Mobility of Workers and Population Between Old and New Capital Cities Using the Interregional Economic Model

sustainability

Article Mobility of Workers and Population between Old and New Capital Cities Using the Interregional Economic Model

Changkeun Lee 1 and Euijune Kim 2,* ID

1 College of Engineering, Seoul National University, Seoul 08826, Korea; [email protected] 2 Department of Agricultural Economics and Rural Development and Research Institute of Agricultural and Life Sciences, Seoul National University, Seoul 08826, Korea * Correspondence: [email protected]; Tel.: +82-2-880-4742

Received: 28 August 2017; Accepted: 14 October 2017; Published: 18 October 2017

Abstract: The purpose of this paper is to analyze the effects of transportation and mobility costs on the mobility of workers and the overall population between old and new capital cities. First of all, mobility costs clearly have a negative effect on utility; higher commuting costs could lead to the spatial dispersion of workers. In addition, if the monthly commuting cost exceeds 1290 USD between Seoul (the old capital) and Sejong (the new capital), it would be efﬁcient for workers in Seoul to move to Sejong. Finally, the interregional population equilibrium could be achieved when the share of transportation cost to commodity price reaches 60.1%.

Keywords: mobility; migration and commuting cost; transportation cost; sustainable growth

1. Introduction Economic concentration in Seoul, the capital city of Korea, has had a negative impact on urban sustainable growth, interregional balanced development, the housing market, and environmental pollution [1]. To tackle this issue with policy tools, the Korean government decided to relocate 36 government ministries and agencies from Seoul to Sejong city (approximately 160 km south of Seoul, the capital city of Korea), the new administrative capital, in 2007, with the Presidential Office, the National Assembly, and all the foreign embassies remaining in Seoul. This location policy is not new for Asian countries. Malaysia constructed a new administrative capital, Putrajaya, in the early 1990s, and has transferred the federal administrative offices to this capital. Indonesia and Japan have discussed the construction of new administrative capital cities since the 1980s. The success of this relocation as a strong population dispersion tool depends on the outflows of government officers and families from Seoul and subsequent relocations of major commercial and financial facilities. For example, the planned population size of Putrajaya in Malaysia is 340,000 by 2025, but the actual size as of 2015 is only 83,000. Sejong City aims to grow into a sustainable self-sufficient city with a population of 500,000 by 2030, but the population size remains at roughly 40% of the population goal. What are the practical policy options for the government to achieve this planning target? In the sense that spatial economic activities have been assessed in terms of transportation costs and agglomeration economy, this paper is concerned with the economic contribution of transportation and mobility costs to the migration between the old and the new capital cities. The purpose of this paper is to analyze the effects of transportation costs on the mobility of workers and the general population between the old and new capital cities using a two-region growth model. Previous studies have analyzed a spatial framework between two regions, in each of which workers can reside or work. They divided mobility on the interregional level into commuting and migration depending on relocation decisions between two regions [2–4]. This paper attempts to

Sustainability 2017, 9, 1872; doi:10.3390/su9101872 www.mdpi.com/journal/sustainability Sustainability 2017, 9, 1872 2 of 15 examine the impacts of transportation and mobility costs on consumers’ utility and the spatial distribution of workers. Transportation cost is logistically deﬁned as the shipping (trade) cost of commodities, whereas mobility costs are the costs of commuting and migration of workers [3]. In addition, the ﬁnancial subsidies to move workers from the old capital to the new capital are derived from the comparative analysis of the theoretical model. The paper proceeds as follows: Section2 presents a literature review on the effect of transportation costs and migration; Section3 develops a simple two-region model; Section4 explores the comparative analysis; Section5 performs a numerical simulation with the use of transportation and commuting costs; and Section6 summarizes this paper and discusses further research issues.

2. Literature Review

2.1. Effects of Transportation and Mobility Costs Traditionally, in spatial economics, some literature has focused on the commute of workers on the intraregional level, but other literature has studied relocation decisions on the interregional level with respect to transportation and mobility costs. Transportation and mobility costs are traditionally key factors that affect the relocation of economic activities such as commuting or migration. Here, we present some examples of the effect of transportation costs on economic activities. Lower transportation costs, economies of scale, product differentiation, and positive general equilibrium feedback apparently work against the development of remote and sparsely populated suburb areas [5]. Kilkenny (1998) reviewed the relationship between transportation cost, mobility, and the rural development of firms and workers. Changes in transportation costs affected regional wage rates, thus determining the location of production cost-oriented firms and affecting the spatial mobility of firms and workers. A reduced transportation cost could result in the optimal number of firms and the concentration of firms in each region [6]. Tabuchi et al. (2005) analyzed the effects of a decrease in intercity transportation cost on the spatial distribution of the population in multiregional economies. The decrease in transportation cost triggered an agglomeration process in which large cities attracted workers and firms from the small cities [7]. However, Tabuchi (1998) demonstrated that when the transportation cost was low enough to overcome the advantages of agglomeration, dispersion prevailed under equilibrium within a two-region framework [8]. Murata and Thisse (2005) examined how low transportation cost facilitated the dispersion of economic activities within a general equilibrium model [9]. Alstadt et al. (2012) analyzed the relationship between transportation access, connectivity and local economic outcomes within an industry. The local 40-min and the regional three-hour market sizes in the trade and service industrial sectors were consistently strong factors that affected industry employment concentration, industry labor productivity, and foreign export proportion. However, these factors were less strong in the manufacturing, construction, and industrial utility sectors [10]. Allio (2016) found that if trade costs are low, the firms of each region access almost the same market wherever they settle, and workers consume products indifferently from the two regions. Thus, when trade costs increase, the agglomeration forces overpass the dispersion [11]. From the analysis of mobility costs, Suh (1988) defined conditions where intercity commuting was plausible. Workers lived in two strip cities that differed in terms of distance from the center, average rental prices, and commuting cost, with the absence of migration cost. When the income gap was large enough relative to the distance between the two cities and to the commuting cost, the residents of the low-income city tended to commute for work to the high-income city, despite the commuting cost [12]. Pinto (2002) observed that a reduction in commuting cost could lead to mobility [2]. Murata and Thisse (2005) assumed that workers could be mobile and free to choose a region where they preferred to work and live. They showed that a high commuting cost fostered economic activities [9]. Anas et al. (1998) and Anas and Rhee (2007) indicated that toll fees, as a commuting cost, reduced inefficient suburb-to-city commuting, as demonstrated in a simple city–suburb model with cross-commuting [13,14]. Baum-Snow (2007a; 2007b) found that in metropolitan areas where the Sustainability 2017, 9, 1872 3 of 15 intra-highway system was more developed, the population would be less concentrated at the center of the metropolitan city. Therefore, the degree of suburbanization was higher [15,16]. Using a two-city model, Sorek (2009) showed how workers’ migration or commuting decisions depended on commuting or migration cost and on commuting time. The migrants were the most able workers of the suburb. Suburb workers exhibited moderate ability to commute to work in the metropolis, and became the least able workers in suburbs. This showed that a reduction in commuting time could moderate, stop, or reverse the migration process. Potential intercity commuting time sharply declined with the development of transport technology. Therefore, commuting beyond the monocentric framework or between distant cities where workers could reside and work is made possible [3]. Xu and Li (2016) stressed the relation between commuting time and dispersion or agglomeration. They revealed that, from the empirical evidence, service employment decreased by 7%, but manufacturing employment increased by 21% in noncore areas in Japan [17]. In short, reducing intercity transportation costs could induce the concentration or dispersion of production factors. Higher commuting cost mostly resulted in population dispersion in a multiregional economy. The lower commuting time caused by the development of transportation technologies could result in population dispersion to suburban areas.

2.2. Migration Market-driven factors and public sector programs induce migration. For market-driven factors, Todaro (1969) and Harris and Todaro (1970) emphasized that a relatively higher permanent income or urban–rural differences in expected earnings attracted a steady stream of rural migrants into urban areas based on the market mechanism [18,19]. Cristopher and McMaster (1990) concluded that the market mechanism could remove regional inequality in economic prosperity. Interregional migration was found to respond to changes in regional wages and differences in employment opportunities. Migration induced by changes in unemployment rates restored the system to equilibrium [20]. Cushing and Poot (2004) stressed that migration was a result of a forward-looking behavior to maximize an individual’s or a household’s expected future benefit against cost [21]. Kancs (2011) studied the determinants of migration, such as market potential, wages, and cost of living in European regions [22]. For a public sector program, Tiebout (1956) suggested that an increase in consumer voter knowledge could improve the allocation of government expenditures [23]. Porell (1982) examined the effect of economic incentives and quality of life factors such as climate, parks, sports events, crime, density, and public welfare payments [24]. Cristopher and McMaster (1990) determined the necessity of a regional policy that could move jobs to a depressed region to eliminate the disequilibrium of the unemployment differential. In addition, mobility in acquiring jobs and knowledge relevant to the location of the industry and workers could improve the allocation of private resources [20]. Marshall et al. (2005) estimated the positive effects of public sector dispersal in Great Britain [25]. Mckinnish (2007) identified welfare migration effects based on the Aid to Families with Dependent Children policy in the United States (US) [26]. Glazer et al. (2008) analyzed the power of income tax policy to affect property values and induce migration [27]. Koethenbuerger (2014) showed that competing in taxes (transfers) renders migration flows less (more) elastic with respect to changes in fiscal policy [28]. Rijnks et al. (2016) found that migration motives are mainly related to residential qualities such as quality of life, livability, environmental quality, and labor market proximity. They highlighted the importance of the regional context in anticipating and designing a regional policy concerning population dynamics [29]. In summary, the differences in regional wages and employment opportunities affect migration. However, for promoting migration, the regional policy (e.g., tax system), the relocation of industry, and public sector dispersal are important tools. To attract migration, government expenditures need to be allocated to improve quality of life (QOL). Sustainability 2017, 9, 1872 4 of 15

and public sector dispersal are important tools. To attract migration, government expenditures need Sustainabilityto be allocated2017, 9to, 1872 improve quality of life (QOL). 4 of 15

3.3. TheThe ModelModel WeWe assumeassume aa simplesimple two-regiontwo-region (the(the oldold capitalcapital andand thethe newnew capital,capital, FigureFigure1 )1) growth growth model model basedbased onon AlonsoAlonso (1964),(1964), KrugmanKrugman (1991),(1991), andand SorekSorek (2009).(2009). ThisThis modelmodel identiﬁesidentifies thethe impactsimpacts ofof transportationtransportation and mobility mobility costs costs on on the the regional regional econ economiesomies [3,30,31]. [3,30,31 Travel]. Travel refers refers to mobility to mobility travel travelsuch as such commuting as commuting and migration, and migration, with withmobility mobility costs. costs. Commuting Commuting cost costis incurred is incurred between between two tworegions, regions, but butnot notwithin within each each regi region.on. Migration Migration cost cost refers refers to to the the costs costs implicated implicated in relocating.relocating. CommoditiesCommodities areare tradedtraded betweenbetween twotwo regions,regions, andand soso transportationtransportation cost,cost, suchsuch asas thethe shippingshipping (trade)(trade) costcost of commodities,of commodities, is incurred is incurred in iceberg in form.iceberg Each form. region Each produces region different produces commodities. different Thecommodities. labor input The (worker) labor input is assumed (worker) to beis theassumed only productionto be the only factor. production Agglomeration factor. Agglomeration economies are representedeconomies are as arepresented function of theas population.a function of Commuting the population. and migration Commuting costs, and transportation migration costs, cost, andtransportation total labor inputscost, and are exogenous.total labor inputs Labor inputsare ex canogenous. be disaggregated Labor inputs into ca fourn be groupsdisaggregated with respect into tofour living groups and with working respect locations. to living The and four working groups loca are astions. follows: The four living groups and working are as follows: in the old living capital; and livingworking and in working the old in capital; the new living capital; and living working in the oldin the capital, new but capital; working living in thein newthe old capital; capital, and thebut oppositeworking ofin thethe thirdnew capital; group. and the opposite of the third group.

FigureFigure 1.1. StructureStructure ofof thethe two-regiontwo-region model.model.

LaborLabor isis suppliedsupplied byby thethe household.household. HouseHouse membersmembers produceproduce KK ++ 11 timestimes laborlabor inputinput inin eacheach house.house. TheThe total total population population in eachin each region region is shown is sh asown in Equation as in Equation (1). The size(1). ofThe the size total of population the total ispopulation ﬁxed. is fixed. PopulationPopulation(Each (Each regionregion hashas non-zeronon-zero population) population) 2 =+2 NLKiij(1) (1) Ni =  Lij(K + 1) (1) ∑j=1 j=1

NNii:: PopulationPopulation inin regionregion ii;; LLijij:: Labor inputinput livingliving inin regionregion ii andand workingworking inin regionregion jj;; KK ≥≥ 0. 2 N = ∑2 Ni (2) = i=1 NN i (2) Production is determined by a Cobb–Douglasi=1 function for labor inputs and agglomeration economies. The latter implies that the personal interactions involved in the production and output sales Production is determined by a Cobb–Douglas function for labor inputs and agglomeration contribute to the productivity of ﬁrms. The price decreases with the population because g(N ) represents economies. The latter implies that the personal interactions involved in the productioni and output scale effect, which represents agglomeration economies as urbanization economies, as measured by sales contribute to the productivity of firms. The price decreases with the population because g(Ni) population in each region [32]. In this study, the population size is affected by relocation decisions, represents scale effect, which represents agglomeration economies as urbanization economies, as depending on transportation cost and mobility costs. Each household supplies homogenous labor, and measured by population in each region [32]. In this study, the population size is affected by the total labor inputs refer to the total man/hour. In terms of living and working locations in Table1, relocation decisions, depending on transportation cost and mobility costs. Each household supplies for example, output X in the old capital is produced by L (workers living and working in the old homogenous labor, and the total labor inputs refer to the11 total man/hour. In terms of living and capital) and L21 (workers living in the new capital, but working in the old capital). working locations in Table 1, for example, output X in the old capital is produced by L11 (workers living and working in the old capital) and L21 (workers living in the new capital, but working in the old capital). Sustainability 2017, 9, 1872 5 of 15

Table 1. Four groups with respect to living and working locations.

Case I Case II Case III Case IV (1, 1) (1, 2) (2, 1) (2, 2) living and working in living in the old capital, but living in the new capital, but living and working in the old capital working in the new capital working in the old capital the new capital Note: (i, j) = (living, working).

Production δ θ Xi = A g(Ni) Lii Lji (j 6= i) (3)

Xi: Aggregate output in region i; Ai: Scale factor; Lii: Labor input living and working in region i; Lji: Labor input living in region j and working in region i; g(Ni): Agglomeration economies function of population in region i; δ + θ = 1; 0 < δ, θ < 1. Firms maximize their proﬁt. The conditional input demand functions for each worker are as follows under perfect competition. Demand of each worker in region i δ Xi pi Lii = (4) wi

θ Xi pi Lji = (j 6= i) (5) wi Price in region i w = i pi δ θ (6) A g(Ni)δ θ Only the household is assumed to supply labor and consume the commodities in each house in this model. Consumers maximize the utility to consume two different regional commodities. The regional import is consumed at the transportation cost-inclusive price because of the shipping (trade) of the commodities. The transportation cost (t) is assumed to be greater than 0. Utility i αij k βij Uij = zij zij (i 6= k) (7)

i z ij: Commodities produced in region i that are consumed by workers living in region i and working in region j; k z ij: Commodities produced in region k that are consumed by workers living in region i and working in region j; αij + βij = 1; 0 < αij, βij < 1. The household income is determined by the wage level. Total monthly income of a household is shown in Equation (8). yij = wj H − 2d cij − mij (8) where yij is the monthly income of the household, excluding the mobility costs. H indicates the total monthly working time. This study did not adopt a time constraint, because a simple two-region growth model was used instead of a time-extended model. In addition, d is the working days in a month, and cij represents the commuting cost between the two regions. mij is the migration cost, which is incurred only when the living site is changed. Consequently, the budget constraint function of the Sustainability 2017, 9, 1872 6 of 15 household is shown in Equation (9). In addition, the Marshallian demands for each commodity are presented in Equations (11) and (12). Demand of the house i 0 k yij = pizij + pi zij (9) 0 pi = pk tki (10)

i αij yij zij = (11) pi

k βij yij zij = 0 (12) pi where pi is the price of a commodity in region i, and p’i represents the price of a commodity in region k (pk) plus the transportation cost from region k to region i (tki). Finally, the maximized utility level (Uij = Vij + εij) is derived from Equation (13).

αij βij αij βij yij Vij = (13) αij 0 βij pi (pi)

The choice of living and working locations could be achieved through the maximized utility, Equation (13). This choice could be speciﬁed in the form of a probability. Assuming that εij is independently identically distributed and follows Gumbel distribution (mean, zero, and variance, σ2: σ2 = π2/6λ2), the choice probability of living and working sites is equal to Equation (14). λ is called the taste heterogeneity parameter. If λ approaches inﬁnity (∞), the taste heterogeneity disappears.

∗ exp λ Vij ψij = ∗ (j 6= i) (14) ∑ exp λ Vks ∀ (k, s)

The probability that a randomly identiﬁed household chooses the living and working sites (i, j) to maximize the utility is calculated with the quadrinomial logit model (Prij = Prob [Uij > Uks; ∀(i, j) 6= (k, s)] = Prob [Vij + εij > Vks + εks; ∀(i, j) 6= (k, s)], ∑ Prij = 1) [14]. The expected welfare measure can be expressed as follows:

1 W = E[max Uij] = ln exp(λ Vij) (15) ∀( ) ∑ i,j λ i,j

The general equilibrium is computed from the market clearing for output, labor, and competitive market. Product market k Xk = ∑ Lψijzij (16) i,j,k Labor market Lii + Lji = ∑ Lψki H (17) k, i Competitive market w − i = pi δ θ 0 (18) A g(Ni)δ θ Sustainability 2017, 9, 1872 7 of 15

w p −=i 0 i δθδθ (18) Ag() Ni

Sustainability4. Comparative2017, 9, Analysis 1872 7 of 15

4.1. Transportation and Mobility Costs and Utilities 4. Comparative Analysis We assume two alternative mobility scenarios with regard to workers and population mobility 4.1.from Transportation the original andcase Mobility of living Costs and andworking Utilities in the old capital. The symmetric spatial distribution of populationWe assume is initially two alternative assumed: mobilityN1 = N2. scenarios with regard to workers and population mobility fromAlternative the original I: Changing case of the living working and site working from the in old the capital old capital. (i = 1) to The the symmetric new capital spatial (j = 2) distribution of population is initially assumed: N1 = N2. From L11 to L12, only the workers can change the working site through commuting. The Alternative I: Changing the working site from the old capital (i = 1) to the new capital (j = 2) population of the old capital does not change. The real income earned by a worker living in the old From L11 to L12, only the workers can change the working site through commuting. The population capital but working in the new capital decreases because of commuting cost c12. The utility V12 is of the old capital does not change. The real income earned by a worker living in the old capital but negative in L12. This result may be related to the commuting cost. working in the new capital decreases because of commuting cost c12. The utility V12 is negative in L12. −ν δθ 11/ N This result may be relatedVAepH to theφδθ commuting() cost. −+αα −+ββ 11= 11 1 11 12' 11 12 −ν δθ pp() 22/ N 11 (19) VAepHdcφδθ(2)−ν /N δ θ − V 12 12φ (Ae 1 1 δ θ 2p H) 12 − + 11 11 1 −α11+α12 0 β11 β12 = p1 (p1) (19) ( −ν2/N2 δ θ − ) V12 φ12∂VAe δ∂θV p2 H 2∂dcV12 ∂V 11 > 12 < 21 > 22 < 0 , 0 , 0, 0 ∂V∂L ∂V∂L ∂V∂L ∂V∂L 11 12> 0, 12 12< 0, 21 12> 0, 22 12< 0 ∂L ∂L ∂L ∂L ∝ 12 12 12 12 (φ = ∝ ∙ ) ∝ij βij (φij = ∝ij ·βij ) InIn thisthis case,case, eveneven ifif the the workers’ workers’ mobility mobility occurs,occurs, thethe totaltotal populationpopulation inin eacheach regionregion doesdoes notnot change.change. Additional subsidy subsidy or or incentives incentives are are needed needed to to induce induce commuting commuting to tothe the new new capital capital on onthe condition of the utility V11 < V12 because 2dc12 > w2H. Figure 2 shows that the gap between two utilities the condition of the utility V11 < V12 because 2dc12 > w2H. Figure2 shows that the gap between two utilitiesincreases increases according according to the torising the rising commuting commuting cost. cost.Commuting Commuting cost costnegatively negatively affects affects the the utility utility of ofworkers workers living living in in the the old old capital, capital, but but working working in in the the new new capital. capital.

FigureFigure 2. 2.Commuting Commutingcost cost and and utilities. utilities.

Figure 3 shows how the transportation cost affects the ratio of utilities. Transportation cost Figure3 shows how the transportation cost affects the ratio of utilities. Transportation cost affects affects the real income and the commodity’s price. β11 and β12, the parameters of the preference for the real income and the commodity’s price. β11 and β12, the parameters of the preference for the the commodity produced in the new capital, affect the ratio of the two utilities. If a worker who lives commodity produced in the new capital, affect the ratio of the two utilities. If a worker who lives in the old capital but works in the new capital prefers the commodity produced in the new capital in the old capital but works in the new capital prefers the commodity produced in the new capital more than a worker who lives and works in the old capital, the gap of utilities increases with the more than a worker who lives and works in the old capital, the gap of utilities increases with the transportation cost. The increasing transportation cost influences the price and affects the utility transportation cost. The increasing transportation cost inﬂuences the price and affects the utility negatively. Additionally, the production of this commodity in the new capital increases, and negatively. Additionally, the production of this commodity in the new capital increases, and ultimately ultimately raises the nominal wage in the new capital. This effect increases the welfare of the raises the nominal wage in the new capital. This effect increases the welfare of the population, population, including the workers living in the old capital, but working in the new capital. including the workers living in the old capital, but working in the new capital. Sustainability 2017, 9, 1872 8 of 15

Sustainability 2017, 9, 1872 8 of 15 Sustainability 2017, 9, 1872 8 of 15

Figure 3. Transportation cost and utilities.

Alternative II: Migrating to the new capital and changing the working site FigureFigure 3. 3. TransportationTransportation cost and utilities. From L11 to L22, the population, including the workers, migrates to the new capital, and the Alternativeworking site II: Migrating also changes. to the The new population capital and changingin the new the workingcapital increases. site The nominal wage in the new capital also increases, whereas the nominal wage in the old capital decreases. Migration cost is From L11 to L22, the population, including the workers, migrates to the new capital, and the From L11 to L22, the population, including the workers, migrates to the new capital, and the workingincurred. site The also utility changes. V22 is Thepositive population in L22. This in the result new is capital caused increases. by the increasing The nominal wage wage in the in newthe workingcapital. site also changes. The population in the new capital increases. The nominal wage in the new capital capital also also increases, increases, whereas whereas the the nominal nominal wage wage in in the the old old capital capital decreases. decreases. Migration Migration cost cost is −ν δθ incurred. The utility V22 is positive in11 /LN22. This result is caused by the increasing wage in the new is incurred. The utilityVAepHV φδθis positive() in L . This result−− isα causedββ by the increasingα wage in the 11= 22 1122 1 11'' 11 22 22 capital. −ν δθ p11()ppp () 22 (20) new capital. φδθ22/ N − VAepHm22 22() 2 22 −ν−ν/ 1N/N1δθδ θ V11 φδθφ11 (Ae 11 δ θ p1 H) −α 0 −β11 0 β22 α VAepH11= 11() 1 p −−α 11 (p'') ββ(p ) p α 22 = −ν /N δ θ 1 111 112 222 22 (20) V22 φ ∂(VAe−ν 2 2δθδ∂θ p H − m∂V) p11()ppp∂V () 22 (20) φδθ22 11 22 21 < VAepHm22 22()0 2>0 22 0 , 0 ∂∂VL ∂V∂L ∂∂VL ∂V∂L 1122 < 0,, 2222 > 0,, 1222 > 0, 2122< 0 ∂VL ∂∂L ∂∂LV ∂∂LV 2211 < V2222 2212 > 2221 < Migration decreases the population0 in the>0 old capital. 0It, is possible0 that V22 > V11 if w2H is larger Migration decreases the∂ populationL ∂ inL the old capital.∂L It is possible∂L that V22 > V11 if w2H is larger than m2 [N22/(N12 + N22)]. If the22 household, 22income, is large22 enough22 to compensate for the migration than m [N 2/(N 2 + N 2)]. If the household income is large enough to compensate for the migration cost without2 2 any1 subsidy2 or incentive, migration benefits the population, including the workers. costMigration without any decreases subsidy the or population incentive, in migration the old capital. beneﬁts It theis possible population, that V including22 > V11 if w the2H workers.is larger Figure 4 shows2 2 that 2the gap between the two utilities increases according to the rising migration thanFigure m42 shows[N2 /(N that1 + N the2 )]. gap If the between household the two income utilities is increaseslarge enough according to compensate to the rising for migration the migration cost. cost. Migration cost affects the utility of worker migrating to the new capital. costMigration without cost any affects subsidy the utility or incentive, of worker migration migrating benefits to the newthe population, capital. including the workers. Figure 4 shows that the gap between the two utilities increases according to the rising migration cost. Migration cost affects the utility of worker migrating to the new capital.

FigureFigure 4.4. MigrationMigration costcost andand utilities.utilities.

In Figure 5, as the transportation cost t12 increases, the price of the commodity produced in the In Figure5, as the transportationFigure cost 4. Migrationt12 increases, cost and the utilities. price of the commodity produced in the old capital increases. Hence, the utility of the workers living in the new capital after migration is old capital increases. Hence, the utility of the workers living in the new capital after migration is negatively affected. The gap of utilities widens according to the increasing transportation cost t12. negativelyIn Figure affected. 5, as the The transportation gap of utilities cost widens t12 increases, according the price to the of increasing the commodity transportation produced cost in thet12 . However, when the transportation cost t21 increases, the gap of utilities decreases. This result is oldHowever, capital when increases. the transportation Hence, the utility cost t21 ofincreases, the workers the gapliving of utilitiesin the new decreases. capital This after result migration is related is related to the price of the commodity produced in the new capital, which the workers living and negativelyto the price affected. of the commodity The gap of produced utilities inwidens the new according capital, whichto the theincreasing workers transportation living and working cost t12 in. working in the old capital pay. This result negatively affects the utility V11. However,the old capital when pay. the This transportation result negatively cost t affects21 increases, the utility the Vgap11. of utilities decreases. This result is related to the price of the commodity produced in the new capital, which the workers living and working in the old capital pay. This result negatively affects the utility V11. Sustainability 2017, 9, 1872 9 of 15 Sustainability 2017, 9, 1872 9 of 15

Figure 5. Transportation cost and utilities.

In summary, as the population including the workers migrates to the new capital, the nominal In summary, as the population including the workers migrates to the new capital, the nominal wage in the new capital increases, whereas the nominal wage in the old capital decreases. Utility is wage in the new capital increases, whereas the nominal wage in the old capital decreases. Utility is also directly related to the nominal wage or real income. Transportation cost negatively affects the also directly related to the nominal wage or real income. Transportation cost negatively affects the price of the commodity and the utility. The effects of commuting and migration costs on the utility price of the commodity and the utility. The effects of commuting and migration costs on the utility are negative. A financial subsidy is needed to enable workers to commute from the old capital to the are negative. A ﬁnancial subsidy is needed to enable workers to commute from the old capital to the new capital. new capital.

4.2. Agglomeration Effect and Utilities Agglomeration economies arise from the total populationpopulation in eacheach region.region. The utility may be affected by agglomeration factors, parameters, and population size. The agglomeration effects of the increasing region sizesize cancan induceinduce urbanurban costs,costs, suchsuch asas congestioncongestion oror disamenity.disamenity. −ν −ν = 11/ N = 22/ N gN()1 e−ν1/N1 , gN()2 e−ν2/N2 s.t. ν > 0 (21) g(N1) = e ,g(N2) = e s.t. ν > 0 (21)

Alternative I: Changing the working sitesite fromfrom thethe oldold capitalcapital (i(i == 1) to thethe newnew capitalcapital (j(j == 2)

−−−−ν δθ −α 0 −β β V ==−φδθφ (Ae ν2/ NN 22 δδ θθ p H − 2dc ) p α 1212 (p' ) 12 12 (22) 12VAepHdcpp12 1212(2)()2 212 1 11 (22)

In Alternative I, the population in each region is constant, and the utility changes in a declining degree or or according according to to elasticity elasticity ν.ν The. The utility utility is opposite is opposite in ν in. Thus,ν. Thus, the utility the utility of the ofworkers the workers living livingin the inold the capital old capital but working but working in the in thenew new capital capital is isaffected affected only only by by a adeclining declining degree degree of agglomeration economies. Alternative II: Migrating toto thethe newnew capitalcapital andand changingchanging thethe workingworking sitesite

− −−−−νν2/ NN2 δθδ θ −αα22 ' 0 ββ22 V22 ==−φδθφ22(Ae 22δ θ p2 H − m22) p2 22(p2) 22 (23) VAepHmpp22 22()() 2 22 2 2 (23)

The population, including the workers, migrates to the new capital, and the working site also changes. Therefore, the population in the new capitalcapital increases. The utility of the workers living and working in the new capital increases due to the improvedimproved agglomeration effects. In the change of ν,, the slope of the utility is less steep.steep. Finally, even if transportationtransportation and mobility costs negatively affect the utility, agglomerationagglomeration economies improve in the increasing population through migration.migration. The utility of the workers living and working in the new capital increases duedue toto thethe improvedimproved agglomerationagglomeration effects.effects.

5. Numerical Simulation Empirically, it is is set set that that the the old old capital capital is isSeou Seoul,l, and and the the new new capital capital is Sejong is Sejong City City(Sejong). (Sejong). The Thenumber number of workers of workers living living in Seoul in Seoul and and Sejong Sejong are are 11 11 million million and and 3.5 3.5 million, million, respectively. respectively. The The initial data are obtained from Statistics Korea. This analysis discusses the spatial dispersion of workers depending on relocation decisions between Seoul and Sejong, as well as their effect on regional Sustainability 2017, 9, 1872 10 of 15 data are obtained from Statistics Korea. This analysis discusses the spatial dispersion of workers Sustainability 2017, 9, 1872 10 of 15 dependingSustainability on 2017 relocation, 9, 1872 decisions between Seoul and Sejong, as well as their effect on10 regional of 15 economies. The change in commuting and transportation cost is considered under static conditions. economies.economies. TheThe changechange inin commutingcommuting andand transportatitransportationon costcost isis consideredconsidered underunder staticstatic conditions.conditions. The dispersion of workers in each living and working site is interpreted as the change rate of the initial TheThe dispersiondispersion ofof workersworkers inin eacheach livingliving andand workinworkingg sitesite isis interpretedinterpreted asas thethe changechange raterate ofof thethe value set to 100. Figures6 and7 illustrate the effects of change in commuting and transportation cost initialinitial valuevalue setset toto 100.100. FiguresFigures 66 andand 77 illustrateillustrate thethe effectseffects ofof changechange inin commutingcommuting andand on the dispersion of workers, respectively. The ﬁrst dimension indicates the case of living in Seoul, transportationtransportation costcost onon thethe dispersiondispersion ofof workers,workers, respectively.respectively. TheThe firstfirst dimensiondimension indicatesindicates thethe casecase butofof working livingliving inin in Seoul,Seoul, Sejong. butbut The workingworking second inin Sejong. dimensionSejong. TheThe issecondsecond the case dimensiondimension of living isis and thethe workingcasecase ofof livingliving in Sejong. andand workingworking The change inin rateSejong.Sejong. of the TheThe dispersion changechange of raterate workers ofof thethe steeply dispersiondispersion responds ofof workersworkers to the change steeplysteeply in respondsresponds transportation toto thethe cost, changechange as shown inin intransportation Figuretransportation7. As the cost,cost, commuting asas shownshown costinin FigureFigure increases, 7.7. AsAs th thethee commuting numbercommuting of workerscostcost increases,increases, living thethe and numbernumber working ofof workersworkers in Sejong sharplylivingliving increases. andand workingworking However, inin SejongSejong the sharplysharply choice increases. probabilityincreases. However,However, of living thethe in Seoul, choicechoice but probabilityprobability working ofof in livingliving Sejong inin increases Seoul,Seoul, marginally,butbut workingworking despite inin SejongSejong the commuting increasesincreases marginally,marginally, cost. despitedespite thethe commutingcommuting cost.cost.

FigureFigureFigure 6. 6.6.Effect EffectEffect of ofofchange changechange in inin communingcommuning cost cost onon thethe the dispersiondispersion dispersion ofof of workers.workers. workers.

FigureFigureFigure 7. 7.7.Effect EffectEffect of ofofchange changechange in inin transportation transportationtransportation costcost onon thethe the dispersiondispersion dispersion ofof of workers.workers. workers.

InIn conjunctionconjunction withwith FigureFigure 6,6, FigureFigure 88 showsshows thethe relationshiprelationship betweenbetween thethe changechange ofof workersworkers In conjunction with Figure6, Figure8 shows the relationship between the change of workers living livingliving inin SeoulSeoul butbut workingworking inin Sejong,Sejong, andand thethe changechange ofof commutingcommuting cost.cost. ThisThis indicatesindicates thatthat in Seoul but working in Sejong, and the change of commuting cost. This indicates that commuting commutingcommuting stopsstops whenwhen thethe monthlymonthly commutingcommuting costcost exceedsexceeds 12901290 USD—aboutUSD—about 26.1%26.1% ofof thethe stopsmonthlymonthly when averageaverage the monthly incomeincome commuting ofof urbanurban householdshouseholds cost exceeds withwith 1290 fourfour USD—about membersmembers inin Korea—atKorea—at 26.1% of theconstantconstant monthly price.price. average TheThe incomehigherhigher of commutingcommuting urban households costcost resultsresults with fourinin thethe members dispersiondispersion in Korea—at ofof workersworkers constant toto Sejong.Sejong. price. ThisThis The implies higherimplies commutingthatthat thethe costpopulationpopulation results in maymay the increaseincrease dispersion naturallynaturally of workers andand fostfost toerer Sejong. thethe economiceconomic This implies activitiesactivities that inin Sejong.Sejong. the population may increase naturallyFigureFigure and 9 foster9 showsshows the thethe economic positivepositive activitiesrelationshiprelationship in Sejong.betweenbetween thethe numbernumber ofof workersworkers livingliving inin SejongSejong andand thetheFigure higherhigher9 shows transportationtransportation the positive cost.cost. relationship ThisThis impliesimplies between thethe dispersiondispersion the number ofof of workersworkers workers fromfrom living SeoulSeoul in Sejong toto Sejong.Sejong. and the higherKrugmanKrugman transportation (1991)(1991) andand cost. KilkennyKilkenny This implies (1998)(1998) theprovedproved dispersion thatthat ththe ofe concentrationconcentration workers from inin Seoul thethe oldold to Sejong. capitalcapital Krugmanisis favoredfavored (1991) byby thethe reductionreduction inin transportationtransportation costcost [6,31],[6,31], whilewhile MurataMurata andand ThisseThisse (2005)(2005) suggestedsuggested thatthat aa higherhigher transportationtransportation costcost fostersfosters laborlabor concentrationconcentration andand agglomerationagglomeration inin thethe regionregion [9].[9]. AtAt aa lowerlower Sustainability 2017, 9, 1872 11 of 15

Sustainabilityand Kilkenny 2017,(1998) 9, 1872 proved that the concentration in the old capital is favored by the reduction11 of in15 Sustainabilitytransportation 2017, 9 cost, 1872 [6 ,31], while Murata and Thisse (2005) suggested that a higher transportation11 of 15 transportationcost fosters labor cost, concentration more workers and live agglomeration in Seoul, and inthe the population region [9]. ultimately At a lower increases. transportation Originally, cost, transportation11more million workers workers, cost, live in moreout Seoul, of workers the and total the li ve14.5 population in million Seoul, andworkers ultimately the population in increases.the two ultimatelyregions, Originally, live increases. in 11 Seoul. million Originally, However, workers, 11sinceout million of transportation the workers, total 14.5 out millioncost of is the rising, workers total the 14.5 in number themillion two of regions,workers workers livein living the in Seoul.twoin Sejong regions, However, is increasing. live sincein Seoul. transportation If the However, share of sincetransportationcost istransportation rising, the cost number tocost commodity’s is of rising, workers the price livingnumber reaches in Sejongof workers up isto increasing. 60.1%, living the in IfSejongworkers the share is increasing.will of be transportation balanced If the betweenshare cost of to transportationSeoulcommodity’s and Sejong. price cost to reaches commodity’s up to 60.1%, price the reaches workers up to will 60.1%, be balanced the workers between will Seoulbe balanced and Sejong. between Seoul and Sejong.

Figure 8. ChangeChange of workers living in Seoul but working in Sejong. Figure 8. Change of workers living in Seoul but working in Sejong.

12 12

10 10

8 8 Seoul 6 SeoulSejong 6 Sejong Number of Workers Living

in Each Region (Million Persons) (Million Region in Each 4 Number of Workers Living

in Each Region (Million Persons) (Million Region in Each 4 Share of Transportation cost to 2 ShareCommodity’s of Transportation Price (%) cost to 2 Commodity’s Price (%)

0 0 0 10305070 0 10305070 Figure 9. Transportation cost and dispersion of workers between the two regions. FigureFigure 9. 9. TransportationTransportation cost cost an andd dispersion dispersion of of workers workers between between the the two two regions. regions. Figures 10 and 11 illustrate the relationship between the transportation or commuting cost and utilities.FiguresFigures The 10 10higher andand 11 11transportation illustrateillustrate the the relationshipor relationship commuting between between cost negatively the the transportation transportation affects the or or utilities,commuting commuting even cost cost if theyand and utilities.contributeutilities. The The to higher the higher dispersion transportation transportation of workers. or or commuting commuting The effect cost costof increasingnegatively negatively transportationaffects affects the the utilities, utilities, cost oneven even utilities if if they they is contributegreatercontribute than to to thatthe the ofdispersion dispersion increasing of of commuting workers. workers. The Thecost. effect effect of of increasing increasing transportation transportation cost cost on on utilities utilities is is greatergreater than than that that of of increasing increasing commuting commuting cost. cost. Sustainability 2017, 9, 1872 12 of 15 Sustainability 2017, 9, 1872 12 of 15 SustainabilitySustainability 20172017,, 99,, 18721872 1212 ofof 1515

Figure 10. Impact of change in commuting cost on utilities. FigureFigure 10. 10. ImpactImpact of of change change in in commuting commuting cost cost on on utilities. utilities.

Figure 11. Impact of change in transportation cost on utilities. FigureFigure 11. 11. ImpactImpact of of change change in in transp transportationtransportationortation cost cost on on utilities. utilities.

FiguresFiguresFigures 121212 andandand 131313 showshowshow thatthatthat outputoutputoutput ininin SejongSejongSejong increasesincreasesincreases withwithwith thethethe risingrisingrising transportationtransportationtransportation andandand commutingFigures cost.12 and This 13 is showrelated that to the output scale ineffect Sejong of agglomeration increases with economies. the rising transportation and commutingcommuting cost. cost. This This is is related related to to the the sc scalescaleale effect effect ofof agglomerationagglomeration economies.economies.

Figure 12. Impact of change in commuting cost on output. FigureFigure 12. 12. ImpactImpact of of change change in in commuting commuting cost cost on on output. output. Sustainability 2017, 9, 1872 13 of 15 Sustainability 2017, 9, 1872 13 of 15

FigureFigure 13. 13. ImpactImpact of of change change in in tran transportationsportation cost cost on on output. output.

Consequently, thethe lower lower transportation transportation and and commuting commuting costs costs foster foster the concentration the concentration of workers of workersin Seoul. in Paradoxically, Seoul. Paradoxically, the higher the transportation higher transportation and commuting and costscommuting induce costs the dispersion induce the of dispersionworkers to of Sejong, workers and to positively Sejong, affectand positively the output affect growth. the However,output growth. the social However, welfare the decreases, social welfareas indicated decreases, by Kilkenny as indicated (1998) [6by]. KilkennyKilkenny (1998)(1998) pointed [6]. Kilkenny out that (1998) rural developmentpointed out couldthat rural only developmentbe achieved at could a lower only overall be achieved welfare at [a6 ].lower In the over senseall welfare that 1290 [6]. USD In the is sense the maximum that 1290 amountUSD is the for maximumthe commuters amount to payfor the from commuters Seoul to Sejong, to pay thefrom government Seoul to Sejong, needs the to government restrict the ﬁnancial needs to subsidy restrict theallocated financial to themsubsidy in allocated order to increaseto them in the order population to increase size the of Sejong.population If the size share of Sejong. of transportation If the share ofcost transportation to commodity cost price to reachescommodi 60.1%,ty price the reaches interregional 60.1%, population the interregional equilibrium population could beequilibrium achieved. couldIn addition, be achieved. for the sustainableIn addition, growth for the of sustainable Sejong, it is growth necessary of toSejong, implement it is necessary in-migration to policyimplement tools in-migrationsuch as improvement policy tools of livingsuch as quality improvement (e.g., housing of living supply quality and (e.g., amenities) housing and supply the development and amenities) of andpublic the infrastructure development facilitiesof public (e.g., infrastructure transportation facili andties (e.g., disaster transportation prevention). and disaster prevention).

6. Conclusions Conclusions This paper paper analyzes analyzes the the effects effects of of transportation and and mobility mobility costs costs on on the mobility of workers and population population between between the the old old and and new new capital capital cities cities using using a two-region a two-region growth growth model. model. First First of all, of thereall, there is clearly is clearly a negative a negative effect effect of oftransportation transportation and and mobility mobility costs costs on on utility, utility, and and the agglomeration economies economies in in Sejong Sejong (the (the new capital) could improve with increasing population throughthrough migration. These These agglomeration agglomeration economies economies positively positively lead lead to to output output growth growth with with scale effect.effect. Higher Higher transportation transportation and and commuting commuting costs costs co coulduld result result in in the the spatial spatial dispersion dispersion of of workers. workers. InIn addition,addition, ifif thethe monthly monthly commuting commuting cost cost exceeds exceeds 1290 1290 USD USD between between the oldthe andold newand capitalnew capital cities, cities,it would it would be efficient be efficient for workers for workers in Seoul in to moveSeoul toto Sejong.move to Finally, Sejong. the Finally, interregional the interregional population populationequilibrium equilibrium could be achieved could be whenachieved the when share the of transportation share of transportation cost to commodity cost to commodity price reaches price reaches60.1%. This60.1%. result This can result identify can what identify kinds what of financial kinds subsidiesof financial and subsidies policy tools and on policy population tools andon populationcommuters and are necessarycommuters for are the necessary mutual development for the mutual of development a few core cities of a such few ascore old cities and newsuch capitalas old andcities new in termscapital of cities population in terms distribution. of population What distri isbution. an effect What of the is commuteran effect of costthe commuter on the population cost on thedispersion population between dispersion the cities? between What the are cities? the effectivenessWhat are the andeffectiveness efficiency and of regional efficiency development of regional developmenttools with respect tools towith spatial respect income to spatial disparity? income How disparity? does spatial How accessibility does spatial from accessibility the infrastructure from the infrastructuredevelopment affectdevelopment regional economicaffect regional integration? econom Inic particular, integration? the impactIn particular, of transportation the impact costs of transportationon the mobility costs from on this the paper mobility could from contribute this pa toper policy could formulation contribute and to policy processes formulation of population and processesand location of population of Japan, Indonesia, and locati andon of other Japan, countries Indonesia, that haveand othe discussedr countries the construction that have discussed of a new theadministrative construction capital of a new city. administrative capital city. As for further research issues, one is to quantifyquantify thethe time value and mobility costs in monetary terms.terms. It It would would be be interesting interesting to to extend extend the the two-region two-region growth growth model model to to a a dynamic dynamic one one with with forward-lookingforward-looking behavior behavior of of households, producer producers,s, and and national and local governments between overlapping generations. generations. Another Another future future research research area area could could be be exploring exploring the the optimal optimal size size of of the population through using agglomeration economies and scale effects of distances and factor inputs. Sustainability 2017, 9, 1872 14 of 15 population through using agglomeration economies and scale effects of distances and factor inputs. Since actual relocation patterns take the form of polycentric cities, it is necessary to specify a spatial model with multiple workplaces and residential areas in mixed urban structures, the heterogeneous quality of schooling, and urban functions for QOL [33].

Author Contributions: Changkeun Lee and Euijune Kim developed a motivation and research structure; all authors specified a model structure and read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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