Autarky more likely than complete specialization

Transcription

1 Autrky more likely thn complete specilition Antonio Quesd Deprtment d Economi, Universitt Rovir i Virgili, Avingud de l Universitt, 4304 Reus, Spin 3th Jnury Astrct This pper mesures the strength of comprtive dvntge s source of interntionl trde y forcing countries to choose etween two extreme situtions: utrky nd complete specilition. It is shown in the stndrd Ricrdin model with two countries, two commodities, one input, nd liner production possiilities frontiers tht utrky is more likely thn complete specilition when: (i) for ech country, no point on production possiilities frontier is more likely to e chosen in utrky thn nother one; nd (ii) trde occurs if nd only if oth countries cn increse the consumption of ech commodity. Keywords: Autrky, comprtive dvntge, liner production possiilities frontier, Preto principle, proility of trding. JEL Clssifiction: F, D5 E-mil ddress: q@urv.ct. Finncil support from the Spnish Ministerio de Educción y Cienci (reserch projects SEJ nd SEJ C0-0) nd from the Deprtment d Universitts, Recerc i Societt de l Informció (Generlitt de Ctluny, reserch project 005SGR00949) is grtefully cknowledged.

2 . Introduction Ricrdo s (8, ch. 7) nlysis of foreign trde seems to suggest tht countries should specilie completely: Under system of perfectly free commerce, ech country nturlly devotes its cpitl nd lour to such employments s re most eneficil to ech. ( ) It is this principle which determines tht wine shll e mde in Frnce nd Portugl, tht corn shll e grown in Americ nd Polnd, nd tht hrdwre nd other goods shll e mnufctured in Englnd. Textooks on the principles of economics tend to e somewht miguous when explining the implictions of comprtive dvntge. Consider, for instnce, these three textooks: Lipsey nd Chrystl (004, ch. 33), Stiglit nd Wlsh (006, ch. 9) nd Miller (008, ch. 33). All of them discuss comprtive dvntge in the interpersonl cse first: Lipsey nd Chrystl (004, p. 60) hve doctor who is d crpenter; Stiglit nd Wlsh (006, p. 47), the president of compny nd her secretry; nd Miller (008, pp. 836), cretive dvertising specilist nd computer rtist. The nlysis in the two first cses suggests tht specilition is complete: the doctor does not devote time to e crpenter, wheres the president rings in new clients nd the secretry types letters. In Miller s cse, complete specilition is clerly identified s the outcome: the d specilist specilied only in writing d copy nd the computer whi specilied only in creting computer rt renderings. By deling with comprtive dvntge in the interpersonl cse efore the interntionl trde cse, the three textooks contriute to give the impression tht there is no sustntil difference etween the conclusions otined in ech cse. Two of them re explicit in this respect: fter the nlysis of the interpersonl cse, Lipsey nd Chrystl (004, p. 60) hold tht The sme principle lso pplies to ntions ; nd Stiglit nd Wlsh (006, p. 47) stte tht The principle of comprtive dvntge pplies to individuls s well s countries. Miller (008, p. 834) simply sys tht The est wy to understnd the gins from trde mong ntions is first to understnd the output gins from specilition etween individuls. Consequently, eing complete specilition the pprent outcome of the existence of comprtive dvntge in the interpersonl cse, it ppers tht it should lso e the outcome in the interntionl trde cse. But ll the uthors use specilie miguously. Miller (008, p. 838) sttes, in model involving the United Sttes, Indi nd the production of softwre nd personl computers, tht U.S. residents will specilie in the ctivity in which they hve comprtive dvntge. Since, in

3 Miller s (008, pp ) nlysis, the lterntive to utrky is complete specilition, one is led to elieve tht specilition is complete. Stiglit nd Wlsh (006, p. 46) hold tht individuls nd countries specilie in those goods in whose production they re reltively, not solutely, most efficient. Stiglit nd Wlsh s (006, pp ) exmple, which involves Chin, the United Sttes, textiles nd irplnes, hints t incomplete specilition. The uthors confirm this impression y stting tht comprtive dvntge my not led to complete specilition. But incomplete specilition is rtificilly introduced y redefining commodities: wht previously ws the commodity textiles lter ecomes two commodities, inexpensive textiles nd higher-qulity textiles. This redefinition just egs the question: cn country specilie in inexpensive textiles incompletely? Lipsey nd Chrystl (004, p. 63) dd qulifiction in their specilition result: If trde is possile t some terms of trde etween the two countries opportunity costs of production, ech country will specilie in the production of the good in which it hs comprtive dvntge. Lipsey nd Chrystl s (004, p. 6) Tle 33. explins the gins from specilition y considering incomplete specilition, ecuse countries produce little more of some commodity ut do not ndon the production of the other commodity. This points to interpreting specilie s prtilly specilie, which is not consistent with their usge of specilie in the interpersonl cse, which points to completely specilie. One my contend tht hving to clrify whether specilition is complete or not is minor point, s comprtive dvntge ensures tht some prtil specilition is lwys enough for countries to hve incentive to trde. Tht is vlid ojection. But then, on the one hnd, why insisting in deling first with the interpersonl cse nd suggesting solution (complete specilition) tht is not the intended solution for the interntionl trde cse? And, on the other hnd, precision is lwys vlule: presenting prtil specilition s the solution identifies the medicine ut not the dose; presenting complete specilition s the solution identifies oth the medicine nd the dose. The source of the miguity in the textook explntion of the theory of comprtive dvntge proly lies in the fct tht it strcts from the countries initil position. When tht initil position is mde explicit, it ecomes ovious tht hving oth countries initilly producing together more of commodity X thn wht the country hving comprtive dvntge in the production of X could produce implies tht 3

4 specilition cnnot e the solution. For similr reson, if ig country fces smll country, it is difficult to justify tht complete specilition will lwys e the solution. Motivted y those miguities, this pper ims to provide n nswer to the question of how likely it is for country to choose to completely specilie when the lterntive is utrky, which is the pir of lterntives considered in some exmples presenting the theory of comprtive dvntge, such s those in Wikipedi (00) nd Miller (008, pp ). Why is this restriction to two lterntives worth considering? On the one hnd, it is conceivle tht these two could e the relevnt lterntives when some trde greement etween two countries is eing negotited, s one of the two countries my demnd tht oth countries completely specilie for the trde greement to e cceptle. This condition might e resonle if comprtive dvntge would led only one country c to completely specilie, ecuse in tht cse c would ssume the risky position of hving the supply of some commodity fully depend on nother country c'. In these circumstnces, c could invoke reciprocity when sking c' to solutely rely on c for the supply of the other commodity. Autrky nd complete specilition my lso e the sic options when the economic integrtion etween two regions of the sme country is the result of politicl decision: in country, it is rrely the cse tht everything is produced everywhere. On the other hnd, from conceptul point of view, it might e worth compring the two extreme situtions. In fct, utrky is represented y just one possiility (no mount of ny commodity exchnged with nother country), while openness consists of n infinite set of possiilities (the smllest mount of some commodity exchnged with nother country mkes utrky the defeted option). It is therefore priori esy for openness to ecome the winning lterntive, despite the fct tht mny exchnge situtions re closer to utrky thn to full openness. One wy of removing this pro trde is is to fce utrky with just the complete opposite: full openness rising from complete specilition. The nlysis is crried out in the stndrd Ricrdin model (the one with two countries, two commodities, one input nd liner production possiilities frontiers) y dding two ssumptions. First, ny point on country s production possiilities frontier is eqully likely to represent the initil sitution of the country. And second, given the initil sitution of ech country, complete specilition occurs if, y dopting it, oth countries cn otin, with respect to their initil positions, more of some commodity nd t lest s much of the other. 4

5 It is shown tht these two ssumptions mke utrky more likely choice thn complete specilition (nd, in the present context, trde). Accordingly, if in the Ricrdin model countries re forced to choose etween utrky (full closedness) nd complete specilition (full openness), the more likely outcome is utrky.. Model There re two countries, nd ; two commodities, X nd Y; nd the only input is lour, L. Country is ssumed to e endowed with the mount L > 0 of lour, wheres country is ssumed to e endowed with the mount L > 0. In ech country, ll the ville lour is pplied to the production of some commodity. Though this is the usul ssumption, it need not e presumed tht X nd Y re the only commodities. A more generl interprettion is tht, for country i {, }, the mount of lour L i cn only e pplied to the production of commodities X nd Y. In this context, utrky is reltive to X nd Y. In country, Y = L Y is the production function of commodity Y nd X = L X is the production function of commodity X, where: (i) nd re positive rel numers representing oth the mrginl nd the verge productivity of lour; nd (ii) for α {X, Y}, L α is the mount of lour in country ssigned to the production of commodity α. Similrly, for country, Y = L Y nd X = L X re the production functions of, respectively, commodity Y nd commodity X, with nd eing positive rel numers. The production of ech commodity in country is represented y point of the country s production possiilities frontier. These frontiers re for country nd for country. Y = L Y = L X () X () Without loss of generlity, country is supposed to hve comprtive dvntge in the production of commodity X, so < nd, hence, country hs comprtive dvntge in the production of commodity Y. 5

6 It is ssumed tht countries choose utrky or complete specilition. This ssumption llows the representtion of production possiilities frontiers in n Edgeworth ox; see Fig., drwn ssuming <, L < L nd L > L. For ny two points p nd q on n Edgeworth ox, define pq to e the distnce etween the two points. Given the initil positions of the two countries, complete specilition (nd, therefore, trde) is defined to occur if nd only if the rectngle whose lower left corner is country s initil position hs non-empty intersection with the rectngle whose upper right corner is country s initil position. For instnce, in Fig., g represents the initil position of country nd h the initil position of country. In this cse, complete specilition occurs ecuse the intersection of the two rectngles (the shded re) is non-empty. In fct, when country completely specilies in the production of X nd in the production of Y, ny point in the shded re cn e reched through trde nd in ny such point oth countries otin more of some commodity nd not less of the other. L X Country L c PPF d Y L PPF h e Y g f Country X L Fig.. Production possiilities frontiers in n Edgeworth ox In Fig., complete specilition still occurs if, given g, the initil position of country lies etween points d nd e (oth included). Consequently, if no point long PPF is more likely to represent country s initil position, the proility tht complete specilition occurs when g is country s initil position is the distnce de divided y the distnce cf: fvourle cses divided y totl numer of cses. By verging over ll the points on PPF, proility tht complete specilition (nd, therefore, trde) occurs cn e defined. It will e shown tht this proility is lwys smller thn ½. 6

7 3. Anlysis Let () nd () define the production possiilities frontiers of countries nd, with <. Set A =, B = L nd L =. The prmeter A mesures how productive L country is producing commodity Y in comprison with country. Anlogously, B mesures how productive country is producing commodity X in comprison with country. In ddition, L mesures how lrge the lour force is in country in comprison with tht of country. Note tht < mounts to A < B. There re three cses to consider. L L k c PPF d j i L L PPF g e h f L L Fig.. Computing the proility of trding when L < L nd L L (Cse ) Cse : L < L nd L L ; tht is, A < B L. This cse is represented in Fig. de ih. For every point g on PPF, the proility of trding is, which equls. Any kf jf such g cn e ssocited with unique vlue [0, L ]. Given the corresponding to g, hf in Fig. is itself, ij is L nd jf is L. Therefore, ih is. In view of this, the proility p () of trding (when point on PPF is chosen so tht ih is the mount produced of commodity Y) is p () = =. Fig. 3 shows the jf L grph of the function p () for [0, L ]. 7

8 p () L L L Fig. 3. The proility function of trding when L < L nd L L (Cse ) Assuming tht country cn choose ny vlue of with the sme proility, the L verge proility of trding in Cse is p =, which is equivlent to L p = L(B A). (3) Cse : L < L nd L > L ; tht is, A < < B. In this cse, s shown in Fig. 4, L PPF intersects wht for country is the horiontl xis (t point such s d in Fig. 4) efore intersecting (t point such s c in Fig. ) wht for country is the verticl xis. This leds to two possiilities, depending on whether country chooses point ove or elow the point g identified in Fig. 4. At tht point or elow, the nlysis is exctly s in Cse. Aove point g, the resulting proility is smller thn the one resulting in Cse ecuse PPF stops t d. Cse : the point c chosen y country is g or lies elow g long PPF. This occurs when 0 L ; see Fig. 4. Following the nlysis in Cse, the proility of je hk trding t c is, which equls. Since hk is df if, the proility p () of trding (when point on PPF is chosen so tht L is the mount produced of hk commodity Y) is p () = = if L, with 0 L. 8

9 L L d PPF i L PPF j h L g e k c f L L L Fig. 4. Computing the proility of trding when L < L nd L > L (Cse ) Cse : the point c chosen y country is ove g long PPF. This occurs when L de ih > L ; see Fig. 5. Now, the proility of trding t c is, which equls. df if Since ih = L, the proility p () of trding (when point in PPF is chosen so ih tht > L is the mount produced of commodity Y) is p () = = L = if L, with L > L. Fig. 6 shows the grph of the function p () for [0, L L ]. L L PPF c d L PPF i L e h L g L L L f Fig. 5. Computing the proility of trding when L < L nd L > L (Cse ) 9

10 p () L L L L L L Fig. 6. The proility function of trding when L < L nd L > L (Cse ) Assuming tht country cn choose ny vlue of with the sme proility, the L L proility of choosing L (so tht Cse pplies) is = =, L L BL in which cse the verge proility of trding is, which is equivlent to A. On the other hnd, the proility of choosing > L (so Cse B pplies) is, mking the verge proility of trding to e equl to BL L, which is equivlent to A L. In sum, the verge L B A proility of trding in cse is p = + A L = BL B BL B AL + AB, which cn e equivlently expressed s BL p = A L + B B L A. (4) Cse 3: L L ; tht is, A < B. In this cse, s shown in Fig. 7, PPF intersects L the verticl xis of country outside the Edgeworth ox (the ssumption A < B implies tht PPF cnnot intersect, s in Cse, the verticl xis of country, which mens tht L > L ). This gives rise to three possiilities, depending on whether country chooses point on PPF ove the point g in Fig. 7, etween g nd e, or elow e. 0

11 L PPF L L g d PPF i h j L e n k c L L L Fig. 7. Computing the proility of trding when L L (Cse 3) f Cse 3: the point c chosen y country is e or lies elow e long PPF. This occurs for 0 L ; see Fig. 7. The resulting cse is nlogous to Cse (nd Cse ). So jn following the nlysis in Cse, the proility of trding t c in Fig. 7 is, which df hk equls. Since hk is if, the proility p 3 () of trding (when point on PPF is chosen so tht L is the mount produced of commodity Y) is p 3 () = hk = if L, with 0 L. L PPF L L L g c d e PPF j i h L L L L f Fig. 8. Computing the proility of trding when L L (Cse 3)

12 Cse 3: the point c chosen y country lies etween g nd e long PPF. This occurs when L > > L ; see Fig. 8. The resulting cse is nlogous to Cse. Thus, dj ih the proility of trding t c in Fig. 8 is, which equls. Since ih = L, the df if proility p 3 () of trding (when point on PPF is chosen so tht L > > L is ih the mount produced of commodity Y) is p 3 () = = L =, with L if L L > > L. Cse 3c: the point chosen y country lies ove g long PPF. This occurs when L L. At ny such point no trde occurs, ecuse country is lredy producing more commodity Y thn country cn produce. p 3 () L L L L L Fig. 9. The proility function of trding when L L (Cse 3) Fig. 9 shows the grph of the function p 3 () for [0, L ], where p 3 () = 0 when [ L, L ]. Assuming tht country cn choose ny vlue of with the sme likelihood, the verge proility in Cse 3 nd Cse 3 is = A L. Given tht the proility tht [0, L ] is =, it follows tht B L AL A the verge proility of trding in Cse 3 is p 3 =, which cn e AL B equivlently expressed s p 3 = AL BL. (5)

13 4. Result Tle 0 summries the nlysis crried out in Section 3. The first column identifies the three possile cses tht cn rise when A < B (the cse A = B is not interesting nd the cse A > B is simply the cse A < B with the nmes of the countries exchnged). The second column defines the conditions chrcteriing ech cse. The third column lists the results (3), (4) nd (5), which estlish the verge proility of trding in ech cse. The fourth column shows, for ech cse, the necessry nd sufficient condition for the proility of trding to e smller thn the proility of not trding. Cse rises when proility p of trding condition for p < / 0 < AL < BL (BL AL) BL < + AL A AL 0 < AL < < BL AL + BL > BL B AL 3 AL < BL or 0 < < BL AL AL BL > BL AL Tle 0. Results nd conditions for not trding to e more prole thn trding Proposition. Let () nd () define the production possiilities frontiers of two countries, nd, which my produce only two commodities, X nd Y, where,,,, L nd L re positive constnts such tht < (so country hs comprtive dvntge in the production of X nd country hs comprtive dvntge in the production of Y). For point (X, Y ) stisfying () nd point (X, Y ) stisfying (), define trde to occur if nd only if X + X < L nd Y + Y < L (so specilition sed on comprtive dvntge llows oth countries to consume more of ech commodity). Assume tht, for ech country, no point long the production possiilities frontier is more likely to e initilly chosen thn nother point. Then the proility of not trding is lwys greter thn the proility of trding. Proof. The proof mounts to verifying tht, for ech of the three cses in Tle 0, the inequlity in the fourth column holds. In Cse, the ssumptions AL > 0 nd BL AL imply BL < + AL. In Cse, since AL > 0, is lwys smller thn. As AL 3

14 AL result, the ssumption BL > yields BL >. In Cse 3, the ssumption AL AL implies 0, so the ssumption > 0 gurntees >. AL BL BL AL 5. Comments Proposition incorportes two ssumptions into the sic Ricrdin model of trde. One refers to the initil sitution of the countries: it is ssumed tht ny point on country s production possiilities frontier is eqully likely to e the point where the decision to engge or not in trde hs to e mde. This is resonle if, priori, ny socil preference estlishing the socilly most preferred point on production possiilities frontier is eqully dmissile. The second ssumption is perhps more ojectionle ecuse it constrints to the utmost the possiility of trding: trde only occurs if oth countries cn get more of ech commodity. This excludes the cse in which the socil preference is represented y the stndrd convex, decresing nd smooth indifference curves. This notwithstnding, the socil preferences implicitly dopted in the pper (with L-shped indifference curves) cn e viewed s limit cse of the stndrd indifference curves. In this respect, (3), (4) nd (5) specify lower ounds for the proility of trding in more generl model in which socil preferences re simply ssumed to e monotonic. It is pprent tht mny types of socil preferences will generte proilities lrger thn those in (3), (4) nd (5). But then the point would e tht this increse in the proility of trding will depend on the specific type of preference considered. For instnce, one cn define socil preferences so tht, in Fig., the two countries will trde if they strt from c nd g. But one cn define socil preferences leding to the opposite outcome. By contrst, it seems resonle to presume tht, under ny dmissile socil preference, trde will occur in Fig. when the countries re initilly t g nd h. It therefore mkes sense to consider the question of how likely it is to trde y just pying ttention to cses in which it seems to e eyond dispute tht trde cn occur. This resoning leds to second justifiction tht relies on the Preto principle. In Fig., with countries t c nd g, the superiority of nother sitution reched through trde does not follow from the Preto principle, ecuse if there is trde etween the two countries, the consumption of some commodity must e reduced in t lest one country. As consequence, some individul in some country must reduce his consumption of 4

15 some commodity. Hence, the superiority of the outcome of trde over the outcome of utrky depends on how individuls, first, nd society, next, determine the wy in which more consumption of some commodity compenstes the loss of welfre due to the reduction in consumption of some other commodity. Since it is not ovious when one s consumption cn e scrificed for the good of society, it is plusile to consider tht the good of society my justify voiding putting society in sitution in which such choices or judgements must e mde. In tht cse, the only rule estlishing when trde is unojectionle is the Preto principle: to hve more of some commodity ut not less of the other. So (3), (4) nd (5) cn e seen s mesures of how likely it is to hve Preto improvements through trde. Finlly, (3), (4) nd (5) re lso useful to determine wht chnges in A, B nd L under utrky mke trde susequently more or less likely. Roughly speking, Cse represents the sitution in which country is smll, ecuse the mximum tht country could produce of ech commodity is less thn the mximum tht country could produce. Cse 3 represents the reverse sitution: country is the smll country. So, in sense, Cse nd Cse 3 descrie the sme sitution. In fct, in oth cses, the proility of trding decreses with A nd increses with B nd L: < 0, 3 < 0, > 0, 3 > 0, > 0 nd 3 > 0. Considering Cse A A B B L L, these results men tht the proility tht trde occurs increses if country : (i) ecomes comprtively less productive in the commodity in whose production the country does not hve comprtive dvntge (A decreses); (ii) ecomes comprtively more productive in the commodity in whose production the country hs comprtive dvntge (B increses); or (iii) ecomes comprtively more populted (L increses), therey ecoming closer in sie to the ig country. Cse represents the intermedite sitution in which ech country is ig in the industry producing the commodity in whose production the country hs comprtive dvntge. Cse seems to e the one in which it is intuitively more likely for trde to occur, ecuse ig country does not seem to e in need to trde with smll country (Cse nd Cse 3). Unexpectedly, the pprently intuitive results from Cse nd Cse 3 fil: L = A B, = A nd = A, so ll the B B L L BL derivtives cn e positive or negtive. It is therefore possile to hve > 0, which A occurs when BL > ; or to hve < 0, which occurs when AL < ; or to hve B L 5

16 < 0, which occurs when (AL)(BL) <. It is even possile for the three results to hold simultneously (for instnce, with BL =. nd AL = 0.4), in which cse the proility of trding decreses when country ecomes, t the sme, smller nd more (less) productive in the commodity in whose production the country hs (does not hve) comprtive dvntge. References Lipsey, R. G. nd K. A. Chrystl (004): Economics, 0th edition. Oxford University Press: Oxford. Miller, R. L. (008): Economics Tody, 4th edition, Interntionl Edition. Person: Boston. Ricrdo, D. (8): On the Principles of Politicl Economy nd Txtion, 3r edition. John Murry: London, Stiglit, J. E. nd C. E. Wlsh (006): Economics, 4th edition. W. W. Norton: New York. Wikipedi (00): Comprtive dvntge, ccessed the 3th Jnury 00, 6