Agglomeration benefits and costs of investing in urban transport infrastructure

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AGGLOMERATION BENEFITS AND COSTS OF INVESTING IN URBAN TRANSPORT	 	
INFRASTRUCTURE	* 	
 	
Haakon Vennemo	 1,2 	
 	1School of Business, 	Oslo Metropolitan University, Norway	 	 	
2 Vista Analyse	 AS, 	Meltzers	 gate 4, 0257 Oslo	, Norway	 	
 	
E-mail	: haakon.vennemo@vista	-analyse.no	 	
 	
Received 	6 January 2023; accepted 	8 March	 2023; published 	30 March	 2023	 	
 	
 
Abstract. 	Theory and evidence suggest that a city owes its existence to 	an 	agglomeration benefit. An investment in urban transportation 	
infrastructure may increase this benefit. While some years ago the agglomeration benefit of urban transportation was just a v	ague 	idea, 	
recently its size has been estimated and the idea has gained concreteness and respectability. However, the theoretical litera	ture has 	
emphasized the agglomeration benefit that arise	s through immigration and higher population, while the empirical lite	rature has emphasized 	
the benefit that arises from effective density at constant population. A third strand of the literature has discussed transpo	rtation of goods. 	
We bring together the	se theoretical and empirical literatures, and discuss which agglomerat	ion benefits and costs are relevant for major 	
categories of urban passenger and freight transport investment.	 	
 
Keywords:	 transport	; aggl	omeration;	 effe	ctive density;	 cost	-benefit analysis	 	
 
Reference 	to this paper should be made as follows	: Vennemo, H. 	2023	. Agglomeration benefits and costs of investing in urban transport 	
infrastructure	. Insights into Regional Development	, 5(1), 59	-71. http://doi.org/10.9770/IRD.202	3.5.1(4)	 	
 
JEL Classifications:	 R13, R42, H43, H54	 	
 
Additional disciplines 	Transport planning 	 	
 	
1. Introduction	 	
A city exists because it offers economic advantages. It provides specialized inputs and sustains specialized 
industries. It inspires entrepreneurs and is a magnet for talent. It supports increasing returns to scale industries and 
allows sharing of public g	oods. Up to a point, the advantages of cities are greater than the well	-known 	
disadvantages of e.g., congestion, pollution, crime and the cost of housing. 	 	
 
Urban transport infrastructure is an essential part of a city. Transport infrastructure increases t	he proximity 	
between people, businesses and goods, and contributes to the city’s advantages and disadvantages. Transport 
makes an urban area more “city	-like”. Yet, a transport planner may find the contribution of an investment in 	
transport infrastructure t	o be elusive. How does traditional cost	-benefit analysis internalize agglomeration 	
 	 	 	* The research	 is support	ed by the Norwegian Research Council Grant no 267	 697,	 ’Impact’	.

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benefits? Do all transport investments generate equal effects? Are agglomeration benefits more important than the 
contribution to congestion and pollution? 	 	
 
In the literatu	re on urban economics one distinguishes between agglomeration benefits (sometimes called ‘wider 	
economic benefits’) associated with market imperfections, and user benefits. However, there are gaps in our 
understanding of how urban transport investments eng	age with these ideas. The theoretical literature uses 	
concepts and indicators that are not entirely satisfactory from a practical point of view, and the empirical 
literatures uses concepts that are not clearly based in theory.	 	
 
In this paper we aim to brin	g together the theoretical and empirical analysis of these issues. In particular, we 	
provide a micro	-foundation for the concept of effective density, or market potential, which is often used in 	
empirical work. The micro	-foundation allows us to distinguish 	between agglomeration benefits in a stable 	
population as opposed to those that depend on migration to a city. The previous literature on impacts of 
transportation investments has only emphasized agglomeration benefits arising from immigration. We show that	 	
these are in fact smaller than immigration’s external costs.	 	
 
In a modern city there are several forms of physical transport: Commuters travel to work in the morning, and back 
in the afternoon. Business 	travellers	 go back and forth on errands and to meeti	ngs during work hours. Leisure 	
travel is for shopping and football practice and all the other things that households do in their spare time. Then 
there is transport of goods, freight, of which we will recognize two kinds: Transport of final goods that are 
consumed and transport of intermediate goods used to make final goods. To the extent that investments targets 
specific purposes of transport, there are different constituents of benefits and costs that come into play. We 
demonstrate how agglomeration benef	its and user benefits enter and exit as we consider transport of different 	
kinds. 	 	
 	
2. Previous literature 	 	
 
The theoretical literature on benefits of urban transport infrastructure is derived from the literature on urban areas 
and cities. Existing models 	treat transport modes and transport costs differently. Some emphasize transport of 	
commuters. Agglomeration benefits enter these models through migration and higher population. Others 
emphasize transport of goods, often modelled in terms of iceberg costs. 	In these models, agglomeration benefits 	
sometimes do not arise at all.	 	
 
An important early contribution is Duranton and Puga (2004), see also Duranton and Puga (2014). Building on 
Abdel	-Rahman and Fujita (1990), they present a model of a city economy with 	market imperfections. Migration 	
to the city provides for a bigger city with more talent that interacts with the market imperfections and generate 
agglomeration benefits. The model also emphasizes costly commuting costs. Commuting costs provides a 
dispersio	n force. The size of the city hangs in the balance between agglomeration benefits, user benefits and 	
commuting costs. Transport of people enters the picture through commutes. Transport of goods is limited: The 
intermediates of the model cannot be transport	ed out of the city, while final goods can be transported at zero cost.	 	
 
Models of a single city are similar in design to small open economy. By contrast, models of urban and sometimes 
rural systems are like models of the global economy. Important early con	tributions include Krugman (1991, 	
Fuijita and Krugman (1995) and Helpman (1998). These models exclude transport of individuals, but they include 
iceberg costs of transporting differentiated goods. Transport of goods gives rise to an agglomeration force. 
Kr	ugman (1991) combines iceberg costs of differentiated goods with costless transport of homogenous goods, 	
Helpman (1998) assumes that the homogenous good cannot be transported, while Fujita and Krugman (1995) 
assume positive costs of transporting the homoge	nous good. The transport or non	-transport of homogenous goods 	
gives a dispersion force.

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The early models of cities and urban systems have recently been ela	borated e.g., by Behrens et al.	 (2014), 	
Redding and Turner (2015) and Redding and Rossi	-Hansberg (2017). These authors solve a general equilibrium 	
system of n locations that each produce differentiated goods. In Redding and Turner (2015) and Redding and 
Rossi	-Hansberg (2017) there are i	ceberg costs of transporting differentiated goods to other cities. In Behrens et al. 	
differentiated goods cannot be exported, but individuals (the input factor) can migrate at zero cost.	 	
 
The empirical literature on transport and agglomeration makes heavy 	use of the concept “effective density” or 	
“market potential” (the two are used interchangeably), see e.g., the survey of Ahlfeldt and Pietrostefani (2019). In 
the empirical literature effective density refers to the synergies of ideas and human capital alo	ng the lines of 	
Marshall (1890) and endogenous growth models (Lucas, 1988; Romer, 1990). Graham (2007) and Graham et al., 
(2010a) are two examples of empirical work that postulates an index of effective density as a sum of employment 
in adjacent locations,	 with distance from “our location” as weights. Instead of geographical distance as weights 	
one may use generalized cost of transport including time and pecuniary cost, as in Graham et al., (2010b). 	 	
 
In the theoretical literature the concept is often attri	buted to Harris (1954). Harris defines it as “an abstract index 	
of the intensity of possible contacts in markets”. Contemporary models of urban systems have interpreted the 
concept in the form of market access of goods (Krugman, 1993, Eaton and Kortum, 199	3), particularly associated 	
with foreign trade (Donaldson and Hornbeck, 2016). Hence, although the name may be the same the connotations 
are different in the empirical and theoretical literatures: The theoretical literature emphasizes market access of 
good	s, while the empirical literature emphasizes density of ideas. The theory papers on market potential are not 	
really helpful in explaining the empirical models. 	 	
 
Analyzing the impact of a transport investment on agglomeration is like analyzing a perturbati	on of the city or 	
urban system. A small number of previous papers have done this. Venables (2007) has a model containing an 
increasing returns to scale production function, a cost of commuting, and an income tax. He finds that a transport 
investment that l	owers the cost of commuting has a direct impact on the aggregate cost of commuting plus an 	
external agglomeration benefit and cost to the extent that the investment induces migration to the city. Venables 
also shows how an income tax interacts with the oth	er market imperfections.	 	
 
Kanemoto (2013) also considers the impact of an investment to lower the cost of commutes. Kanemoto has an 
explicit microeconomic underpinning of the aggregate production function, and he has several cities. However, 
like Venables,	 Kanemoto does not discuss agglomeration benefits in a given population, nor does he discuss 	
different transportation aims and modes.	 	
 
Our paper makes three contributions to the literature on transport and agglomeration. First, we show how 
transport invest	ment may generate agglomeration benefits in a given population and that this is the proper channel 	
since agglomeration benefits of immigration are dwarfed by agglomeration costs. Second, we provide a 
satisfactory theoretical underpinning for the concept of	 effective density. Third, we discuss agglomeration 	
benefits of all relevant transportation aims and modes, including recreational travel and freight.	 	
 	
3. The model	 	
 
We present here a model of a city economy that features agglomeration. We use upper case lett	ers for aggregate 	
variables, lower	-case letters for individual level variables, and (where necessary) lower	-case letters with a bar for 	
average variables. For parameters we use lower case Greek letters.

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3.1	 Commuting cost and land rent	 	
Our modeling of commuting costs and land rent follows Duranton and Puga (2004) and is by now fairly standard. 
A short summary is offered. Commuting cost and land rent determine the spatial extent of the city. The individual 
commuting cost 	c is a function o	f distance traveled, 	x, and a parameter τ that summarizes the quality of 	
infrastructure service	:	 	
 	(1) 	
A longer distance (high 	x) increases costs, while improved infrastructure service (high τ) decreases cost. All 	
workplaces are located at the same location in the city, the Central Business District (CBD). 	 	
Everybody is equal and therefore, in equilibrium the sum of commuting cost 	and land rental cost will be the same 	
for all. Land rent at the border is zero and there is no congestion immediately outside the border.	 	
There are 	N individuals in the city. Everybody lives somewhere on a disk of area 	N and radius 	 from the 	
CBD. Subsuming the square root into the function 	c(x,τ)	 this gives the following relation between commuting cost 	
and rental cost of land:	 	
 	(2) 	
 	 	
Equation 	(2) says that the sum of commuting cost and rental cost of land is the same everywhere in the city, 	
including at the border where land rent is zero. In particular, the equation holds for an individual experiencing 
average commuting costs (	) and a	verage land rent (	), which we state as equation 	(3): 	
 	(3) 	
3.2	 Production technology of the final good	 	
Production of the final good and intermediates again follows the standard model, which is a love of variety 
production function and fixed costs of making intermediates. The city produces a final good 	Y by means of a 	mass 	
m of intermediates 	y(s)	: 	
 	(4) 	
The parameter 	σ determines the curvature of the production function, the elasticity of substitution. 	 	
 	
3.3	 Production technology of intermediates	 	
Intermediates are produced by increasing	 returns to scale technologies:	 	
 	(5) 	
β indicates variable cost, 	α indicates fixed cost, and 	l(s)	 is input of human capital in production of the 	
intermediate. To begin with we assume that intermediates are not exported. Intermediate producers then face 
downward sloping demand curves from the local final goods sector, and profit maximization implies:	 	
 	(6) 	
Intermediates use identical production technologies where 	q is the common price of intermediates and 	w is the 	
common wage of human capital in the city. A common wage and no other primitive inputs imply that there is one

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final goods sector in equilibrium. Free entry into production of intermediates implies zero profits, which 
determine a common production l	evel of intermediates 	y by means of equations (5), (6) and (7)	: 	
 	(7) 	
 	(8) 	
Equation (5) determines the common level of human capital 	l in each intermediate:	 	
 	(9) 	
With a fixed level of human capital 	H in the city, the mass of intermediates can be found:	 	
 	(10	) 	
3.4	 Effective density	 	
We depart from the standard model and assume that each individual is endowed with 	h units of human capital. 	
We let 	denote the intellectual influence of individual 	j on individual 	i. 	 is a scalar between and 1. 	
The network literature (e.g., Topa and Zenou, 2015) usually assumes that 	 is either if there is no contact 	
between 	i and 	j, or 1 if there is unhindered contact. These are extreme outcomes. Most links between peo	ple face 	
transaction costs in the form of culture, distance, frequency of interaction etc that suggest that an intermediate 
value between and 1 is appropriate. 	 	
We assume that the links between people can be improved by better communication technologies:	 	
 	 (11	) 	
c1…c	n are the costs of communication technologies between 	i and 	j. Individuals in the city may also receive 	
influence from outside the city. Such influence is incorporated into equation 	 (11	). 	
We are concerned with ordinary physical transportation, whether business travel where people meet 
professionall	y in meetings and seminars and professional dinners, or leisure travel where ideas may be shared on 	
the sidelines of a football field or during a chance meeting at a café, or commutes where people of common 
interests may end up talking at the subway statio	n. Suppress other explanatory variables and let τ be an indicator 	
of infrastructure quality that decreases the cost of transportation in the manner of equation 	(1). 	
Adding over all influencers gives aggregate influence on individual 	i: 	
 	(12	) 	
Equation 	(12	) is our expression for effective density. It is an index, or weighted sum of human capital elsewhere 	
in the urban area that one considers a city. The index allows significant flexibility. If the influence from 
employees, say, to entrepreneurs is a priori z	ero, the relevant 	g(i,j)	 are always zero and 	g is lower than it would 	
have been otherwise. If 	g(i,j)	 of some 	j are equal, e.g., because these	 j share the same location, equation 	(12	) will 	
cluster the relevant 	h(j)	 into groups. Such a clustering is common in empirical formulations.	 	
In equation 	(13	), 	is 	average	 influence on individual 	i. In general, the average influence depends on 	
the cost of communication 	vis	-à-vis	 everybody else, and this cost will differ depending on one’s location in the 	
city. We suppress this locational difference and assume that the average influence on all individuals is the same 
and denoted 	g. Total influence on each individual is 	gH	: 	
 	 	 	(13	)

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In equation 	(13	) we ignore any influence of population (	N) on effective density (	g). The interpretation is that 	
population growth is accompanied by proportional spatial growth.	† 	
 
Stronger intel	lectual influences increase productivity among intermediate producers. For instance, among the self	-	
employed influence and inspiration from others may spur innovation to develop new processes that reduce cost 
and improve productivity. Among employees the i	nfluence from others may inspire to improve work procedures 	
and product lines, again improving productivity. We propose a formulation for productivity improvement as 
follows:	 	
 	(14	) 	
 	(15	) 	
 are benchmark parameters of productivity when there is no influence from others. 	 is the elasticity 	
on productivity when intellectual influence increases (i.e. learning), or better: the externality of effective density.	 	
 	
3.5	 Aggregate production	 	
Pulling together equations 	(4), (8), (10	), (14	) and 	(15	), we obtain the aggregate production function of the final 	
good:	 	
 	(16	) 	
A complicated function of constants have been subsumed into 	Y by an appropriate choice of units. The price of 	
the final good is the numeraire. We assume that our city is an island in a sea of cities and that the final good sector 
participates in a large ma	rket subject to free entry, and zero profits prevail. Zero profits imply a wage rate equal to 	
Y/N	, or 	 	
 	(17	) 	
 	
3.6	 Utility and welfare	 	
We assume that income from land rent is divided equally between the individuals of the	 city. Since the price of 	
the final good is the numeraire it is straightforward to calculate indirect utility of each individual in the city (	v) as 	
wage income plus the average share of land rents, less rental cost, less commuting cost. In other words, ind	irect 	
utility equals net income in this economy of one final good. 	 	
Inserting equations 	(3) and 	(17	) we obtain:	 	
 	(18	) 	
Equation 	(18	) is a key equation for what follows. It states that a city is a trade	-off between positive learning 	
externalities (indicated by the exponent 	θ) and sharing externalities (the e	xponent 	σ) on the one hand, and 	
congestion costs 	 on the other. The city population generates learning (	θ) and sharing (	σ) externalities, which 	
reinforce each other 	, but city size also influences average congestion costs 	. Infrastructure (	τ) 	
influences agglomeration directly in the term 	 Previous models have included this impact only through 	
growth in population (	N). 	
 
People are free to migrate between our city and the outside world, and equilibrium city 	size obtains when 	
individual utility inside the city equals individual utility outside. Individual utility outside the city is fixed at 	, 	
hence 	 in equilibrium. Viewed as a function of city size N the model admits two equilibria, 	of which one is 	
stable and the other is unstable (Duranton and Puga (2004, 2014)). A stable equilibrium requires 	. This 	
requirement states that the equilibrium city is bigger than what would have been optimal. Intuitively, migration to 
 	 	 	† Recall that everybody lives on a disk of size N. Here we 	deviate from a recent paper by Davis and Dingel (2019). Davis and Dingel argue 	
that a larger N encourages learning. There are some other differences between our paper and Davis and Dingel (2019) as well. 	In particular, 	
learning is optimal in their model, t	here is no external agglomeration benefit.

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the cit	y eats away at the surplus of the city until the point where the congestion cost equals the positive 	
externalities.	 	
 	
4. Cost	-benefit te	st for investment in transport	 	
We use the model to set up a cost	-benefit test of an investment in transport infrastructure. 	The test comprises 	
agglomeration benefits, external costs, and user benefits.	 	
 	
4.1	 Preliminaries	 	
There are altogether 	 members of the economy inside and outside the city, and to measure the benefit of a 	
transport project we use a simple welfare function:	 	
 	(19	) 	
We submit that an investment to improve transport infrastructure should 	pass the cost	-benefit test	 	
 	(20	) 	
For simplicity we disregard the investment cost of constructing τ. Adding a non	-zero investment cost would only 	
change the hurdle of the cost	-benefit test. In 	(20	) 	 is the displacement effect, the effect of people 	
migrating between the city and the outside world. To the first order, the displacement effect generates zero utility. 
What remains as a potential benefit is the impact on individual utility, multiplied by c	ity population.	 	
To indicate the impact on individual utility we make the standard assumption in cost	-benefit analysis that the 	
economy is initially in equilibrium and the project under consideration will benefit the economy if 	 is positive. 	
The effect on individual utility can generally be written as	 	
 	(21	) 	
It is useful to sign the terms of 	(21	). In equilibrium we know that 	 is negative. Further, 	τ is optimally arranged 	
prior to any project that is new to the economy. This means 	initially. It	 follows that 	 is positive when 	 	
is positive. In plain words: Transport infrastructure that improves individual utility directly (	 > 0) will attract 	
migrants to the city (	. This seems a reasonable feature of the model. 	 	
Armed with these preliminaries we are ready to work out the cost	-benefit test of specific, new transportation aims 	
and modes. 	 	
 	
4.2	 Cost	-benefit test for commutes 	 	
We find the impact on welfare of an increase in	 τ that affects the average cost of commutes, 	: 	
 	
 	(22	) 	
We spell out the terms of 	(22	). When τ increases the first term in 	(22	) is the percentage increase in effective 	
density 	 times the elasticity of productivity with respect to effective density (	θ), times production. This 	
term is the ex	ternal agglomeration benefit of much empirical work. In empirical work 	θ is often found to be 	
around 0.04 (Ahlfeldt and Pietrostefani, 2019). 	 	
The second term in 	(22	), 	, is the decrease in average transportation and congestion cost for commutes that the 	
improvement brings about, times the number of inhabitants in the city. This term is the user benefit of the	 	
investment and the only term of this model that would be included in a traditional cost	-benefit appraisal.

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The third term in equation 	(22	), 	 , collects the effects of a larger population. Inside the 	
brackets the first term, 	 combines the sharing and learning externalities of a larger population, where 	
the sharing externality implies that more intermediate varieties can be supported, and the learning externality 
implies that a higher human capital base generates more synergies	, more learning. The second impact inside the 	
brackets, 	 is the increase in average congestion cost when new inhabitants arrive, multiplied by population. 	 	
The bracketed term in the second line of equation 	(22	) equals 	, which we know is negative in an economy that 	
starts out from equilibrium. The cost increase in congestion is more important than 	the benefit increase through 	
sharing and learning. Hence there is no external benefit of the bracketed terms in total, rather the expression 
points to an external cost. Still, the previous literature has emphasized the agglomeration benefit inherent in the	 	
expression and not the overall sign (Venables, 2007).	 	
 	
4.3	 Cost	-benefit test for recreational travel	 	
Commutes are carried out in order to generate income and production. Residential travel, by contrast, is done to 
increase utility. In the model so far, all one does in ones spare time is to consume 	Y. We now assume there are 	
two goods for citizens to choos	e from, namely the consumption good 	Y and time 	T spent on recreation in the form 	
of contact with friends and family etc. Labor supply stays the same. Individual consumption of recreation is 	t and 	
T=tN	. 	
Y has a price of 1 as before. The unit cost of recreat	ion is 	. More precisely,	 	 is the cost of travelling to gain 	
access to the recreational service (i.e. friends, family). 	We integrate recreational travel into the analysis by 	
inserting its price into the indirect utility function of households, see equation 	(23	). 
 	(23	) 	
Similarly to the cost of commutes we assume that improvements in infrastructure 	τ lower the price of recreational 	
travel, and that a larger population 	N increases the price of recreational travel (average length of time spent 	
travelling, congestion) hence 	. Let 	 as before, and consider a project that increases the 	
indicator τ. In this setup the indicator τ allows for more conveni	ent recreational travel 	and 	commutes, since both 	
travels occur on the same roads, railways etc. We obtain	 	
 	(24	) 	
From Roy’s identity we have 	 Hence, equation 	(24	) is positive if and only if:	 	
 	(25	) 	
From equation 	(25	) a project that promotes recreational travel gives a user benefit that is proportional to 	
recreational transport consumption, 	. 	Furthermore it increases effective	 density 	as an external benefit, 	
. The impact on effective density may be further disentangled using 	 (11	), since we now have two items, 	
commutes and recreational travel, that contribute (through a higher 	τ) to higher effective density. In plain terms 	
recreational contact may transfer knowledge and influence, adding to the impact of commutes. Most empirical 
an	alysis does not distinguish travel by purpose when calculating external agglomeration impacts of higher 	
effective density. Implicitly, recreational travel is treated on par with commutes, highlighting the relevance of 
including recreational travel in the t	heory model. 	 	
The	 project may also reduce travel costs for commuters, 	. 	
These improvements in welfare set in motion migration to the city. Population increases, which gives rise to 
positive learning and sharing externalities, but also further congestion and impediments to recreational services.

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Around a stable equilibrium the 	congestion and impediments dominate, the net impact of immigration is an 	
external cost. 	 	
Compared to commutes the difference when assessing recreational travel is the a) the stronger economic benefit 
of increased density 	, b) the user benefi	t 	 and c) the additional external economic cost associated with 	
population growth, 	 . 	
 	
4.4	 Cost	-benefit test for transport of final goods	 	
As noted earlier in the paper, there is a strand in the literature on market access, effective 	density and 	
agglomeration benefits that is concerned with trade in goods and transport of goods. We now extend our model to 
trade in goods. First, we consider trade in the final good. We ignore recreation (the previous section). 	 	
 
To model trade in goods w	e assume that the economy has access to a final good 	X that can be imported for 	
consumption at price 	px. Consumption of the final good that is domestically produced, is 	Z. From equation 	(18	) 	
the budget constraint of the economy is 	 	
 	(26	) 	
 
For each consumer, equation 	(26	) modifies indirect utility as follows: 	 	
 	(27	) 	
 
We assume iceberg costs in transporting good 	X to our city. An investment to reduce iceberg costs will reduce 	px. 	
 
Similarly to above, we have that 	 in a stable equilibrium.	 	
 
By means of equation 	(27	) and Roy’s identity we obtain	 	
 	(28	) 	
 
Since the investment to reduce iceberg costs will reduce 	px the cost	-benefit test is formulated in the negative.	 	
Equation 	(28	) is negative if and only if	 	
 	(29	) 	
 
The equation tells us that a decrease in iceberg freight cost produces a user benefit in proportion to imports of the 
final good, plus a net external cost of migration to the city. The net external cost consists of a gross ex	ternal 	
benefit and a larger gross external cost, like in the other cases we have examined. The reason, of course, is that 
lower freight costs improve transport lines of goods, lower prices and increase the standard of living in the city. 
People realize thi	s and move to the city in response. There is a beneficial impact of sharing and learning, but in 	
the neighborhood of equilibrium this benefit is dominated by costs of congestion. In contrast to improvements in 
commuting costs or recreational costs within t	he city, lower freight costs do not bring people closer together and 	
has no consequence for effective density of a given population.

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4.5	 Cost	-benefit test for transport of intermediates	 	
To conclude the taxonomy of transport modes and aims we consider transport of intermediate goods. In addition 
to domestic intermediate goods we assume that it is possible to purchase from other regions 	n intermediate goods 	
x1…x	n at fixed prices 	q1…q	n. The purchase is financed by sales of the final good Y. The production function 	(4) is 	
modified to.	 	
 	 	
 	(30	) 	
The regional budget constraint is modified to 	 	
 	(31	) 	
The budget constraint equals city utility. Assume freight costs decrease and 	qi goes down. 	(31	) is a money metric 	
utility function and Hotelling’s lemma immediately gives 	. The cost	-benefit test is again 	
formulated in the negative: 	 	
 	(32	) 	
(32	) bears similarities to 	(29	). (32	) tells us that a decrease in the cost of an intermediate gives a user benefit in 	
proportion to consumption of that interme	diate, plus an external economic cost as the primary benefit is eaten 	
away by migration to the city. External economic benefits are absent in the aggregate despite the sharing and 
learning externalities.	 	
Discussion and conclusion	 	
The previous theoretical 	literature on costs and benefits of urban transportation has associated agglomeration 	
benefits with immigration. We have developed a simple model that allows agglomeration benefits in a city 
structure of a given population size. This is the maintained assu	mption in much empirical work. Along the way 	
we have shown that in the neighborhood of equilibrium the external agglomeration benefit of immigration 
actually is dominated by an external congestion cost. Further, we have shown that investments to improve 
transport facilities for people in cities will entail agglomeration benefits to a given population, while investments 
to improve the transportation of goods influence population size. While these investments bring agglomeration 
benefits, they entail larger e	xternal costs and the net external effect is negative.	 	
 
External benefits and costs, and traditional user benefits, associated with different transport purposes are 
summarized in 	Table 	1.

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Table 	1. Types of transport, types of benefit	 	
 	External economic benefits and costs	 	User benefits	 	
Type of transport	 	
Benefit 
(through 
effective 
density)	 	
Cost 	(net effect of 	
congestion, productivity)	 	
 Recreation	 	Transport 
accessibility 	 	
Consump	-tion	 	Lower cost of 
production	 	
Recreational 	
travel	 	X 	X 	X 	X 	 	 	
Commutes	 	X 	X 	 	X 	 	 	
Freight, final 	
goods	 	 	X 	 	 	X 	 	
Freight, 	
intermediate 	
goods	 	
 	X 	 	 	
 	
X 	
 
Table 	1 reiterates that only transport projects that increase transportation of people produce agglomeration 	
benefits at given population size. The agglomeration benefits at given population size are	 positive in nature. 	 	
 
All urban transport projects 	– whether passenger or freight 	– facilitate a response in terms of immigration. With 	
immigration a number of benefits and costs are set into motion. Learning and sharing externalities are enhanced, 
commut	ing costs rise, and environmental amenities may be strained. However, to the first order the costs of 	
immigration are larger than the benefits. The reason is that immigration is a response to the benefit of a transport 
project. The benefit implies that cit	y life is more attractive and immigration results. Immigration eats away at the 	
surplus until it is eliminated. If it were never eliminated marginal utility would remain higher in cities, and city 
growth would be a runaway process (unstable equilibrium). H	ence, the agglomeration benefits requiring 	
migration are arguably less interesting than those at given population. By implication improving transport of 
goods is less likely to bring about agglomeration benefits than transport of people, and projects that 	improve both 	
commutes and recreational travel could be the most fruitful of all.	 	
 
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Funding: 	Support by the Norwegian Research Council Grant no 267	 697,	 ’Impact’ is gratefully acknowledged.	 	
 
Acknowledgement:	 Thanks to Steinar Strøm, Michael Hoel, Wiljar Hansen, 	Rasmus Bøgh Holmen, 	seminar 	participants at 	
OsloMet and participants at the 42nd Annual Meeting of the Norwegian Association of Economists for valuable comments 
on an earlier draft. This research was conducted while the author was affiliated with the School of Business at Oslo 
Metrop	olitan University	. 	
 
Declaration of Interests: 	I declare no conflict of interests.	 	
 
 
Haakon VENNEMO	, PhD and Professor, is an expert in environmental economics, energy economics and development 	
issues, with a broad knowledge of macro and micro	-economics in 	general. He has project experience from a large number of 	
countries in Asia, Africa and Latin	-America and is an experienced project manager as well as participant. In China he has a 	
continuous project experience since 1996. Haakon is also engaged in domest	ic Norwegian policy issues, where he primarily 	
does economic analysis of policy suggestions of interest to the public and private sector; market analysis and evaluations. 
Energy, environment and welfare issues are important in his Norwegian portfolio, but 	he conducts work in a large number of 	
areas. Haakon has taken part in several hundred policy research projects, and has been project manager in more than a 
hundred. He is also a very experienced quality controller. Haakon Vennemo has strong academic creden	tials and about 40 	
publications in referee journals and books. He is Adjunct Professor of Economics at the Business School of Oslo 
Metropolitan University.	 	
ORCID ID	: https://orcid.org/	0000	-0002	-4862	-9583	 	
 
 
 
 
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