Volume 29, Issue Wage Subsdy and Sector-Specfc Unemployment: A New Economc Geography Approach Yenhuang Chen Chnese Culture Unversty Lhong Zhao Chna HuanQu Contractng & Engneerng Corporaton Abstract Ths paper uses a new economc geography approach to examne the effects of wage subsdy, whch s undertake to bolster up the ndustral development. Ths paper also hghlghts the effects of trade lberalzaton and nternatonal captal moblty. In partcular, sector-specfc unemployment s ntroduced n the monopolstcally compettve sector of the home country. Ctaton: Yenhuang Chen and Lhong Zhao, (2009) ''Wage Subsdy and Sector-Specfc Unemployment: A New Economc Geography Approach'', Economcs Bulletn, Vol. 29 no. pp. 426-436. Submtted: Jun 2008. Publshed: March 25, 2009.
. Introducton Many emprcal surveys reveal that a large share of nternatonal trade has taken place between smlar countres. Actually, there s evdence that ntra-ndustry trade occurs not only n ndustral countres but also n developng countres. 2 There has been a prolferaton of studes n the feld of nternatonal trade under the context of nter-ndustry trade, but ntra-ndustry trade has receved less attenton untl recent decades. Comparatve advantage, based on whch the nter-ndustry trade emerges, s not powerful enough to explan the trade between smlar countres. It s the concept of economes of scale that s used to explan ths sort of trade. Monopolstc competton à la Dxt and Stgltz (977) ncorporates mportant features, such as product varety, consumer preference and market entry. Economsts extensvely employ the monopolstcally compettve approach to establsh an ntra-ndustry trade model. Krugman s (980) model of ntra-ndustry trade ntegrates producton dfferentaton, economes of scale and mperfect competton. Now, ths model has developed nto the theory of New Economc Geography (hereafter NEG) to analyze ndustral locaton. NEG manly nvestgates the endogenous emergence of ndustral agglomeraton by ncorporatng monopolstc competton, economes of scale and ceberg transport costs. Krugman (99) proves that frms and workers tend to agglomerate together, prmarly because of the mpact of ncreasng returns and transport costs upon labor mgraton. Involvng two vertcally lnked ndustres, both of whch are mperfectly compettve, Venables (996) shows that lnkages between upstream and downstream can be equally effectve wth labor mgraton n endogenously determnng equlbrum locatons. On the bass of a smlar method, Krugman and Venables (995) address the relatonshp among globalzaton, agglomeraton and nternatonal nequaltes, whle Forsld and Mdelfart (2005) explore ndustral polcy mplcatons. These papers rely on the sharp assumpton that labor s the sngle prmary factor for producton. Amng to explore the crucal role of captal on trade lberalzaton, ths paper develops a more general framework, where both captal and labor serve as prmary factors for producton. 3 Ever snce the nfluental papers by Krugman (980 and 99), NEG has attracted a great deal of attenton n the lterature, whch s evdenced by the launch of the Journal of Economc Geography n 200. Currently, applcatons of the theory of NEG have been popularzed to the felds of nternatonal trade, regonal economcs, economc growth, and/or economc ntegraton. In the real world, because of the uneven development between the urban and the rural, the phenomenon of unemployment s nevtable. On the other hand, due to some poltcally related reasons or the barganng power of unons, the mnmum wage s wdely wtnessed n the urban areas of many countres. Harrs and Todaro (970) analyze the formaton of urban unemployment whch s caused by nsttutonally fxed See, for example, Greenaway and Mlner (986), Helpman (987) and Krugman and Obstfeld (2003). 2 See, for example, Tharakan (984). 3 The large bulk of one-country general-equlbrum models utlze both captal and labor as prmary factors for producton. However, the ntroducton of captal nto NEG model s stll relatvely scarce.
urban mnmum wage, pavng the way for a seres of subsequent dscusson. To our lmted knowledge, there have been no attempts to analyze the unemployment ssue n the NEG framework, whch motvates us to fll ths gap. Besdes ths novel contrbuton, the present paper also ntroduces wage subsdy nto the economy and nvestgates ts effects. Wage subsdy s usually descrbed as a prescrbng polcy suffcng to mtgate the negatve effects of labor market dstorton. As noted n Husby (993), an alternatve polcy that combnes a mnmum wage and a wage subsdy s superor to ether by tself. Such a combnaton can assst the low wage worker, avod dsemployment effects, and maxmze market effcency (p. 30). Accordng to the concluson by Husby (993), ths paper mplements wage subsdy n the urban area rather than rural area, snce the mnmum wage only prevals n the urban area. The remander of ths paper s organzed as follows. Secton 2 formulates a NEG model. In partcular, sector-specfc unemployment and wage subsdy are smultaneously ntroduced n the monopolstcally compettve sector of the home country. Secton 3 conducts numercal smulaton for analyss. Conclusons are drawn n Secton 4. 2. The Model Suppose that the world s composed of two countres: the home (ndexed by ) and the foregn (ndexed by 2). The consumers n each country consume a group of dfferentated manufactured goods and a homogeneous agrcultural good. The manufactured goods are produced by a monopolstcally compettve sector (ndexed by X) wth ncreasng-returns-to-scale technology, and the agrcultural good s produced by a perfectly compettve sector (ndexed by Y) wth constant-returns-to-scale technology. Sectors X and Y are assumed to be urban manufacturng and rural agrculture, respectvely. Followng Krugman (980 and 99), the agrcultural good can be traded costlessly between countres n order to smplfy the model. However, the trade of manufactured goods s subject to transport costs, whch take the ceberg form. More precsely, f one unt of manufactured goods s traded from one country to another, only / t ( t > ) unt wll arrve. The utlty functons of all consumers are assumed to be dentcal. We adopt smple Cobb-Douglas preferences: U = D δ Y δ, () where D and Y are the consumpton of the composte manufactured good and of the agrcultural good, and δ [0,] s the ncome share on the composte manufactured good. As n Dxt and Stgltz (977), the consumpton of the composte manufactured good s defned as: σ /( σ ) ( σ )/ σ x h h, (2) D= where x h s the consumpton of varety h and σ > s the elastcty of substtuton between each par of dfferentated manufactured goods. The prce ndex of the composte manufactured good n country s denoted by q : 2
/( σ ) σ σ q = np + nj( tpj),, j =,2, j, (3) where p s the prce of manufactured goods produced n country, 4 and n s the number of varetes of n country. It s noteworthy that, n equlbrum, each monopolstcally compettve frm n the urban area produces a sngle varety of n dfferentated manufactured goods Let w X, w Y and r be the urban wage, the rural wage and the captal rental n country, respectvely. In the home country, sector-specfc unemployment s ntroduced nto the manufacturng sector by assumng that the urban wage s rgdly set above the market-clearng level. Therefore, labor wll mgrate from the rural area nto the urban area untl the rural wage rate equals the expected urban wage rate: where ew = w, (4) X Y e = LX /( LX + U ) (5) s the urban employment rate, and U and L X are the unemployed and employed labor n the urban area, respectvely. The rural wage rate s flexble, so no unemployment occurs n the agrcultural sector. In the foregn country, we assume that both urban and rural wage rates are flexble, rulng out the possblty of unemployment and leadng to the same level of urban and rural wage rates,.e., w X2 = w Y2 w 2. In the producton sde, the producton of both sectors utlzes labor and captal. Perfect competton and costless trade are assumed n the agrcultural sector, so that n both countres margnal cost functons equal the world prce of the agrculture good: g ( wy, r ) =, 2 g ( w2, r 2) =, (6) where the agrcultural good s chosen as the numérare and g s the margnal cost functon of the agrcultural sector n country. The domestc government undertakes a specfc wage subsdy n the manufacturng sector, and thus the domestc manufacturng frm wll act as f the labor cost s w X ( s), where s s the subsdy rate, nstead of w X. Then we can defne the margnal cost of each manufacturng frm n the home country as m (w X ( s), r ). Wrte t as m (w X, r,s) n order to smplfy the exposton. No subsdy s offered n the foregn country, therefore the margnal cost of each manufacturng frm n the foregn country appears as m 2 (w 2, r 2 ). Each manufacturng frm seeks proft maxmzaton by choosng ts prce. We focus on symmetrc equlbra,.e., each frm adopts the same technology to produce. The cost functon for a representatve frm can be expressed as (F+ x )m, where Fm s the fxed cost. Consderng the preference à la Dxt and Stgltz (977), the representatve frm seeks proft maxmzaton accordng to the equalty between margnal revenue and margnal cost: 4 Under symmetrc assumpton, all manufacturng frms (n the same country) wll charge the same prce n equlbrum. 3
p = ( / σ ) m, (7) where σ s the elastcty of demand. Ths equaton mples that n equlbrum, the prce of manufactured goods s a mark-up over the margnal cost. Under monopolstc competton, free entry elmnates the proft of each frm: p ) x = ( F + x m, (8) where x s the output level of each manufacturng frm n country. 5 Vewng equatons (7) and (8) and choosng F=/( σ ), these gve that x =. Due to zero-proft condton, the equlbrum output level of each manufacturng frm must satsfy: x = = p q δ I + p t q δ I, (9) σ σ σ σ σ j j where I s the natonal ncome n country. Note that the frst term on the rght sde s country s demand for a varety of manufactured good produced n country, whle the second term s country j s demand for the varety of manufactured good produced n country. 6 The natonal ncome n country s defned as: 7 I = wxlx + wyly + rk = wyl + rk, (0) where L and K are the labor and captal endowments n country, respectvely. Factor markets clearng requres that, n equlbrum, the supply of both factors s equal to the demand. Usng Shephard s Lemma, we can obtan the followng factor market equlbrum condtons: Yg + n( x + F) m + U = L, () w w Yg + n( x + F) m = K, (2) r r where the subscrpts of margnal cost functons denote partal dervatve. In sum, the general equlbrum s specfed by equatons (3), (4), (5), (6), (7), (9), (0), () and (2), whch can be solved for Y, I, n, w Y, w 2, r, e, U, p and q. The parameters of the model are L, K, w X, σ and δ, whch are exogenously gven. 3. Numercal Smulaton Snce ths model s too complcated to solve analytcally, we n ths secton assgn key values to parameters and specfy specfc technologes to conduct numercal smulaton as usual n such models. 8 Suppose that the margnal cost functons of the agrcultural sector and of the manufacturng sector n both countres are: 5 Under symmetrc assumpton, all manufacturng frms (n the same country) wll have the same output level n equlbrum. 6 Detaled dervatons of the demand functons see Fujta et al. (999). 7 In the home country, L= L + L + U. Takng nto account the defnton of e yelds I = w L + rk. X Y 8 See, for example, Krugman and Venables (995) and Fujta et al. (999). Y 4
g ( w, r) = w r, α α Y Y g ( w, r ) = w r ; 2 α α 2 2 2 2 m ( w r β β X, r, s) = [ wx ( s)], m ( w, r ) = w r. 2 β β 2 2 2 2 Meanwhle, we assgn these values to the exogenous parameters: 9 δ = 0.5, w =.5, σ = 5, α = 2/ 3, β = / 3, L = L2 = K = K2 = 00. X The objectve of ths secton s not to calculate the estmate of the effects of wage subsdy, snce t goes beyond the scope of ths paper. Rather, the objectve s to explore the drecton of the change n each varable and to see the lkely sze of these effects. In what follows, we assume that labor s always specfc to each country but moble between sectors wthn each country. Our analyss begns wth the scenaro n whch captal s also specfc to each country, but t s moble between sectors wthn each country. Later, we wll relax the constrant on nternatonal captal moblty. Suppose that the domestc wage subsdy s set at s=0.2. Table summarzes the smulaton result of the effects of trade lberalzaton. 0 Table. Effects of trade lberalzaton when captal s specfc to each country and s=0.2 t=2.5 t=2.0 t=.5 e 0.680 0.682 0.686 U 2.809 2.567.994 n 76.203 75.235 73.56 n 2 80.34 8.389 83.29 p.294.289.280 p 2.25.255.263 Y 9.297 92.83 95.45 Y 2 99.608 98.260 95.956 w Y.020.023.028 w 2 0.998 0.996 0.990 We can see from each column n Table that the prce of manufactured goods n the home country s hgher than that n the foregn country (p > p 2 ). The reason s that the mnmum wage n the urban area of home country makes the producton cost of manufactured goods n the home country hgher. Table also shows that the varetes of manufactured goods n the home country are less than those n the foregn country (n < n 2 ), as a result, ntra-ndustry occurs and the home (foregn) country s a net mporter (exporter). Moreover, the foregn labor receves a lower wage than the domestc labor (w 2 < w Y < w X ), and the foregn country tends to produce more agrcultural good (Y 2 > Y ). As long as the mnmum urban wage s hgher than the domestc rural wage, urban unemployment prevals n the home country. The trend of trade lberalzaton has totally dfferent results across countres. Intally (the case of t = 2. 5 ), the foregn country produces more varetes of 9 The condton thatα > β mples that manufactured goods are relatvely captal ntensve. 0 Throughout ths paper, we use the term trade lberalzaton sorely n the sense of a decrease n transport costs. 5
manufactured goods than does the home country (n < n 2 ). Ownng to ncreasng-returns-to-scale technology adopted n the producton of manufactured goods, trade lberalzaton attracts the domestc manufacturng to the foregn country and wdens the dfference n the varety. Ths phenomenon s so-called dendustralzaton. Let the dfference between n and n 2 represent the volume of ntra-ndustry trade. The smulaton result shows that the volume of ntra-ndustry trade ncreases wth the trend of trade lberalzaton. For the foregn country, the varety expanson consttutes an element of gans from ntra-ndustry trade. On the other hand, trade lberalzaton wll generate resource re-allocaton. In ths model, the demand for captal n the manufacturng sector decreases (ncreases) n the home (foregn) country, leadng to an expanson (a constrcton) n the supply of captal n the agrcultural sector n the home (foregn) country snce captal s mmoble between countres. These results ncrease the domestc rural wage, whch wll attract some of the unemployed labor to the rural area, and thus the level of employed labor and employment rate change n the same drecton as the domestc rural wage. In the meanwhle, these results decrease the foregn wage, and thus ncrease (decrease) the output level of agrcultural good n the home (foregn) country. In sum, we can obtan the followng lemma. Lemma. When captal s specfc to each country, the trend of trade lberalzaton has totally dfferent results across countres. It leads to a decrease (an ncrease) n the prce of manufactured goods n the home (foregn) country, a decrease (an ncrease) n the varetes of manufactured goods produced n the home (foregn) country, and an ncrease (a decrease) n the output level of agrcultural good n the home (foregn) country. These results postvely mpact upon the rural wage, the level of employed labor and employment rate n the home country but negatvely mpact upon the wage n the foregn country. Another ssue we concern about s the effects of wage subsdy. Suppose that the transport costs are fxed at t=.5. Table 2 summarzes the smulaton result. Table 2. Effects of wage subsdy when captal s specfc to each country and t=.5 s=0.2 s=0.4 s=0.5 e 0.686 0.685 0.690 U.994 9.040 24.974 n 73.56 95.892 5.69 n 2 83.29 70.60 60.248 p.280.65.085 p 2.263.24.76 Y 95.45 6.050 30.239 Y 2 95.956.568 23.95 w Y.028.027.035 w 2 0.990.030.063 Intally (the case of s=0.2), the foregn country produces more varetes of manufactured goods than does the home country (n < n 2 ), and the home (foregn) country s a net mporter (exporter). However n the cases of s=0.4 and s=0.5, that 6
wll be reversed (n > n 2 ) and the home (foregn) country becomes the net exporter (mporter). The volume of ntra-ndustry trade s always ncreasng. Wage subsdy exerts a cost-reducng effect from the pont vew of manufacturng frms, therefore the prce of manufactured goods n the home country decreases wth the ncrease n wage subsdy and thus the producton of domestc manufacturng s promoted at the expense of foregn manufacturng. The home country demands more manufactured goods but less agrcultural good, so the producton of foregn agrculture s promoted at the expense of domestc agrculture. Therefore, balance of trade can be mantaned. These results ncrease the foregn wage. In the home country, theses results make the urban area more attractve and nduce some of the agrcultural labor to mgrate to the urban area where they may be employed. It wll negatvely mpact upon the level of employed labor n the home country. The change n domestc rural wage depends on the degree of wage subsdy, so does the urban employment rate. In sum, we can obtan the followng lemma. Lemma 2. When captal s specfc to each country, an ncrease n the wage subsdy leads to a decrease n the prce of manufactured goods n both countres, an ncrease (a decrease) n the varetes of manufactured goods n the home (foregn) country, and a decrease (an ncrease) n the output level of agrcultural good n the home (foregn) country. These results negatvely mpact upon the level of employed labor n the urban area n the home country but postvely mpact upon the wage n the foregn country. In order to dentfy the features of nternatonal captal moblty, we next analyze the other scenaro, n whch no constrant on captal moblty s placed,.e., captal s moble both between sectors and countres. In equlbrum, both countres have the same captal rental. Tables 3 and 4 summarze the smulaton results of the effects of trade lberalzaton when the wage subsdy s set at s=0.2, and the effects of wage subsdy when transport costs are set at t=.5, respectvely. Table 3. Effects of trade lberalzaton when captal s moble nternatonally and s=0.2 t=2.5 t=2.0 t=.5 e 0.673 0.672 0.67 U 2.976 2.447 9.25 n 73.29 70.206 5.333 n 2 83.250 86.308 06.075 p.33.33.37 p 2.239.239.242 Y 9.352 93.668 08.684 Y 2 99.776 97.809 85.063 w Y.009.009.006 w 2 0.673 0.672 0.67 Compared wth Table, we fnd that smlar effects exst between wth and wthout nternatonal captal moblty n the employed level of the home country, the varetes of manufactured goods n both countres and the output levels of agrcultural good n both countres. In addton, we can demonstrate that nternatonal captal moblty enhances the effects of trade lberalzaton upon these varables. However, when 7
transport costs are not that hgh, dfferent effects exst n the urban employment rate, the prce of manufactured goods and the rural wage n the home country. When captal s allowed to be moble nternatonally, the scale of domestc (foregn) manufacturng s less (larger) than that wthout nternatonal captal moblty. It ndcates that the captal removes from the home country to the foregn country, whch n turn makes the scale of domestc (foregn) manufacturng shrnk (expand). When transport costs are not that hgh, the scale of domestc (foregn) manufacturng shrnks (expands) quckly wth the trend of trade lberalzaton. Therefore, we can argue that nternatonal captal moblty accelerates the dendustralzaton of the home country. Moreover, n vew of the ncreasng-returns-to-scale technology n the producton of manufactured goods of both countres, the prce of manufactured goods n the home (foregn) country s hgher (lower) than that wthout nternatonal captal moblty. Table 4. Effects of wage subsdy when captal s moble nternatonally and t=.5 s=0.2 s=0.4 s=0.5 e 0.67 0.686 0.706 U 9.25 9.23 27.662 n 5.333 97.452 4.685 n 2 06.075 69.227 38.889 p.37.62.053 p 2.242.25.8 Y 08.684 59.940 9.582 Y 2 85.063 2.256 35.789 w Y.006.029.058 w 2 0.67 0.686 0.706 In contrast wth Table 2, an ncrease n wage subsdy unambguously ncreases the rural wage and urban employment rate n the home country. Nonetheless, smlar effects exst between wth and wthout nternatonal captal moblty upon other varables. Compared wth Table 2, nternatonal captal moblty enhances the effects of wage subsdy. When captal s allowed to be moble nternatonally, the scale of domestc (foregn) manufacturng expands (shrnks) much more quckly than that wthout nternatonal captal moblty, suggestng that the captal removes from the foregn country to the home country. Smlarly, the scale of domestc (foregn) agrculture shrnks (expands) much more quckly than that wthout nternatonal captal moblty. Therefore, f the rate of wage subsdy contnues to ncrease, the home country wll become a manufacturng core but an agrcultural perphery, whle the foregn country wll become an agrcultural core but a manufacturng perphery. The smulaton result shows that such a rate of wage subsdy that ndustral agglomeraton occurs les between 0.5 and 0.52. Therefore, we can obtan the followng proposton. Proposton. No matter whether the wage subsdy or the trend of trade lberalzaton works, nternatonal captal moblty accelerates the dendustralzaton of the home country. 8
4. Conclusons Ths paper sets up a NEG model wth sector-specfc unemployment to examne the effects of wage subsdy and trade lberalzaton. There are two alternatve scenaros: frst, captal s specfc to each country and second, captal s moble nternatonally. When captal s specfc to each country, t s shown that trade lberalzaton attracts the domestc manufacturng to the foregn country, resultng n postve effect upon employment but dendustralzaton. Furthermore, wage subsdy promotes the producton of domestc manufacturng at the expense of foregn manufacturng. When captal s moble nternatonally, the drecton of captal moblty s completely dfferent wth respect to whch element works. However, no matter whether the wage subsdy or the trend of trade lberalzaton works, nternatonal captal moblty accelerates the dendustralzaton of the home country. These conclusons are of partcular nterest to the polcy makers n developng countres. 9
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