New Economic Geography of Superstar Cities

Transcription

1 New Economic Geography of Superstar Cities Bochao Zhang and Yuming Fu 2 May 204 Abstracts Gyourko, Mayer and Sinai ( Superstar Cities American Economic Journal: Economic Policy 5(4), 203) document the widening house price dispersion across US cities over the past half a century and demonstrate that such dispersion can arise as a result of changes in aggregate demand rather than changes in local conditions. In particular, cities with less elastic housing supply become more expensive as aggregate demand increases; hence they become more exclusive to high-income households and are perceived to be superstar cities. We present a more general model, where income sorting arises due to (i) diversity of local non-traded services being a luxury good, (ii) increasing return to local demand for differentiated non-traded services, (iii) comparative advantage for low-skill workers to specialize in non-traded sector. In equilibrium, cities differentiate endogenously to cater to different preferences across income groups with respect to the bundle of local service diversity and housing cost, and household utility is non-decreasing with skill level. Our model can simulate the impact of change in population size and skill distribution on house price dispersion, income sorting, and welfare across the skill spectrum. We show that middle-income traded sector workers tend to suffer from rising skill disparity, which makes access to local-service diversity increasingly more expensive as house price dispersion widens. However, the house price dispersion will eventually be limited by high-income households reliance on low-skill workers for supplying local service diversity. Key words: income sorting; house price dispersion; increasing return; taste for variety. JEL classification: J3 R R3 The Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive, Singapore 7566 ( bochao.zhang@nus.edu.sg). 2 The Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive, Singapore 7566 ( yuming.fu@nus.edu.sg).

2 . Introduction House price dispersion across US metropolitan areas has widened considerably since World War II. Gyourko, Mayer and Sinai (203) to be referred to as GMS (203) thereafter offer a fundamental insight that the dispersion can widen as a result of aggregate demand increase rather than local condition changes. GMS (203) show that, when heterogeneous tastes for cities are uncorrelated with income, asymmetric housing supply elasticity across cities is sufficient to produce elevated house price dispersion when aggregate demand increases. Cities with inelastic housing supply referred to as superstar cities in GMS (203) become more expensive, hence more exclusive to high-income households, as a result of increased aggregate demand. The present paper presents a more general model to account for house price dispersion across cities in response to aggregate demand change in an economy. Our model does not rely on asymmetric housing supply elasticity, which is not necessarily sustainable when the supply elasticity can be regulated by local governments (e.g. Hilber & Robert-Nicoud, 203). In addition, our model endogenizes the heterogeneous tastes for cities and provides clearer basis for evaluating the welfare impact of house price dispersion across income segments. Our model is rooted in the tradition of the new economic geography literature (Fujita, Krugman, & Venables, 200; Krugman, 99) by emphasizing the role of increasing return at the city level in sustaining asymmetric spatial equilibrium. We assume a nonhomothetic utitlity function, where diversity of local nontraded services is a luxury good. Individuals also consume a homogeneous traded numéraire good and housing. Individuals are endowed with heterogeneous skill levels and can choose to specialize in either the traded-good sector or the nontraded-service sector. We assume away agglomeration economies in traded-sector employment to focus on the increasing returns in the nontraded-service sector. We assume the traded-sector productivity to be proportional to labor skill but is independent of location, whereas the nontraded-sector productivity is independent of skill but depends on local demand size due to the

3 requirement of a fixed cost for each variety of nontraded service. In such a setting, low skilled worker will choose to specialize in nontraded sector; they will enjoy the same utility regardless of their skill and location in equilibrium. The price of the composite nontraded services diverges between cities as they specialize to cater to the demand for nontraded services by different skill groups; such divergence is compensated by house price divergence. Our model can simulate the impact of change in population size and skill distribution on house price dispersion, income sorting, and welfare across the skill spectrum. We show that middle-income traded sector workers tend to suffer from rising skill disparity, which makes access to local-service diversity increasingly more expensive as house price dispersion widens. However, the house price dispersion will eventually be limited by high-income households reliance on low-skill workers for supplying local service diversity. In addition to producing the stylized facts about the geographic dispersion of income and housing prices documented in GMS (203), our model yields other predictions consistent with the empirical literature. First, superstar cities tend to be larger, as the cost advantage of nontraded service variety is endogenous with respect local demand. This is consistent with the finding that large Europe and US cities outperformed their smaller counterparts with respect to consumption benefits (Edward L. Glaeser, Kolko, & Saiz, 200). Second, the willingness to pay to locate in large cities increases with skill level, which is consistent with the evidence reported in Lee (200) and Fu and Liao (204). Third, our model shows that the larger, superstar, cities would also be more diversified with respect to worker skills. Essentially, our theory emphasizes that the high-skill and the low-skill can be complementary through nontraded service sector. This prediction is consistent with the stylized fact that both high-skill and low-skill workers disproportionately sort into large cities (Combes, Duranton, Gobillon, & Roux, 202; Eeckhout, Pinheiro, & Schmidheiny, 200). Skill sorting across cities is extensively documented in the literature (Bacolod, Blum, & Strange, 2009; Combes, et al., 202; Henderson, 974). Most studies focus on productive advantages of skill sorting, such as skill complementarity in production (Baum-Snow & 2

4 Pavan, 202, 203; Berry & Glaeser, 2005; Combes, Duranton, & Gobillon, 2008; Giannetti, 200, 2003; Edward L Glaeser & Resseger, 200; Matano & Naticchioni, 202; Mion & Naticchioni, 2009), learning externality (D. R. Davis & Dingel, 202), and sharing of intermediate inputs (J. C. Davis & Henderson, 2008; Hendricks, 20). Behrens et al (200), Venables (20) and Davis and Dingel (202) are recent examples that provide microfoundation for asymmetric spatial equilibrium with agglomeration economies in traded-good production and skill sorting that emerge from symmetric locations. Our present paper is in the same spirit as these examples but focuses instead on agglomeration economies in nontraded service production and skill sorting driven by consumption benefits. Glaeser et al. (200), Adamson et al. (2004), Gottlieb and Glaeser (2006), and Lee (200) highlight the consumption benefits of skill sorting and offer evidence that higher skill workers value consumer amenities more highly (i.e. nonhomothetic utility with the income elasticity of demand for nontraded consumer amenities greater than unity). Like GMS (203), these studies assume exogenous distribution of consumer amenities. Recent literature also highlights the non-monotonic pattern of skill sorting across cities. In particular, Eeckhout et al. (200) and Combes et al. (202) document greater skill dispersion in larger cities. Eeckhout et al. (200) explains this pattern by assuming large cities are more productive and hence have greater demand for both very high and very low skills that are relative scarce. Davis and Dingel (202), on the other hand, assume that nontraded service sector does not depend on skills and, consequently, relatively low-skill workers specialize in nontraded service employment. Low-skill workers co-locate with high skill workers as the former rely on the demand for nontraded services by the latter for their employment opportunities. We adopt Davis and Dingel (202) s assumption. Empirical evidence show that the presence of high-skill workers improves employment outcomes for low-skill workers, especially for those employed in nontraded service sector. Moretti (200), for example, finds that one additional skilled job in the traded sector generates 2.5 jobs in local goods and services sector in U.S. cities. More evidence can be found in Moretti and Thulin (203), Manning (2004), and Kaplanis 3

5 (200). Our model is presented in section 2. The sorting equilibrium is characterized in section 3. Numerical examples of the equilibrium evolution with changing aggregate skill dispersion and population size are shown in section 4. Section 5 concludes. 2. The Model We consider an economy with two cities at symmetric locations. The economy has a population of perfectly mobile workers with heterogeneous skill levels. They consume housing in one of the two cities, a numeraire traded good, and a bundle of differentiated nontraded services. They have a taste for variety of nontraded services and their utility function is nonhomothetic such that the income elasticity of demand for the nontraded services is greater than unity. The productivity of traded-good producers equals to their skill level but is independent of location, whereas the productivity of nontraded-service producers is independent of their skill level but is subject to increasing return with respect to local demand (market thickness). The housing supply in each city is imperfectly elastic so that housing price dispersion widens as housing consumptions in two cities diverge. In such a setting, we show that the relatively low-skill workers will choose to specialize in producing nontraded services and cities will specialize with respect to different diversity of local services to cater to different income segments. The city that offers a greater diversity of local services (low nontraded-service price) and a higher compensating housing price the superstar city caters to high skill workers, who have greater willingness to pay for local service diversity, and also attracts a greater proportion of low-skill workers to provide nontraded services. 2.. Consumption In our model, individuals consume three goods: traded goods, X, a composite of nontraded service goods, S, and housing goods, H. Previous studies have shown that the income elasticity of demand for housing expenditure is less than (Albouy, 2008; E. L. Glaeser, Kahn, & Rappaport, 2008; Moretti, 203). We assume that both housing and 4

6 traded goods are necessary goods, thus income elasticity of demand for nontraded service goods is greater than. This is the key assumption that drives spatial sorting of skills in our model. Consumers preference is defined by the indirect utility function, I P () V(, I G, P) G G, where I is individual income and P is the price index of a composite of housing and traded goods, given by, Ph PX P, (2) where P h is price of housing and P X is price of traded goods. The price index is in the form of Cobb-Douglas, which implies that expenditure share of housing is constant within the composite, and the share is given by. Because we use traded goods as numéraire, P X always equals to. Further, we assume that people have a taste for diversity of nontraded service goods. The price index of nontraded service varieties, G, is defined by, (3), where p( i ) is the price of variety i, n is the range of varieties produced and is the elasticity of substitution between any two varieties. Parameters are restricted, such that 0, 0, 0,. measures the degree of non-homotheticity of the utility. If 0, the utility is homothetic. Income elasticity of demand for housing and traded goods are given by. Using Roy s identity, we can derive the demand for each goods. Demand for traded goods is, 5

7 V / P G P I V / I I G X (4) Q X Housing demand is given by, (5) Q h V / Ph G P I V / I I G P Demand for nontraded-service variety i is given by, V / p( i) I G G P (6) QSi, V / I G p( i) I G h Note that income need to be sufficiently high to generate both a positive demand for nontraded services and a positive utility. When, the demand for nontraded services is positive whenever the utility is positive Production Nontraded Service Sector We assume the production technology is the same for all nontraded service varieties and in all locations. Labor is the only input. Each worker has one unit of labor to produce nontraded service goods. To specialize in producing any variety, worker must pay a fixed labor cost, F, to acquire certain trainings. In addition, each unit of service good also requires a constant marginal labor input c. Producing a quantity of zi () of any variety requires l (7) unit of labor input, defined by, Because of consumers' preference for diversity and the fixed cost associated with labor specialization, each team produces a unique variety. Consider a particular team facing a wage rate,w, for workers in nontraded service sector. Then, with variety price pi (), firm s profit p () i is given by, (8). Demand for variety i, zi (), is given by (4). Because the price elasticity of demand is 6

8 constant, the profit-maximization behavior of a firm implies a constant mark-up over the marginal cost of production, (9) In equilibrium, free entry and exist condition drives the profit to zero, (0), Therefore, the optimal output level for all teams in all locations is given by, (), The associated equilibrium labor input is given by, (2) We perform normalization by letting. Therefore, (3) z( i) (4) ( ) * p i * = Fs, = w. Traded Goods Sector Although workers have equal amount of labor, we assume they have heterogeneous skills, which reflect their productivity in traded goods sector. Skill can be represented by a one-dimensional indicator,b, which is distributed according to a density function, kb (), on a finite support. Workers are free to choose between traded good sector and nontraded service sector. Because nontraded service sector does not make use of worker s heterogeneity, high-skill workers have no productivity advantage in producing nontraded service goods. By comparative advantage, as in Roy (95), high-skill workers will work in traded sector that compensates their skills. Housing Sector To generate congestion costs, we adopt a standard internal structure for cities (Alonso, 7

9 964; Behrens, et al., 200; Muth, 969). Each location is endowed with housing sites that serve as residences and that do not require labor input. Residents commute from home to working places in the central business district. We denote as the housing price in city c, incorporating both land rents and commuting costs. This leads to a simple increasing relation between housing prices,, and aggregate housing consumption, Q c, of the form, with 3. Equilibrium This section develops equilibrium conditions in a two-city system. In our model, there are two identical locations, city and city 2. Workers optimally choose their city, occupation and consumption. The total mass of population is L, and population s skill is distributed with density function k( b ). In this study, we do not focus on the process that the asymmetric equilibrium emerges; instead, we take the asymmetric equilibrium as given, and discuss its evolution, as macro factors change. To build intuition and understand the basic properties of asymmetric equilibrium, we depict utility curve of the traded workers in an arbitrary city, say city, which is represented by the red line in Figure. To simplify our analysis, we assume. Because only the traded sector makes use of workers skill, by comparative advantage, only the most skilled workers specialize in producing the traded goods. We denote by b 2 the skill cutoff, above which the workers produce traded goods. Hence, the traded workers are ranked by their skills, from b 2 to b. Their utility curve is upwards sloping, and workers with higher skill, thus more income, gain higher utility. From equation (), the slope of the curve is. G 8

10 Figure Suppose the service price index in another city, say city 2, is higher than what it is in city. Housing price being held constant, the utility curve rotates clockwise and becomes less steep, represented by the red dot line. Since the new utility curve is below that of city, the traded workers with any level of skill always gain higher utility in city. The intuition is straightforward. The traded workers can earn same wage in both cities, hence, when choosing locations, they only need to compare the prices of housing and service goods in two cities. Living in city means paying lower price for service goods, meanwhile, paying the same price for housing. Thus, any traded worker will always prefer city to city 2. In this case, city 2 will not exist without the economic basis. To compensate the traded workers for the higher service price, city 2 must offer housing goods at lower price. As housing becomes cheaper, the utility curve of city 2 will shift up to the extent that some traded workers will choose to live there. Although the exact positions of two utility curves must be determined in general equilibrium, it is clear that housing price dispersion always exist, as long as the two cities offer nontraded service goods at different prices. We summarize our first finding in proposition I. 9

11 Proposition I (Price dispersion) In asymmetric equilibrium, housing price dispersion always exists; the housing price is higher in the city with lower service price. Without loss of any generality, we maintain our assumption that city is the city with higher housing costs, but lower service price index, i.e., P h, > P h,2 and G < G2. Because nontraded service goods are luxury in nature, the traded workers with high skill, thus high income, appreciate the lower service price index more than the low-income workers. The high-skill workers will sort into the city with higher housing price, but lower service price index. We formalize our finding in Proposition II. Proposition II (Skill sorting of traded workers) In asymmetric equilibrium, the high-skill traded workers sort into the city with high housing cost and low price index; the middle-skill traded workers sort into the city with high price index and low housing cost. We formalize the proof in Appendix. The intuition behind proposition II is straightforward. Location is irrelevant to the income of traded workers. Housing price has the same effect on everyone in the same city, therefore, the high-skill worker necessarily spend greater amount of their income on nontraded service goods. Thus, they benefit more from living in the high-rent city with lower price of service goods. Meanwhile, the high housing price in the large city will push some middle-skill traded workers out of the city. In equilibrium, there exists a cutoff traded worker, who is indifferent between two cities. The more skilled workers choose to live in the superstar city with low service price, while those of middle skill choose the small city. Proposition II claims that the asymmetric equilibrium is characterized by perfect sorting of traded workers. Under the assumption that skill distribution is continuous, there exists a cutoff skill b that separates the traded workers in city and city 2, as shown in Figure. 0

12 We write the conditions for asymmetric equilibrium as equation (5) through (25). We denote by the wage rate in nontraded service sector of city i. Equation (5) defines the cutoff skill b, such that the workers with skill b are indifferent between two cities, b P b P 2 (5) G G G2 G2 Equation (6) defines the cutoff skill b 2, such that the workers with skill b 2 are indifferent between two traded and nontraded service sector, (6) b2 = w2 Equation (36) describes the condition underlying spatial equilibrium. Nontraded service workers must be indifferent between two cities, w P w 2 P 2 (7) G G G2 G2 The total population of nontraded service workers in the whole economy is, and we denote by f the proportion of them that live in city. Hence, the population of nontraded service workers in city is. Equations (8) and (9) define the service price index in each city, (8) (9) Equations (20) and (2) define the zero-profit conditions for nontraded service supply. (20) G b t G P w G P F L dt K( b2 ) w b G t G G w G

13 (2) G 2 b t G2 P 2 w 2 G 2 P 2 F L dt K( b2 ) w b 2 2 G t G2 G2 w2 G2 On the right-hand side is the aggregate demand for individual variety in each city, which must equals to F, to assure that the producers earn zero profit. Equation (22) through (25) define the clearing of housing markets in both cities. b G P G P (22) Qh, L t k() t dt LK( b2 ) w b t G Ph w G Ph,, G P G P Q L t k() t dt LK( b ) w b (23) h,2 b t G2 Ph,2 w2 G2 Ph,2 (24) (25) In asymmetric equilibrium, our model predicts that low-skill workers are overrepresented in large cities, as stated in the following proposition. Proposition III (overrepresentation of low-skill service workers in the larger city) In asymmetric equilibrium, the superstar city employs a larger proportion of low-skill nontraded-service workers. We formalize the proof in Appendix. The intuition is straightforward. In the large city, nontraded service workers earn lower wage than the cutoff traded worker, who is indifferent between two cities. Thus, the low-skill workers do not appreciate the low service price index as much as the traded workers. To compensate the low-skill service workers for the higher housing price, the superstar city must pay higher wage to them. In the end, the population of low-skill workers, as well as the number of service varieties they produce, grows to the extent that the service price index in the superstar city is lower, despite that the price of each single variety is higher. The asymmetric equilibrium of our model can account for not only the persistent housing 2

14 price dispersion between superstar cities and second-tier cities, but the empirical finding that both high-skill and low-skill workers are overrepresented in the large cities. 4. Numerical Comparative Statics In this section, we numerically solve the asymmetric equilibrium of our model, under the assumption that skill is uniformly distributed. Using a particular group of parameters, we present our baseline case in table. It shows that the superstar city, city, consists of 6 percentage of the total population. The traded workers in large city are more skillful than those in small city. In the superstar city, the housing price is also higher. To be compensated for the higher housing price, the nontraded service workers in the superstar city earn higher wage. However, due to the larger size of the service sector, the service price index in the superstar city is lower, as opposed to small city. Table. Two-city Asymmetric Equilibrium Main features City City 2 Population Traded workers skill Population of service workers Wage of service workers Service price index Housing price Notes: To produce the table, we choose parameters as follows, L =,, F = and b ~ U (,0). Our model predicts that the workers in both traded sector and nontraded service sector earn higher wage in the superstar cities. Although the prediction of our model is similar to Gyourko, Mayer and Sinai (203), the economic mechanisms in two papers are quite different. In their model, the superstar city is exclusively occupied by the high-income 3

15 workers. The low-income workers are bid out from superstar cities, because of the inelasticity of housing supply. In our model, the higher wage in traded sector is a result of skill sorting. The wage premium in nontraded service sector serves as a compensation for the higher housing costs in superstar cities. Deriving from our baseline case, we perform two comparative statics experiments. First, we raise the upper support of kb () to make the skill distribution more dispersed. The effects of raising b are twofold. First, as the most skilled traded workers earn higher income, the aggregate demand for nontraded services is higher. Second, raising b leads to a reduction in the density of low-skill workers; thus, the supply of nontraded service workers tends to decrease. As b increases from 0 to 20, the skill cutoff for superstar city increases from 7 to 4.5, as shown in Figure 2. When more high income workers move to the large city, housing price is bid up; therefore, some middle-skill traded workers are pushed out from the superstar cities First Cutoff Skill Upper Support of Skill Distribution Figure 2 Figure 3 shows that the skill cutoff for nontraded service sector also tends to increase. Some of the least skilled traded workers switch to service sector, catering to an increasing demand for service goods, as well as a lack of service workers. 4

16 0 Second Cutoff Skill Upper Support of Skill Distribution Figure City City 2 Housing Price Upper Support of Skill Distribution Figure 4 In addition, as shown in figure 4, greater skill dispersion enhances the divergence of housing price between superstar city and small city. Our prediction is consistent with documented empirical evidence that greater income dispersion is positively associated with widening gap in housing price between large cities and small cities (Gyourko, Mayer & Sinai, 203). Despite of the greater difference in housing price, population gap does not necessarily become wider. In our example, the population gap shrinks a little, as shown in Figure 5. 5

17 City City Population Upper Support of Skill Distribution Figure Produce traded goods in city Produce traded goods in city 2 Produce services.4 Utility of Workers with Skill of Upper Support of Skill Distribution Figure 6 To explore the welfare implications across skill spectrum, we respectively depict the utility paths of the workers with skill of, 6 and 0 in figure 6 to 8. The red lines in the figure are the utility that workers are supposed to gain by producing traded goods in city. The blue line is the utility from producing the traded goods in city 2. The green line represents producing nontraded services in either city. The workers will choose the combination of location and occupation that delivers the highest utility. As shown in figure 6, the workers with skill always choose to produce nontraded 6

18 services, and they benefit from the greater disparity of skill. For the workers with skill of 6, shown in figure 7, they are initially traded producers in the small city. However, as the upper support of skill distribution increases to 2, these workers find it profitable to switch to nontraded service sector. As for the workers with skill 0, presented in figure 8, the situation is more complicated. At the beginning, it is the best decision for them to produce traded goods in city. Nevertheless, as greater amount of high-skill workers emerge and choose to live in city, they are pushed out from the superstar cities. In our example, these workers move from city to city 2, when b reaches 4. In this process, their utility always decreases. From these figures, some general conclusions can be reached. As skill distribution becomes more dispersed, the nontraded service workers are always better off, while the middle-skill traded workers tend to suffer Produce traded goods in city Produce traded goods in city 2 Produce services Utility of Workers with Skill of Upper Support of Skill Distribution Figure 7 7

19 Produce traded goods in city Produce traded goods in city 2 Produce services Utility of Workers with skill of Upper Support of Skill Distribution Figure 8 In our second experiment, we maintain the skill distribution and raise the total population in the whole economy, from to 2.5. Greater population size means higher demand for nontraded service goods, as more high-skill workers are present in economy. On the other hand, the presence of greater amount of low-skill workers also increases the labor supply in the nontraded service sector. Due to the benefits from increasing return, the nontraded service price indices of two cities both decrease (Figure 3). The skill cutoff for superstar cities becomes lower (figure 9) and some middle-skill traded workers are pulled to the superstar cities. It is also due to the increasing return in the service sector that the sector employs lower proportion of total population (figure 4), and the workers employed become less skilled (figure 0). As population size becomes larger, the dispersion of housing price widens (figure ), so does the gap in population (figure 2). To fully understand the welfare implications of population growth, we analyze its utility effects on the workers from different skill groups. Consistent with our first experiment, we also depict utility paths for the workers with skill, 6 and 0. As shown in figure 5 to 7, they all benefit from population growth. 8

20 First Skill Cutoff Population Size Figure Second Skill Cutoff Population Size Figure City City 2.2 City Population Population Size Figure 9

21 2.8 City City 2.6 Housing Price Population Size Figure City City 2 Local Service Price Index Population Size Figure City City Population Ratio of Traded to Service Sector Population Size Figure 4 20

22 .8.6 Produce traded goods in city Produce traded goods in city 2 Produce services Utility of Workers with Skill Population Size Figure Produce traded goods in city Produce traded goods in city 2 Produce services Utility of Workers with Skill Population Size Figure Produce traded goods in city Produce traded goods in city 2 Produce services Utility of Workers with Skill Population Size Figure 7 2

23 5. Conclusion We have presented a theory of emergent superstar cities, which accounts for increasing geographic dispersion in housing prices and income as an endogenous outcome of consumer sorting across cities to take advantage of increasing returns in the supply of differentiated nontraded services. The model also accounts for the skill dispersion in large, superstar, cities, distinguished with greater variety of nontraded service. With rising income inequality in US, many cities seek to tackle local income equality. Our model shows that such local efforts may not be effective. In fact, the presence of high income households in a city can benefit the low-skill workers by creating greater demand for nontraded services that employ low skill workers. 22

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27 Appendix Proofs of Propositions Proposition I (Skill sorting of traded workers) In asymmetric equilibrium, the high-skill traded workers sort into the city with high housing price and low service price index; the middle-skill traded workers sort into the city with high service price index and low housing price. Proof: From the indirect utility function (), we have, (A) 2 V I I G G 0 High income and low service price index are complementary. If there exists a traded worker with income * b, who is indifferent between two cities, * * P b P2 b. G G G G 2 2 The single crossing condition (A) ensures that the traded workers with income b * b prefer the city with lower service price index and higher housing price. Q.E.D Proposition II (overrepresentation of the low-kill in large city) In asymmetric equilibrium, the large city holds greater amount of low-skill workers. Proof: We prove this proposition in two steps: Step. City pays higher wage to the workers in nontraded service sector, i.e., 26

28 w > w. 2 Suppose that. Because w2 = b2 < b, proposition II says that nontraded service workers will strictly prefer city 2, and this conflicts with the condition that nontraded service workers are indifferent between two cities. Therefore, city must pay higher wage to the nontraded service workers to make the nontraded service workers indifferent between two cities. Step 2. City must hold larger number of low-skill workers. Because city pays higher wage to the workers in nontraded service sector, from (8), the price of a single service variety is higher. To maintain a lower price index, city must produce greater amount of varieties. Therefore, city must hold larger number of low-skill workers. Q.E.D 27