URBAN SUBCENTER FORMATION

1
URBAN SUBCENTER FORMATION BY ROBERT
W. HELSLEY ARTHUR M. SULLIVAN FOR REGIONAL
SCIENCE AND URBAN ECONOMICS
(21/1991) PRESENTED BY
FLORIAN F. FUHRMANN
2
Introduction
The conventional monocentric model of urban
employment was suggested to be largely
irrelevant. Employment is decentralizing to the
suburbs and centralizing within the
suburbs. Currently two approaches I. Citys
production and residential sectors are either
segregated or integrated. II. Firms can export
their output from either a central export node
or a circumferential suburban highway. This
article takes a third approachIII. Development
of sub centers is affected by fixed costs of
public capital, differences in production
technologies and interactions between production
locations. Objective is to show how, in a
growing, sub centers arise from the familiar
tradeoff between external scale economies in
production and diseconomies of transportation.
3
This approach uses 3 different models with
several assumptions gt A planning model (1)
with identical technologies gt (2) with
different technologies gt (3) with
non-reciprocal externalities Assumptions 1. A
myopic planner allocates a growing population to
one of two production locations
2. Public capital must be
installed prior to development of production
site 3. There are
external scale economies in production and
diseconomies of scale in transportation
4. The planner only cares about
welfare in the current
planning period Population increases by n
workers per period, the planner is to allocate
this population growth to the two locations to
maximize the aggregate social value of output.
Three phases I.) an initial phase of
exclusive city center development
II.) a phase of exclusive
sub center development III.) a final
phase of simultaneous development
4
(1) A planning model with identical
technologies Social value of output Vit Qit -
C (Nit,G) IitG (general for (1,2,3))
where output Qit ? (Nit) F (Nit,G). i
center,sub center For ? ? 01, ? satisfies
MSVC(Nct-1?tn)MSVS((t-1)n- Nct-1(1-
?t)n) Where the marginal social value of labor
for each location is given by MSVi
(Nit) ? (Nit) F (Nit,G) ? (Nit) FN (Nit,G)-
CN(Nit,G)
t period
MSV
MSVS
MSVC
G
A
A
MSV
NS
NC
NS1
NS2
NC1
NC2
n
5
(2) A planning model with different
technologies Now we have a different output
equation Qit si ? (Nit) F
(Nit,G), where si is productivity of
labor and sslt
sc. The introduction of sslt1 decreases MSVs,
for a given Ns, MSVs
(Nst)s1-MSVs (Nst)slt1gt0
MSV
MSVC
MSVS
G
B
B
MSV
NS
NC
NS1
NS2
NC1
NC2
n
6
(3) Non-reciprocal externalities We assume that
external scale economies are only generated in
the city center and that they spillover to the
sub center. City center output Qct ?
(Nct) F (Nct,G) Sub center output Qst ?
(µNct-1) F (Nst,G), µlt1 Since MSVs(Nst) lt 0,
the slope of MSVs is negative
MSV
MSVC
MSVS
G
C
C
MSV
NS
NC
NS1
NC1
NC2
7
A computational model of (3) Functional forms of
the different technologies Qct a(Nct)e
(Nct)a (Gc)1- a, Qst a(µNct-1)e (Nst)a
(Gc)1- a, C(Nit,G) c1(Nct/G)c2(Nct/G)2c3(Nct/
G)3, Vit Qit - C (Nit,G) IitG.
Vit
VMPc
MCc
MCs
MSVc
VMPs
Population of CC
Maximum at Nc 129
MSVs
8
Parameter values Benchmark Larger c3 Smaller e Smaller µ
C3 ( congestion cost) 0.000008 0.0000107 0.000008 0.000008
e (scale economies) 0.35 0.35 0.31 0.35
µ ( spillovers ) 0.10 0.10 0.10 0.08
Computational results
Nc at peak of MSVc 129 108 97 129
tc (end phase 1 ) 17 15 14 19
Nc at ts 171 151 141 191
tc (end phase 2) 17.5 15.4 14.6 19.4
Nc at tc 171 151 141 191
Ns at tc 6 5 7 5
T ( end of phase 3 ) 62.6 52.8 49.6 60.8
NcT ( terminal C size ) 413 351 334 431
NsT ( terminal S size ) 215 179 164 196
NT ( terminal size ) 628 530 498 610
NcT/N at t30 0.904 0.857 0.837 0.927
NcT/N 0.659 0.664 0.672 0.680
? at t20 0.90 0.80 0.80 0.90
? at t40 0.40 0.40 0.40 0.50
? at t60 0.39 -------------- ------------------ -----------------
9

• Sensitivity analysis
• An increase in c3 increases the diseconomies
  from transportation and
• thus decreases the population at which MSVc is
  maximized.
• Also if c3 increases, the fraction of population
  allocated to the central
• city at each t decreases and ?t decreases more
  rapidly over time.
• A decrease in e shifts the central citys MSV
  curve downward. The
• downward shift of MSVc decreases the amount of
  labor at which MSV
• reaches its maximum. A decrease in e also
  shortens the first phase of
• development. Changes in e also affect the
  duration of phase 3.
• A decrease in µ does not affect MSVc ,but shifts
  MSVs downward
• the first phase of development lasts longer.
• A decrease in µ also affects the duration of
  phase 3.

10
Comparing the three models The three models
differ in their predictions about the relative
size of the central city when the metropolitan
area stops growing, and the duration of the
second development phase. The third model, in
which the external scale economies in production
are non-reciprocal, predicts the development of a
dominant central city and a relatively short or
non-existing second phase of development.
11
Summary and extensions The analysis in this
paper uses a number of assumptions that present
opportunities for further work 1.Our planner
is myopic and only cares about welfare in the
current period. Solution Give the planner
ability to plan into future. gtsub
centers would develop much earlier 2.It would be
interesting to characterize an equilibrium with
profit maximizing land developers. Will this
equilibrium be Pareto efficient? Probably not,
we hope to examine the market equilibrium.