additional jobs in
weight-gaining industries via this transport-related agglomeration
force. Weight-losing industries, however, will shun the market and will
instead locate at the source of the raw material. Therefore, the existence
of a big-city market may spawn separate employment concentrations
at faraway natural-resource sites where factories built to serve the
5. The best factory location may sometimes lie at a “transshipment” point between the
mine and the market, where the shipment must be unloaded and reloaded for some
reason. Exercise 1.1 considers such a case, assuming that an unbridged river cuts the
road between the mine and market, necessitating unloading, transfer to a barge, and
reloading of the shipment.
6. With multiple markets and mines, it can be shown that the optimal location is usually
some intermediate point, so that a market or mine location is not best.
market ﬁnd it best to locate. Concentrated employment in one spot may
thus cause additional remote employment concentrations to arise as a
result of transport-related forces.
1.5 The Interaction of Scale Economies and Transportation Costs
in the Formation of Cities
Although the desire to minimize transport costs can pull a factory
toward a particular location, these costs can also play a role in the
overall organization of production. In particular, transport costs can
help determine whether production is centralized in one large factory
or divided among a number of smaller establishments. The analysis in
section 1.2 showed that a single large factory was best, but transport
costs played no role in that analysis.
To illustrate the interaction between scale economies and transport
costs, and to show how this interaction can affect the formation of
cities, consider a simple model adapted from Krugman 1991. Suppose
that the economy has ﬁve regions and a total population of N, with
N/5 people living in each region. The regions are represented as squares
in ﬁgure 1.7. Each person consumes one unit of a manufactured good,
which is produced with scale economies. In this setting, scale economies are best seen via the cost function C(Q), which gives the total cost
of producing Q units of the manufactured good. Scale economies mean
that the cost per unit of output declines as Q increases, with the factory
becoming more efﬁcient as the level of output expands. Thus, C(Q)/Q
falls as Q rises.
Scale economies versus transport costs.
Why Cities Exist
The economy must produce N units of manufactured good to serve
the population. Two different arrangements of production are possible:
centralized and dispersed. Under dispersed production, a small factory,
producing N/5 units of output, would be located in each of the ﬁve
regions. These factories are represented by the small circles in ﬁgure
1.7. The cost per unit of output in each factory is C(N/5)/(N/5) ≡ λ.
Under centralized production, one large factory, represented by the
large circle, would be located in the central region, producing N units
of output at a cost per unit equal to C(N)/N ≡ θ. With scale economies,
the cost per unit of output is lower in a large factory than in a small
one, with θ x0. This consumer has disposable income of y – tx1, less than
that of the central-city consumer. As a result, the consumer ’s budget
line has a smaller intercept than the central-city budget line, as can be
seen in the ﬁgure. The main question concerns the price per square foot
of housing at this suburban location, denoted by p1. What magnitude
must this price have in order to ensure that the suburban consumer is
just as well off as the central-city consumer? The answer is that p1 must
lead to a budget line that allows the suburban consumer to reach the
same indifference curve as her central-city counterpart. For this outcome
to be possible, the suburban budget line, with its lower intercept, must
be ﬂatter than the central-city line. When the budget line is ﬂatter by
just the right degree, the utility-maximizing point will lie on the indifference curve reached by the central-city consumer, as seen in the ﬁgure.
But since the slope of the budget line equals the negative of the housing
price, it follows that a ﬂatter budget line (with a negative slope closer
to zero) must have a lower price. Therefore, the suburban price p1 must
Analyzing Urban Spatial Structure
be lower than the central-city price p0, so that p1 x0 and r = r1
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