Aerotropolis - Editorial Express

Aerotropolis - Editorial Express

Aerotropolis: an aviation-linked space∗ Ricardo Flores-Fillol†- Rosella Nicolini‡ March 2006 Abstract This paper examines the conditions allowing for...

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Aerotropolis: an aviation-linked space∗ Ricardo Flores-Fillol†- Rosella Nicolini‡ March 2006

Abstract This paper examines the conditions allowing for the formation of aeropolitan areas as large industrial areas with high concentration of commercial activities in the surroundings of cargo airports. Land competition around airports takes place among service operators, firms and farmers, when firms deliver part of their production by plane. Besides supplying aviation and non-aviation services to firms, service operators generate externalities that firms can take advantage of as far as they are close enough to the airport center. Our framework allows to select a stable land equilibrium involving service operators, firms and farmers characterized by the spatial sequence Airport-Industrial Park-Rural Area (A-I-R), irrespective of the category of the airport (cargo or passenger). Aerotropolis-type configurations arise around cargo airports when there is an intense use of the airport by the firms and a sufficiently high level of externalities. Keywords: Aerotropolis; externalities; bid-rent function JEL Classification: L29, L90, R14



We are grateful to Jan Brueckner, Nicolas Boccard, Xavier Martínez-Giralt and Inés Macho-Stadler for their comments and suggestions. R. Flores-Fillol acknowledges the financial support from the Spanish Ministry of Education and Science (SEC2002-02506 and BEC2003-01132) and Generalitat de Catalunya (2005SGR00836). R. Nicolini acknowledges support by the Ramón y Cajal contract, Barcelona Economics Program CREA, research grants 2005SGR00470 and SEJ2005-01427/ECON. † Departament d’Economia i d’Història Econòmica, Edifici B, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain. Tel.: +34935811811; fax: +34935812012; email: [email protected] ‡ Instituto de Análisis Económico (IAE) - CSIC and CREA, Barcelona Economics. Address: IAE, Campus de la UAB, 08193 Bellaterra (Barcelona), Spain. Tel.: +34935806612; fax: +34935801452; email: [email protected]

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Introduction

Logistics become more and more an issue because firms need to be more and more flexible. Speed and agility are already as important as price and quality for firms that adopt justin-time strategies. Firms choose their location to enhance their accessibility to markets. Logistics are not seen anymore as costs to be minimized, but as value-added activities that need to be optimized. Quoting Mr. Lueck (AMB vice president and asset manager): "You can have the best product, the best R&D and the best marketing, but if you can’t get your product to the user through the supply chain efficiently, you will lose... Logistics are a value link in the supply chain, providing more than a way to move a box from here to there". Fast delivery is a key element (see Leinbach and Bowen, 2004 for empirical evidence). Airports are seen (especially by e-tailers) as a new kind of Central Business District (CBD) with enough capacity to leverage air commerce into high profits. In that spirit, Kasarda (2000) introduced for the first time the idea of aerotropolis (airport city), namely a large industrial area characterized by a high concentration of commercial activities in the surroundings of some cargo airports. Arend et al. (2004) assess that aerotropoli may extend up to 32 kilometers (20 miles), including a number of activities and infrastructures like retail and distribution centers, light industrial parks, office and research parks, districts zoned for specific purposes, foreign trade zones, entertainment and conference facilities and even residential developments that contribute substantially to the competitiveness of firms belonging to this area. This paper aims at analyzing the conditions that allow for the formation of aeropolitan areas by applying the idea of sprawl to study the distribution of activities around an airport. Our study concentrate on two main issues: 1. Figure out the possible land sprawl configuration as a stable equilibrium in the sourroundings of an airport, 2. Detect the conditions supporting the creation of an aerotropolis. Glaeser and Kahn (2004) argue that decentralization and density are the basic features characterizing the concept of sprawl. The canonical setting focuses on urban sprawl, and usually refers to the spreading of employment and population in a metropolitan area as well as its concentration in living and working areas. The land equilibrium is driven by the value each type of agent pegs to a land plot at a each possible distance from the airport center. Starting from the model for the location of divisible activities developed by Von-Thünen (1826), various models have tried to explain the configuration of cities where households

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commute to the CBD and form urban agglomerations around it.1 As pointed out by Fujita and Thisse (2002), the novelty of Von-Thünen is to introduce the notion of bid-rent function: land is not homogeneous and is assigned to the highest bidder. A piece of land at a particular location can be associated with a commodity whose price is not fixed by the market demand and supply. According to Alonso (1964), who adopted the Von-Thünen agricultural model to an urban context, the rent each agent can bid at each location is explained by the savings in transport costs with respect to a more distant site. Hence, land rises a spatial heterogeneity and agents stop bidding for the most distant land since no further savings can be enjoyed. Fujita and Thisse (2002) prove that the spatial heterogeneity generated by an exogenous center (the CBD) allows to escape from the Spatial Impossibility Theorem.2 This study grants most of its features to the urban theory. In that spirit, we consider how commercial firms, service operators and farmers compete for land. By service operators we are referring to all firms developing activities associated to the usage of the airport. Service operators provide aviation and non-aviation services to commercial firms. Aviation services account for air transportation activities whereas non-aviation services include a number of complementary facilities (e.g. freighter docks, bonded warehouse, mechanical handling, refrigerated storage, fresh meat inspection, mortuary, animal quarantine, livestock handling, health officials, security for valuables, decompression chamber, express/courier center, equipment for dangerous and radioactive goods, large or heavy cargo etc.).3 Although we adopt the basic features of general urban models, we extend the analysis to consider the presence of externalities as a further variable affecting each agent location choice. Our setting is simple. There is a group of service operators supplying a range of services in the proximity of an airport, and firms need to settle close to them to exploit those services. The proximity to the airport let firms benefit from externalities that smooth their operating costs. The externalities are generated by service operators and capture the easiness for firms to access to many complementary activities (basically services) they need for carrying out their regular activity. The spatial concentration of these services in the proximity of an airport prevents firms from wasting time in searching the most suitable ones and reduces their operative costs. In such a way, firms earn speediness in delivering their products and make the value-added of their activity increase. Therefore, externalities are modeled as intangible assets that partially reduce firms operative costs and whose 1

See Fujita and Thisse (2002) for a complete overview of the evolution of this literature in economics of agglomeration. 2 Spatial Impossibility Theorem: there is no competitive equilibrium involving transportation in a tworegion economy with a finite number of consumers and firms; homogeneous space; costly transport; and preferences locally non-satiated (Fujita and Thisse, 2002, pp. 35). 3 The reader can browse at www.azworldairports.com and find the most important non-aviation services provided in the major worldwide airports.

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exploitation is strongly associated with location (in the spirit of Chipman, 1970). The idea of introducing externalities as a further force driving agent location choices is not new. There exists other studies stressing the importance of externalities in determining urban patterns. Let us recall the study by Brueckner et al. (1997) in which the relative location of income groups depend on the spatial distribution of amenities in a city; as well as the contribution by Cavailhès et al. (2004) that explains the presence of periurban belts around cities (occupied by both households and farmers) as a consequence of the choice of households to live in the same area as farmers since they value the rural amenities created by farming activities. The size of the benefits generated by the externalities turn out to be crucial for the formation of an aerotropolis. As aerotropolis, we intend a dense industrial area where firms exploit the externalities sourced by service operators in the surroundings of a cargo airport. The forces driving the structure of the urban sprawl are basically the presence of externalities and the proportion of the production firms need to deliver by air commerce. Once the condition to fix the creation of an urban sprawl are fixed, we derive the second result of the study: determining the basic features originating an aerotropolis. We are able to detect the conditions for the existence of an aerotropolis by comparison between the equilibrium in the cargo and the passenger settings. Finally, another distinguishing feature of our framework is the presence of transport costs as a quadratic function of the Euclidean distance form each location to an exogenous fixed central business district (CBD). Our idea is to replicate a setting in which the exploitation of the intangible benefits (externalities) is strongly associated with the location. As far as the firm distances from the CBD, the impact of such externalities becomes small, but the decline of the impact is progressive (and not proportional) with the distance.4 This paper is structured as follows. Section 2 presents some empirical evidence motivating the analysis. Section 3 presents the model, introduces the equilibrium analysis and isolates the required conditions for aeropolitan areas to arise. Section 4 provides some case studies supporting the theoretical results and, finally, Section 5 concludes.

2

Empirical Evidence

In this section we provide some empirical evidence about the importance of air transport in order to support some assumptions of the framework we develop.5 4

In this respect, empirical evidence can be found in Henderson (2003) or Glaeser and Kahn (2004). We would like to thank M. Serret (IMADE, Spain), The Agency of Development of Alava (Spain), E. Maniecki (Chamber of Industry and Commerce of Cologne, Germany), Economic Promotion Board Region Frankfurt RhineMain (Germany), M.V. Cicogna (ENAC, Italy), W. Küstner (Wirtschaftsfoerderung Region Stuttgart GmbH, Germany) for data and information provided. 5

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The International Civil Aviation Organization (ICAO) estimates that about 4.5% of the world GDP may be attributed to air transport and its effects upon industries providing either aviation-specific inputs or consumer products. In simple terms, every US $100 of output produced and every 100 jobs created by air transport trigger additional demand of US $325 and in turn 610 jobs in other industries. The total economic contribution of air transport can be measured by looking at the employment and income effects derived from its direct economic activities on the one hand, and from its indirect and induced activities (better known as multiplier effect) on the other hand. As one can expect, most of these employment and income effects take place at regional level are higher than at national and vary substantially from airport to airport depending on the relationship between the firms and service operators.6 The concept of aerotropolis (a large industrial area characterized by a high concentration of commercial activities in the surroundings of some cargo airports) derives from a refinement of the study of the economic effects induced by an airport in its surroundings. It is relatively new. Some aerotropolis projects already exist and others are under construction and taking shape. Arend et al. (2004) mention several examples of aerotropolis. Amsterdam-Shiphol (AMS) is one of the best examples of mature aerotropolis since it is surrounded by logistic and office parks; merchandise marts; hotels and entertainment complexes; and there is rail service to Amsterdam, other important cities in Western Europe and major logistic centers. The cases of Memphis (MEM) and Louisville (SDF) in United States; and the cases of Köln-Bonn (CLG) and Vitoria-Foronda (VIT) in Europe (Germany and Spain respectively) are also the center of well established aeropolitan areas. Conversely, Dallas-Ft. Worth (DFW) is one of the clearest examples of aerotropolis under construction. Particularly, at the east of the airport, "Las Colinas" area is expanding to accommodate 790, 000 sqm of light industrial space, 121, 000 sqm of retail, 13, 000 family homes, 3, 700 hotel rooms and more than 75 restaurants. Companies like AT&T, Hewlett-Packard, Exxon, Abbot Laboratories, GTE or Microsoft are already there (Kasarda, 2000). Another example of aerotropolis under construction is the logistic integrated area "PLAZA" in Zaragoza (Spain).7 Given the commercial underpinning orientation of an aerotropolis, it is quite intuitive to think of aerotropoli creating around cargo airports. In Europe, the specialization between cargo and passenger airports is less pronounced since the major airports in cargo are also prominent in passenger activities. Although any airport develops both cargo and passenger activities, they are usually classified into two categories (cargo or passenger) by looking at the dominant nature of their operations (see Airports Council International for quantitiative statistics). For instance, 6

Referring to ICAO circular (2004) for a few quantitative data.

7

Data can be obtained at www.plazadosmil.com.

4

Memphis (MEM) and Louisville (SDF) are usually classified as cargo airports. They are are air-express "mega-hubs" since they are the air base of FedEx and UPS respectively. Consequently e-tailers that normally work in partnership with FedEx and UPS have strong incentives to settle close to these airports.8

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The model

The building blocks of our model grant a lot to Cavailhès et al. (2004) and Fujita and Thisse (2002). Space is represented by the real line X = (−∞, ∞) with the central business district (CBD) lying at the origin. The CBD is an exogenous fixed point and it corresponds to the airport terminals.We define any spatial distance from it as x ∈ X , with x > 0. There are three types of agents competing for land: (i) a continuum of identical service operators of mass NA and density na (x) ≥ 0 at x ∈ X ; (ii) a continuum of identical firms of mass NI and density ni (x) ≥ 0 at x ∈ X; and (iii) a continuum of farmers of mass NF density nf (x) ≥ 0 at x ∈ X, characterized by bidding a fixed (agricultural) rent Rf . Land is finite and the total area occupied by service operators, firms and farmers at each x ∈ X is fixed and normalized to 1 (as in Cavailhès et al.): na (x)Sa (x) + ni (x)Si (x) + nf (x)Sf (x) = 1.

(1)

Sa (x), Si (x) and Sa (x) stand for the sizes of land plots and na (x)Sa (x), ni (x)Si (x) and nf (x)Sf (x) denote the total amount of land being used by each type of agent at a certain location x ∈ X. Both service operators and firms maximize profits by choosing their optimal land plot at each location x ∈ X. The economy is assumed to be open and agents make zero profits and can freely move. Land is assigned to the highest bidder and therefore the land equilibrium is driven by the value each type of agent pegs to a land plot at a each possible distance from the airport center. We define an Airport space (A) as a specialized service operator area (i.e. na (x) > 0 and ni (x) = nf (x) = 0); an Industrial Park (I) as a specialized firm area (i.e. ni (x) > 0 and na (x) = nf (x) = 0); and finally a Rural Area (R) as an area where only farmers live (i.e. nf (x) > 0 and na (x) = ni (x) = 0). The relative positions of the areas A, I and R with respect to the CBD are endogenously determined by the bid-rent functions obtained at equilibrium.9 8 For instance, Barnesandnoble.com, Planetrx.com, Toysrus.com or Williamsonoma.com are settled at MEM surroundings; whereas and Nike.com, Drugemporiun.com or Gess.com are settled at SDF surroundings. 9 A basic approach to the concept of bid-rent function can be found in Zenou (2005).

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As argued in Section 2, airports can be classified into cargo and passenger type. Since there are some structural features distinguishing the two categories of airports, we present separately the case of a cargo and a passenger airport. A comparison between the equilibrium in the two scenarios allows to detect the conditions guaranteeing the existence of an aerotropolis.

3.1

The Cargo airport

First we concentrate on the cargo case, by thinking of an airport endowed with a specific infrastructure devoted to cargo activities. 3.1.1

Firm maximization behavior

A firm located at x ∈ X produces a quantity of good equal to qi (x). We assume that firms have to deliver by plane a proportion α of their production, i.e. qic (x) is the quantity of good delivered through the airport where qic (x) = αqi (x) and α ∈ (0, 1). Firms get a net price p for each unit of good they sell and have to pay d (airport tariff) for each unit of the production they deliver by plane with p, d ≥ 0. Firms benefit from externalities generated by service operators. The externalities capture the presence of external economies arising in an airport neighborhood where the agglomeration of service operators gains in terms of speed, agility and complementarities that are very important to produce value-added activities.10 We assume that the presence of externalities reduces the costs firms incur in delivering through the airport. The amount of externalities absorbed by a firm at x ∈ X is represented by Ai (x), whose value is associated with firm location and the land plot of the service operators (SA ): Ai (x) =

θSA , tx2

(2)

where θ, t > 0. Hence, the externalities depend positively (via the parameter θ) on the overall land in which by service operators settle (i.e. the size of the airport), while they melt with the distance from the airport terminals.11 In order to capture this feature, transport costs are defined as a quadratic function of the Euclidean distance from the CBD (tx2 ).12 Therefore, intangible assets Ai (x) smooth the cost for firms of aviation services (dqic (x)) 10

For instance, Leinbach and Bowen (2004) provide a complete study of this phenomenon for the case of Singapore-Changi (SIN). 11 This expression embodies the simulataneous importance firms deserve to be close enough to the aiport (they need an easy access to the airport terminals) as well as the size of the externalities they can enjoy. 12 Empirical evidence can be found in Henderson (2003) and Glaeser and Kahn (2004).

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and their exploitation is strongly associated with firm location. However, as shown by the empirical evidence, firms demand both aviation and nonaviation services (that include a number of complementary facilities) from service operators. Bi (x) captures the non-aviation expenditures of a firm located at x ∈ X. Finally, firms have to pay a land rent Ri (x). Therefore, the profit function for a firm located at x ∈ X is: π i (x) = pqi (x) − Ri (x)Si (x) −

dqic (x) − Bi (x). Ai (x)

(3)

Firms’ production function takes the form qi (x) = Si (x)γ , where γ stands for the elasticity of production with respect to firm’s plot size and γ ∈ (0, 1), i.e. firms have decreasing returns in land size. There is a competition race for land plots between the different group of agents. Firms have an interest in land and we assume that the elasticity of their production with respect to the land is quite high. Non-aviation expenditures are determined by: Bi (x) =

β 2 (tx ) = βtx, x

(4)

with β > 0. Bi (x) is composed by two elements: βx represents the degree of use of nonaviation services (decreasing with distance), and the transportation costs (tx2 ). By replacing (2) and (4) into (3), we get the objective function that firms maximize with respect to Si (x): M ax pSi (x)γ − Ri (x)Si (x) − Si (x)

dqic (x) θSA tx2

− βtx

The result of the maximization program yields the following optimal land plot for a firm located at x ∈ X: Si∗ (x) =

Ã

γ(p −

αdtx2 θSA )

Ri (x)

1 ! 1−γ

.

Assumption 1 : p>

dq c (x) αdtx2 , =⇒ pqi (x) > i θSA Ai (x) 7

(5)

i.e. for any firm at x ∈ X, gross profits (namely before using the airport) are greater than aviation costs. Therefore, Si∗ (x) is always positive. Competition for land among firms implies that they make zero profits. The zero profits condition leads to: Ri∗ (x)

=

µ

1−γ βtx

¶ 1−γ γ

¶1 µ αdtx2 γ γ p− , θSA

(6)

where Ri∗ (x) is the bid-rent function for firms, i.e. the highest price a firm is willing to pay for a piece of land at x ∈ X. By plugging (6) into (5) we obtain:

Si∗∗ (x)



=

βtx ³ (1 − γ) p −

The size of the airport can be written as SA = are identical SA = NA (x)Sa (x). Hence, Si∗∗ (x)



=

R

1 γ

´ . 2

αdtx θSA

x∈X

Sa (x)dx, and since service operators

βtx

³ (1 − γ) p −

αdtx2 θNA Sa (x)

1 γ

´

(7)

The service operators’ optimization problem needs to be solved in order to obtain the values for Si∗∗ (x) and Ri∗ (x) and analyze the land equilibrium. Each service operator maximizes the following profit function: π a (x) =

(d − c)QC + Ba (x) − Ra (x)Sa (x), Na

(8)

where d is the airport tariff paid by firms, c the operating unit cost service operators have to bear and d > c > 0. Finally, Ba (x) are the non-aviation profits and Ra (x) the land rent for a service operator located at x ∈ X.13 Service operators do not care particularly the 13

As pointed out in ICAO (2004) and Passatore (1998), each airport balance sheet is characterized by this double source of revenues: aviation and non-aviation services. We mention a few examples. According to Passatore (1998), in 1996 the revenues of the Stuttgart Airport (STR) can be split into 73% corresponding to aviation and 27% to non-aviation income, while the total income of Frankfurt-Main (FRA) was composed by 66% of aviation and 34% of non-aviation.

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closeness to the airport center. production delivered through the airport can be written as Qc = R Thec overall industry c (x), because firms are identical. Since q c (x) = αS (x)γ then, q (x)dx = N q i i i i x∈X i Qc = Ni αSi (x)γ .

(9)

The non-aviation profits earned by a service operator take this form: β Sa (x), x

Ba (x) =

(10)

i.e. they depend on firms’ degree of use of non-aviation services ( βx ) and on the size of the service operator supplying the service. By plugging (7) into (9) and both (9) and (10) into (8) we get the objective function that service operators maximize with respect to Sa (x):

M ax Sa (x)

(d − c)ni (x)αSi (x)γ β + Sa (x) − Ra (x)Sa (x), Na x

s.t. Si (x) = Si∗∗ (x) =

Ã

!1 γ

´ ³ βtx 2 (1−γ) p− θNαdtx S (x) A a

.

This result yields the following optimal value:

Sa∗ (x) =

where k(x) =

µ

k(x)αdθtx2 β −Ra (x) x

¶1 2

pθNa

+ αdtx2 ,

(11)

Ni (d−c)αβtx . (1−γ)

Assumption 2 β > Ra (x), x i.e. non-aviation profits got by a service operator are higher than the value of the land rent it has to pay at a given location x ∈ X. Therefore, Sa∗ (x) is always positive. 9

As before, the zero profits condition leads to: µ ¶ θNi (d − c) β e Ra (x) = 1− , x d(1 − γ)

(12)

where Rae (x) is the equilibrium bid-rent function for service operators, i.e. the highest price a service operator is willing to pay for a piece of land at x ∈ X. Assumption 3 Let

θNi (d−c) d(1−γ)

≤ 1, then Rae (x) ≥ 0.

By plugging (12) into (11) we obtain the equilibrium land size: Sae (x) =

2αdtx2 . θNA p

(13)

The equilibrium firm size and bid-rent function are obtained by plugging (13) into (6) and (7): Rie (x)

=

µ

1−γ βtx

¶ 1−γ γ

γ

³p´1 γ

2

,

(14)

and Sie (x)

=

µ

2βtx (1 − γ)p

¶1 γ

.

(15)

At equilibrium, one can observe that for both firms and service operators land rent is decreasing in x because land loses its value as agents distance from the CBD. Consequently, land size is increasing in x since lower rents allow agents to occupy larger plots. Finally, since it is assumed that farmers take the residual land, Sfe (x) is determined by (1): ´1 ³ γ 2βtx 1 1 2αdtx2 e e e Sf (x) = nf (x) (1 − na (x)Sa (x) − ni (x)Si (x)) = nf (x) (1 − na (x) NA θp − ni (x) (1−γ)p ), e

and they pay for it a constant (agricultural) rent (Rfe (x) = Rf ).

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3.1.2

Equilibrium analysis

© eª At equilibrium, the highest bidder gets the use of the land, i.e. Re (x) = max Rae (x), Rie (x), Rf . Proposition 1 In the neighborhood of a cargo airport, there are two possible (not trivial) land sprawls: I-A-R (Industrial park-Airport-Rural area), and A-I-R (Airport-Industrial park-Rural area) equilibria. Proof. e

1. Rf < min {Rae (x), Rie (x)} holds at equilibrium because otherwise either the service operators or the firms (or both) get no land. 2. For any γ ∈ (0, 1) with γ 6= 12 , both Rae (x) and Rie (x) are decreasing and convex and 1

2 γ βt i cross only once at x = xA ≡ [ βγ (1 − θ(d−c)N d(1−γ) )( p ) ( 1−γ ) the proof of the single-crossing condition).

1−γ γ

γ

] 2γ−1 (see Appendix A for

(a) If γ < 12 , then Rae (x) < Rie (x) for ∀ x < xA and, so, the land sprawl turns out to be I-A-R (b) If γ > 12 , then Rae (x) > Rie (x) for ∀ x < xA and the correspondent land sprawl is A-I-R

Corollary 1 The elasticity of the production of firms with respect to land is relatively high, hence the most suitable space equilibrium is the A-I-R one. In this case the CBD turns out to be the centre of the airport. An A-I-R-type land equilibrium is presented in Figure 3 below:14 14

Figure 3 is drawn by selecting the following paramenters: γ = 23 , t = p = 6, θ = 1.

11

3 , 10

β = 2, d = 4, c = 1, NI = 13 ,

Figure 3: The A-I-R Land Equilibrium The distance xA fixes the limit of A and xI bounds the I area. At the equilibrium, land plots are assigned to the highest bidder group (namely, service operators, Z firms or farmers) xA

and, as a consequence, land appears to be fully specialized. Therefore, na (x)dx = NA 0 Z xI and ni (x)dx = NI . Moreover, since no land is vacant, na (x) = S e1(x) for all x < xA ; xA

and ni (x) =

a

1 Sie (x)

for all x ∈ (xA , xI ).

Corollary 2 At an A-I-R land equilibrium, the farmer’s bid-rent function is bounded from above. 1

Proof. The A-I-R configuration requires xA < xI where xI ≡ [( Rγe )( p2 ) γ ( 1−γ βt ) e

MAX

This condition leads to Rf < Rf

γ

γ

] 1−γ .

f

1

3γ−2γ 2 −1 ( 1−γ ) 2γ−1 ( ≡ [( γp 2 ) βt

1 θNI (d−c) β(1− d(1−γ) )

1

) γ ]1−γ and

therefore, the farmer’s bid-rent function cannot be higher than a given threshold.

12

1−γ γ

At equilibrium, Assumptions 1 and 2 are always satisfied (see Appendix B).15 All firms in the industrial area enjoy the same amount of externalities, that can be obtained by plugging (13) into (2): Aei =

2αd . p

The higher is the proportion of production firms deliver by plane (α), the lower is the price with respect to the service operators’ tariff ( pd ), and the more firms are able to absorb externalities

3.2

The Passenger airport

We mostly replicate the analysis performed for the cargo case. For sake of simplicity, we keep on with the same notation for parameters, while we add primes to variables for distingush them from the previous case, but still keeping the same meaning. 3.2.1

Firm maximization behavior

The aviation services supplied by service operators are mainly addressed to passenger transport and, marginally, to cargo activity. Cargo activity is considered by service operators as a by-product of their passenger operations. Firm’s total (qi0 (x)) at x ∈ X) production can be split into two parts and just a proportion (α) is delivered by plane. As a consequence, the profit function for a firm located at x ∈ X turns out to be: £ ¤ dαq 0 (x) − Bi0 (x), π 0i (x) = p αqi0 (x) + (1 − α)qi0 (x) − Ri0 (x)Si0 (x) − 0 i Ai (x)

(16)

We assume that the share of products delivered by air transport (α) is supplied on a marginal cost basis, i.e. p = d and externalities play no role ( A0i (x) = 1) and, hence, (16) reduces to: π 0i (x) = (1 − α)pqi0 (x) − Ri0 (x)Si0 (x) − Bi0 (x).

(17)

Equation (17) shows that firm profits are independent from the airport size (SA ). Hence, firms’ maximization program can be computed irrespective of service operators’ decisions. (with qi0 (x) = Si0 (x)γ ) : M0 ax (1 − α)pSi0 (x)γ − Ri0 (x)Si0 (x) − Bi0 (x). Si (x)

15

Therefore, the only parameter constraint comes from Assumption 3.

13

Firms maximization with respect to Si0 (x) yields the following optimal land plot: Si0∗ (x)

=

µ

(1 − α)γp Ri0 (x)



1 1−γ

.

(18)

By applying the zero profits condition, we get the equilibrium bid-rent function for firms: Ri0e (x)

=

µ

1−γ βtx

¶ 1−γ γ

1

γ[(1 − α)p] γ .

(19)

Finally, the equilibrium plot size for firms is obtained by plugging (19) into (18): Si0e (x)

=

µ

βtx (1 − γ)(1 − α)p

¶1 γ

.

(20)

Passing to service operators, each of them maximizes the following profit function: π 0a (x) =

(d − c) Q0 (T + µ 0 ) + Ba0 (x) − Ra0 (x)Sa0 (x), NA SA

(21)

0

Q where (d−c) 0 ) captures aviation profits coming from passenger transportation. SerNA (T + µ SA vices operators located in the proximity of passenger airports specialise in services addressed to passenger traffic. More precisely, T refers to profits issuing from tourist transport, while 0 µ SQ0 refers to the earnings related to business trips (µ > 0), and (d − c) is the net benefit for A each unit of trasport activity. Profits associated with business trips depend on the intensity of the airport use, which is measured as a trade-off between the dynamism of the region (the more active, the more business trips) and the size of the airport.16 . As in the cargo case, commercial firms and service operators are homogeneous (with mass NI and NA , re0 = N S 0 (x). Since cargo activities are considered spectively), hence Q0 = NI Si0 (x)γ and SA A a by service operators as a by-product of their passenger operations (i.e. a complementary facility), they are included in non-aviation profits (Ba0 (x) = βx Sa0 (x)). The maximization program is :

M ax Sa0 (x)

(d − c) Q0 (T + µ 0 ) + Ba0 (x) − Ra0 (x)Sa0 (x) NA SA

16

In that sense, a small airport in a very active region yields a high intensity of airport use and hence high profits related to business trips.

14

0 = N S 0 (x). s.t. Q0 = NI Si0 (x)γ , SA A a

Service operator maximization with respect to Sa0 (x) yields the following optimal land plot size (and by considering (20): Sa0∗ (x) =

Ã

µβtxNI (1 − γ)(1 − α)pNA 2 ( βx − Ra0 (x))

!1 2

.

(22)

Finally, one can obtain the equilibrium bid-rent function and plot size for a service operator: " # µ ¶2 T (d − c)(1 − γ)(1 − α)p β 0e Ra (x) = 1− , (23) x 2β NI µt and Sa0e (x) =

2µNi βtx . NA T (1 − γ)(1 − α)p

(24)

In the passenger case, Assumption 2 holds as in the cargo case to guarantee a positive land plot for service operators. Conversely, we need to redefine Assumption 3. Assumption 30 Let

³

T 2β

´2

(d−c)(1−γ)(1−α)p NI µt

≤ 1, then Ra0e (x) ≥ 0 .

As in the cargo case, land rent is decreasing in distance (x) and land size is increasing in x. Finally, farmers take the residual land: Sf0e (x) = n0 1(x) (1 − n0a (x)Sa0e (x) − n0i (x)Si0e (x)) = µf ´ ´1 ¶ ³ ³ γ 2µNi βtx βtx 1 0 = nf (x) 1 − na (x) NA T (1−γ)(1−α)p − ni (x) (1−γ)(1−α)p , and they pay for it a 0e

constant rent (Rf0e (x) = Rf ). 3.2.2

Equilibrium analysis

Proposition 2 As in the cargo case, in the neighborhood of a passenger airport, there exists two stable stable land equilibrium: I-A-R and A-I-R. Proof. SeeµProof of Proposition 1. Nevertheless, here, Ra0e (x) and Ri0e (x) cross at x = x0A ≡ ¶ ³ ´2 1−γ γ (1−γ)(1−α)(d−c)p β βt T [ 1 − 2β ( 1−γ ) γ ] 2γ−1 for any γ ∈ (0, 1) with γ 6= 12 (see 1 Ni µt γ((1−α)p) γ

Appendix A for the proof of the single-crossing condition).

15

Again, Corollary 1 still holds and we may select the A-I-R equilibrium as the most suitable. At equilibrium, Assumption 2 is fulfilled and the only constraint comes from Assumption 0 3 . Both fin the cargo and the passenger cases, the land equilibrium implies an A-I-R configuration. Nevertheless, the two structures are not identical and the distinguishing features of the A region and I region differ in the two scenarios (due to the different crossing points). A comparison between the equilibrium in the cargo and the passenger settings allows to detect the conditions guaranteeing the existence of an aerotropolis.

3.3

The formation of an aerotropolis: the cargo and the passenger cases

Lemma 1 Let α > 12 , in case of a cargo airport: i) the capacity of firms to enjoy externalities in the surroundings of a cargo airport is higher (Aei > Ae0 i ); ii) firms are willing to pay a higher land rent (Rie (x) > Ri0e (x)) and they obtain a smaller land plot (Sie (x) < Si0e (x)), when they are close enough to a cargo airport. Proof. e0 i) The externalities absorbed by firms in the two scenarios are Aei = 2αd p and Ai = 1 rep 1 spectively. Hence, Aei > Ae0 i holds for α > 2d , namely α > 2 for p = d. ³ ´ 1−γ ¡ ¢ 1 ´ 1−γ ´1 ´1 ³ ³ ³ 1 γ γ γ γ 1−γ p γ 1−γ 2βtx βtx 1 γ ii) βtx γ 2 > βtx γ ((1 − α)p) holds for α > 2 ; and (1−γ)p < (1−γ)(1−α)p holds for α > 12 .

The higher the proportion of production that is delivered by plane (α), the more externalities firms are able to absorb in the cargo scenario and hence, the difference Aei − Ae0 i increases. Therefore, given a threshold for α, the agglomeration of activities around cargo airports implies gains in terms of speed, agility and complementarities that are valued by firms. In this situation, firms are willing to pay a higher price for land plots in case of a cargo airport since they enjoy more externalities. Consequently, land plots are smaller due to the higher rent. Corollary 3 If Lemma 1 holds, industrial parks are denser in firms in the case of cargo airports. Proof. An industrial park is a specialized firm area where no land is vacant. Density is given by ni (x) = S e1(x) and n0i (x) = S 0e1(x) in the cargo and passenger cases respectively. i i Hence Sie (x) < Si0e (x) implies ni (x) > n0i (x). This result insists in the idea of higher agglomeration of activities around cargo airports.

16

Lemma 2 Let θ > θ : i) service operators are willing to pay a lower land rent (Rae (x) < Ra0e (x)), when close to a cargo airport; ii) the cargo is smaller than (xA < x0A ), ¶ µ in the passenger airport ´ ³ 2 (1−γ)(1−α)p(d−c) 1 d(1−γ) T γ with θ ≡ ( . [2(1 − α)] − 1 + 2β 1 ) NI µt NI (d−c)[2(1−α)] γ

Proof. ³ i) βx 1 −

θnNI (d−c) d(1−γ)

´

< 1

β x

µ ³ ´2 T 1 − 2β

2 γ βt I ii) [ βγ (1− θ(d−c)N d(1−γ) )( p ) ( 1−γ )

1−γ γ

γ

β

] 2γ−1 < [

1

γ((1−α)p) γ

holds for θ > θ (expression in Lemma 2).



(1−γ) d(1−α) ) µt . holds for θ > θ1 ≡ ( T2N Iβ µ ¶ ³ ´2 1−γ γ (1−γ)(1−α)(d−c)p βt T γ ] 2γ−1 1 − 2β ( ) NI µt 1−γ

(1−γ)(1−α)p(d−c) NI µt

It is possible to check that the second condition over θ is more stringent (i.e. θ > θ1 ), once Assumption 30 is fulfilled. More precisely, θ > θ1 holds for any p > 1 and ³ ´2 µt 2β for (1−γ)(1−α)p = 1. Finally, since Assumption 3 fixes an upper bound for θ (i.e. T θ < θ ≡

d(1−γ) (d−c) ),

we need to prove that the interval θ − θ exists. One may check that ³ ´2 µt 2β θ < θ holds if 1 < (1−γ)(1−α)p which is always true because it is exactly the condition T imposed by Assumption 30. As a result, when externalities are sufficiently important (i.e. θ > θ), service operators are willing to pay a lower price for land plots in presence of a cargo airport. Under these circumstances, passenger airports are bigger than cargo airports at equilibrium. Corollary 4 If Lemmas 1 and 2 hold, industrial areas are larger in case of a cargo airport. e

0e

Proof. For a given agricultural rent (i.e. Rf = Rf ), we get xI > x0I because Rie (x) > Ri0e (x). Since xA < x0A , then (xI − xA ) > (x0I − x0A ). Hence, industrial parks are denser and larger around a cargo airport. Proposition 3 If Lemmas 1 and 2 hold, an aerotropolis arises surrounding a cargo airport, because industrial parks are larger and denser. An aerotropolis is empirically defined as a large and dense industrial area located in the surroundings of some cargo airports where commercial activities concentrate. Our analysis helps to identify the requirements for the emergence of aeropolitan areas. These conditions are basically two: an intense use of the airport by the firms (a high α); and a sufficiently high level of externalities (a high θ). When these conditions are fulfilled, service operators 17

value more passenger airports whereas firms value more cargo airports. In addition, cargo are smaller than passenger airports and industrial areas are larger and denser in firms in presence of a cargo airport. Therefore, an aerotropolis arises. An aerotropolis-type configuration is shown in Figure 4 below:17

Figure 4: The Aerotropolis

4

A few case studies

In this section we present some case studies in order to provide some empirical support to our theoretical results. Relying on the distinction between cargo and passenger airports, a small sample of European airports is selected for both categories. A comparison between them should give some insights on the way to distinguish aerotropolis-type configurations from other industrial areas. The selected airports are: Madrid-Barajas (MAD), Vitoria-Foronda (VIT), FrankfurtMain (FRA) and Köln-Bonn (CLG). The former two are Spanish and the latter two are 17

Figure 4 is drawn by selecting the following paramenters: γ = 23 , t = 6 p = 6, θ = 1 (as in Figure 3) and µ = 2, α = 11 , T = 34 .

18

3 , 10

β = 2, d = 4, c = 1,NI = 13 ,

German. On one hand, MAD and FRA are passenger-type airports (although they are also cargo hubs). On the other hand, VIT and CLG are the most important cargo-specialized airports in each country.18 Hence, the selected sample also allows for a cross-country comparison. Although MAD and FRA combine passenger and cargo activities, they can be labeled as passenger airports by looking at the predominant nature of their operations. In 2004, FRA recorded a traffic of 51.10 millions of passengers and 1.75 millions of linear metric tons of delivered goods; and MAD recorded a traffic of 38.71 millions of passengers and 0.34 millions of linear metric tons of delivered goods. In these airports, combination carriers (that transport both passengers and cargo) are the type of companies that mainly operate. CLG is the second busiest cargo hub in Germany just after FRA, and VIT is the third Spanish cargo airport after MAD and Barcelona (BCN). In 2004, CLG recorded a traffic of 8.4 millions of passengers and 0.6 millions of linear metric tons of delivered goods; and VIT recorded a traffic of 0.095 millions of passengers and 0.04 millions of linear metric tons of delivered goods. These airports are the base for integrated carriers which provide doorto-door express delivery service. More precisely, FedEx and UPS operate in CLG, whereas FedEx, DHL and TNT operate in VIT.

4.1

A-I-R space configuration

This subsection aims at developing an applied study on the land distribution around airports in order to detect A-I-R land configurations. • Vitoria-Foronda (VIT). The airport extends over an area of 150, 000 sqm in the proximity of Vitoria’s industrial area. According to the information supplied by the Agency of Development of Alava,19 the spatial distribution of activities follows this pattern: 18

Data from Airport International (issue june/july 2005) for FRA and CLG; and Annual Report of AENA (2004) for MAD and VIT. 19 "Álava Agencia de Desarrollo" in Spanish. This agency depends on the Provincial Government of Alava. Alava is the Spanish province whose capital is Vitoria (see www.alavaagenciadesarrollo.es).

19

Figure 5: VIT (25 km around) Figure 6: VIT (40 km around) Taking VIT airport as the reference point (i.e. the CBD) and focusing on the space located within a radius of 25 km, the land distribution seems to fit to the A-I-R scheme20 and the industrial parks surrounding VIT locate on average 13.12 km away from the airport. When we enlarge the radius to 40 km, new industrial agglomerations appear and seem to be located in the closeness of the town rather than the airport. Therefore, in case of VIT, the A-I-R land equilibrium is observed approximately up to a radius of 25 km when considering the airport as CBD. When we consider a greater distance from the CBD, the externality effects sourcing from service operators smooth (see Henderson, 2003) and we need to consider other arguments in order to explain the land configuration. • Madrid-Barajas (MAD). This airport area measures around 39, 000, 000 sqm.21 According to the data supplied by the Institute of Development of Madrid (IMADE),22 the industrial parks surrounding MAD (within a radius of 25 km) locate on average at 12 km away from the airport. The spatial distribution of activities replicates the same pattern of VIT. As far as the distance from the airport increases, the externalities decay and the spatial distribution becomes less clear. However, conversely to VIT, even within a 40 km radius the industrial agglomerations seem to fit to the A-I-R spatial sequence. 20

No analytical difference is made between urban and rural areas since we are interested in firm (and not household) agglomerations. 21 This is the total surface working from January 2006. The MAD airport recently expanded from 24, 000, 000 to 39, 000, 000 sqm. 22 "Instituto Madrileño de Desarrollo" in Spanish. This Institute depends on the Regional Government of Madrid (see www.imade.es).

20

Figure 8: MAD (40 km around)

Figure 7: MAD (25 km around)

• Köln-Bonn (CLG). It is the second busiest cargo hub in Germany and settles approximately at the same distance from Köln and Bonn (around 15 km). The airport extends over 450, 000 sqm and is characterized by a large number of industrial parks surrounding it. There are around 90 parks including both the existing ones and those under construction within a radius of 40 km, according to the data supplied by the Chamber of Industry and Commerce of Cologne.23

Figure 9: CLG (25 km around) Figure 10: CLG (40 km around) Within a radius of 25 km, industrial parks are located on average at 15.55 km far from the airport, i.e. a bit farther that in VIT and MAD cases. It is interesting to compare the industrial sprawl sketched in Figures 9 and 10. Within the smaller radius, most of the industrial areas are found between the airport and the cities. However, within the larger radius, the industrial distribution is more scattered and some of parks appear beyond the cities. In any case, the A-I-R land equilibrium seems to hold in both scenarios. • Frankfurt-Main (FRA). [IN PROGRESS] 23

"Industrie-und Handelshammer zu Köln" in German (see www.ihk-koeln.de/index.jsp).

21

The airport is located close to the city. There is an important industrial park located between the city and the airport, at a distance of 10 km form the airport. The following picture clarifies such a spatial scheme, which fits quite well into the A-I-R scheme.

Figure 9: FRA (25 km around)

4.2

Aerotropolis

As it has been shown in the previous sections, an aerotropolis requires some conditions to arise (in terms of α and θ). It has been also shown that cargo airports are smaller than passenger airports (i.e. xA < x0A ) and that industrial areas are larger and denser in firms in presence of a cargo airport (i.e. (xI − xA ) > (x0I − x0A ) and ni (x) > n0i (x)). Since it is known that CLG and VIT surroundings feature an aerotropolis-type configuration, it is interesting to check if the conditions described before are fulfilled. The following table summarizes observed data:24 Airport VIT MAD CLG FRA

Airport Extension (sqm)

Weighted Average Distance (km)

xA

Proxy for (xI -xA )

Firm Density ( P Si (x) )·100

150, 000 39, 000, 000 450, 000 ?

13.12 12 15.55

0.008 0.004 0.005

i

Proxy for ni (x)

Table 1: VIT, MAD, CLG and FRA surroundings (25 km around) Looking at airport extension, it appears that the size of cargo airports is smaller. Focusing on the space structure within a radius of 25 km (to have neat A-I-R land structures), 24

Data sources: Agency of Development of Alava (VIT), IMADE (MAD), Chamber of Industry and Commerce of Cologne (CLG) and Economic Promotion Board Region Frankfurt RhineMain (FRA).

22

in order to fix the limit of an aerotropolis, we propose a weighted average distance of industrial parks with respect to the airport25 as a proxy for bounding the industrial zone (i.e. (xI − xA )). Intuitively, the bigger the weighted average distance, the larger the industrial area. As one can expect, we observe greater distances in the case of cargo airports such as CLG and VIT. Finally, we concentrate on firm density in industrial areas in order to study the last distinguishing feature of an aerotropolis. We proxy it by the number P of firms settled (denoted by i) with respect to the total surface of all industrial parks ( Si (x)). Again, a higher firm density seems to be detected in the cargo cases, confirming the suggested features of aerotropolis schemes.26 Some cross-country comments: the analysis seems to be consistent across countries [IN PROGRESS]

5

Concluding remarks

The increasing importance of the e-commerce makes airports be considered as a new type of Central Business District (CBD) with enough capacity to leverage air commerce into high profits.27 This paper applies the current urban theory to study the spatial distribution of activities around airports and provide some insights about the formation of aerotropoli. Aerotropoli are defined as large industrial areas characterized by a high concentration of commercial activities in the surroundings of some cargo airports. Land competition around airports takes place among service operators, firms and farmers, where firms need to deliver part of their production by plane. Service operators, in addition of supplying aviation and non-aviation services to firms, generate externalities that firms can take advantage of as far as they are close enough to the airport center. The externalities are the key factor explaining land distribution. According to the relative size of the externalities with respect to the transport costs, agents associate a value to each unit of land. Finally, location is determined fby the comparison of each agent’s bid-rent function. In this framework, we select a stable land equilibrium involving service operators, firms and farmers characterized by the spatial sequence Airport-Industrial Park-Rural Area (A-I-R), irrespective of the category of the airport (cargo or passenger). 25 It is the average of distances of each industrial park with respect to the airport, weighted by the relative number of firms belonging to each park. 26 More detailed information on the number of parks (corresponding to 2004) can be found in Appendix C. Nevertheless, the density index is computed by excluding the parks that were either not active or under construction by the end of 2004. 27 “...these days the magnets for business are airports...airports are becoming the centres of cities of their own” (The Economist 24/11/2005).

23

Aerotropoli arise around cargo airports when firms use quite intensively airport services and the level of externalities is high. Under these circumstances, service operators peg more value to land in case of passenger airports whereas firms value more cargo airports. The size of cargo airports turns out to be smaller than that of passenger airports while industrial areas are larger and denser in the case of a cargo airport. Empirical evidence basically supports these theoretical statements. A direct implication issuing from this type of analysis addresses to policy matters. Once stated the importance of the externalities associated with an airport, one can think of the economic effects produced by public policies supporting the creation of aerotropolis. The economic contribution of air transport in terms of employment and income has important effects at regional level. Consequently, regional governments may be interested in trying to implement the required conditions allowing for the formation of aerotropoli. Some policy recommendations would suggest to foster logistic platforms close to cargo airports, and to promote and encourage the partnership between firms and service operators. In such a framework, the intense collaboration among agents would guarantee a sufficiently high level of externalities to ensure the existence of an aerotropolis. Most of the analysis that remains to be done concerns the empirical analysis of the features distinguishing the aerotropolis-type configurations from other industrial areas. At the moment, the quality of data and the lack of complete time series prevents from dealing with complete econometric estimations which would help to fix the determinants of the formation aerotropolis spaces.

References [1] Alonso, W. (1964), “Location and Land Use”, Harvard University Press. [2] Arend, M., Bruns, A., McCurry, J.W. (2004), “The 2004 Global Infrastructure Report”, Site Selection Magazine. [3] Brueckner, J.K., Thisse, J.F., Zenou, Y. (1999), “Why Central Paris is Rich and Downtown Detroit Poor? An Amenity Based Theory”, European Economic Review, 43, 91-107. [4] Cavailhès, J, Peeters, D., Sekeris, E., Thisse, J.F. (2004), “The Periurban City: Why to Live Between the Suburbs and the Countryside”, Regional Science and Urban Economics, 34, 681-703. [5] Chipman, J.S. (1970), “External economies of scale and Competitive Equilibria”, Quarterly Journal of Economics, 87, 347-385. [6] Economist, The (24/Nov/2005): “Business on the Fly". 24

[7] Fujita, M., Thisse, J.F. (2002), “Economics of Agglomeration. Cities, Industrial Location and Regional Growth”, Cambridge University Press. [8] Glaeser, E.L., Kahn, M.E. (2004), “Sprawl and Urban Growth", Handbook of Regional and Urban Economics (Henderson, J.V. and Thisse, J.F. Eds), 2482-2527. [9] Henderson, J.V. (2003), "Marshall’s Scale Economies", Journal of Urban Economics, 53, 1-28. [10] ICAO (2004), "Economic Contribution of Civil Aviation", circular 292-AT/124. [11] Kasarda, J.D. (2000), "Logistics and the Rise of Aerotropolis", Real Estate Issues, winter 2000/2001, 43-48. [12] Leinbach, Th.R., Bowen, J.T.Jr (2004), "Air Cargo Services and the Electronics Industry in Southeast Asia", Journal of Economic Geography, 4, 299-321. [13] Passatore, R.(Ed) (1998), "Gli Aeroporti Europei: Profili Organizzativi ed Economici", Instituto Poligrafico e Zecca dello Stato, Roma. [14] Thünen, J.H. von (1826), "Der Isolierte Staat in Bezeiehung auf landwirtschaft und Nationalökonomie". Hamburg: Perthes. English translation: "The Isolated State". Oxford: Pergammon Press (1966). [15] Zenou, Y. (2005), "Urban Labor Economic Theory. Efficiency Wages, Job Search and Urban Ghettos". Mimeo.

25

A

Appendix: single-crossing condition

The bid-rent function of service operators and that of firms cross at xA (in the cargo case) and at x0A (in the passenger case). We prove that xA and x0A are the only points equalizing both bid-rent functions (single-crossing condition) by showing that both bid-rent functions are decreasing and convex.

1. The cargo airport. In the cargo case, the first and second derivatives of service operators and firms’ bid-rent functions are (12) and (14): (a)

(b)

(c)

(d)

β(1−

∂Rae (x) ∂x

θ(d−c)Ni

)

d(1−γ)δ i i = − . This expression is negative for 1 > θ(d−c)N d(1−γ) , which x2 is always true when Assumption 3 is satisfied. Therefore Rae (x) is downward sloping.

∂ 2 Rae (x) ∂x2

2β(1−

θ(d−c)Ni )

d(1−γ) = . Again by Assumption 3, this expression is positive and x3 e therefore Ra (x) is convex.

∂Rie (x) ∂x

=− sloping ∂ 2 Rie (x) ∂x2

1 −γ

2

2

1

p γ (1−γ)2 ( 1−γ ) txβ tx2 β

γ−1 1 γ pγ

(1−γ)2 ( 1−γ ) txβ tx3 β

1−2γ γ

, which is negative and hence Rie (x) is downward

1−2γ γ

1 −γ

2

1

p γ (1−2γ)(1−γ)3 ( 1−γ ) txβ

1−3γ γ

= + . When γ ∈ ( 12 , 1), t2 x4 β 2 γ which is a necessary condition for an A-I-R-type land equilibrium to arise, the first term in the expression is positive and the second one is negative. Therefore, the expression will be positive when the first term is higher than the second, 2

γ−1 1 γ pγ

(1−γ)2 ( 1−γ ) txβ tx3 β

1−2γ γ

> i.e. which is always the case.

1 −γ

2

1

p γ (1−2γ)(1−γ)3 ( 1−γ ) txβ t2 x4 β 2 γ

1−3γ γ

. This is true for γ >

1 4

2 The passenger airport. In the passenger case, the first and second derivatives of service operators and firms’ bid-rent functions are (23) and (19): (a)

∂Ra0e (x) ∂x

β(1−

(1−α)(d−c)pT 2 (1−γ)δ 0i ) 4β 2 µtNi 2 x

2

(1−γ) =− . This expression is negative for 1 > (1−α)pT , 4β 2 µtNi 0e which is always true when Assumption 30 is satisfied. Therefore Ra (x) is downward sloping.

26

(b)

2β(1− (1−α)(d−c)pT 2

∂ 2 Ra0e (x) ∂x2

2 (1−γ)

4β µtNi x3

)

= . Again by Assumption 30, this expression is positive and therefore Ra0e (x) is convex. 1−2γ

(c)

∂Ri0e (x) ∂x

1

(1−γ)2 ( 1−γ ) γ [(1−α)p] γ txβ − tx2 β

= ward sloping.

, which is negative and hence Ri0e (x) is down-

1−3γ

(d)

1−2γ

1

1

( 1−2γ )(1−γ)3 ( 1−γ ) γ [(1−α)p] γ 2(1−γ)2 ( 1−γ ) γ [(1−α)p] γ ∂ 2 Ri0e (x) γ txβ txβ = + . When γ ∈ 2 2 ∂x tx3 β t2 x4 β 1 ( 2 , 1), the first term in the expression is negative and the second term positive.

Therefore, the expression will be positive when the first term is lower than the second, i.e. true for γ >

B

( 1−2γ )(1−γ)3 ( 1−γ ) γ txβ

1−3γ γ

t2 x4 β 2 1 4

1−2γ

1

[(1−α)p] γ

<

2(1−γ)2 ( 1−γ ) γ txβ tx3 β

1

[(1−α)p] γ

. This is

which is always the case.

Appendix: Assumptions 1 and 2

In this appendix we provide the proof that Assumption 1 and Assumption 2 are always satisfied at equilibrium. • Assumption 1. Since SA =

na (x)Sa (x) λA (x) ,

by plugging this value into (13) SA becomes: e SA =

2αdtx2 . θp

Assumption 1 states that p>

αdtx2 . θSA

This inequality, by replacing (25), yields p >

p 2

• Assumption 2.

Assumption 2 states that β > Ra (x). x 27

which is always satisfied.

(25)

Finally, this inequality, by replacing (12), yields δiθ(d−c) d(1−γ) > 0, that is always satisfied because both the numerator and the denominator are positive.

C

Appendix : Industrial parks

Table 2: Industrial parks around VIT

Table 3: Industrial parks around MAD

28

Table 4: Industrial parks around CLG. 29

30