Labor Requirements by Country and Good

Spring 2003 Eon 455 Answers to roblem Set 2 Harvey Lapan 1. Consider the Riardian model, with two ountries, the U.S. and the U.K. Eah ountry has a total labor supply of 2,000 worker hours, and labor requirements in eah ountry are given by: Labor Requirements by Country and Good Calulators Wheat United States 8 hours/alulator 4 hours/bushel United Kingdom 10 hours/alulator 2 hours/bushel (a)the U.K has an absolute advantage in wheat and the U.S. in alulators beause the U.K has lower labor requirements (higher produtivity) in wheat than the U.S. does and the U.S. has lower labor requirements (higher produtivity) in alulators than does the U.K. (i)for this ase it is lear the U.S. has the omparative advantage in alulators and the U.K in wheat. The opportunity ost of produing alulators in the U.S. is 2 bushels of wheat, the opportunity ost of alulator prodution in the U.K. is 5 bushels of wheat. Conversely, the opportunity ost of wheat in the U.S. is one-half (1/2) alulator, in the U.K. it is one-fifth (1/5) alulator. (b)derive and sketh the prodution possibility frontier for eah ountry. Let QC=Calulator Output, LC = labor used in alulator prodution; QW = Wheat Output, LW=labor used in wheat prodution For the US: LC+LW=2000; QC=(LC/8) or LC=8QC; For the UK: LC+LW=2000; QC=(LC/10) or LC=10QC; QW=(LW/4) so: QW=(2000-LC)/4=500-2QC QW=(LW/2 so: QW=(2000-LC)/2=1000-5QC Wheat Output US rodution ossibility Frontier 600 500 400 300 200 100 0 0 50 100 150 200 250 300 Calulator Output Wheat Output UK rodution ossible Frontier 1200 1000 800 600 400 200 0 0 50 100 150 200 250 Calulator Output 1

(i)suppose the U.S. originally produes and onsumes 125 alulators and 250 bushels of wheat, while the UK produes and onsumes 100 alulators and 500 bushels of wheat (so total world output is 225 alulators and 750 bushels of wheat). Let the UK inrease wheat prodution by C units (up to a maximum inrease of 500 in the UK); this will ause UK alulator prodution to derease by (C/5). Let the U.S. inrease alulator prodution by D units (up to a maximum inrease of 125 alulators); this will ause U.S. wheat prodution to fall by (2D). Thus, from a world perspetive: Change Wheat rodution = C 2D> 0 if C > 2D D C 5 > 0 if C<5D Change Calulator rodution = ( ) Thus, for any hange in the two ountries suh that: 5D> C > 2D world output of both goods inrease. {e.g., if the UK inreases wheat prodution by (C=) 200 and U.S. inreases alulator prodution by 75). Naturally, one one ountry is fully speialized, it an produe no more of the good in whih it has a omparative advantage. (ii) The world prodution possibility frontier is suh that - at most - only one ountry should produe both goods. Thus, for low levels of alulator output, the UK should speialize in wheat, while the US produes both goods; while for large levels of alulator output, the US speializes in alulators, while the UK produes both goods. Formally, letting F represent food (wheat) output and C represent alulator output, where the supersript T represents total (world) output: C 250; F = 1, 000, C = 0; F = 500 2 C ; F = 1,500 2C T uk uk us US T T ( ) 450 C T 250; C us = 250, F us = 0; F uk = 1000 5 C uk ; F T = 1, 000 5 C T 250 In the figure below, the line segment labeled US represents the situation where the US produes both goods (and the line segment is the US ppf shifted up by UK food prodution of 1000), and the segment labeled UK represents the ase where the UK produes both goods (and is the UK ppf shifted right by maximum US alulator prodution). The point V is the vertex point where eah ountry speializes in the good in whih it has a omparative advantage. Food 1500 US 1000 V UK 250 450 Calulators World rodution ossibility Frontier 2

()In the absene of trade, autarky (no trade) relative pries would be: us uk ( f ) = 2 ( bushels / alulator), and ( f ) = 5 ( bushels / alulator), where is the prie of alulators, f is the prie of food (wheat), and the supersript indiates whih ountry. (i)if the prie of wheat is $6.00, then the U.S. will export alulators if > $12, and will import alulators if < $12 (if = $12 then U.S. ould export or import). For the U.K., it will export alulators if > $30 and import alulator if < $30. (These pries follow from the autarky relative prie. If this is not lear, remember that labor will work where it gets its highest return; the return for working in the alulator industry is: ( a l) and the return for working in the food (wheat) industry is ( f a lf ) where a li is the amount of labor required to produe good i). (ii)if they trade at a prie of wheat = $6, and a prie of alulators = $18.00, this means that for eah unit of alulators exported, they an afford to import three units of wheat (and for eah unit of wheat exported, they an afford to import one/third unit of alulators). Thus, if the U.S. is originally produing both goods, it an inrease alulator prodution by X units, derease wheat prodution by 2X units, and if it exports Y units of alulators (imports 3Y units of food), for X > Y and 3Y 2X 3Y 2 > X > Y ) its > (or, for both: ( ) onsumption of both goods will inrease. The same idea holds for the UK (whih produes more wheat, fewer alulators and imports alulators). Only relative prie matters beause the trade budget onstraint is (say, from US Calulator exports, or Food imports = ( ) = ( f )( exp ) perspetive): ( ) f Food imports alulator orts NEW LABOR REQUIREMENT TABLE: Hourly Labor Requirements by Country and Good Calulator Wheat United States 2 hours/alulator 1 hour/bushel United Kingdom 10 hours/alulator 2 hours/bushel (e)now the U.S. has an absolute advantage in both goods. (i)however, the U.K. still has a omparative advantage in wheat as the opportunity ost of alulator prodution (in terms of wheat) is higher in the UK than in the US. (ii)this redution in US labor requirements (inrease in labor produtivities) will not affet autarky (no trade) relative pries of goods in the U.S. as the opportunity ost is unhanged. The U.S. real wage will inrease due to the produtivity inrease. The impat of this hange in labor produtivities on post-trade pries is that the relative prie of alulators will fall sine greater U.S. alulator prodution reates exess supply (remember that the US will not produe wheat and the UK will not produe alulators if both ountries speialize). The UK will gain by the inreased produtivity in the US (due to heaper alulator imports); the US is helped by the higher produtivity but hurt by heaper pries for alulator exports so it is possible (though not likely) that the US is atually worse off due to the inreased US produtivity. (f)same proess as earlier; if the UK inreases wheat prodution by C units, UK alulator prodution falls by (C/5). If the U.S. inreases alulator prodution by D units, U.S. wheat prodution falls by (2D). Total world output of both goods inreases if 5D> C > 2D. (g)if labor migration is allowed, then the answer depends upon the labor produtivity of the immigrant workers (or labor requirements for produing with the immigrant worker). If the immigrants who move to a new 3

ountry have the same produtivity as the workers who originally lived there, then under the first (labor requirement) table, all wheat will be produed in the UK, all alulators in the US, and labor will move to equalize real wages - aording to demands for the two goods [Sine wheat is produed in the UK: 2 UK f = W ; sine alulators are produed in the US: 8 us uk us = W. Sine labor mobility equalizes wages: W = W = W. Hene, f = 2 W; = 8W whih implies: ( f ) = 4. Demand for the goods, at this relative prie, determines output, and thus how muh labor is needed in eah ountry]. For the seond table, both goods would be produed in the US and all labor would move to the US. Of ourse, if the migration of workers did not affet their own produtivity (i.e., UK workers who moved to the US had the same produtivity as UK workers who stayed at home) then the migration would not have any impat on output. If produtivity levels hanged as migrants entered the ountry then some interior equilibrium ould emerge. Disussing this situation requires a more omplete model of prodution with more than one input. 2. To illustrate how the model an be extended to more than two ountries, onsider the following example Labor Requirements by Country and Good Calulators Wheat United States 8 hours/alulator 4 hour/bushel United Kingdom 12 hour/alulator 3 hours/bushel Mexio 10 hours/alulator 2 hours/bushel (a)the US has an absolute advantage in alulators, Mexio in wheat, the UK in neither. (b)the opportunity ost of alulator prodution in the US is 2 bushels; in Mexio the opportunity ost of alulator prodution is 5 bushels; and in the UK the opportunity ost of alulator prodution is 4 bushels. So, ompared to Mexio, the UK has a omparative advantage in alulator prodution. ()Compared to the US, the UK has a omparative advantage in wheat prodution (see part b). Thus, the US has a omparative advantage in alulator prodution, regardless as to whether the omparison is with Mexio or the UK; and Mexio has a omparative advantage in wheat prodution, regardless as to whether the omparison is with the US or the UK. But the UK s omparative advantage depends upon to whom it is being ompared. (d)autarky relative pries in eah ountry reflet the opportunity ost; thus: us uk mex In US: ( f ) = 2; In UK: ( f ) = 4; In Mexio: ( f ) = 5; where the units (omitted) are: bushels/alulator. 4

(e)the world supply urve for alulators looks like: S / f 5 4 2 Calulators (f)under free trade, the US will export alulators and Mexio will export wheat (beause eah has a omparative advantage in that good ompared to any other ountry). However, whih good the UK exports depends upon demand and supply (ountry size). 3. To illustrate how the model an be extended to more than two goods, onsider the following example Labor Requirements by Country and Good Calulator Wheat DVDs Shoes United States 8 hours/alulator 4 hours/bushel 3 hours/dvd 6 hours/shoe Mexio 10 hours/alulator 2 hours/bushel 12 hours/dvd 4 hours/shoe (a) The U.S. has an absolute advantage in alulators and DVDs, Mexio has an absolute advantage in wheat and shoes. (b)the U.S. has a omparative advantage in DVDs sine the opportunity ost of DVD prodution in the US is: (3/4) wheat, or (1/2) shoe, or (3/8) alulator; whereas in Mexio the opportunity ost of DVD prodution is: 6 wheat, 3 shoes, or (6/5) alulator. [Another way to say the same thing is: in Mexio the labor requirement to produe DVDs is 4 times that for the US, whereas for all other goods the labor requirement in Mexio is less than four times the US labor requirement]. That is, regardless of whether the opportunity ost of DVD prodution is measured in terms of lost wheat output, lost shoes output, or lost alulator output, that ost is lower in the US than in Mexio. For the same reason, Mexio has a omparative advantage in wheat {i.e., the opportunity ost of produing wheat in Mexio is: (1/5) alulator, (1/2) shoe or (1/6)DVD; whereas the opportunity ost of wheat prodution in the US is: (1/2) alulator, (2/3) shoe or (4/3) DVD}. The amount of output lost produing wheat in Mexio is less than the amount lost when wheat is produed in the US, regardless of the output in whih you measure this loss. However, for alulators or shoes, you annot say unambiguously whih ountry has the omparative advantage sine it depends in terms of whih good you measure the opportunity ost. Thus, for example, the opportunity ost of alulator prodution is: in the US to produe 1 alulator osts: (8/3) DVD or 2 wheat or (4/3) shoes; in Mexio to produe 1 alulator osts: (5/6) DVD, 5 wheat or (5/2) shoes 5

So, as ompared to DVDs, alulator prodution is (relatively) heaper in Mexio than in the US, but as ompared to wheat or shoes, alulator prodution is (relatively) heaper in the US. Similarly, for shoes, ompared to alulators or DVDs, shoes are heaper to produe in Mexio; but ompared to wheat, shoes are heaper to produe in the US. ()Autarky relative pries in eah ountry reflet opportunity osts; so, as above: In US: ( f ) = ( d f ) = ( ) ( s f ) = ( ) In UK: ( f ) = ( d f ) = ( s f ) = 2 bushels / alulator; 3 4 bushels / DVD; 3 2 bushels / shoe 5 bushels / alulator; 6 bushels / DVD; 2 bushels / shoe where the subsripts refer to alulators (), food or wheat (f), DVDs (d), and shoes (s). (d)if trade were allowed, the US would export DVDs and import wheat, but whih ountry would export alulators or shoes depends upon demand, ountry size, et. This follows the earlier statements about omparative advantage and an be seen by omparing relative osts below. (e)let W denote the wage in the U.S., and W denote the wage in Mexio (measured in the same units, e.g., dollars/hour). The marginal prodution osts in eah ountry are: us us us us US: MC = 8 W; MCf = 4 W; MCd = 3 W; MCs = 6W mex mex mex mex UK: MC = 10 W ; MC = 2 W ; MC = 12 W ; MC = 4W f d s To see where a good is produed, ompare marginal osts in eah ountry. = 4 2 = 2 > 1 - i.e., if W us mex For example, if ( MC f MC f ) ( W W ) ( W W ) < 2W - then Mexio is the low ost produer of wheat (food) and hene wheat will be produed in Mexio. Applying the same logi to eah good implies the following: ( ) 4 4 ( WW) ( 5 4) WW > : all goods will be produed in Mexio > > ; DVDs will be produed in the US; wheat, shoes and alulator will be produed in Mexio ( 54) > ( WW) > ( 23) : DVDs and alulators will be produed in the US; shoes and wheat will be produed in Mexio ( 23) > ( WW) > ( 12) : DVDs, alulators and shoes will be produed in the US; wheat will be produed in the Mexio WW < 12 : all goods will be produed in the US h b g (f)suppose an original trading equilibrium ours in whih Mexio exports only one good (hene, wheat), 23 > WW > 12, or equivalently: and the U.S. exports the other three goods (this implies ( ) ( ) ( ) 2 ( W W) ( 3 2) > > ). As the Mexian work fore grows, this will inrease the supply of wheat, dereasing its relative prie (and hene dereasing the wage in Mexio as ompared to US wages and hene as ompared to the W = 32W ), then shoes will also be produed prie of import goods). If the Mexian wage falls enough ( to ( ) in Mexio (as well as in the US). Further inreases in the Mexian labor fore will eventually ause Mexio to 6

produe all the shoes (and wheat), until the Mexian wage drops even further. If Mexian wages drop enough { ie., W < ( 45) W}, then alulators will also be produed in Mexio. Thus, labor fore growth will effet relative wages between ountries and hene the relative pries of goods, as well as where goods are produed (exept for the two extreme goods, as Mexio will always produe wheat and the US DVDs). (g)if Mexian produtivity in all setors doubles (labor requirements are halved), the hourly labor requirements and marginal osts beome: Calulator Wheat DVDs Shoes United States 8 hours/alulator 4 hours/bushel 3 hours/dvd 6 hours/shoe Mexio 5 hours/alulator 1 hours/bushel 6 hours/dvd 2 hours/shoe MC in US 8W 4W 3W 6W MC in Mexio 5W W 6W 2W MCUS/MCMex (8W/5W) (4W/W) (W/2W) (3W/W) US produes nothing if: US produes only DVDs if: US produes DVDs & alulators if: US produes all exept wheat if: US produes all if: W>2W 2W>W>(5/8)W (5/8)W>W>(1/3)W (1/3)W>W>(1/4)W (1/4)W>W Thus, suppose Mexian produtivity doubles (and Mexio only produes wheat); if Mexian wages also double, then prodution osts in Mexio (as ompared to the US) are unhanged, but output of wheat doubles. To restore equilibrium, the relative prie of wheat must fall. To say the same thing another way, higher Mexian wages and inome inreases the demand for all other goods, so that the relative prie of all other goods inreases (ompared to wheat). This implies that the Mexian wage must inrease by less (in terms of US wages) than a fator of 2 (i.e., by less than the produtivity inrease). Sine Mexian wages inrease by less than Mexian produtivity, Mexian osts fall relative to the US, and if this fall is large enough Mexio will start produing additional goods (first, shoes and wheat). Thus, in terms of prodution patterns and the relative prie of goods, the inrease in Mexian produtivity has an effet that is very similar to the impat of an inrease in the Mexian labor fore (sine the produtivity inrease inreases the effetive Mexian labor fore and has the same effet on the Mexian prodution possibility frontier as would a doubling of the labor fore). So, the inrease in Mexian produtivity: (i)may/will lead Mexio to export additional goods, first shoes, then perhaps alulators; (ii)will ause the relative prie of Mexian exports wheat and perhaps shoes to fall ompared to other goods still produed only in the US; and (iii)will probably raise Mexian wages ompared to the US (note the two offsetting fators: higher produtivity inreases Mexian wages, but lower pries for goods Mexio produes lowers Mexian relative wages; if demand for wheat, and perhaps shoes, is very inelasti it is possible but not likely that Mexian wages fall ompared to the US). Sine the relative prie of Mexian exports whih are US imports dereases, the inreased produtivity in Mexio benefits the US (i.e., raises the US real wage in terms of its import goods and is unhanged in terms of its export goods). 7