A Microeconomic Foundation for Optimum Currency Areas: The Case for Perfect Capital Mobility and Immobile Labor Forces

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1 Theoretcal Economcs Letters htt://dx.do.org/0.4236/tel Publshed Onlne October 202 (htt:// A Mcroeconomc Foundaton for Otmum Currency Areas: The Case for Perfect Catal Moblty and Immoble Labor Forces Masayuk Otak Insttute of Socal Scence Unversty of Tokyo Tokyo Jaan Emal: ohtak@ss.u-tokyo.ac.j Receved June 6 202; revsed July 2 202; acceted August 202 ABSTRACT Ths artcle rovdes a mcroeconomc foundaton for Mundell s otmum currency area theory. We consder twn countres where labor forces are fxed to each country although the real catal moves nternatonally. When the central bank n each country behaves non-cooeratvely t wll rase the domestc nterest rate to attract more real catal and ncrease the rent of her resdences. However the ferce cometton between the central banks ultmately exacerbates the dsarty n ncome dstrbuton. Moreover when the real catal or the fnancal ntermedary as ts agent does not have a natonalty the worsened ncome dstrbuton also results n the neffcent resource allocaton. Thus such twn countres should unfy ther central banks and coordnate ther monetary and nterest olces. In other words these countres consttute an otmum currency area. Keywords: Otmum Currency Area; Catal wthout a Natonalty; Non-Cooeratve Game between Central Banks; Dsarty n ncome Dstrbuton; Ineffcency of Resource Allocaton. Introducton Income dsarty s not lmted to develong countres. Advanced economes also face ths growng roblem. Ths artcle consders why such an undesrable economc consequence s nvoked when constructng a mcroeconomc foundaton for the otmum currency area theory orgnatng from Mundell s [] semnal work. As Mundell [] emhaszes the moblty of roducton resources lays a crucal role when we consder whch economes should consttute an otmum currency area. We deal wth the case n whch both labor forces are mmoble and have a natonalty but real catal wth no natonalty can move nternatonally at the owners or ther agents (banks securty comanes and etc. ) dscreton. Such a settng s lausble when we observe that foregn drect nvestment s generally referable to certfyng work vsas. When small twn countres wth dentcal economc structure are n ths stuaton ther central banks comete to nvte more real catals to enrch ther economy as long as the countres attan full emloyment. Nonetheless such cometton has the followng devastatng conesquence. If one central bank ursues a hgh-nterest olcy to attract more real catal the other central bank counteroffers wth a hgher nterest rate. Such a cumulatve rocess does not cease untl a surlus from workng that s the benefts of the hgh nterest olcy vansh entrely. Consequently the non-cooeratve behavor of two central banks brngs about a serous ncome dsarty between catal and labor. Furthermore snce catals or fnancal ntermedares as ther agents are assumed to have no natonalty the emergng dsarty also results n the large welfare losses for these two natons. The unfcaton of two central banks s desrable for overcomng such a dffculty. The small twn countres should be at least economcally ntegrated. Then the same amount of money s suled to ensure full emloyment and the nterest rates offered to non-natonalty real catals become dentcal at the lowest level. Accordngly each country s suled wth an amount of real catal and thus the ncome dsarty and neffcent resource allocaton wthn the natons are entrely resolved. That s the small twn countres consttute an otmum currency area whenever the real catal moblty s comlete. The remander of ths aer s structured as follows. In Secton 2 we construct a small twn country model based on Otak [2]. In Secton 3 we comare the non-cooeratve and cooeratve monetary olces and rove the nevtablty of otmum currency areas. In Secton 4 we Coyrght 202 ScRes.

2 396 M. OTAKI summarze the analyses and results. In Secton 5 we rovde bref concludng remarks. 2. The Model 2.. Structure of the Model We use a two-erod overlang generaton model n a roducton economy wth money. The world conssts of twn countres A and B whose economc structures are dentcal and the rest of the world. Each country has resdents who cannot move elsewhere and who lve n two erods wth the densty [0 ]. Each resdent secalzes n roducng one dfferentated goods wth the hel of real catals when he/she s young. Real catal whose owners have no natonalty exsts wth the densty [0] [02]. Hence each resdent can otentally deloy the real catals wth the densty [0 ]. Catal ncome s also earned when the owner s young and then catal tself s assed to a descendant. Once an owner determnes the locaton of hs/her catal he/she lves n that country even after hs retrement. The mnmum rate of return from the rest of the world ( r ) s guaranteed to all catal owners. Furthermore for smlcty a unt real catal combned wth a resdent s busness sklls roduces a unt good. The ncome dstrbuton between resdents and catal owners s determned by a negotaton. The negotaton rocess whch was develoed by Otak [2] s assumed to be the followng two-stage game. Frst a resdent determnes how much catal to deloy n order to maxmze hs/her ncome from busness sklls. Second gven the volume of catal deloyed and goods roduced the resdents and owners mutually determne the ncome dstrbuton n accordance wth the asymmetrc Nash barganng soluton. In addton there s a central bank n each country whch ursues the socal welfare of her resdents. Each central bank s olcy varables are the nomnal money suly and the real nterest rate (.e. the rate of return for catal). We assume that a central bank manulates the real nterest rate by ntervenng n the negotaton rocess between her resdents and the non-natonalty catal owners or fnancal ntermedares that are agents of catal owners. That s a central bank can control the barganng ower of her resdents through moral suason Constructon of the Model Indvdual s Utlty and Consumton Functons We assume that all ndvduals (ncludng catal owners) have the same concave and lnear homogenous lfetme functon: 2 0 U u c c c c z dz where c z s the consumton of good z durng the th stage of lfe. We can derve the followng corresondng ndrect utlty functon IU : IU Yt yt Yt yt t t t t t where Yt s the nomnal ncome and t s the rce ndex defned by 0 t d t z z. Furthermore the consumton functon of the younger generaton C s t () C c y. (2) Fnally the demand functon for good z s where d y z d Dz y (3) s the aggregate demand Producton Process by the Two-Stage Game To develo the aforementoned roducton rocess we consder the followng two-stage game. ) Each resdent maxmzes hs/her ncome from busness sklls by deloyng non-natonalty catals; 2) The resdent and catal owners or fnancal ntermedares negotate ther ncome dstrbuton n accordance wth the asymmetrc Nash barganng soluton the threaten ont of whch s 0 r. We must solve ths roblem by backward nducton. In the second stage game the corresondng generalzed Nash roduct G z s GP z z r r r (4) where s the degree of tolerance that s resdents dscount rate aled to the negotaton rocess wth catal owners or ther agents. s the modfed (actual) dscount rate; that s denotes the ower of moral suason of country s central bank to decrease the resdents dscount rate to nduce more catal radly nto the domestc economy. r s the domestc rate of return for a unt catal. The shae of the roduct s derved from two roertes of the model. Frst the objectve functon s lnear on the real ncome as ndcated by (). Second the roducton (or demand) volume s already determned by the frst stage of the game. Maxmzng (4) wth resect to r we obtan the equ lbrum domestc rate of return r : r z r. (5) See Rubnsten [3] for a detal nterretaton concernng the asymmetrc Nash barganng soluton. Coyrght 202 ScRes.

3 M. OTAKI 397 Takng (5) nto consderaton the maxmzaton roblem of the frst stage can be exressed as The soluton to (6) s z max zr Dz z max z r z z z r Dz (6). (7) Hence the rce level s constant over tme and the equlbrum nflaton rate s. Substtutng (3) and (7) nto (6) we obtan z d where y denotes the real GDP of country. From () t s clear that (8) corresonds to the socal welfare of resdents n country The Market Equlbrum In both countres money s suled through the unexected transfer to the older generaton; thus takng (2) nto consderaton the equlbrum condton for the domestc aggregate goods market becomes d d d m y c y m y c where m denotes the real money suly wthn country. The second term of (9) corresonds to the aggregate exendture of the older generaton. Owng to the erfect moblty the real catal market acheves equlbrum when k y = f = d j 2 f > j j 0 f < (8) (9) (0) where k s the amount of catal that has been nvested n country. The model contans fve tyes of endogenous varable d r y k two tyes of exogenous varable m and fve structural Equatons (5) and (7)-(0). Thus the model s closed The Non-Cooeratve Game between Central Banks and the Dsarty n Income Dstrbuton Because of the nternatonal moblty of real catals and the reresentaton of socal welfare (8) each central bank s eager to attract more catal and enrch ts country. Such cometton s descrbed by the followng two-stage game. In the frst stage central banks determne ( ). Next they decde how much money they suly (.e. ( m m )). To solve the equlbrum of ths game we must begn wth the second stage. Snce the outcomes of the frst stage are summarzed by (0) takng the socal welfare (8) and the equlbrum condton for each aggregated goods market (9) nto consderaton the best resonse of each central bank s to mantan the full-emloyment equlbrum whch s defned as the amount of real catal that s assocated wth ts country. Hence the followng domnant strategy n ths game corresonds to the result of the frst-stage game. That s m j 2 f > 0 f < j = f =. j () Snce full-emloyment s assured n the second stage central banks strve to nvte as much real catal as ossble. The followng theorem holds concernng the unqueness of the Nash equlbrum: Theorem. The unque Nash equlbrum s characterzed by m 0 (2) Proof. <Suffcency> If (2) s satsfed there s no actve ncentve to dverge the strateges because no addtonal gan s obtaned by lesser m. Hence (2) s a Nash equlbrum. <Necessty> Suose that s strctly ostve n some Nash equlbrum. Then j j. j By selectng a slghtly larger than j mroves her socal welfare as much as j 0. country Thus there s an ncentve to dverge from the equlbrum. Ths s a contradcton. The economc mlcaton of Theorem s qute serous. As long as two central banks extend the non-cooeratve game to attract more catal the ncome dsarty deeens aganst ther ntentons. Owng to the cometton resdents earnngs from busness sklls are utterly absorbed by the catal ncome. Snce as seen n (8) the socal welfare of resdents s roortonal to ther ncome the deeenng ncome dsarty also results n a less effcent economy. Such a henomenon s romnent n East Asa for examle. In ths area foregn drect nvestments flow manly from Jaan and Chna to other countres. Although the catal accumulaton suffcently advances and a lmted Coyrght 202 ScRes.

4 398 M. OTAKI number of catalsts and banks surrsngly become rch the labor ncome of most resdents ncludng those n Jaan and Chna stagnates. Income dsarty s one of the most urgent roblems n East Asa. 3. The Otmum Currency Area as the Unfcaton of Central Banks In the revous secton we showed that the non-cooeratve actons of central banks have qute harmful effects on both countres. In ths sense we roose the unfcaton of central banks. Accordng to Mundell [] a currency area s defned as follows: A sngle currency mles a sngle central bank (wth note-ssung ower) and therefore a otentally elastc suly of nterregonal means of ayment. (. 568) We adot ths defnton of a currency area. When central banks are unfed and a currency area s formed the twn countres A and B can be treated as a sngle country and hence monetary coordnaton becomes ossble. Because of the symmetry of the countres the otmal coordnaton olcy s also symmetrc. Hence the two-ste game extended n 2.3 requres equal allocaton of real catal. Thus we obtan m m and 0. It s evdent that the socal welfare of each country (8) becomes. Ths s the maxmal value that each country attans. In ths sense these twn countres together consttute an otmum currency area Results and Analyses We reconsder the theory of otmum currency area from the ersectve of resource allocaton and ncome dstrbuton. The obtaned results are as follows. We concentrate on the case of twn countres under erfect catal moblty and mmoble labor forces. Ths assumton seems natural f we consder the sgnfcance of the exstence of naton states. When each central bank ursues ts natonal nterests that s the socal welfare of ts mmoble labor force (.e. the resdents) dre economc consequences emerge. Each central bank s led to adot an artfcal hgh nterest olcy because more catal nduced by a rate slghtly hgher than the rates of ts rval central bank brngs about hgher ncomes for the busness sklls ossessed by the resdents 2 Hamada [4] and [5] also analyze not only how ast monetary ntegratons were generated but also what olces were desrable to sustan such unon although hs models are bascally statc and fnd dffculty n exressng functons of money exlctly. 3 Casella [6] analyses the utlty of monetary unon as the savng of transacton costs. However the substance of such costs s not necessarly clear. Although Basev Delbono and Delncolo [7] argue that there are mcroeconomc benefts from the monetary ntegraton they do not fnd the exstence of the ferce zero-sum game between the central banks that we deal here. That s both studes do not drectly connect wth the theoretcal relatonsh between factor moblty and the necessty of a currency area that s the most serous concern of Mundell []. of that central bank s naton. However such comettve and escalatng nterest-rasng s devastatng and cumulatve and t does not end untl all the resdents ncome s absorbed by the real catal wthout natonalty. Thus a serous ncome dsarty and a large decrease n socal welfare occur. It s clear that the naton s not an otmum currency area. When the two central banks are unfed and the monetary coordnaton becomes ossble such catastrohc cometton ceases. Real catal s allocated equally by abolshng the comettve and artfcal hgh-nterest olcy. Just enough external money s suled to ensure the full-emloyment equlbrum n each country. Thus the socal welfare acheves ts maxmum. In other words our twn countres under erfect catal moblty consttute an otmum currency area. It s also noteworthy that our aroach s based on a rgorous dynamc mcroeconomc foundaton and thus enables the economc welfare analyss. In ths sense we succeed n udatng and extendng the theory of Mundell [] Concludng Remarks We obtan the result that twn-countres wth erfect catal moblty should form a currency area n the sense of Mundell []. We must note some lmtaton of our work. The frst s the dffculty of central bank unfcaton. Bureaucrats who oerate the unfed central bank may be of dfferent natonaltes. Dfferences due to culture ethncty tradton and etc. are not as easy to overcome as our theory assumes. It takes more tme than we exect to ensure fare olcy coordnaton. As Hamada [5] argues n general any monetary ntegraton cannot works well wthout accomlshng oltcal ntegraton beforehand at least hstorcally. The second concerns the glut of foregn drect nvestment. In realty the volume and range of moble real catal s large and wde. It s feared that the world as a whole may become a unque otmum currency area. Nevertheless t s certan that such a tremendous and enlarged organzaton would never work well. It may be more ractcal to lace a levy on nternatonal catal movement lke the Tobn tax. REFERENCES [] R. A. Mundell A Theory of Otmum Currency Areas Amercan Economc Revew Vol. 5 No [2] M. Otak A Welfare Economcs Foundaton for the Full- Emloyment Polcy Economcs Letters Vol. 02 No do:0.06/j.econlet [3] A. Rubnsten Perfect Equlbrum n a Barganng Model Econometrca Vol. 50 No do:0.2307/9253 Coyrght 202 ScRes.

5 M. OTAKI 399 [4] K. Hamada On the Poltcal Economy of Monetary Integraton In: R. Z. Alber Ed. Natonal Monetary Polces and the Internatonal Fnancal System Unversty of Chcago Press Chcago 974. [5] K. Hamada On the Coordnaton of Monetary Polces n a Monetary Unon Paer Presented at the Colloquum on New Economc Aroach to the Study of Internatonal Integraton Euroean Unversty Insttute 979. [6] A. Cassella Partcaton n a Monetary Unon Amercan Economc Revew Vol. 82 No [7] G. Besev F. Delbono and V. Delncolo Internatonal Monetary Cooeraton and Economc Influence Journal of Internatonal Economcs Vol Coyrght 202 ScRes.