City formation with complex landscapes

• DOI: http://doi.org/10.1002/isaf.1418
• Author: James R. Fain
• Published date: 01 October 2017
• Date: 01 October 2017

RESEARCH ARTICLE

City formation with complex landscapes

James R. Fain

Oklahoma State University, Stillwater, OK,

USA

Correspondence

James R. Fain, Oklahoma State University,

Stillwater, OK, USA

Email: jim.fain@okstate.edu

Summary

Using simulation methods I explore some of the properties of the new economic geography

model using a complex landscape. I introduce landscape complexity by allowing the existence

of limited pathways that can be traversed at a lower cost than most other paths. I also introduce

a river that may be crossed at limited points and may be used to transport goods. I find that

adding complexity substantially alters how many cities form and where they form. Compared with

a simple landscape, complex landscapes produce a distribution of city sizes that more closely

resemble the actual distribution of city sizes.

KEYWORDS

new economic geography; complex landscapes,simulations, transportation costs

1|INTRODUCTION

Johann von Thünen (1966) began his seminal work, Isolated State,by

stating “Imagine a very large town, at the center of a fertile plain which

is crossed by no navigable river or canal”. With this sentence von

Thünen laid out a simple, idealized landscape: no river or canal, and a

flat plain that is equally easy to traverse in all directions. Subsequent

researchers have made frequent use of this idealized setting, as

allowing the landscape on which cities may form to be simple, instead

of complex, makes the research work more tractable. This, of course, is

a common practice; models are frequently developed in a simple

framework and the simplifying assumptions are later relaxed.

The new economic geography (NEG) model has served as the

framework for a great deal of the recent research in city formation.

Most of the model development in this area has employed a simple

landscape with uniform transportation costs. As one might expect,

the model was developed using the calculus‐based techniques that

are widely used in economics. To further simplify the problem, in many

early formulations of the model the landscape upon which cities form

is a one‐dimensional space. The NEG model can generalize to higher

dimensional spaces, but the calculus‐based calculations become

unwieldy in this setting. In this paper I employ computer‐based simula-

tions to explore the operation of the NEG model of city formation in

two‐dimensional space when the landscape is complex.

Computer‐based simulations are frequently used to evaluate and

illustrate the workings of the NEG model. In fact, simulations are used

even when the landscape is both simple and one‐dimensional. For

example, Fujita, Krugman, and Venables (1999) employed simulations

in almost every chapter to solve numerical examples in a simple one‐

dimensional landscape. DeMaagd and Moore (2007) used computer‐

based simulations to explore the properties of the NEG model in

two‐dimensional space. In this paper I extend their work to include

complex landscapes.

I introduce two types of complexity to the landscape. First, I con-

sider the possibility that some pathways through the landscape can be

traversed at a lower cost than most other pathways. If such paths exist,

then cities should be more likely to form on or along these corridors to

take advantage of the lower transportation costs. The second type of

complexity I introduce is adding a non‐trivial river to the landscape.

The river is large enough to be a barrier to movement—it can only be

crossed at certain locations, where a bridge, ford or ferry exists. I con-

sider scenarios in which the river is both navigable and non‐navigable.

Adding complexity to the landscape means that the cost of

transporting goods is no longer uniform across the space: some path-

ways have a relatively lower cost of moving goods and other pathways

have a relatively higher cost. Transportation costs are a key element of

the NEG model, so switching from a simple to a complex landscape will

alter the model's outcomes. As a result of this switch, the number of

cities that form and where they form will likely change. The distribu-

tion of city sizes will be altered as well. The degree to which complex

landscapes affect city formation has not been studied in the context

of a formal model.

The idea that complex landscapes impact urban development is

not new. In his work regarding Chicago's emergence as a major city,

Cronon (1991) introduces to the discussion of cities the concepts of

“first nature”and “second nature”. Cronon classifies as “first nature”

Received: 13 April 2017 Revised: 1 October 2017 Accepted: 15 October 2017

DOI: 10.1002/isaf.1418

Intell Sys Acc Fin Mgmt. 2017;24:125–137. Copyright © 2017 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/isaf 125