An Essay on Urban Economic Theory

326 Pages·1999·7.291 MB·English

by  Yorgos Y. Papageorgiou, David Pines (auth.)

An Essay on
URBAN ECONOMIC THEORY
AdvancesinUrbanandRegional Economics
VOLUME 1
SeriesEditor
RichardAmott,BostonCollege, US.A.
An Essayon
URBAN ECONOMIC THEORY
by
YORGOS Y. PAPAGEORGIOU
McMaster University
and
DAVIDPINES
Tel Aviv University
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Papageorgiou, Y. Y.
An essay on urban economic theory / by Yorgos Y. Papageorgiou and
David Pines.
p. cm. - (Advances in urban and regional economics ; v. 1)
Includes bibliographical references (p. ) and index.
ISBN 978-1-4613-7245-5 ISBN 978-1-4615-4947-5 (eBook)
DOI 10.1007/978-1-4615-4947-5
1. Urban economics. 1. Pines, David. II. Title III. Series.
HT321. P34 1998
330.9173'2-dc21 98-44115
CIP
Copyright <C> 1999 Springer Science+Business Media New York
Originally published by KIuwer Academic Publishers in 1999
Softcover reprint of the hardcover 1s t edition 1999
AlI rights reserved. No part of this publication may be reproduced, stored in
a retrieval system or transmitted in any form or by any means, mechanica1,
photo-copying, recording, or otherwise, without the prior written permis sion of
the publisher, Springer Science+Business Media, LLC
Printed on acid-free paper.
To Tamar and to Maria
Contents
ListofFigures xiii
List ofTables xv
Preface xvii
Acknowledgements XIX
1 Introduction 1
1.1 Scope ofthis Book . . . . . . . . . . . . . . . . . 1
1.2 Fundamental Determinants ofSpatial Structure. 2
1.3 Historical Sketch . . . . . . . . . . . . . . . . . . 4
1.3.1 Urban Land Use and Rent Theory .... 4
1.3.2 Size and Functional Distribution ofCities 11
1.3.3 Economic Geography of Cities 14
1.3.4 Some Final Comments . 17
1.4 Book Outline . . . . . 18
1.5 Appendix: Notation. 20
1.5.1 Latin Symbols 20
1.5.2 Greek Symbols 24
1.6 References . 25
I The Monocentric City 31
2 Urban Equilibrium 33
2.1 Conceptual Framework. . . . . . . . . . . . . . . . . 33
2.1.1 Landscape and the Shape ofthe Urban Area 33
2.1.2 Preferences . . . . . . . . . . 35
2.1.3 Prices . . . . . . . . . . . . . . . . . . . . . . 36
2.2 The Structure ofUrban Equilibrium . . . . . . . . . 36
2.2.1 Land Ownership, Property Rights, and the Disposal of
Urban Rent . . . . . . . . . . . . . . . . . . . . . . . . .. 36
viii Contents
2.2.2 Individual Decisions . . . . . . . . . 37
2.2.3 Clearing the Urban Land Market .. 39
2.2.4 Clearing the Available Land Market 39
2.2.5 Rent Disposal and Income Determination 40
2.2.6 Definition ofa Competitive Equilibrium 41
2.2.7 Closing the Model . 42
2.3 Properties ofthe Equilibrium Allocation . . . . 43
2.3.1 The Shape ofthe Urban Area . 43
2.3.2 The Principle ofZero Marginal Location Costs 43
2.3.3 Population Density . . . . . . . . . . . . 45
2.3.4 Negative Exponential Rent and Density 46
2.3.5 Aggregate Relationships at Equilibrium 48
2.4 Appendices . . . . . . . . . . . . . . 50
2.4.1 Alternative Choice Problems 50
2.4.2 A Fundamental Issue. 53
2.5 References . 54
3 Comparative Statics 57
3.1 Open Renter City. 58
3.1.1 Initial Endowment 58
3.1.2 Agricultural Rent. 59
3.1.3 Utility Level ... 60
3.1.4 Transportation Technology 61
3.1.5 Land Reclamation 63
3.1.6 Public Good .. 63
3.2 Closed Renter City . . . . 64
3.2.1 Population Size .. 65
3.2.2 Agricultural Rent. 67
3.2.3 Transportation Technology 68
3.2.4 Land Reclamation 71
3.2.5 Public Good . 72
3.2.6 Initial Endowment . 74
3.3 Theoretical Implications and Empirical Evidence 75
3.3.1 Agricultural Rent. . . . . . . . . . . . . . 77
3.3.2 Economic Growth and Suburbanisation . 78
3.3.3 Population Growth and Suburbanisation . 79
3.4 Appendix: Closed Mixed and Owner Cities. 81
3.4.1 Effects on Utility . 81
3.4.2 Initial Endowment 83
3.4.3 Population Size . . 86
3.4.4 Agricultural Rent . 88
3.4.5 Share in Profits from Land Development. 91
3.4.6 Transportation Technology 92
3.4.7 Land Reclamation 92
3.4.8 Public Good 94
3.5 References . 94
Contents
IX
4 Optimality ofthe Equilibrium Allocation 97
4.1 Allocations that Maximise Social Welfare 97
4.1.1 Social Welfare FUnction . . . . . . 97
4.1.2 Conditions for Maximising Social Welfare 99
4.1.3 Properties ofthe Optimal Allocation. . 101
4.2 Decentralisation................... . 104
4.3 How to Treat Equals? .. . . . . . . . . . . . . . . 106
4.4 Appendix: Equilibrium Allocation and Pareto Efficiency . 109
4.5 References........................... . 111
5 Extensions 113
5.1 Utility and Location . . . . . . . 113
5.1.1 The Value ofTime . . . . 113
5.1.2 Environmental Quality. . 115
5.2 Production ... . . . . . . . . . 117
5.2.1 Comparative Statics . . . 118
5.2.2 Sudden Urban Growth. . 119
5.3 Heterogeneous Population . 121
5.3.1 The Slope Test . . . . 121
5.3.2 The Value ofTime . . 123
5.3.3 Comparative Statics . 124
5.4 The City as a Central Place System . 128
5.4.1 The Model . 128
5.4.2 Some Equilibrium Properties . 131
5.4.3 Negative Exponential Rent and Density . 133
5.5 Appendices . . . . . . . . . . . . . . . . . 135
5.5.1 Proofof (5.10) . 135
5.5.2 Counter-Example to Result 5.2 . . 136
5.6 References................. . 139
6 Urban Housing 141
6.1 Nondurable Housing Production . 142
6.1.1 A Model with Households and Housing Producers . 142
6.1.2 A Model with Housing Produced by Households . 143
6.2 Durable Housing Production . 146
6.2.1 Supply ofHousing . . . . . . . . . . . . . . . . . 146
6.2.2 Demand for Housing . . . . . . . . . . . . . . . . 160
6.2.3 Spatial Structure ofa Durable Housing Market . 162
6.3 Appendices . . . . . . . 164
6.3.1 Proofof (6.18) . 164
6.3.2 Proofof (6.20) . 164
6.3.3 Proofof (6.21) . 165
6.3.4 Proofof (6.22) . 166
6.3.5 Proofof (6.24) . 166
6.4 References....... . 167
x Contents
7 Transportation Infrastructure 169
7.1 Competitive Market for Urban Transportation 170
7.2 Market Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.2.1 Monitoring the UseofTransportation Infrastructure and
Non-Excludability . . . . . . . . . . . . . 172
7.2.2 Returns to Scale . . . . . . . . . . . . . . 173
7.3 Public Supply ofTransportation Infrastructure . 175
7.3.1 First-Best Allocation . . 177
7.3.2 Second-Best Allocation . 178
7.4 Appendices . . . . . . . . . . . . 181
7.4.1 Proofof (7.6) ..... . 181
7.4.2 First-Best Allocation Problem . 182
7.4.3 Second-Best Allocation Problem . 185
7.4.4 ProofofLemma 7.1 . 186
7.4.5 ProofofResult 7.3 . 187
7.5 References.......... . 188
8 From Monocentricity to Polycentricity 191
8.1 The Alleged Failure ofthe EDF ... · 191
8.2 The Monocentric City and the EDF . . · 193
8.3 The Density Gradient and City Size . . · 195
8.4 Is the Monocentric Paradigm Obsolete? .196
8.5 References . · 199
II Polycentric Urban Structures 203
9 Agglomeration 205
9.1 The Benefits and Costs ofAgglomeration . 205
9.2 Modelling Agglomeration . 210
9.2.1 Von Thiinen and the Monocentric City. . 210
9.2.2 Internal City Structure .... . 213
9.2.3 Distribution ofCity Sizes . . . . 215
9.2.4 Economic Geography ofCities . 220
9.3 References................ . 229
10 The Polycentric City 235
10.1 Club Theory . 236
10.1.1 Elements ofClub Theory . 237
10.1.2 Extensions . 242
10.1.3 Clubs as Institutions ofCollective Economic Activity. . 244
10.1.4 Spatial Clubs . . . . . . . . . . . . . . . . . . 246
10.1.5 The Henry George Rule . . . . . . . . . . . . 247
10.2 The City as an Optimal Complex ofSpatial Clubs . 248
10.2.1 The Model . 249
10.2.2 The Optimal Club Complex . . . . . . . . . . 252
Contents xi
10.2.3 Decentralisation . 253
10.3 Monocentricity Versus Polycentricity . 254
10.3.1 Monocentric Configuration . 255
10.3.2 Polycentric Configuration . 256
10.3.3 Optimal Configuration . . 257
10.3.4 Comparative Statics . . . . 258
10.4 Appendices . . . . . . . . . . . . . 262
10.4.1 Optimality ofthe Club Equilibrium and Decentralisation 262
10.4.2 ProofofResult 10.1 . 263
10.5 References 263
11 Specialisation and Trade 267
11.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 267
11.2 An Extended Club-LPG Model . . . . . . . . . . . . . 269
11.3 A Reduced Form ofthe Optimal Allocation Problem . 271
11.4 Gains from Trade Versus the Loss from Inefficient City Size . 277
11.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 278
11.5.1 Consumption and Production Groups with a Pure Local
Public Good 278
11.5.2 ConsumptionandProductionGroupswithanImpureLo-
cal Public Good . 279
11.5.3 Consumption Groups with a Crowding Effect . 280
11.6 References. . . . . . . . . . . . . . . . . . . . . . . . 282
12 Externalities, Nonconvexity and Agglomeration 283
12.1 Introduction. . . . . . . . . . . . . . . . . . . 283
12.2 What is an Externality? . . . . . . . . . . . . . . . . 285
12.3 The Population Distribution Among Cities .... . 287
12.3.1 External Scale Diseconomies and Economies in an Old
Debate. . . . . . . . . . . . . . . . . .287
12.3.2 The Gaps MSC - MV and MSP - w .290
12.3.3 Variation ofGaps with City Size . . . 291
12.4 The Role ofNonconvexity . . . . . . . . . . . 293
12.4.1 The Utility-Size Configuration Revisited. . 293
12.4.2 Equilibrium, Stability and Market Bias . . 297
12.4.3 Externalities, Nonconvexity and the Direction ofMarket
Bias . . . . . . . . . . . . 297
12.5 Concluding Comments. . . . . . 300
12.6 Appendix: Gap Calculations. . 301
12.7 References. . . . . . . . . . . . . 303
Author Index 305
Subject Index 309