Labor Productivity by Country and Good United States Shirts 10 shirts/day 6 shirts/day Food 30 bushels/day 2 bushels/day. 2bushels.

Transcription

1 Fall 010 Econ 455 Anwr to Problm St Harvy Lapan 1. Conidr a Ricardian modl o comparativ advantag. Thr ar two countri, th U.S. and. Each country can produc two good, hirt (S and ood (F. Aum th US ha 1000 workr and ha 5000 workr. Labor productivity in ach country i: Labor Productivity by Country and Good Unitd Stat Shirt 10 hirt/day 6 hirt/day Food 30 buhl/day buhl/day (ath US ha th abolut advantag in both good bcau th US marginal productivity o labor i highr or both good. (ith opportunity cot o producing ood in th U.S. i 1/3 hirt pr buhl inc on workr can produc 30 buhl or 10 hirt o i w mov a workr rom hirt production to ood production w hav: ΔS MPLS 10hirt 1 US : = = = hirt / buhl. Similarly, th opportunity cot o ood production in ΔF MPLF 30buhl 3 ΔS MPLS 6hirt i: : = = = 3 hirt / buhl. Thu, th US ha th lowr opportunity cot ΔF MPLF buhl o producing ood. O cour, that man ha th lowr opportunity cot o producing hirt. Th opportunity ΔF MPLF 30buhl cot o producing hirt in: US : = = = 3 buhl / hirt, whra or : ΔS MPLS 10hirt ΔF MPLF buhl 1 : = = = buhl / hirt. ΔS MPL 6hirt 3 S (iio cour, a hown abov, th US ha th comparativ advantag in ood and ha th comparativ advantag in hirt. (bdriv and ktch th production poibility rontir or ach country. For US: # Shirt Q = 10L = 10( 1000 L = 10,000 10( Q 30 = ( Q 3 a L = ( Q 30 For : # Shirt Q = 6L = 6( 5000 L = 30,000 6( Q = 30,000 3Q a Q = L 1

2 Shirt Shirt B B Food Food US Production Poibility Frontir Chin Production Poibility Frontir (ith point B rprnt th original US production (and conumption o 5000 hirt and unit o ood, whil B rprnt Chin production (and conumption o hirt and 5000 unit o ood. Lt incra hirt production by S unit (up to a maximum production o in ; thi will cau Chin ood production to all by (S/3 unit {moving in th dirction hown by th arrow}. Lt th U.S. incra ood production by D unit (up to a maximum o unit o ood; thi will cau U.S. hirt production to all by (D/3 {again, moving in th dirction hown by th arrow}. Thu, rom a world prpctiv: Chang Food Production = D ( S 3 > 0 i D > ( S 3 Chang Shirt Production = S ( D 3 > 0 i D < 3S Thu, or any chang in th two countri uch that: 3S > D > ( S 3 (or, quivalntly, 3D S ( D 3 > > world output o both good incra. {.g., i incra hirt production by 100 and U.S. incra ood production by 100. Naturally, onc on country i ully pcializd, it can produc no mor o th good in which it ha a comparativ advantag. (iith world production poibility rontir i uch that - at mot - only on country produc both good. For low lvl o ood output, hould pcializ in hirt, whil th US produc both good; whil or larg lvl o ood output, th US pcializ in ood and produc both good. Formally: T u u T T ( ( Q 30000; Q = 0, Q = 30000; Q = Q 3 ; Q = Q 3 ( T u u T T T 40,000 Q 30,000; Q = 30,000, Q = 0; Q = 30,000 3 Q ; Q = 30,000 3 Q 30,000 = 10,000 3Q T u = + T u = + In th abov, Q Q Q i world ood output and Q Q Q i world hirt output. u, (cin th abnc o trad, autarky (no trad rlativ pric would b: ( P P 3 ( ood / hi ( P P ( ( ood hirt indicat th country. = rt and = 13 /, whr P i th pric o ood, P i th pric o hirt, and th uprcript u US Ral Wag: ( ( W P = 30 unit ood / day; W P = 10 hirt / day Chin Ral Wag: ( ( W P = unit ood / day; W P = 6hirt / day u

3 (d I trad i allowd, ach country will xport th good in which it ha a comparativ advantag thu, th US xport ood, xport hirt. Auming ach country wind up ully pcializd (which will happn i country iz ar not too dirnt, thn pot-trad ( ( P P w 13 < < 3. In th US, th rlativ pric o hirt all, and thu th ral wag in trm o hirt (th import good ri whil th ral wag in trm o ood i unchangd. In, th rlativ pric o ood all (rlativ pric o hirt ri and hnc th ral wag in trm o ood ri, whil in trm o hirt it i unchangd. Thu, th ral wag in ach country ri in trm o th import good. (W know that i th world rlativ pric, ( ( P P w 13 < < 3, thn ach country will pcializ. Hnc, th mthod i to aum ach country do pcializ, calculat dmand undr that aumption, and i th rulting pric i conitnt with th aumption (thi will happn i th dmand curv look lik D1 in th igur on th nxt pag. I th quilibrium rlativ pric or hirt you calculat i l than (1/3, you know th aumption wa al, and in quilibrium will produc both good (th dmand curv look lik D. Similarly, i th quilibrium rlativ pric you calculat wr gratr than 3, thn again th aumption i al and th U.S. will produc both good (th dmand curv look lik D3 in th igur. u So, auming ach country pcializ, lt W b th US wag and W th Chin wag. Thn, inc ach u country pcializ, W 30 P = W 6. Thu, incom in ach country i: P = ( and ( u u u u I = W L = W 1000 = 30000P and Chi na I = W L = W 5000 = 30000P u I + I 30000P P P Hnc, total dmand or ood i: D = = = P P P Stting dmand qual to upply, auming ach country pcializ, impli: P P S = D = = 1. P P Sinc thi pric i within th aumd rang (dmand look lik D1 th quilibrium i on in which both countri u W W = 30P 6P = 5. Not that hit in pcializ, with th quilibrium pric a givn, which impli ( ( dmand, by changing th rlativ pric o output, will chang th rlativ wag btwn countri. 3

4 P P Supply Shirt 3 D3 (1/3 D1 D Shirt World Equilibrium 3 Ca (iith pot trad ral wag: US: u u ( W P ( W P ( W P ( P P : ( W P ( W P ( W P( P P = 30, = = 30 1 = 30 > 10 = 6, = = 6 1 = 6 > So, in both countri, th ral wag incra in trm o th import good and i unchangd in trm o th xport good, o ovrall both countri gain. A 50% incra in Chin productivity, in both ctor, would - at th original world pric - incra output o hirt, and incra dmand or both hirt and ood (inc th incrad productivity rai th incom o Chin workr and hnc incra thir dmand or both good and inc i pcializd to hirt production. I world pric don t chang, bnit rom thi productivity incra and th US i not actd. Howvr, i i larg nough world pric will chang. In particular, givn th upply o ood, dmand incra o thr i an xc dmand or ood (which i th am a an xc upply o hirt. Thu, th rlativ pric o ood (to hirt mut incra, bniting th US, which xport ood, and hurting, which import ood. Th ovrall impact on i ambiguou, inc th productivity incra bnit, but th pric chang hurt thm. Th US mut bnit. Spciically, with th 50% incra in Chin productivity, auming both countri till pcializ, w hav: 4

5 u u u u I = W L = W = 30000P and I = W L = W 5000 = 9P 5000 = 45000P Givn pric, US incom i not actd, but Chin incom incra by 50% bcau productivity incra by 50%. Uing th dmand unction rom part ( w hav: D u I + I 30000P P P = = = 15, 000 +, 500 P P P P P P 3 Stting upply qual to dmand: S = D = , 500 = = or P P P = Notic that th rlativ pric o hirt ha alln (th rlativ pric o ood ha rin but rmain pcializd in hirt; th ct on ral wag in ach country i: u u W P = 30, W P = W P P P = 30 3 = 45 US: ( ( ( ( ( : ( W P ( W P ( W P ( P P ( = 9, = = 9 3 = 6 So, th productivity incra in, which cau hirt pric to all (ood pric to ri, cau th US ral wag to ri in trm o hirt. Chin ral wag in trm o hirt ri bcau o th productivity incra, but Chin ral wag in trm o ood i unchangd (bcau th pric o ood incra. Both countri gain rom th productivity growth in. Not that th pciic rult dpnd upon th dmand unction but th gnral concluion will b imilar with dirnt dmand unction. g Suppo a third country, Argntina i allowd to trad with th US and. Aum th productivity o labor in ach country i givn by: Unitd Stat Argntina Shirt 10 hirt/day 6 hirt/day hirt/day Food 30 buhl/day buhl/day 8 buhl/day i How will th addition o Argntina to thi agrmnt act which good th US xport and which good xport? Can you tll which good Argntina will xport? (a vrbal, not a quantitativ, anwr i xpctd hr. I you look at autarky pric, uing th am logic a arlir, you hav: ( P P ( P P ( ( P P US Argntina = 3; = 1 3 ; = 4 Now Argntina i th lowt cot upplir o ood (hight cot upplir o hirt, and th low cot upplir o hirt. I trad occur among all 3 countri, Argntina will xport ood, will xport hirt but th US trad pattrn i uncrtain. In trm o comparativ advantag, th US ha a comparativ advantag in hirt whn compard to Argntina, but th US ha a comparativ advantag in ood whn compard to. Thu, without mor inormation, w cannot b ur which good th US would xport. ii How will th addition o Argntina to th US- trad agrmnt act th (r trad quilibrium rlativ pric o hirt (in trm o ood? A vrbal anwr uic. Sinc th world rlativ pric o ood bor Argntina joind th trading group wa abov (1/3, Argntina will want to pcializ in ood. Thu, allowing Argntina to trad will incra th upply o ood and th dmand or hirt. Thu, th world rlativ pric o hirt will ri (i.., th world rlativ pric o ood all du to Argntina joining th trad group. 5

6 iii How will th addition o Argntina to th US- trad agrmnt act wlar (ral wag in th US and in? Will both countri ncarily bnit by allowing Argntina to join? Will Argntina bnit by joining thi r trad zon? Explain carully. Sinc Argntina addition to th r trad zon will lowr th pric o ood a Chin import will gain (compard to th ituation in which jut tradd with th US. Argntina, o cour, gain a compard to autarky. On th othr hand, i th US continu to xport ood, it will lo a th world pric o ood all. It i poibl th US could chang rom a ood xportr to a hirt xportr (i Argntina production wr uicintly larg, in which ca th US may gain or lo. Th main point i that whil th world a a whol potntially gain in that it i poibl to incra world output o all good not vry country ncarily gain unl it i compnatd. Thu, it would b poibl or all countri to b bttr o atr Argntina join th r trad zon but, without compnation, not vry country mut gain.. To illutrat how th modl can b xtndd to mor than two good, conidr th ollowing xampl Labor Productivity by Country and Good Sho Shirt TV Food CD Unitd Stat 1 ho/day 4 hirt/day 4 TV/day 16 buhl/day 1 CD/day 4 ho/day hirt/day 1 TV/day buhl/day CD/day US/Chin Productivity (a In which good( do th U.S. hav an abolut advantag? In which good( do hav an abolut advantag? Th U.S. ha an abolut advantag in all good. (b In which country i th opportunity cot o producing TV lowr? I th anwr i ambiguou, xplain why. Th qution i: th opportunity cot o producing TV in trm o WHICH othr good? I w look at th lat row o th Tabl abov (not givn in th problm t itl, w US rlativ productivity (compard to in producing TV i highr than th rlativ productivity or ho or hirt, but lowr than th rlativ productivity in producing ood and CD. Thu, th opportunity cot o producing TV a compard to ho or hirt i lowr in th US; BUT th opportunity cot o producing TV a compard to Food or CD, i highr in th US. Not akd but rom th Tabl w that th US ha th lowr opportunity cot o producing ood, maurd in trm o ANY o th othr good, and ha th lowr opportunity cot o producing hirt, maurd in trm o ANY o th othr good. (c Find autarky rlativ pric in ach country (or implicty, xpr th pric o ach good in trm o ood. Autarky rlativ pric in trm o ood. Ltting ood b th itm in which valu ar maurd (what i calld th numrair, w hav or ach country, i th good i producd, W = Px MPLx or vry good x, whr MPL x i P MPL MPL x th labor productivity; hnc: =, or Px = P and thu: P MPLx MPL x 6

7 P MPL ho ood 4 Phirt PTV PCD 4 US : = = ood / ho; = 4 ood / hirt; = 4 ood / TV ; = ood / CD P MPL 3 P P P 3 ood ho ood ood ood P MPL ho ood 1 Phirt PTV PCD : = = ood / ho; = 1 ood / hirt; = ood / TV; =1 ood / CD P MPL P P P ood ho ood ood ood (d I trad wr allowd, what can you prdict about th pattrn o trad? (i.., which good th U.S. xport and which it import? Explain. I r trad wr allowd, w would prdict that th US would dinitly xport ood, and that would dinitly xport hirt, bcau ach country ha a comparativ advantag in that good a compard to any othr good. What othr good th countri xportd would dpnd on dmand and country iz. Howvr, i th US only xport two good, w know it would b ood and CD (bcau th US ha a comparativ advantag in CD, a compard to TV, hirt or ho; i th US xportd 3 good, it would b ood, CD and TV; and i th US xportd 4 good, it would b all good xcpt hirt. Similar logic appli to (by jut looking abov at what th US i not xporting. ( Lt W dnot th wag in th U.S., and W dnot th Chin wag. Show whr ach good i producd bad upon th ratio o wag ( W / W btwn th two countri. Th ratio o marginal cot or ach good look lik thi: MC MC u x x u ( W MPLx ( W MPLx MPLx = = ω u MPLx whr: ω ( WW. Thu, or all good: u u u u u MCho 4 ω MChirt ω MCTV 1 ω MC ood ω MCCD ω = ω ; ; ; ; = = ω = = ω ω ω = = = = = MC 1 3 MC 4 MC 4 4 MC 16 8 MC 1 6 ho hirt TV ood CD Good will b producd whr th cot i lowt. Thu, i th ratio o US to Chin MC i l than on or a givn good, production o that good occur in th US; i th ratio i gratr than on, production occur in and whn it qual on, production may occur in both countri. Hnc: I ω <, all good will b producd in th US and non in (thi cannot b an quilibrium; I < ω < 3 thn hirt will b producd in, all othr good in th US; I 3< ω < 4 thn ho and hirt will b producd in, th othr thr good in th US; I 4< ω < 6 thn ood and CD will b producd in th US, th othr 3 good in ; I 6< ω < 8 thn only ood will b producd in th US, th othr our good in ; I ω > 8, no good will b producd in th US (which cannot b an quilibrium bcau o unmploymnt. (Naturally, i w hav an quality, uch a ω = 3, thn on o th good (hr, ho could b producd in both countri. 7

8 ( Givn rlativ labor uppli or ach country, draw a graph to how how th quilibrium rlativ wag (US wag to Chin wag i dtrmind. Explain th graph. Th igur look omthing lik that blow. Th numbr hown on th vrtical cal rprnt th rlativ wag at which it i qually cotly to produc on o th good in both countri. At ω = 8, th cot o producing ood i th am in th US and ; vrything l i chapr to produc in. Thu, atω = 8, th (rlativ dmand or US labor i horizontal, inc th prcnt o world ood production that occur in th US could b btwn 0 and 100% at that pric. Onc th rlativ wag all blow 8, thn dinitly all ood production i in th US. A ω dcra, th rlativ cot (pric o ood production all, compard to othr good, thrby incraing dmand or ood and hnc th dmand or US labor (to produc ood thi xplain th downward loping portion o th labor dmand curv. Onc th rlativ wag rach 6, th cot o CD production ar th am in both countri, and again labor dmand i horizontal (ininitly latic ovr om rang. Onc all CD ar producd in th US, it tak urthr dclin in th rlativ wag to timulat dmand or US labor. Th rlativ dmand and rlativ upply curv jointly dtrmin th rlativ wag. Givn th initial rlativ upply o US labor, th initial quilibrium i at a point lik A. W/W * US: no good US: ood L u /L 8 6 US: CD and ood Shit du lowr Chin labor Supply 4 3 A US: TV, CD and ood E US: all xcpt hirt US: all good : no good L/L * (g U th graph to dicu how a dclin in th Chin working population (du to th on child policy will act: (1US ral wag; (th t o good th US xport; (3th rlativ pric o good; and (4Chin ral wag.. Sinc productivit ar not hiting, jut th Chin population (and work orc, what happn i hown in th am graph (abov by hiting th rlativ labor upply to th right that i, th US work orc, rlativ to th Chin work orc, incra in iz. Thi i hown by th dottd vrtical lin. Th nw quilibrium rlativ wag i hown at point E, o th US wag all rlativ to th Chin wag. Morovr, inc productiviti ar not changing w know: (1th US ral wag in trm o it original xport i unchangd but th ral wag in trm o all import all (du to th incra in th Chin rlativ wag; (th t o good th US xport incra in thi ca, it now xport TV, a wll a ood and CD; (3th rlativ pric o good xport ri that i, th rlativ pric o hirt and ho - and th rlativ pric o it import all (including TV, inc TV production 8

9 mov rom to th US; and (4inc productiviti ar unchangd, th Chin ral wag ri. That i, in trm o it currnt xport (ho, hirt, th ral wag i unchangd; but in trm o currnt import TV, CD and ood th ral wag ri. Thu, th Chin population contraction bnit but hurt th US. 3. (Spciic Factor Modl, Chaptr 3 Labor i th only mobil actor, capital (K i pciic to ctor C, land (T i pciic to ood production. Tchnology and rourc contraint ar: ( 1 1 ( ; θ( 1 ( 1 C = K Lc F = T L ; θ > 0; rourc contraint: Lc + L = L a Driv th production poibility rontir or thi conomy (that i, xpr C a a unction o F, and alo o th rourc availabl: K,T,L and θ. Bcau thr i only on variabl input, th production poibility rontir can b drivd through ubtitution: c ( 1 1 ( ( ( ( c c c ; 1 θ( 1 ( ( ( ( θ θ ( ( θ yild th pp. C = K L C = K L L = C K F = T L F = T L L = F T L + L = L C K + F T = L b U labor dmand to: ; i Givn output pric, how graphically how th quilibrium wag rat and th allocation o labor btwn th two ctor i dtrmind. T In th igur blow, L rprnt th total upply o labor; labor dmand or ctor F i maurd rom th point 0, in th uual dirction a w mov to th right, labor dmand in F i incraing. Labor dmand or ctor C ha bn lippd ovr, o th dmand or labor in ctor C i maurd rom th right vrtical lin, and a w mov to th lt, th dmand or labor in C i incraing (th arrow at th bottom o th igur alo how thi. Equilibrium occur whr th two curv intrct which i whr total labor dmand qual total labor upply; thi i point A, with quilibrium wag W, and with (0, L T unit o labor mployd in ctor F, and ( L, L unit o labor mployd in ctor C. 9

10 W B C P. MPL P c. MPL c A W H 0 L L L c L T ii Show mathmatically how th quilibrium wag rat and th upply curv or ach good (C, F i dtrmind (a a unction o output pric. Alo, dicu how th rturn to land and capital ar dtrmind. To driv th labor dmand curv, t th marginal valu product o labor qual to th wag: * C = L K P C L = P L K = W L = K P W ; ( ( ( ( ( ( c c c c c c c * θ ( ( ( ( ( ( F = θ L T P F L = P L T = W L = T θ P W Adding labor dmand and tting it qual to upply yild th quilibrium wag: 1 * * L + Lc = L T( θp W + K( Pc W = L W = ( 1 ( T L( θp + ( K L( Pc Not that: doubling pric cau wag to doubl (again, th pur inlation ct; and that doubling all input ha no ct on wag (bcau o contant rturn to cal. A or th quilibrium upply curv: Th can b ound in on o two way: (1uing labor dmand in ach ctor, i you plug that back into th production unction, and valuat at th quilibrium wag, you gt th ( gnral quilibrium upply curv; (or, you can gt th gnral quilibrium upply curv rom th production poibility rontir, by inding th point whr th lop o th rontir qual th rlativ pric ratio. You hould u both mthod to convinc yourl that thy giv th am rult. Mthod 1: PK C = L K ;L = K P W C = = ( ( ( 1 1 * c c c c c 1 W ( T L( θ P + ( K L( Pc PK 10

11 1 * θ PT θ PT 1 W ( T L( θ P + ( K L( Pc 1 ( ( ( θ F = θ L T ;L = T P W F = = Mthod : dq c = P From th pp, production occur whr (abolut valu o lop = pric ratio; that i: dq Pc From th pp: dc FK P θ CT ( C K + ( F θ T = L ( C K dc + ( F θ T df = 0 = = ρ F = ρ df θ CT P c K whr ρ rprnt th rlativ pric o ood. Subtituting back in to th pp giv th upply curv: ( ( θ ( ( ρ θ ( 1 θ ( ρ θ 4 C K + F T = L C K + C T K T = L C K + T = LK L K CT L T C = F = F = 1 1 θ ρθ ; ρ 1 1 K ( K + ρθt ( K + ρθt Now, th may not look lik th am rult a mthod 1, but thy ar. For xampl, uing th rult rom mthod 1, w hav: 1 1 PK c KL KL T K c c c C = = = 1 ( T L( θp + ( K L( P P T( θp + K( P θ ρ + Similarly, you can how th upply curv or F i th am, rgardl o th mthod ud. Svral thing to not about th upply curv: (1I both output pric doubl, thr i no chang in upply o ithr good thi i pur inlation ; (I all input doubl, th output o both good doubl (givn pric thi i contant rturn to cal; (3You hould b abl to that th upply o C incra a K incra but dcra a T incra; convrly, or F, th upply o F dcra a K incra, but incra a T incra. Thi i th ct o pciic actor. (4For th mobil actor, labor, uppli o both good incra a L incra. (5Givn output pric, an incra in productivity in ctor F (an incra in θ incra output o good F and dcra output o good C. (6And, o cour, an incra in th pric o a good incra th upply o that good and dcra th upply o th othr good. A or th rturn to land and capital: Graphically, inc you can think o landownr a conumr o labor, th rturn to landownr can b maurd by th conumr urplu ara nxt to th dmand or labor in ctor F: that i, in trm o th prviou igur, th ara o {B,W,A} would giv th total rturn to land. Similarly, th rturn to capital can b maurd by th ara nxt to th labor dmand curv in ctor C: thi would b ara {C,H,A} Mathmatically, th rturn to land (pr acr can b maurd in ithr o two way thy giv th am rult bcau o contant rturn to cal. Lt R T tand or th rturn to land. Thn: 11

12 PF WL R F T = = P T T Th irt way i th total proit, pr acr, atr paying labor cot; th cond way i th marginal valu product o land. Undr contant rturn to cal, th two maur ar idntical. Hnc: F θ P ( 1 1 RT = P = L T. T Uing th dmand or labor in ctor F, 1 * θ P T ( θ ( θ ( ( θ ( θ L = T P W R = P L T = P T P W T = Similarly, th rturn to capital ( R K i ound rom: PC c WLc C Pc R = = P = L K K K c c ( 1 1 K. From th labor dmand in C: ( ( c 1 1 P Pc W = Lc K RK = 4W Finally, uing th quilibrium wag calculatd abov, w gt th quilibrium rturn to land and capital: P θ P 1 W ( T L( θ P + ( K L( Pc θ R T = = ; 4 Pc Pc K = = 1 4W ( T L( θ P + ( K L( Pc R ; iii Uing your rult in part ii, givn output pric, how how an incra in th amount o land (T availabl or production act: (1th quantity upplid o ach good; (th ral rturn to land; (3th ral rturn to capital; and (4th ral wag rat. (1 Mathmatically, rom our arlir rult: C F 1 1 L K C L Kθ ρ = = < 0; ( K + ρθt T ( K + ρθt 1 3 T ( ( ( ( 4W ( ( + ( ρθ L T F ρθ L ρθ L T ρ θ ρθ L ρ θ T K = = = K + ρθt K + ρθt K + ρθt K + ρθt > 0 That i, an incra in th pciic actor ud to produc ood, givn output pric, lad to an incra in th output o ood and a dcra in th output o th othr good. In trm o rturn to actor, givn th output pric, w would xpct th incra in th amount o land 1

13 to rduc th rturn to land (diminihing marginal productivity, incra th dmand or labor and thu incra th wag rat, and hnc through thi indirct ct rduc th rturn on capital. Mathmatically: R R T 4 4 ( θ P L = = ( T L( θp ( K L( P 4 T L P K L P θ P R T 1 3 T + c ( ( θ + ( ( c ( Pc L( θ P P c R K K = 1 = 3 T ( T L( θp + ( K L( Pc 4 ( T L( θp + ( K L( Pc 1 ( θ P L ( 1 W W = ( T L( θ P + ( K L( Pc = > 1 T ( ( 0 4 T L θ P + ( K L( Pc P Pc Sinc RT = and R K = it i clar w jut nd to know how th wag rat chang to know 4W 4W how th rturn to th othr actor chang. iv. Givn output pric, how how an incra in productivity ( θ act output and th ral rturn to ach input. Uing th arlir rlationhip: 1 1 L K C L KTρθ C = = < 0; 1 3 K + ρθt θ K + ρθt F R R T ( ( θ ( ( ( ( ( ( + ( ρθ L T F ρθ L T ρθ L T ρ θt ρθ L T ρ θ T K = = = K + ρθt K + ρθt K + ρθt K + ρθt P θp ( T L( θp ( K L( P θ c + R T = 0 1 = > 3 θ ( T L( θp + ( K L( Pc ( T L( θp + ( K L( Pc P c R K K = 1 = 3 θ ( T L( θp + ( K L( Pc ( T L( θp + ( K L( Pc ( T L θ Pc ( P ( T L 1 ( 1 W θ P W = ( T L( θ P + ( K L( Pc = > 1 T ( ( 0 T L P + ( K L( Pc < 0 < 0 > 0 < 0 13

14 c Aum two countri, th US and Brazil, ar almot idntical. Thy dir only in that th US ha mor capital than Brazil. i Bad upon your rult rom part (b, what prdiction would you mak concrning th autarky (no trad rlativ pric o ood in th Brazil a compard to th US? By analogy to th xrci abov, givn output pric, an incra in a pciic actor incra output o th good that u that pciic actor and rduc output o th good (givn output pric; thu, an incra in th amount o capital, givn output pric, incra th upply o clothing and dcra th upply o ood; alo, givn output pric, th incra in capital incra th wag rat, and dcra th rturn on land and capital. Now, th gratr availability o capital and incrad upply o clothing will lad clothing pric to all (ood pric to ri in th US, a compard to Brazil. A clothing pric all (ood pric ri, th rturn on capital dcra, th rturn on land incra, and th ral wag in trm o clothing ri, but th ral wag in trm o ood all. So, in comparing th US to Brazil, th rlativ pric o ood will b highr in th US; th ral rturn on capital will b lowr in th US, both bcau o th abundanc o capital and bcau thi abundanc lad to a dcra in th rlativ pric o clothing. Th ral wag in trm o clothing will b highr in th US but w cannot ay or ur about th ral wag in trm o ood (inc mor capital incra th wag, but highr ood pric rduc th ral wag in trm o ood, lading to an ambiguou impact. Similarly, inc th gratr availability o capital dpr th rturn on land (du to highr wag BUT th highr pric o ood rai th rturn to land, w cannot b ur how th rturn on land compar btwn th two countri. ii I trad i allowd btwn th two countri, what will th pattrn o trad b and how will th rlativ pric o clothing chang in ach country? I trad i allowd btwn th US and Brazil, clarly th US will xport clothing and Brazil will xport ood. Hnc, trad cau th rlativ pric o clothing to ri in th US and to all in Brazil (th oppoit or th rlativ pric o ood. iii How do trad act th ral rturn to ach actor in ach country? Do th country a a whol potntially gain rom trad? In th US, th incrad rlativ pric o clothing: rai th ral rturn to capital, lowr th ral rturn to land and ha an ambiguou act on wag: th ral rturn to labor ri in trm o ood but all in trm o clothing. Thu, du to trad, land ownr lo, capitalit gain, and th impact on workr i ambiguou. In Brazil, th oppoit happn. Th incrad rlativ pric o ood (dcrad rlativ pric o clothing rai th ral rturn to land, lowr th ral rturn to capital, and ha an ambiguou impact on th ral wag. Th ral wag in trm o ood all, th ral wag in trm o clothing ri. Both countri potntially gain rom trad in that it i poibl or th winnr in ach country to compnat th lor in that country and hav vrybody bttr o than without trad. But i th compnation do not tak plac, thr will b oppoition to trad. 14