The Northern Immigration Policy in a North-South Economy Model

Transcription

1 The Pakitan Development Review 44 : (Summer 005) pp The orthern Immigration Policy in a orth-south Economy Model TARO ABE Wooton (1985) conidered the immigration into Findlay (1980) orth-south model and examined how the north relaxation of immigration policy influence income in both region. Baed on Wooton (1985), thi paper ha performed the ame analyi auming there to be a complete capital mobility between the north and the outh. The major finding are a follow: In the long-run, the relaxation of the north immigration policy doe not affect the per capita income of both the northern labour and immigrant worker. When the north practie a dicriminative reditribution policy againt the immigrant worker, the per capita income in the north will increae becaue reditribution of income from the immigrant worker to the northern labour a a reult of the policy relaxation i taking place. 1. ITRODUCTIO The iue of how the influx of immigrant from the outhern economie to the north ha affected the economy in a north-outh model ha alway been dicued. A the globaliation of the world economy accelerate, thi iue i back in the potlight. In a Heckher-Ohlin model, which i commonly ued when international trade i coming into play, free trade i aid to equalie factor price and hence there i no incentive for factor to move from one country to another. In uch a model, it i aumed that all countrie are identical except in their two factor endowment capital and labour. Contrary to uch uppoition, Findlay (1980) feature a model that include the aymmetry between the north and the outh. There are two aumption that illutrate thi aymmetrical relationhip between the two region. For one, it i aumed that complete pecialiation hold uch that the north produce an indutrial Taro Abe i baed at the Faculty of Economic, agoya akuin Univerity, Kamihinano, Seto, Aichi, Japan. Author ote: Thi paper i part of the project (o. 581) ponored by the Heiei 15 Science Reearch Subidy granted by Japan Society for the Promotion of Science and i financially upported by the Faculty of Economic of agoya akuin Univerity. I wih to thank Takehi akatani, Tamotu akamura, oritugu akanihi, Hideyuki Adachi, Kazuo Mino, and an anonymou referee of thi journal for their comment. In addition, I would like to thank Khoo ChunKeat, Shin Imoto, Hu Yunfang and the Co-editor of thi journal, Faiz Bilquee, for their help. onethele, the author i reponible for every poible mitake in thi paper.

2 198 Taro Abe good that feature both a conumption and capital input while the outh import capital good from the north and produce a primary good, which alo i a conumption good, uing the imported capital good. The econd aumption ha got omething to do with the elaticity of the labour upply. The northern economy i aumed to be a fully employed economy in which the labour upply i inelatic and all labour i ued in the production proce. Therefore, in the long-run the growth rate i determined by the growth of labour upply, which grow at a contant rate. On the other hand, the outh i a labour urplu economy. The modern ector of the economy that produce primary good can obtain unlimited upply of labour from the traditional ector that produce non-tradable good at a fixed amount of ubitence wage rate. Wooton (1985) ue thi Findlay (1980) model and examine how the relaxation of immigration policy influence the north-outh economy. In Wooton (1985), it i aumed that the northern labour upply conit of immigrant worker at a certain ratio and thi ratio i treated a the policy parameter. An aumption like thi i appropriate for the northern government management of immigrant, uch a that adopted by the Wet ermany or Switzerland after the World War II. Immigrant reide for a period of time in the north, receive income and remit that income to the outh. The northern labour receive both wage and profit income. Wooton (1985) review how the north relaxation of immigration policy influence the per capita income of both the northern and the outhern labour and the potential profit of the policy. The major finding of Wooton (1985) are a follow. In the hort-run when the capital tock i fixed, relaxation of immigration policy will eae the preure on the north labour upply contraint and increae the northern labour per capita income. Although the wage rate fall the rie of profit rate urpae the fall thereon. Since the north per capita income increae, the outh term of trade will alo improve provided that the total income of the immigrant doe not decreae ignificantly. In the long-run, the north immigration policy will not affect the term of trade becaue the term of trade will be adjuted to equalie the growth rate in the two region. The increae of profit rate in the north will raie it capital-labour ratio in the teady tate, hence the north wage rate partially recover from it temporary fall. The outh employment will increae in thi cae provided the total income of the immigrant doe not decreae ignificantly. 1 From what we have een above, we can conclude that the north enjoy the benefit of labour mobility between the two region. The outh, even when the immigrant labourer reduce the remittance of income, will enjoy benefit gained from a contrained labour mobility regardle of the increae in profit reaped from the rie of import demand from the north. 1 For a more detailed dicuion on foreign trade and invetment iue, ee Khan (1984).

3 orthern Immigration Policy in a orth-south Economy 199 On top of that, the tax policy of both the north and the outh i alo dicued. Taking it into conideration, the optimum policy for the north would be to completely free the labour mobility and adminiter a non-dicriminative reditribution policy. A tax levied on the emigrating worker by the outh government will in turn reduce the income of the north and alo it import demand. A a reult, the outh employment could potentially be hurt. Above i the main argument of Wooton (1985). Freedom in capital mobility ha become an iue to be reckoned with in today globaliation of economy. Burgtaller and Saavedra-Rivano (1984) dicu the capital mobility which include the tructural difference between the north and the outh. With an aumption that the good have high malleability, the aid paper introduce capital mobility between the two region into Findlay (1980) model. Thi paper examine how the capital mobility between the two region influence the per capita income thereon but doe not dicu the immigration policy. Baed on Wooton (1985) and Burgtaller and Saavedra-Rivano (1984) thi paper attempt a parallel examination of how the relaxation of immigration policy in the north and the tax policy of both government affect the per capita income in both the region, given there i a complete capital mobility between the north and the outh. The paper i organied into three ection. Section explain the Wooton (1985) model. In Section 3 the analyi i performed adopting the capital mobility into the model and Section 4 conclude the analyi.. THE WOOTO MODEL Thi ection explain the Wooton (1985) model. Subection.1 tate the baic tructure of the model. Section. elaborate the relaxation of immigration policy, and Section.3 the tax policy..1. Baic Structure of the Model The northern economy. The north ue capital and labour, K and L repectively, to produce indutrial good. L conit of the northern labourer a well a the immigrant worker. Therefore, the production function of the north i given by YF(K, L) (1) Suppoe the northern production function i a contant-return to cale production function, furthermore let f denote the per capita production of the north and k denote the capital-labour ratio, we can derive from (1) ff(k) () It i aumed that the production function atifie the Inada condition.

4 00 Taro Abe Since the real wage rate, w, of the north equal it marginal productivity of labour, wf(k) f (k)k (3) And ince the interet rate, r, equal the marginal productivity of capital, rf (k) (4) Suppoe that the labour force of the north, L, grow at n, an exogenouly determined growth rate. Hence, uppoe the initial value of the north labour force i L ~, ~ L L exp( nt) (5) The north temporarily aborb L of immigrant worker from the outh and all of it i employed in the north production ector. Suppoe the north only aborb the immigrant worker up to a certain fraction to the local labour upply, τ, L τl, τ > 0 (6) Both L and L grow at the ame rate. Denote k a the capital per northern labour, the per capita income of the north, y, i given by y w + rk (7) The northern labour enjoy both wage and profit income. Since related to k in uch a way that y L L + L, k i K K k k (8) L + L (1 + τ) L 1+ τ Becaue the immigrant worker do not own capital, their per capita income,, i given by y w (9) The immigrant worker end a fraction of their income, q, back to their home country. Denote Q a the total remittance of money by immigrant worker to the outh, Q qy L (10)

5 orthern Immigration Policy in a orth-south Economy 01 The outhern economy. The modern ector in the outh ue capital and labour, K and L to produce a primary good. Hence the production function i given a Y F ( K, L ) (11) Suppoe thi i a contant-return-to-cale production function, denote f a per capita production and k a capital-labour ratio, it can be rewritten a k f f ( ) (1) The outh production i conumed dometically and exchanged for the north conumption and capital good. There i a traditional ector in the outh called the hinterland that produce only non-tradable good. The hinterland aborb all labour except thoe who work in the production of traded good. Therefore, the modern ector could pull a much labour upply at a fixed wage rate from uch hinterland. Since the real wage rate w in the outh equal it marginal productivity of labour, w f ( k ) f ( k ) k (13) The outh profit rate, r, equal it marginal productivity of capital. Denote p a it term of trade, k r pf ( ) (14) The per capita income, y, of the outh modern ector conit of the per capita factor income f(k) and the remittance from the emigrant to the north. Hence, denote λ a the employment ratio between the two region, we get y f qyτ ( k ) + (15) λp Suppoe a fraction of profit income,, i pent on the invetment good demand, the outh per capita expene on conumption good, e, i given by e f ( k ) f ( k ) k (16) Balance of payment equilibrium. Denote m a the demand function of conumption import per northern labourer. Suppoe a certain fraction of of the north income i aved, the per capita conumption expene in the north i then (1 )y. m i a decreaing function of the outh term of trade, p, and an increaing function of (1 )y. Here we aume the elaticity of conumption expene take a

6 0 Taro Abe value of one. ext, denote m ~ a the demand function of conumption import per immigrant worker from the outh. m ~ i a decreaing function of p and an increaing function of the dipoable income per immigrant worker, ( 1 q ) y. Denote µ a the import demand for conumption per outhern labourer, and aume that µ i a 1 decreaing function of and an increaing function of e. Taking the remittance p from the immigrant worker back to the outh, the balance of payment equilibrium i given by 1 p { m[ p, (1 ) y] + m ~ [ p,(1 q) y ] τ} r k + µ [, e ] λ qyτ (17) p Capital accumulation. ext we will look at the capital accumulation. In the north, a certain fraction of the income i aved and inveted thereon. Since the northern labour growth rate i n, we can expre the dynamic equation of k a k & y (18) nk In the outh, although a certain fraction out of the profit i diverted to capital accumulation, the outh employment growth rate equal it capital accumulation rate becaue from (13) we know that k i a fixed value. Thu the dynamic equation pertaining to the north-outh employment ratio, λ, i given by λ & ( r n) λ (19) Determinant relation of the model. With a total of 17 equation namely ()~(10) and (1)~(19) together with a total of 17 endogenou variable, f(k), k, w, r, L, L, y, k, y, Q, f ( k ), k, r, p, λ, y and e, thi model i cloed. The major determinant relation are a follow. From Equation (5), (18) and (19), uppoe that L, k and λ each take a certain value. L will then be determined in (6) and k in (8). Hence, from Equation (), (3), (4), (7) and (9) f(k), w, r, y and y are determined, repectively. Having the above-mentioned reult, Q i determined in Equation (10). k i then determined in Equation (13), and Equation (1) olved f ( k ). Latly, p i determined in Equation (17) becaue e i a function of p a we know from Equation (15) and (16). Pleae refer to Appendix 1 for tability condition.

7 orthern Immigration Policy in a orth-south Economy 03.. The orth Relaxation of Immigration Policy In thi ection, we will ee how the relaxation of the north immigration policy influence the per capita income in both region in two cenario in the hort-run where both k and λ are fixed and in the long run where both change. 3 Short-run equilibrium analyi. Firt of all, we will ee how the per capita income, y of the immigrant i affected. From Equation (3), (8) and (9) we can derive dy k f ( k) < 0 (0) 1+ τ Thi how that the increae of immigrant will reduce the north real wage rate. ext, we will ee how the income per northern labourer, y, i affected. From Equation (3), (4) and (8) we know that dy τk f ( k) > 0 (1) 1+ τ Thi tell u that the decreae in wage income i offet by the increae in profit income. Denote η a the price elaticity of the import demand of the northern labour, η ~ a the price elaticity of the import demand of the immigrant, by virtue of Equation (17) we can derive the following. dp d τ dy (1 ) (1 ) (1 µ dy pm + pm q + q ) ( τ + y p d{ r k + λµ } dp { m[ p,(1 ) y](1 η) + τm[ p,(1 q) y ](1 η ~ )} ) () By virtue of the tability condition of the balance of payment equilibrium the denumerator of Equation () take a poitive value. Although the firt term of the numerator take a poitive ign, both the ign of the econd term of the numerator dp and cannot be determined becaue there i no way to tell if the total income of the immigrant ha increaed or otherwie. 4 Hence, from Equation (15) it i not poible to tell how the per capita income in the outh, y, i affected. 3 Throughout thi paper it i aumed that good have high malleability that it i poible for capital to move pontaneouly. Thi ort of aumption poe a problem in a hort-run analyi. However, ince the purpoe of thi ection i to compare the Wooton (1985) reult, we will come back to thi problem in future tudie. 4 µ Furthermore, 1 > 0. Pleae refer Appendix. p

8 04 Taro Abe Table 1 um up the hort-run reult of Wooton (1985). 5 Table 1 Wooton(1985) (Short-run) y y py p τ Long-run equilibrium analyi. Long-run equilibrium i defined a a tate in which the capital accumulation rate in the north equal that in the outh. From Equation (3), (4), (7), (8) and (18) we can derive the following. τk f ( k) dk 1+ τ > 0 (3) τ n f ( k) + kf ( k) 1+ τ dy n dk (4) { f ( k) n} k dk 1+ τ > 0 (5) τ n f ( k) + kf ( k) 1+ τ dw dk kf ( k) < 0 (6) Equation (3) and (4) illutrate that the increae of immigrant will puh the north capital accumulation and thu increae it per capita income. On the other hand Equation (5) and (6) how that the increae of immigrant reduce the real wage rate. From Equation (17) we can derive the north-outh employment ratio a dλ dy pm pm q q µ (1 ) + (1 ) + (1 ) y p 1 µ rτy µ [, e ] 1 + nk p µ pλ dy + τ (7) 5 Wooton (1985) ue λy, the outhern income per northern labour to expre the outhern welfare. However, λ α y β i more commonly ued and it i thought that the outhern welfare depend on the ize of α and β. Therefore thi paper doe not ue λy to repreent the outhern welfare.

9 orthern Immigration Policy in a orth-south Economy 05 By virtue of tability condition the denumerator take a poitive value. Although the firt term of the numerator to the right take a poitive ign, it i not poible to determine the ign of the econd term becaue it i not poible to determine whether the income of the immigrant, τ y, will increae or otherwie. Hence, from (15) the effect of y i alo undetermined. The term of trade of the outh do not change becaue they are determined by Equation (13) and (19). From the above reult, we can conclude that although the north favour a free labour mobility, the outh might favour a contrained labour mobility becaue of the uppreing effect of the remittance by the immigrant worker. Table um up the long-run reult of Wooton (1985). Table Wooton(1985) (Long-run) y y py p λ τ Tax Policy Thi ection examine about the tax policy of both government. The northern tax policy. Suppoe that the northern government levie a proportional tax on labour income and reditribute it among the northern worker. Thi baically ay that the immigrant worker are dicriminated in term of wage. Auming a t percent of the wage income i taxed, the per capita income of the immigrant worker will then be ˆ y (1 t) w (8) The per capita income of the northern worker i given by the following becaue the tax i reditributed among the northern worker. wl + twl + rk y ˆ (1 + tτ) w + rk L (9) We will dicu the long term effect of the north relaxation of immigration policy on it per capita income. From Equation (3), (4), (8), (18) and (9) we can derive τ tw (1 t) k f ( k) dk 1+ τ > 0 (30) dt τ n f ( k) + (1 t) kf ( k) 1+ τ

10 06 Taro Abe Furthermore, from (8) dyˆ n dk > 0 (31) Hence the per capita income in the north increae a a reult of the increae in immigrant. So it i fair to ay that the optimal policy for the north will be to completely free the labour mobility in two region even when the tax iue i taken into conideration. When labour mobility i completely free, labour movement from the outh to the north top at the point where the real wage rate in both the region are equal. Hence yˆ pw (3) ext we hall ee what happen when tax policy i introduced in a cenario illutrated by Equation (3) a cenario where labour mobility i completely free. τ i endogenied o that (3) will hold. From Equation (3), (13), (19), (8) and (3) we can derive dk w > 0 (33) dt (1 t) kf ( k) It how that the increae of t reduce the per capita income of the immigrant, ŷ, meanwhile a movement of the immigrant from the north to the outh occurred. Hence by uing Equation (7), (8), (18) and (33) we can derive the following equation and how that an increae of tax reduce the north per capita income. dk t dk (1 + τ) < 0 (34) dt 1 t dt dyˆ n dt dk dt < 0 (35) Thi i due to the fact that tax hike reduce profit rate and in turn reduce capital accumulation. Baed on the above reult, we can conclude that the optimum policy for the north i to completely free labour movement and to implement a non-dicriminative reditribution policy. The outhern tax policy. The outhern government taxe the emigrant worker and reditribute it to the outhern worker. Thi can be illutrated by the increae in q. Uing Equation (17) µ 1 ( pm ~ + ) dλ p τy (36) dq qτ r k + µ µ y pλ

11 orthern Immigration Policy in a orth-south Economy 07 The denumerator take a poitive value by virtue of the tability condition. However, dλ the ign of i unable to be determined becaue there i no aying what ign will the numerator take. In a cenario where labour movement i completely free between the two region, Equation (3) illutrate that it i poible that ( 1 q) yˆ pw. Thi i different from Equation (3) becaue the compulory taxation, q, exit. Therefore, both y and τ change depending on the change of q. We can derive the following uing Equation (17) dλ dq dy µ τy pm (1 ) + ( pm ~ + qy ) + (1 ) dq dq p 1 q qτ r k + µ y pλ (37) The firt and econd term of the numerator take a minu ign a a reult of the north rie of wage rate due to the increae of q. The third term take a poitive ign becaue it how the relaxation of the balance of payment contraint due to the increae of remittance back to the outh. Hence the ign of Equation (37) cannot be determined. From thee reult we know that the employment in the outh decreae hould the tax policy in the outh ignificantly reduce the income in the north. 3. IMMIRATIO POLICY WITH FREE CAPITAL MOVEMET Thi ection perform the ame analyi with a free capital movement. The northern economy remain baically the ame a in the lat ection Baic Structure of the Model Capital movement. Taking a little hint from Burgtaller and Saavedra-Rivano (1984), uppoe that capital movement happen arbitrary o that the profit rate equal in both region. We get r r (38) Denote K S, K, K and K a the outh capital tock, the north capital tock, capital tock ued in the production of indutrial good and capital tock ued in the production of primary good, repectively, the capital balance equation i K S K K + + K (39)

12 08 Taro Abe Divide both ide of (39) by L we can derive the following. 6 k S + k ( 1+ τ) k + k λ (40) K S Where, ks, L K k, L K k and L + L L λ. L The outhern economy. The outhern income conit of wage income, profit income and remittance from the emigrant worker. Hence it per capita income i given by y f ks qyτ ( k ) f ( k ) k + f ( k ) + (41) λ λp The firt and econd term to the right i the real wage rate in the outh, the third i the outh profit income and the lat i the remittance from the worker who have emigrated to the north. Therefore, the per capita conumption expenditure in the outh i K S k e y f ( k ) y f S (4) L λ The econd term to the right i the demand for invetment good in the outh, repreent the fraction of profit income pent on the demand for invetment good. Balance-of-payment equilibrium. Adopting the profit gained in the outh by the north, balance of payment equilibrium i given by: p { ~ m[ p,(1 ) y] + m[ p,(1 q) y ] τ} qyτ + pf ( k λ ks ) 1 pf ( k ) ks + λµ [, e ] p (43) The third term on the right hand ide i the remittance to the outh by the immigrant, the fourth i the profit gained by the north in the outh. Therefore, both term repreent balance of capital. Southern capital accumulation. The capital accumulation in the outh i given by k & nk (44) S r k S S 6 We had K k in the lat ection becaue we were not conidering the capital movement. L However, in both cae k repreent the northern capital per northern worker.

13 orthern Immigration Policy in a orth-south Economy 09 Determinant relation of the model. Thi model i cloed with 18 Equation, ()~(7), (9), (10), (1)~(14), (18), (38), (40)~(44) and 18 endogenou variable, f(k), k, w, r, L, L, y, k, y, Q, ( f k ), k, r, p, k S, λ, y and e. The major relation are a follow. Auming that L, k S and k each take a certain value from equation (5), (18) and (44). Equation (13) then olve k, and baed on that f(k) and r are olved in equation (1) and (14). Uing Equation (3), (4), (7) and (9) we know that both y and y are function of k and Equation (40) how that λ i alo a function of k. Equation(38) tell u that k i a function of p, hence y, y, and λ are alo function of p. By virtue of Equation (41) and (4) both y and e are alo function of p. Taking all thee into conideration, p i olved in Equation (43) and all other variable will then be determined. 3.. Relaxation of Immigration Policy by the orth Thi ection examine how the income in both region i affected in the hort-run where both k S and k are fixed and in the long run where both are flexible when the north increae the immigrant intake from the outh. Short-run equilibrium analyi. Let u tart with how the relaxed immigration policy affect the term of trade. Equation (43) tell u that λ λ µ + λµ ry + r k pm ~ dp τ τ τ (45) Γ On top of that, we know that Γ < 0 by virtue of the tability of the balance of trade equilibrium equation. The firt and econd term of the numerator repreent the change of the outh import of northern conumption good. The third and fourth term how the change in capital balance and the fifth term how the change in the north import of outhern good. dp λ The ign of i undetermined becaue Equation (40) tell u that < 0 τ dp while Equation (41) and (4) tell u that > 0. If >0, by virtue of Equation τ (38) r rie and k fall according to Equation (4). Hence uing Equation (3), (7) and (9) we can conclude that both w and y reduce and y increae. A for y, uing Equation (41) dy qy λp qτ dy + λp qyτ dp λp (46)

14 10 Taro Abe Equation (40) could be rewritten a dk k (1 + τ) dλ k (47) The ign of dλ dk i unable to be determined becaue < 0. Therefore, the dy dp ign of i alo undetermined. Uing the ame logic, if < 0 then k, w and y will increae and both y and r will fall. In thi cae Equation (47) ay that λ will fall becaue k increae. Thu, it i clear that y will increae by virtue of Equation (46). Thee reult differ from that of Wooton (1985) for y alway increae while y decreae in the hort-run. Thi i o becaue the capital-labour ratio, k, in Wooton (1985) mut fall a a reult of the relaxed immigration policy. However, k in thi paper will increae a a reult of the capital movement from the outh to the north when term of trade woren in the tate of balance of payment equilibrium, becaue capital i aumed to be moving arbitrarily. Table 3 um up the hort-run reult of thi paper. Table 3 y Finding in Thi Paper (Short-run) y py p λ τ ± ± ± ± ± Long-run equilibrium analyi. Aume that thi dynamic ytem atifie the tability condition at the proximity of it equilibrium value. 7 Firt let take a look at y and y. A quick reference to it determinant relation at the equilibrium how that k i olved in Equation (13), p in Equation (44), r in Equation (14), and r in Equation (38). Hence k i olved in Equation (4) and w i olved in Equation (3). Latly k and y are olved by virtue of Equation (7) and (18). Since thee determinant relation have nothing to do with τ, dy 0 (48) 7 Pleae refer Appendix 3.

15 orthern Immigration Policy in a orth-south Economy 11 dy 0 (49) Both y and y are not affected by the immigration policy at all. The increae of immigrant will reduce the north capital-labour ratio, k, and increae it profit rate, r, in the initial phae. However, we know from Equation (38) that it will caue a hift of capital from the outh to the north and eventually k will return it initial level. Therefore, r will remain fixed becaue p i determined by Equation (44) and k i determined by Equation (13). The above reult differ from Wooton (1985). We can conclude that when capital could move pontaneouly between the two region uch a that aumed in thi paper, the north doe not benefit from perfect labour mobility in the long-run. ext, we will ee how the per capita income of the outh, y, i affected. We can rewrite Equation (40)~(43) into dλ pm ~ + (1 r k ) + µ + λµ r k + ry µ λ τ (50) λ τ ry ry ( ( k λ ks τ + 1 ) r λn r λ θ kτ 1+ > 0 λ ) (51) (5) The effect on y i undetermined becaue there i no telling how λ i affected. 8 Table 4 um up the long-run reult of thi paper. Table 4 Finding in Thi Paper (Long-run) y y py p λ τ Pleae refer Appendix 4.

16 1 Taro Abe 3.3. Tax Policy Thi ection review the tax policy of both the government. The northern tax policy. Similar to the Wooton (1985) we will tax the wage income in the north and reditribute it to the northern worker. Therefore, Equation (8) and (9) will again be utilied. By virtue of Equation (18) and (9), dk wt > 0 (53) n r dy We can infer from Equation (18) that > 0. Thi how that the effect of the reditribution to the northern worker a a reult of the increae of τ will in turn raie the north capital accumulation. Thu, the optimal policy for the north i to perfectly free the labour movement when the taxation on northern wage income i taken into conideration. Thi reult differ from the cenario where taxation i out of the picture. 9 ext, we will review the tax policy when the north i implementing the optimal immigration policy. That mean our concern i on the tax policy when the intake of immigrant labour upply i determined in uch a way o that dk Equation (3) hold. We know that 0 becaue k i determined uing dt Equation (4) and (14). Hence by uing Equation (18) and (9) we can derive yˆ d dk dt > 0 τw >0 (54) n r by virtue of Equation (9). 10 Since the profit rate in the north i dt determined by the outh profit rate, thi reult i obtained becaue the increae in tax have increaed the capital accumulation a a reult of the higher tax revenue. Baed on the above reult, the optimal policy for the north under a circumtance where capital movement i free i to impoe a dicriminative tax policy on the immigrant worker and to perfectly free the labour movement. Thi finding i differ from that of Wooton (1985) becaue k i not affected by the northern tax policy for the north profit rate i regulated by that of the outh. Wooton (1985) ay that profit rate fall while k rie a a reult of an increae in t. 9 However, when the evaluation i done when tax i firt brought in (t 0) the reult doe not differ from that when tax i not accounted for becaue dk Thi reult i independent from the evaluation timing iue.

17 orthern Immigration Policy in a orth-south Economy 13 The outhern tax policy. The outhern government taxe the emigrant and reditribute the tax to the local outhern worker. We can derive the following baed on Equation (17) dλ τy dr µ 1 ( pm ~ + ) θ ryτ (1 ) f ks + p µ µ λ (55) The denumerator take a poitive ign by virtue of tability condition. Since the denumerator i the ame with that in Equation (36), thi reult i imilar to that of Wooton (1985). ext, uppoe that north ha opted for the optimal policy, in which the north implement a dicriminative reditribution policy againt the immigrant worker and perfectly free the labour movement. In uch a circumtance, when labour movement i at equilibrium, the following equation mut hold. ( 1 r )(1 t) w pw (56) Since both w and pw are olved by Equation (13), (38) and (44) at thi tate, in order for (56) to hold when q change t inevitably have to change a well. Therefore dt dq 1 t 1 r < 0 (57) In order to top the labour movement caued by the increae in q, the northern government i left with only one option that i to reduce the tax levied on labour income. 4. COCLUSIOS We have examined in thi paper how the north relaxation of immigration policy affect the per capita income in both region, in a ituation where capital movement i free in both region. The major finding are a follow. In the hort-run, the relaxation of immigration policy by the north will affect the term of trade by way of the balance of payment equilibrium equation. However, when the term of trade woren, the income per northern worker reduce while the income per immigrant worker increae.

18 14 Taro Abe The relaxation of immigration policy in Wooton (1985) pontaneouly reduce the north capital-labour ratio, however, thi paper how that capital movement from the outh the north occur even when the term of trade woren, a a reult riing k. In the long-run, the north relaxation of immigration policy doe not affect the per capita income of both the northern worker a well a the immigration worker. Thi paper illutrate the following mechanim when the immigration policy i relaxed, k initially fall but ince the profit rate of north, r, will increae becaue of that, capital movement occur at an intant from the outh to the north, returning k to the tarting level. Thi reult ignificantly differ from that of Wooton (1985) in which it ay the north doe not have any incentive to free the labour movement in the long-run under a free capital mobility regime. In a cenario where the north implement a dicriminative reditribution policy againt the immigrant worker, the per capita income in the north will increae becaue the reditribution of income from the immigrant to the northern local worker occur a a reult of the relaxation of the immigration policy. The optimal policy for the north will then be to completely free labour mobility and to implement a dicriminative reditribution policy againt the immigrant worker. Thi paper ha the following limitation. In a hort-run analyi, it i aumed that capital move pontaneouly. Thi paper doe not account for the difference in quality of labour. Skilled and unkilled labour are not treated accordingly. Thee are the remaining iue to be olved in future tudie.

19 orthern Immigration Policy in a orth-south Economy 15 Appendice APPEDIX 1 The following Jacobian could be derived from Equation (18) and (19). a 11 y k a 1 0 a a n p f ( ) λ k 1 k p f ( ) λ λ k Auming a 11 < 0 and p λ < 0 µ 1 p µ e µ 1 e p e p, hence trace<0 and det >0 and thi i table. APPEDIX By virtue of Equation (15)~(17) the numerator of Equation(58) i e µ pf µ Hence 1 > 0. p ( k qy τ p( m + m ~ ) + ) + + λ λ qy τ > 0 By virtue of Equation (18), fact with (7), (38) and (44), APPEDIX 3 y nk at long run equilibrium. Combine thi k w (60) n(1 ) It i neceary that > in order to obtain a meaningful olution for (60). A for dynamic Equation (18) and (44), the Jacobian at the proximity of the equilibrium value ( k are S ) e k and ( ) e

20 16 Taro Abe p b11 r ( k k) + n( 1) k 1 r ( k k) b b b 1 1 r r p k p k S k p S So p p b 11 + b n( 1) + r ( k ) + < 0 k r (61) k k p b 11 b b1b1 nr ( ) > 0 (6) k S S Are the tability condition. Both baed on Equation (40) and (43) p k and p k S could be rewritten a the following p k pm µ (1 r + k Γ ) + λµ k (63) p k S r µ + + λµ k Γ k S (64) p k S take a minu ign by virtue of (60) and (6). However, the ign of undetermined becaue from Equation (40) and (4) < 0. k p k i APPEDIX 4 At long run equilibrium, by virtue of Equation (44) trade, p, i a contant. n p and term of r

21 orthern Immigration Policy in a orth-south Economy 17 We can derive the following uing Equation (40)~(43) pm ~ + (1 ) r k + qy λµ dλ pr k + µ + λµ λ τ The ign of Equation (65) could not be determined becaue (65) λ qy ( ( k λ k S + 1 ) r λ θ ) (66) qy r kτ (1 + ) > 0 (67) τ λn λ We will take a look at the balance of payment equilibrium Equation (43) to ee what doe all thi mean. Subtitute Equation (40) into Equation (43), p { m p y m ~ [,(1 ) ] + [ p,(1 q) y ] τ} 1 pr {(1 + τ) k + k k } k + λµ [, e ] qy τ + pr { k (1 + τ) k} S When τ increae the immigrant demand for the outhern good to the left of the equation increae, too. On the other hand, the third and fourth term to the right balance of capital work favourably for the outh. However, there i no telling if the outh demand for the northern good the econd term on the right dλ will fall or otherwie. Hence i undetermined. Take an example where > 0. When > 0 i extremely large, the λ τ immigration policy of the north magnifie the demand for northern good. Hence it i dλ poible that < 0 ince the north immigration policy exert preure on the outh capital import from the north. REFERECES Burgtaller, A., and. Saavedra-Rivano (1984) Capital Mobility and rowth in a orth-south Model. Journal of Development Economic 15, Findlay, R. (1980) The Term of Trade, Equilibrium rowth in the World Economy. American Economic Review 70:3, Khan, M. A. (1984) International Trade and Foreign Invetment: A Model with Aymmetric Production. The Pakitan Development Review 3:4, p (68)

22 18 Taro Abe Lewi, W. A. (1954) Economic Development with Unlimited Supplie of Labour. Mancheter School of Economic and Social Studie, Saavedra-Rivano,., and I. Wooton (1983) The Choice between International Labour and Capital Mobility in a Model of orth-south Trade. Journal of International Economic 14, Taylor, L. (1981) South-orth and Southern rowth: Bleak Propect From a Structuralit Point of View. Journal of International Economic 11, Wooton, I. (1985) Labour Migration in a Model of orth-south Trade. Economic Modelling :4,