Fall 0 Eon 455 Answers - Proble Set 3 Due Noveber 4, 0 Harvey Lapan. Consder a splfed verson of the Heksher-Ohln odel wth the followng tehnology: To produe loth (C): unts of labor and unts of aptal are requred for eah unt of C. To produe anufatures (M): unts of labor and 4 unts of aptal are requred for eah unt of M. a) Fnd produton osts and output pre n ters of fator pres. Let be the wage rate and R the rental rate on aptal. The hnt gves the answer for anufatures; jt apply the sae reasonng to loth. ( ) = ( + 4 ) ( ) = ( + 4 ); Pr = = ( + 4 ) TC M Q R MC M R e MC P R ( ) = ( + ) ( ) = ( + ); Pr = = ( + ) TC loth Q R MC loth R e MC P R. Fnd fator pres n ters of output pre. Show how an nrease n P affets,r. = + = +. Ths s lke two lnear equatons n two unknowns; one an nvert ths relatonshp and solve for R: P P = + R R = ; substtute ths n the relatonshp for anufatures: P P P P = ( + 4R) = + 4 = ( P ) or = P P P P P P Use the soluton for to solve for R: R = = =. Suarzng: P P P P = ; R = and for both goods to be produed P > P > P How does an nrease n P affet fator pres? Fro above: P ( R) ; P ( 4R) P P = > 0; P P = > ; P P R P = < 0 Th an nrease n the pre of loth lowers the return to aptal and rases the wage rate (sne loth s labor-ntensve and anufatures are aptal-ntensve). Moreover, the wage rate rses by ore (n % ters) than does the pre of loth so the real wage nreases n ters of ether M or loth. b) Fnd the produton possblty fronter (ppf). Let Q, Q denote the outputs of good C and M, respetvely. The resoure onstrants are: Q + Q L sne the tehnology ples: L = Q and L = Q Labor: () f Captal: () Q + 4Q K sne the tehnology ples: K = Q and K = 4Q
The followng fgure shows the produton possblty fronter for ths eonoy; the ponts on, or below, the lne labeled labor onstrant nsure that labor eployed s no larger than avalable labor (wth full eployent on that lne), whle the lne labeled aptal onstrant has the sae nterpretaton. For ths splfed eonoy, the only output level where both nputs are fully eployed s where the two lnes nterset, at pont V, where output s: L K K L Q = ; Q = M Output L/ Labor onstrant Z K/4 New aptal onstrant V Captal onstrant 0 L/ K/ Clothng The feasble produton set s the regon bounded by: {0,(K/4),V,(L/)}, and the produton possblty fronter s the lne segents desrbed by: {(K/4),V,(L/)}. ()Show how an nrease n the supply of aptal shfts the ppf. An nrease n aptal shfts the aptal onstrant outward, as shown by the dotted lne n the fgure. The pont Z represents the new output level where both fators are fully eployed (n ths sple verson, there s a unque produton pont that represents full eployent of both nputs). Note that an nrease n K leads to an nrease n output of the aptal ntensve good (M) and a derease n output of the labor ntensve good as desrbed n lass and n the text. ) Assung the US s aptal abundant and Chna s labor abundant (but they have dental tastes and tehnology), opare autarky pres, then fnd the pattern of trade and dss ts onsequenes. As shown above, gven pres, an nrease n the supply of labor (n Chna) nreases output of the labor ntensve good (C) and dereases output of the aptal ntensve good (M). At gven pres, ths wll
reate an exess supply of good C and an exess deand for good M. Hene, as the supply of labor nreases wthn an eonoy, the equlbru pre of the labor-ntensve good (loth) dereases. Slarly, an nrease n the supply of aptal (US) aes the equlbru autarky relatve pre of the labor ntensve good (loth) to rse. Hene, the autarky relatve pre of good C wll be hgher n the US than n Chna. Ths, fro part (a) ples that the wage rate wll be hgher n the US and the return on aptal wll be hgher n Chna (.e., hna P P hna hna n autarky > > and R < R P P Th, wth trade, the US wll export M (the aptal-ntensve good) and port C (the labor-ntensve P P falls n the US and nreases n Chna. good). As a result of trade, ( ) But, fro (a), ths ples that the wage rate falls n the US and rses n Chna, whle the return on aptal (R) rses n the US and falls n Chna. Fnally, f free trade equalzes oodty pres and both goods are produed n both ountres, t t equalze fator pres (see equatons deternng fator pres n (a)), provded tehnology s the sae n the two ountres. Ths s the fator pre equalzaton theore. d) Modfy the above odel by assung US produtvty n both setors double, whle Chnese tehnology reans unhanged. In the US: Cloth requres: unts of labor and unt of aptal are requred for eah unt of loth. Manufatures requres: unt of labor and unts of aptal are requred for eah unt of M. ) Show how ths doublng of produtvty n the US affets ts autarky output pres and fator pres. In Rardan ters, whle the US has an absolute advantage (tehnologally) n both goods, there s no oparatve advantage due to tehnology. To see ths spefally, we an re-derve the produton possblty fronter for the US: Labor: (a) Q + Q L sne the tehnology ples: L = Q and L = Q Captal: (a) Q + Q K sne the tehnology ples: K = Q and K = Q Ths yelds the full eployent pont of: Q = ( L K ); Qf = ( K L) Th, at full eployent, output of both goods double and th the relatve supply s unhanged. Hene, f deand for both goods also doubles (beae noe doubles) so that relatve deand s unhanged, the doublng of produtvty n both setors wll not affet autarky relatve goods pres and hene wll not affet the pattern of trade between the US and Chna. Turnng to nput pres, ng the log of part (a) of the answer, for the US we have: P = MC = + R; P = MC = + R; solvng for nput pres (n the US) n ters of output pres we have: = P P ; R = P P, whereas for Chna (fro part a): ( ) ( ) 3
hna P P hna P P = ; R = Th, we see that gven output pres the doublng of produtvty n both setors n the US leads to a doublng of the real return to both fators. ) ll free trade equalze fators pres and reove the pressure for fator graton? Sne the doublng of produtvty n both setors n the US leaves relatve autarky pres unhanged, t follows that the pattern of trade s stll deterned by fator endowents so the US wll export M and Chna loth. Trade stll lowers the real return to labor (rases the real return to aptal) n the US sne t lowers the pre of the labor-ntensve good, whereas the opposte happens n Chna. However, trade wll not lead to fator pre equalzaton beae tehnologes are dfferent. As the above exaple shows, f trade equalzes goods pres and both goods are produed n both ountres, then the real return to both fators wll be twe as hgh n the US as n Chna. Th, there wll stll be pressure for fator oveents.. (Fator oveents) There s a sngle good (e.g., food), produed ng land and labor. The aount of land n a ountry s fxed; labor ay be oble aross ountres. US and Mexan tehnology and resoures are: US: ( ) ( ) Mexo: ( ) ( ) Q = 40 T L ; T = 5; L = 00 Q = 30 T L ; T = 00; L = 00 a) For eah ountry, fnd and sketh the labor deand urve. Also, alulate the equlbru wage, return on land and per apta noe n eah ountry (all easured n ters of output). deand Q 40 T 0P US : MPLabor = ( T ) ( L ) P 0 = = ( L ) = T L L PQ L Q US land rent: 0( ) ( ) R= = L T = P T T Sne there s only one good, you an set P =, sne GNP, wages and rental rates are all easured n ters of ths good. Evaluatng at T = 5, L = 00 : 5 5 = 0 = 0 = 30 00 0 ; Slarly for Mexo: R 00 00 40 = 0 = = 5 5 3 Q T T deand 5 Mexo : 5 5 = = ( L ) = T L L L 4
Q L Mexan land rent: R = = 5 T T Evaluatng at T = 00, L = 00 : 00 = 5 = 5 ; 00 R 00 = 5 = 5 00 Below you see the labor deand urve for the US, and how graton shfts the doest labor supply. The labor deand urve for Mexo looks slarly; though egraton fro Mexo (to the US) would redue the labor supply n Mexo. (w/p) A L s L d L s +I (w/p) e (w/p) E G L age Deternaton The returns to land an be easured, n ths dagra, as the onsuer surpl sne we an thnk of landowners as rentng labor, and hene a lower labor pre benefts landowners. In the dagra land rents, at the ntal wage, would be gven by {A,E,(w/P) e }; f wages fall, as shown, land rents nrease by the area {(w/p) e,e,g,(w/p) } b) Assue the U.S. allows soe Mexan workers to enter the U.S., but the nuber s lted by the nuber of vsas ssued (V). The atual nuber of guest workers has to be no larger than ths ( I V). Sne only wages deterne where people work, the atual nuber of guest workers (or grants) wll equal the nuber of vsas, as long as U.S. wages are at least as hgh as Mexan wages. For future purposes, let L = L + I = 00 + I where L s the nuber of people workng n the U.S. and I are guest workers. Slarly, for Mexo L = L I = 00 I 5
. Frst onsder what would happen f there were no restrtons on labor oveents; wages T T would be equalzed so: = 0 ; 5 = L I L I + L L s the populaton, and ( ) ( ) here, L + I, L I are the nuber of workers. Settng wages n the two ountres equal to eah other, and ng the values for aptal, we have T T 0 T T = 0 5 = = L + I L I 5 L + I L I 6 5 00 * 4( L I) ( L I) 5I 4L L 300; I 60 = = + = = = 9 L + I L I So, f V < 60 wages wll not be equalzed and the vsa lt wll be bndng. Th, for V < 60, I = V and we have = 0 ; = 0 > 0 > L V T + V V T L + V R R Slarly for Mexo, 5 T ; R 5 L V R = 0 = < < L V T V V In the US, US workers lose, landownders gan; the opposte happens n Mexo. As for world output: ( ) ( ) ( ) ( ) world Q = Q + Q = 40 T L + V + 30 T L V world Q Q Q T T = = 0 5 V L L L + V L V 5 00 = 0 5 > 0 for V < 60 00 + V 00 V As long as the argnal produt of labor s hgher n the US than n Mexo, the nflow of workers to the US wll rase world output.. As explaned above, f V > 60, sne t only takes 60 workers to equalze wages between the two ountres, then not all the vsas wll be ed. So, a suffently hgh vsa quota s slar to havng no restrtons at all. 6
. Calulate how US and Mexan noe hange as V nreases (the output hange was done above). Fro the defnton of noe n the proble set: T Y = Q V = 40( T ) ( L + V) V = 40( T ) ( L + V) 0 V ( L + V) T = 0 + = 0 + + ( L + V) { ( L V) V} ( T ) ( L V) ( L V) Hene: 3 ( L V) ( L V dy + + ) 3 = 0( T ) + ( L + V) = 0( T ) ( L + V) V > 0 dv Another atheatal way to see the sae thng s: Y Q L Y = Q V = V = V > 0; = sne V L L L V Q = and < 0. Th, as ore workers enter, they fore down the U.S. wage L L whh eans what eployers pay grant workers goes down. In ths ase the U.S. t gan fro unrestrted graton. For Mexo, the stuaton s ore oplated. The Mexan worker earns ore n the U.S., but as ore Mexans work n the U.S. t drves down the wages those workers earn. Hene, Mexo wll n ths stuaton gan by ltng outgraton to the U.S. Forally: ( ) ( ) Y Q Y = Q + V = + + V = + V < V L L L sne, for Mexo, L V ( L V) = 00, =. Sne ( L ) < 0, Mexo s largest gan ours when there s stll a wage gap between the ountres. If you substtute n the atual funtonal fors: ( 5) ( + ) 5 00 = 0 5 + V 0 < 0 at V = 60 3 00 + V 00 V 00 V ( T ) ( ) Y T T == ( ) + V = 0 5 V 0 + 3 V L L + V L V L + V So Mexo would beneft by ltng graton gven that the grants reeve the U.S. 7
wage. If the grant workers have to buy the vsas, or are pad the Mexan wage, then the stuaton s reversed and the U.S. would have the nentve to lt (but not elnate) nflows. As shown already world output would nrease untl argnal produts are equalzed. v. Now, f the vsas are autoned, the equlbru pre (value of the vsa) s the wage gap: P P= ( ); = + < 0. V L L Not surprsngly, the ore vsas sold, the lower ther value. Furtherore, Y Q L Y = Q V + PV = Q V; = V V L L V = + V < ( ) L Y Q L ex Y = Q + I PI = Q + V; = + + V V L L V = ( ) + V > 0 L The Mexan wage rses as V nreases sne there are fewer workers left n Mexo. Hene, n ths ase, Mexo gans as V nreases whle the U.S. gans fro soe graton but unrestrted graton wll not axze the U.S. gan. orld output always nreases untl wages are equalzed, but whether both ountres prefer lted or unrestrted graton depends on how ths nreased output s splt between the ountres. v. As dssed above, whether unrestrted graton s optal for the U.S. depends on the net wages reeved by the guest workers. If they reeve the U.S. wage and do not have to pay for vsas, then unrestrted graton s best. If they reeve the Mexan wage or have to buy the vsa, then t pays to lt graton. Ths latter arguent s uh lke a onopoly arguent for ltng output. ) If guest workers pay taxes n the U.S. but not n Mexo, and f there are no lts on graton fro Mexo to the U.S., then the equlbru ondton for Mexan graton looks lke: ( ) ( Tax) =. In ths expresson, thnk of as representng the annual noe of workers n eah ountry (for the sae nuber of hours of work) and Tax as the annual tax pad by guest workers. Now, n equlbru, the U.S. wage wll be hgher than the Mexan wage, whh eans U.S. labor produtvty wll exeed Mexan labor produtvty, whh eans that world output s not axzed. orld output ould be nreased by larger graton fro Mexo to the U.S. 8
3. (Chapter 8, Trade Poly) Consder a sall ountry (Naragua) wth the followng deand and supply urves for sugar: Supply = 0P s ; Deand = 80 P s Naragua an export (or port) sugar at a gven world pre of: P s = 40. Naragua has an export tarff of t per unt exports. b) The autarky pre n Narague s found fro: X = S D= P 80 = 0 P = 5. So: w aut If t P P = 40 5 = 5 Exports= 0; Qs = Ds = 50, Ps = 5 If the tarff s less than 5, then trade wll our: w ( ) ( ) ( ) t < 5; P = P t = 40 t Q= 400 0 t; D= 80 40 t = 00 + t; X = Q D= 300 t s s s So, as t nreases, doest pre falls, produton falls, onsupton nreases and exports fall. To alulate the hange n surples, t helps to e a graph: P 40 A C K G S 40-t 5 B H 00 00+t 400-0t 400 D Q The hange n PS s area {40,G,H,40-t}; The hange n CS s area {40,B,A,40} Tax revenue s areas {C,K,H,B}. Hene Δ PS = ( ) t ( 400 + 400 0t ) = 400t + 5 t ; Δ CS = ( ) t ( 00 + 00 + t ) = 00t + t TR = tx = t ( 300 t ) = 300t t s tarff revenue. Produer surpl dereases wth the tarff (only t<5 s relevant), onsuer surpl nreases, whereas tarff revenue nreases wth the tarff for t <.5, and then dereases thereafter. Overall: Δ elfare = TR +Δ PS +Δ CS = 6t so that the tarff lowers overall welfare. 9
()If t>5, the tarff s prohbtve, no trade ours and doest pre s 5. b) Copare the doest equlbru when t=5 to the ase where there s no tarff, but there s an export quota of 0 unts. Fro part (a), wth t=5, exports M = 300 t = 0. Th, an export quota of 0 and a tarff of 5 have dental effets on doest pre, onsupton, produton and exports; and hene they have dental effets on onsuer and produer surpl. The only possble dfferene s the tarff revenue (whh s 800 under the tarff); under the quota, exporters ake 5 on eah unt exported and hene wll earn exess profts of 800, unless the quota lenses are autoned off, n whh ase the two poles are dental. If the quotas are gven to foregn porters, then the revenue fro the tarff s lost to the ountry, and so the quota, n that ase, would be nferor to the tarff for the exportng ountry. ) Suppose the governent subsdzes exports at a rate of s per unt of export. Show how ths export subsdy affets Naragua (see Fgure below): ()doest pre doest pre for both onsuers and produers nreases to {40+s} ()Consuer surpl dereases - due to the hgher pre - by area next to deand urve between two s pres area {40,A,B,(40+s)} n fgure; hene: Δ CS = { 80 + 80 s} = { 80s + s } ()Produer surpl nreases due to the hgher pre, by the area next to supply between two pres s area {40,G,H,(40+s)}. Hene: Δ PS = { 400 + 400 + 0s} = { 400s + 5s } (v)governent expendtures: Exports are: S D= 30 + s s 30 + s = 30s+ s Hene: Cost to governent = ( ) ( ) (v)ipat overall welfare: Δ CS +ΔPS Governent Expendtures = < 6s 0, s 0 P Deand 40+s B H S 40 C A G J D Q 80-s 80 400 400+0s The deadweght loss s area ABC and area JGH. 0
. No export quota an fore exports to nrease over the free trade level so there s no quanttatve poly that has the sae pat as an export subsdy. d) If the goal s to derease sugar onsupton, an export subsdy aoplshes ths by rasng doest pre; but the export subsdy also aes doest produton to nrease. th a onsupton tax of 5, there s no hange n produer surpl opared to free trade, whereas the hange n onsuer surpl s the sae as wth an export subsdy of 5. Th, the welfare onsequenes of a onsupton tax of 5 s: Δ PS = 0 ; Δ CS = 80s + s = 00 + 5 = 975 Tax Revenue = 5 ( 50) = 750 elfare Loss = -5; ths s area of trangle ABC. (e part a, when s=5, to get the hange n onsuer surpl and onsupton level). For the export subsdy, fro part a, wth s=5, we have elfare Loss wth export subsdy = 6s = 350 Th, the onsupton tax whh results n the sae level of doest onsupton as the export subsdy has a lower welfare ost beae we do not have the loss assoated wth produng ore expensve sugar and sellng t abroad at a pre that s less than atual produton osts. AND, of ourse, f the dereased sugar onsupton lowers dabetes, and redues health are osts, there s a postve beneft to offset the welfare loss (but ths beneft s the sae wth the export subsdy and the onsupton tax f t s due to redued onsupton). 4. (No ponts prate for those nterested) (More sophstated verson of H-O odel). There are two goods (C and M) and two nputs (K and L). The produton funtons are: 3 3 3 3 = = Q K L ; Q K L where { K,L } are the nputs (aptal, labor) ed n setor C and { } K,L are the nputs ed n setor M. Let denote the wage rate (pre of L) and R the rental rate (ost of ng K, aptal). Fnally, let P,P denote the output pres of goods C and M, respetvely. (a) There are two ways to derve the ost funton one by substtuton, and one by ng non-lnear prograng (whh nvolves ng the Lagrangan funton). By substtuton: Q K β L α =. Solvng for labor yelds: L ( QK ) ( Q ) ( K ) Let β α α β α α β α Total osts are: TC L RK RK ( Q ) ( K ) = =. = + = + () Equaton () expresses total osts as a funton of fator pres, output and aptal nputs. Cost nzaton eans hoose the aptal nput that nzes ths expresson. Th: ( ) d TC dk β α R ( Q ) ( K ) ( β α = ) = α 0 () sne: ( ) d K dk θ = θ ( K ) θ A suffent ondton for an nteror nu s that the frst dervatve of the funton be zero and that
the seond dervatve be postve; t s readly seen that the seond dervatve s postve. Solvng () for K yelds: α ( α+ β) α ( α + β ) β (3) * β α K = ( Q) = Q α R αr where * K denotes the soluton. Substtutng bak for L yelds: β * α R L = Q β ( α+ β) (4) Note that the hoe of nputs depends on relatve fator pres, not absolute fator pres. Also, note that when ( α + β) =, the nput e s proportonal to output. Fnally, substtutng bak nto the ost funton () yelds nu osts: α β ( ) ( ) ( + λ ),, = + = where: λ = * * * C Q R L RK R Q α β ( α + β) β α ( ) ( α + β α β ) (you need to substtute and then splfy the expresson; t s a bt tedo, but you should get the result above): Ths result an be heked beae the dervatve of the ost funton wth respet to nput pre should gve you bak the optal nput e. Hene: ( ) * α α + β dc β ( α + β) ( ) ( ) ( ) α α+ β α α+ β α+ β β = R Q Q α β dr ( α β) β α + = + β α αr whh s ( ) ( ) * K. Slarly, dfferentatng wth respet to gves you ( α β) * L : ( α + β ) * β dc α + β ( α+ β) β ( α+ β) ( α+ β) αr = ( ) ( ) ( ) R Q = Q α β d α β β α + + β α β Use of the Lagrangean funton gves the sae results, of ourse. Brefly, the Lagrangean s: ( α β ) Η L + RK + θ Q L K where θ s the Lagrangean ultpler. Partally dfferentatng yelds, for an nteror soluton: Η = R β α θβ K L = 0 K Η = β α θα K L = 0 L (a) (a)
Η = = θ ( Q L α K β ) 0 (3a) Takng the rato of (a) to (a) yelds: β L R L α R αk K = = β (4a) Hene, the labor ntensty depends on fator pres and n ters of the orgnal produton funton s nreasng n the paraeter on L and dereasng n the paraeter on K. Usng (4a) to solve for L n ters of K, and then substtutng ths nto (3a) yelds the optu aptal nput, whh wll be the sae as above. Then, ng ths soluton for aptal, the soluton for labor s found fro (4a), and the ost urve by pluggng bak nto the objetve funton. You do not need to solve for θ, but f you do you get the followng fro (a) ( K ) ( L ) β α * R R θ = α = α β β α β β ( α+ β) ( ) ( ) ( α β Q ) + (5a) Lookng bak at the ost funton derved above and oparng to (5a), we see that (5a) represents the argnal ost funton. Ths s no ondene; the Lagrangean ultpler n ths proble wll always yeld the argnal ost funton. Fnally, for the spef funtons gven: 3 3 * 3 3 Q = K L α =, β =,( α + β) = so: TC ( Q,, R) = λ R Q 3 3 3 3 * 3 3 Q = K L α =, β =,( α + β) = so: TC ( Q,, R) = λ R Q 3 3 where: 3 λ = = ( 3) ( 3) ( 3) ( 3) ( 3) Clearly, good C s labor ntensve and M s aptal ntensve as we have fro (4a) above: L α R K ω K = = ; = ω K β L L where: ω = R (b) Gven output pres, show how an nrease n the avalable supply of labor hanges output. Fro the ost urves above we have: 3
= λ = and 3 3 MC R P 3 3 MC λ R P = = (b) e an e these two equatons to solve for fator pres n ters of output pre. Takng the rato of argnal osts and settng ths equal to the pre rato (relatve pres) yelds: 3 3 3 MC λ R P 3 3 MC λ R R P = = = ω 3 = ρ where: ρ ; P = ω = (b) P R Pluggng ths bak nto (b) and solvng gves the level of fator pres: P R = λp P = (3b) λp Fro (3) and (4) n part (a) you have the optal aount of nputs n eah setor: ( α+ β) α 3 * β * ω * 3 = = ; = ( ω ) K Q K Q K Q α R ( α+ β) β 3 3 * α R * * = =, = L Q L Q L Q β ω ω (4b) (5b) You an express these nput deands n ters of output pre by substtutng for ( ) Dong so and wrtng the resoure onstrants yelds: L + L = L ρ Q + ρ Q = L (6b) 3 3 f P ω n ters of. P K + K = K ρq + ρ Q = K (7b) 3 3 f Gven pres, equatons (6b) and (7b) are jt lke proble # (.e., the labor and aptal e per unt output are fxed) and an be solved for output levels. Dong so yelds: 3 3 ( 3)( ρ ρ ); ( 3)( ρ ρ ) Q = L K Q = K L Th, gven pres, an nrease n K wll nrease the output of good F, the aptal ntensve good, and derease the output of good C. Also, note that f output pres do not hange, nput pres do not hange sne, fro equaton (3b) above, fator pres an be deterned n ters of only output pres. Th, gven pres, an nrease n L aes the supply of good M to derease and that of good C to nrease (note f both L and K double, output of eah good doubles so the rato of outputs only depends on (K/L)). But total noe nreases as L nreases, so deand for both goods nreases. Hene, to restore equlbru, the pre of good M t nrease (relatve pre of C dereases). Th, the autarky (relatve) pre of good C (the labor ntensve good) s an nreasng funton of the ountry s relatve aptal abundane. Consequently, gven the sae deands and tehnology, the labor abundant ountry 4
wll export the labor ntensve good (C) and port the aptal-ntensve good (M). Further, sne the wage rate dereases, and the rental rate nreases, as the pre of good C falls (.e., the relatve pre of good M nreases), ths eans that the autarky wage rate wll be lower, and the autarky rental rate on aptal hgher, n the labor abundant ountry. Hene, dfferenes n fator supples lead to dfferenes n autarky output pres, whh lead to the dfferenes n nput pres one would expet.. As dssed above, gven output pres, nput pres are deterned and hene hanges f fator supples wll not hange fator pres. () To show how fator pres hange wth output pres, look bak at equaton (3b). P R = λp P = λp P R P R P R P R = = = > λp P λp P R ; = < 0 ; P λp P P P P = =, 0 λp P λp P = > = < P λp These results ply that an nrease n P, the aptal ntensve good, lowers the real return to labor and rases the real return to aptal n ters of ether good (a % nrease n P, nreases the rental rate R by %, and hene ( R P ) nreases as P nreases). Slarly, an nrease n the pre of the labor ntensve good (C) lowers the real return to aptal and rases the real return to labor n ters of ether good. The results show that, as P nreases, nreases proportonately ore than nreases wth P ). Ths s the Stolper-Sauelson result. P (.e., ( P ) (d) Fro part (), t s apparent that the pat of trade on the dstrbuton of noe depends upon how trade affets the relatve pres of goods. If a ountry exports good M (a aptal abundant ountry), then trade aes the relatve pre of M to nrease, and th trade nreases the real return to aptal and lowers the real return to labor. If a ountry exports good C (a labor abundant ountry, suh as Chna), then trades rases the relatve pre of good C, and hene trade nreases the real return to labor and lowers the real return to aptal. Fro part (b), assung ountres have dental tehnologes and tastes, then the autarky relatve pre of good C wll be hgher n the aptal-abundant ountry (equvalently, the autarky relatve pre of good C wll be lower n the labor-abundant ountry). Th, fro part (b), we predt that the aptalabundant ountry (the ountry wth ore aptal per worker, suh as the US) wll export good M and port good C, and that the labor-abundant ountry (the one wth less aptal per worker, suh as Chna) 5
wll export C and port M. Not everybody gans fro trade and hene there wll be groups opposng trade lberalzaton. Fnally, note that free trade assung tehnology s the sae throughout the world - wll lead to equal post-trade fator pres aross the world (.e., the wage rate wll be equalzed between the aptalabundant and labor-abundant ountres, and the sae for the return on labor) provded that ()free trade equalzes the pres of goods.e., gnore transportaton osts and tarffs; and ()both goods are produed n both ountres. (e) If the U.S. s aptal-abundant and the Heksher-Ohln odel an be appled to the world eonoy, the U.S. wll export the aptal-ntensve good (M) and port the labor-ntensve good (C). Trade restrtons (tarffs or quotas) wll rase the doest pre of the port good (C) and th wll nrease the real return to labor and derease the real return to aptal. Hene, we would predt that groups representng labor (Unons, for exaple) would oppose free trade and groups representng aptalsts would favor free trade. Ths s a reasonably aurate desrpton of atual poltal postons (though the realty s a bt ore oplated, of ourse). 6