Fall 2008 Eon 455 Ansers - Problem Set 3 Harvey Lapan 1. Consider a simpliied version o the Heksher-Ohlin model ith the olloing tehnology: To produe loth: three units o labor and one unit o land are required per unit output o loth. To produe ood: one unit o labor and three units o land are required or eah unit o ood. a) Find the prodution possibility rontier (pp). Let Q, Q denote the outputs o good C and F, respetively. The resoure onstraints are: Labor: (1) 3Q + Q L sine the tehnology implies: L = 3Q and L = Q Land: (2) Q + 3Q T sine the tehnology implies: T = Q and T = 3Q The olloing igure shos the prodution possibility rontier or this eonomy; the points on, or belo, the line labeled labor onstraint insure that labor employed is no larger than available labor (ith ull employment on that line), hile the line labeled land onstraint has the same interpretation. For this simpliied eonomy, the only output level here both inputs are ully employed is here the to lines interset, at point V, here output is: 3L T 3T L Q = ; Q = 8 8 Food Output L Labor onstraint W T/3 V Ne land onstraint Land onstraint 0 L/3 T Clothing The easible prodution set is the region bounded by: {0,(T/3),V,(L/3)}, and the prodution possibility rontier is the line segments desribed by: {(T/3),V,(L/3)}. 1
(i)sho ho an inrease in the supply o land shits the pp. An inrease in land shits the land onstraint outard, as shon by the dotted line in the igure. The point W represents the ne output level here both ators are ully employed (in this simple version, there is a unique prodution point that represents ull employment o both inputs). Note that an inrease in T leads to an inrease in output o the land intensive good (F) and a derease in output o the labor intensive good as desribed in lass and in the text. b) Find input pries { W,R } in terms o output pries, assuming both goods are produed and both ators ully ed. Using the tehnology, sine eah unit o C requires 3 units o labor and 1 unit o land, osts are: MC = 3W + R. Similarly, or good F, hih es 3 units o land and 1 unit o labor: MC = 3R+ W. I goods are produed, prie mt equal marginal ost; th: P = 3W + R; P = 3R+ W. Solving or R, W in terms o output pries yields: 3P P 3P P W = ; R= 8 8 (i) Note that an inrease in the prie o good C (the labor intensive good) leads to a derease in the real return on land (i.e., ( R P ) dereases as P inreases, and hene ( R P ) mt also derease) and an W P inrease; this is hy trade, in this model, inrease in the real age i.e., both ( ) W P and ( ) beneits the oners o one ator and hurts the oners o the other ator Similarly, an inrease in ould ae ( R P), i =, to inrease and ( W P), i =, to derease). i i P ) Assuming the US is land abundant and Mexio is labor abundant (but they have idential tastes and tehnology), ind the pattern o trade and diss its onsequenes. As shon above, given pries, an inrease in the supply o land inreases output o the land intensive good (F) and dereases output o the labor intensive good (C). At given pries, this ill reate an exess supply o good F and an exess demand or good C. Hene, as the stok o land inreases ithin an eonomy, the equilibrium prie o the labor-intensive good inreases. Th, the autarky relative prie o good C ill be higher in the US than in Mexio. This, rom the previo part, implies that the age rate ill be higher in the US and the return on land ill be higher in P P Mexio (i.e., in autarky > W > W and R < R P P Th, ith trade, the US ill export F (the land-intensive good) and import C (the labor-intensive good). P P alls in the US and inreases in Mexio. As a result o trade, ( ) But, rom (b), this implies that the age rate alls in the US and rises in Mexio, hile the return on land (R) rises in the US and alls in Mexio. 2
Finally, i ree trade equalizes ommodity pries and both goods are produed in both ountries, it mt equalize ator pries (see equations determining ator pries in (b)), provided tehnology is the same in the to ountries. This is the ator prie equalization theorem. d) Modiy the above model by assuming US produtivity in both setors double: Cloth requires: 1.5 units o labor and 0.5 units o land are required or eah unit o loth. Food requires: 0.5 units o labor and 1.5 units o land are required or eah unit o ood. i) Sho ho this doubling o produtivity in the US aets its autarky output pries and ator pries. In Riardian terms, hile the US has an absolute advantage (tehnologially) in both goods, there is no omparative advantage due to tehnology. To see this speiially, e an re-derive the prodution possibility rontier or the US: Labor: (1a)( 3 2) ( 2) Land: (2a)( 2) ( 3 2) Q Q L + sine the tehnology implies: L ( 3Q 2) + sine the tehnology implies: T ( Q 2) = and L = ( Q 2) = and T = ( 3Q 2) Q Q T 3L T 3T L This yields the ull employment point o: Q = ; Q = 4 4 Th, at ull employment, output o both goods double and th the relative supply is unhanged. Hene, i demand or both goods also doubles (beae inome doubles) so that relative demand is unhanged, the doubling o produtivity in both setors ill not aet autarky relative goods pries and hene ill not aet the pattern o trade beteen the US and Mexio. Turning to input pries, ing the logi o part (b) o the anser, or the US e have: ( 3 2) ( 2 ); ( 2) ( 3 2) P = MC = W + R P = MC = W + R ; solving or input pries (in the US) in terms o output pries e have: 3P P 3P ; P W = R =, hereas or Mexio (rom part b): 4 4 3P P 3P ; P W = R = 8 8 Th, e see that given output pries the doubling o produtivity in both setors in the US leads to a doubling o the real return to both ators. ii) Under ree trade beteen the US and Mexio, ind: (i)the pattern o trade and (ii)ho trade aets ator pries in eah ountry. Sine the doubling o produtivity in both setors in the US leaves relative autarky pries unhanged, it ollos that the pattern o trade is still determined by ator endoments so the US ill export ood and Mexio loth. Trade still loers the real return to labor (raises the real return to land) in the US sine it loers the prie o the labor-intensive good, hereas the opposite happens in Mexio. Hoever, trade ill not lead to ator prie equalization beae 3
tehnologies are dierent. As the above example shos, the real return to both ators ill be tie as high in the US as in Mexio. 2. Consider the standard trade model ith to goods (C, F) and to ountries (US, Japan). Assume in autarky the US has the loer relative prie o good F. a) State the pattern o trade and sho that both ountries gain. Sine the autarky relative prie o good F is loer in the US, under ree trade the US ill export ood and import lothing. The demonstration that both ountries gain rom trade is shon in the piture belo (hih shos the impat rom the US perspetive) C U2 T R U1 V A U2 U1 M Q R T B F The point M represents the autarky prodution and onsumption point or the US. The dashed line, hih represents the orld prie under trade, shos that the orld relative prie o F is higher than the autarky relative prie o F. As a result, US prodution moves to Q (more F produed, less C) and onsumption ours somehere along the dotted line (TQT) hih represents balane o trade equilibrium. Sine it is possible to onsume more o all goods than in autarky (point M), the ountry mt be potentially better o (though not everybody in the ountry mt gain). The main point is that by alloing the ountry to trade at a dierent prie than the autarky prie, the hange in prodution makes onsumption points available to it that dominate the autarky onsumption point. The demonstration that orld output o both goods an inrease is as ollos. In autarky: US US J J dq P P dq = < = hih means that the opportunity ost o produing ood is dq P P dq loer in the US in autarky. Th, by having the US produe more ood (less lothing) and Japan 4
more lothing (less ood) it is possible to inrease orld output o both goods. This rationale is jt the same as or the Riardian model, exept beae prodution osts ere onstant in the Riardian model, the logi implies that in the Riardian model at least one ountry ill speialize. b) Suppose that, in eah ountry, prodution o lothing aes pollution hih damages only loal itizens. I there is no government poliy, this means that in autarky good C is overprodued and its prie is loer than it should be (i eiieny prevailed). This is beae irms do not aount or the pollution osts they impose on others, but they should. Hene, the ountry that imports C (the US) gains rom trade or to reasons the ual reason or gains rom trade PLUS the at that trade loers domesti pollution (as output o C alls). On the other hand, the ountry that exports C (Japan) ould gain or lose rom trade. The trade given pollution beneits Japan or the ual reason. Hoever, beae trade aes output o good C to inrease, and beae it as overprodued in autarky, Japan ould lose (rom the higher pollution levels). There, i there are market ailures, you annot be sure trade is beneiial. ) The US export subsidy or ood means that the domesti (relative) prie o ood in the US ill orld exeed the orld prie: P = P ( 1+ s), here s is the subsidy rate (%). For Japan, the domesti prie equals the orld prie. Given the orld prie, US ood exports inrease (beae the US prie rises); this dereases orld ood pries. Japan, an importer o ood, gains rom the US export subsidy. The US, on the other hand, loses or to reasons given orld pries, the subsidy redues US elare and the loer orld prie, due to the subsidy, also hurts the US. d) A US export subsidy tends to inrease ood prodution and exports, and raises the domesti relative prie o ood. A US import tari raises the domesti relative prie o lothing, and th osets the export subsidy. The overall impat depends on hih is larger. Let s be the export subsidy rate (a %) and t the import tari rate (also a %); then: = ( 1+ ); and P P ( 1 t) P P s ( ) ( 1 ) = + here P, P are orld pries. Th: ( + ) ( 1 t) P P 1+ s P 1 s = =. P P t P + + I s = t, then the to poliies ombined have no real eet. 3. (Labor migration) There is a single good, produed ing land and labor. The amount o land in a ountry is ixed; labor may be mobile aross ountries. US tehnology is: US: Q = ( T ) ( L ) 20 ; Resoure endoments are: T = T = 100; L = 25;. Without ator movements, labor employment ithin an eonomy equals labor endoment. 5
(a) Sho ho inreases in the US labor supply aet the age rate and the rent on land. From proit maximization, labor demand is solution to: Q = = 10 T L = 10 T L L ( ) ( ) ( ) ( ) Q P MPL P =. Let P=1; This implies: L (/P) A L s L d L s +I (/P) e (/P) E G L Wage Determination The above igure shos the labor demand and given the ixed labor supply, the equilibrium age. As the labor supply inreases (shits to the right) it is airly obvio that the real age alls. There are to ays to alulate the return to land. Either land is paid its marginal value produt (so R = P Q T or land reeives total output less hat is paid to labor. ( ) ( ) ( ) Q P L Q Q L L RT = PQ WL R = P R = T T Under onstant returns to sale these to onepts o rent are the same: ie., ( ) ( ) Th: T Q T + L Q L = Q R Q = = 10( L ) ( T ) P T Th, as the US labor ore inreases the return to land inreases. In the igure, in the initial situation the return to land is the area under the labor demand urve above the equilibrium age i.e., the area {A,(/P) e,e}. When the labor supply inreases, this area inreases to {A,(/P),G}; the land rents inrease both beae landoners pay loer ages and also beae the additional orkers employed produe more than they are paid. 6
(b) With L = L = 25, then R = 10( T ) ( L ) = 10( 100) ( 25) = 20; = 10( T ) ( L ) = 5 P P Finally, US inome is: ( ) ( ) ( ) ( ) Y = Q= 20 T L = 20 100 25 = 1, 000. Note that this is the same as adding up ator payments: Y = WL + RT = 20*25 + 5*100 = 1,000 () Let Mexian orkers move to the US. I I represents the number o immigrant orkers, then: L = L + I = 25 + I. ( ) ( ) i. Clearly, as I inreases, US ages all but the return on land rises. Landoners ill avor immigration (or eonomis reasons) hereas orkers ill oppose it. ii. I Mexian orkers are paid the US age, ho does immigration aet the US? US net national inome is output less ages paid to immigrants, th: net m m Y = Q W I = 20( T ) ( 25 + I) W I m I the immigrants are paid the US age, then: = 10( ) ( 25 + ) W T I (or simpliity, e e output as the numeraire, so P 1). Simpliying: ( ) ( ) ( ) ( ) ( ) ( ) [ ] net Y = 20 T 25 + I 10 T 25 + I I = 10 T 25 + I 50 + I It is airly easy to see that immigration mt raise US inome. Formally, you ould dierentiate ith respet to I: net Y net dy di ( ) ( ) 32 [ ] ( ) ( ) T I I T I ( T ) ( I) 32 [ I] = 5 25 50 10 25 5 25 + + + + = + > 0 iii. iv. O ourse, rom the US perspetive, employers ill be better o i the immigrant orkers are paid the (loer) Mexian age. And, given the number o immigrants, paying the guest orkers a loer age means a higher net inome or the US (and loer or Mexio). I you allo ree immigration beteen the to ountries, and only eonomi ators ditate migration, then ree immigration ill equalize ages beteen the to ountries. (d) I all orkers are given (ree) health insurane paid by the US government, and i it is not inaned by a tax on orkers, then hat happens is the ost to the US o employing an additional immigrant orker is the age the orker reeives PLUS the ost o the health insurane. Hene, it is possible that alloing immigration ould loer the standard o living or the US sine immigrant orkers are reeiving more than their marginal value produt (it is like a age subsidy). O ourse, in reality (but not in my question), these orkers also pay taxes hih ould at least 7
partly oset the impat o ree health insurane. (e) Finally, suppose the prodution untion or ood in Mexio is: ( ) ( ) m m m 10 m Q = T L here T = 100, is the amount o ixed land in Mexio, number o orkers employed in Mexio and the Mexian population is L = 25. i. Sho ho immigration aets total orld output: ( ) ( ) ( ) ( ) m L is the Q = Q + Q = 20 T L + I + 10 T L I here T = T = 100 and L = L = 25. Th: ( ) ( ) ( ) ( ) ( ) ( ) Q = 20 100 25 + I + 10 100 25 I = 200 25 + I + 100 25 I Verbally, sine initially the marginal produt o labor ill be higher in the US, as labor moves rom Mexio to the US orld output mt inrease; this ontinues to our until the marginal produts are the same in the to ountries. Hene: dq ( 25 I ) = 10025 ( + I) 5025 ( I) = 5025 ( I) 2 1 di ( 25 + I ) Clearly, at I=0, this derivative is positive, indiating migration rom Mexio to US inreases orld output. dq ii. Maximizing orld output entails setting = 0 (and heking that the seond order di ondition holds, hih it does). From above: ( 25 ) ( 25 + I ) dq I = 0 2 = 1 4( 25 I) = ( 25 + I) I = 15 di Th, ith I=15, L = 25 + 15 = 40, L = 25 15 = 10 and the age ill be the same in both ountries: W = 10( 100) ( 40) = 5( 10 ) ; W = 5( 100) ( 10) = 5( 10) Assuming no market ailures, ree immigration beteen the to ountries ill maximize orld output. 8