URBAN SUBCENTER FORMATION BY ROBERT W. HELSLEY & ARTHUR M. SULLIVAN FOR REGIONAL SCIENCE AND URBAN ECONOMICS (21/1991) PRESENTED BY FLORIAN F. FUHRMANN

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. City’s 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 approach:III. 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.

This approach uses 3 different models with several assumptions: => A planning model (1) with identical technologies => (2) with different technologies => (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

(1): A planning model with identical technologies Social value of output: V i t = Q i t - C (N i t,G) – I i t G (general for (1,2,3)) where output Q i t = Ψ (N i t ) F (N i t,G). i = center,sub center For θ Є [0;1], θ satisfies: MSV C (N c t-1 +θ t n)=MSV S ((t-1)n- N c t-1 +(1- θ t )n) Where the marginal social value of labor for each location is given by: MSV i (N i t ) = Ψ (N i t ) F (N i t,G)+ Ψ (N i t ) F N (N i t,G)- C N (N i t,G) NSNS NCNC NS1NS1 NS2NS2 MSV S MSV C MSV AA G NC1NC1 NC2NC2 MSV* t= period n

(2) A planning model with different technologies Now we have a different output equation : Q i t =σ i Ψ (N i t ) F (N i t,G), where σ i is productivity of labor and σ s < σ c. The introduction of σ s <1 decreases MSV s, for a given N s, MSV s (N s t ) σ=1 -MSV s (N s t ) σ 0 NSNS NCNC N’ S 1 N’ S 2 MSV S MSV C B B G N’ C 1 N’ C 2 MSV* MSV n

(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 : Q c t = Ψ (N c t ) F (N c t,G) Sub center output: Q s t = Ψ (μN c t-1 ) F (N s t,G), μ<1 Since MSV s ’(N s t ) < 0, the slope of MSV s is negative: NSNS NCNC N* S 1 MSV C C N’ C 1 N’ C 2 MSV* MSV C MSV S G

A computational model of (3) Functional forms of the different technologies: Q c t = a(N c t ) ε (N c t ) α (G c ) 1- α, Q s t = a(μN c t-1 ) ε (N s t ) α (G c ) 1- α, C(N i t,G) = c 1 (N c t /G)+c 2 (N c t /G) 2 +c 3 (N c t /G) 3, V i t = Q i t - C (N i t,G) – I i t G. Population of CC VitVit MSV c MC c VMP c Maximum at N c =129 VMP s MC s MSV s

Parameter valuesBenchmarkLarger c 3 Smaller εSmaller μ C 3 ( congestion cost) ε (scale economies) μ ( spillovers ) Computational results : N c at peak of MSV c t c (end phase 1 ) N c at t s t c (end phase 2) N c at t c N s at t c 6575 T ( end of phase 3 ) N c T ( terminal C size ) N s T ( terminal S size ) N T ( terminal size ) N c T /N at t= N c T /N θ at t= θ at t= θ at t=

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

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.

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. =>sub 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.