Homework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.


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1 Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed by recognizing tht mximum world output of C is just the verticl sum of mximum ntionl outputs. From tht point, if there is ny demnd for F, it will be provided by the country with comprtive dvntge in F production. In the text, this is the Foreign country. Thus, the slope of the world PPF will be identicl to tht of the Foreign country s PPF. Foreign will continue to provide F (s well s C, Home is specilized to C production), until it is specilized in the production of F, t point 1. From tht point, dditionl demnd for F must come from the Home country, which will be producing both goods until it too is specilized in production of F. b. ht is the menu of the worst combintions of outputs? Show tht it is mde up of two liner segments. The dshed line in the bove digrm is the menu of ntionlly efficient but globlly inefficient points. [i.e. the truly worst point would be the origin zero output from either country.] This is generted by perverse speciliztion. Tht is, from the point of globlly mximum output of C, if demnd for F is first served by the Home country, until it is speicilized, t point 2, nd then by the Foreign country, we construct the dshed frontier. 2. In the discussion of Section 5.6 suppose tht both Home nd Foreign countries produce commodity 3. Recll tht the sitution in section 5.6 involves lrge country producing 3 goods (1,2,3),
2 nd second country producing good 3, nd possibly other goods.. ht cn be sid bout the distribution of income between countries if Home demnd switches smll mount from commodity 2 to some commodity produced brod? Answering these questions involves using the zeroprofit conditions i.e. P j # Lj w nd P j * # LJ *w* nd recognizing tht if good 3 is produced in common P 3 = P 3 *. Using these two fcts, nd fixed Lj, we get key impliction: P 3 = P 3 * Y Lj w = LJ *w*, so if price of good 3 is unchnged between equilibri, wges must be unchnged. Thus, there re two cses to consider. First, the incresed demnd for Foreign lbor (in the form of incresed demnd for Foreign goods) rises w*/w. But this must result in L3 w < L3 *w*, nd shift of ll good 3 production to the Home country. Alterntively, the Home country is lrge nd Foreign is specilized to production of good 3, before nd fter the chnged demnd. Becuse reltive prices re determined by production conditions in the lrge (i.e. Home) country, reltive prices re unchnged, both countries continue to produce good 3, so w*/w is unchnged. b. If Home technology for producing commodity 1 improves? Fix the price of good 3 t $1. Since there is no chnge in technology in the production of good 3, there will be no chnge in wges in either country. The price of good 1 will then fll by n mount equl to the mount of the productivity increse in production of good 1. This will led to gins for both countries, with the gins being proportionl to the mount of good 1 consumed. 3. Suppose costs of production depend only on lbor costs, nd tht to produce unit of ech commodity in ech country tkes the number of lborhours shown: LA LB Home Foreign In which commodity does the Home country possess the gretest comprtive dvntge? For mking comprisons with n > 2 goods, it is useful to recll tht unit cost for good j is c j = Lj w. Furthermore, with trde the lw of one price implies tht there cn only be one price for good j nd p j = c j in ll countries with positive output. Thus, if Lj w < Lj *w*, then only the Home country will produce good j. Rerrnging, we hve condition which sttes tht if:
3 Lj * Lj * w < Home produces j. w Similrly, if Lj w > Lj *w*, then only the Foreign country will produce good j, nd we hve: Lj * Lj * w > Foreign produces j. w Tking these together mens tht we cn crete chin, ordering industries by degree of Home dvntge. Using the dt in the bove tble, we hve: 10 LB 10 LA = < = < = * * *. LB LA 3 which implies tht the Home country hs the gretest comprtive dvntge in the production of commodity C. Note tht these rtios re bsolute dvntge comprisons nd re not informtive bout production nd trde without wge dt. But we cn use this chin to identify the extreme members. b. If the Foreign wge rte is $1 per lbor hour nd freetrde equilibrium is reched, wht is the most tht the Home wge rte cn be? hy? Recll tht which countries produce which goods is determined by the reltive wge in the two countries w*/w. ith Foreign wge of $1, the Home country must be ble to produce t lest one good, so the w*/w cnnot be less thn 10/7. ith Foreign wge of $1, the Home wge rte cn be t most 7/10. c. If the Foreign wge rte is $1 per lborhour, wht would possible Home wge rte be so tht the Home country cn produce only one commodity? hich commodity would tht be? This question sks to to find Home wge, given Foreign wge of $1, such tht Home is just priced out of producing good B. This will occur if w*/w > 2. Thus, the Home country cn produce only one commodity, C, for ny wge greter thn ½.
4 4. In Ricrdin world, with lbor the only fctor of production being pid, the following tble gives the constnt lbor costs per unit of producing different commodities for countries " nd $. het L Crs Tnkers LT Rectors LR Trctors LX " $ In which commodities does country " hve n bsolute dvntge? hy? Country " hs n bsolute dvntge in the production of rectors nd trctors. Recll tht bsolute dvntge involves direct comprison of lbor productivities. Since LR < LR * nd LX < LX * we hve our nswer. Note tht we could compre lbor productivities directly by looking t MPPLs: " LR > " LR * nd " LX > " LX *. b. In which commodities does country $ hve comprtive dvntge? hy? As in the previous question, we need to construct the chin: α LX β LX α α α LR LT < β < β < β < LR LT < < < < But, without informtion on reltive wges, we cnnot sy where the chin will be broken. $ will certinly hve comprtive dvntge in whet, but beyond tht we cnnot sy. c. hich country would export tnkers? Explin. Country " will export trctors, if it exports nything. Tnkers, in the middle of the chin cnnot be predicted without informtion on w $ /w ". 5. Consider the world to consist of two countries (Home nd Foreign) mde up of individuls with identicl nd homothetic tste ptterns. Portry these by set of smoothly bowedin indifference curves. Suppose production in the Home country requires two lbor hours per unit of food nd only one lborhour per unit of clothing, wheres the Foreign country s figures for food nd clothing re just the opposite. The Foreign country s lbor force consists of 1 million lbor hours.. If the Home country is smll reltive to the Foreign country, one of the countries will produce both goods. hich country? ht will be food s reltive price? α L β L
5 It is useful to strt by explicitly showing the opportunity cost rtios: Home Home 2 1 = > = = 1 2 For For. The smll country lwys specilizes. Since the smll country is price tker, the world price is fixed by the lrge country s utrky price rtio. Thus, if Foreign is lrge, the world reltive price of Food is ½ nd the Home country will specilize in clothing. The Foreign country will produce both goods. b. If the Home country is lrge reltive to the Foreign country, one of the countries will produce both goods. hich country? ht will be food s reltive price? The sitution here is just reversed. The world price is now set by the, now lrge, Home country s utrky reltive price of food, which is 2. The, now smll, Foreign country will specilize in its comprtive dvntge industry, in this cse food. And the Home country will produce both goods. c. Construct world supply nd demnd schedules for food, with p = P F /P C on the verticl xis nd world food output on the horizontl. * * p w S The supply curve hs two horizontl components nd one verticl. For D # þ F, e.g. 1, tht demnd will be stisfied by the country with comprtive dvntge in food, i.e. the Foreign country. At the Foreign speciliztion point, þ F, there re rnge of prices consistent with ech country being specilized in its comprtive dvntge good e.g. world demnd curve 2. If demnd is sufficiently gret tht output of food from the Home country is lso required, i.e. D $ þ F (e.g. t demnd curve 3), the world price will be set by technicl conditions in the Home country. This determines the other horizontl component. þ* F Q + Q* F F
6 orkbook questions, 1, 2, 4, nd 8 1. Absolute versus Comprtive Advntge: Suppose tht in the US four mnhours re required to produce ech unit of clothing nd ech unit of food. In Cnd, one mnhour is required for ech unit of clothing nd two mnhours re required for unit of food.. hich country hs n bsolute dvntge in ech good? To strt with, it is useful to collect these ssumptions into simple tble: US 4 4 Cnd 1 2 Note tht bsolute dvntge comprisions involve bilterl comprisons of productivity by industry. Thus, Cnd hs n bsolute dvntge in the production of both goods, i.e.: 1 < 4, nd 2 < 4. b. hich country hs comprtive dvntge in ech good? Recll tht comprtive dvntge comprisons involve compring reltive productivity. Thus, we need to compre: US US 4 1 = = 1 > = = 4 2 Cn Cn. This comprison shows tht Cnd hs lower opportunity cost/utrky price of clothing. Thus, Cnd hs comprtive dvntge in clothing. c. Assuming tht ech country hs 40 mnhours of lbor vilble for production, drw the production possibilities frontiers for ech country. (Put food on the verticl xis). ht do the slopes of these frontiers indicte?
7 As we derived in clss, the slopes of these curves show the opportunity costs of clothing in terms of food. Tht is, the number of units of food tht must be given up to secure one more unit of clothing. d. Drw the world production possibilities frontier. ht does it s slope indicte? As drwn, the world production possibilities frontier shows output being produced by the most efficient country. Just s in the individul countries, the slope shows the opportunity cost of clothing in terms of food, in this cse to the world economy s whole. Since equilibrium occurs on the prt of the world PPF whose slope is determined by Cndin production conditions, this mens tht the world termsoftrde will be equl to the
8 utrky MRT in Cnd. This implies, by the wy, tht ll gins from trde will ccrue to the US. e. If consumers in both countries hve Leontief preferences, consuming clothing nd food in fixed proportion of onetoone, wht is the trde pttern? If we drw in the incomeconsumption line, which is fixed for Leontief preferences, we see tht Cnd will produce both goods, while the US will be specilized to food. Thus, the US will export food nd import clothing, while Cnd does the reverse. f. If the lbor force in the US increses by fctor of 20, will nything hppen to the trde pttern? This increse in the endowment of lbor will result in new world equilibrium, in which the US is producing both goods nd Cnd is specilized to clothing, with the world price determined by the opportunity cost rtio in the US. However, the trde pttern remins the sme: US will export food nd import clothing, while Cnd does the reverse. This is determined by comprtive dvntge, fct determined by technology, which ws unchnged by the increse in US popultion. 2. Commodity prices nd fctorl terms of trde: Suppose the lbor coefficients in the food nd clothing industries re s follows: PC P F * * 4 1 PC 10 = = = nd * = = = 8 2 P 5 = 4 * = 10 = 8 * = 5 Suppose lso tht the Home country hs 16 units of lbor nd the Foreign country hs 30.. Drw the production possibilities frontier for ech country nd clculte ech country s utrky prices. Since utrky reltive prices will be equl to the opportunity cost rtio (i.e. the MRT) we cn clculte the prices s: F 2 *. 1 Thus, utrky price of clothing in the Home country is ½ unit of food, while the utrky price of clothing in the Foreign country is 2 units of food. The PPFs for the two countries re shown in the following grph.
9 b. Drw the world production possibilities frontier. ht must the world reltive price of food in terms of clothing be in order for both countries to specilize in food? In clothing? Over wht rnge of prices will countries specilize in the good in which ech hs comprtive dvntge? PF > 2 P C will result in both countries specilizing in food, nd countries to specilize in clothing. If 1 2 PF < < P C 2 PF < 1 P 2 C for both ech country will specilize to its
10 comprtive dvntge good. c. Suppose tht the world price rtio is equl to 1. Clculte the reltive wges, w/w*. If prices re equl, both countries re specilized to their comprtive dvntge goods nd P C = w = *w* = P F *, so 4w = 5w* nd w/w* = 5/4. d. Now suppose tht there is n increse in world demnd for clothing so tht the reltive price of clothing rises to 3/2. ht hppens to the reltive wge between the Home nd Foreign country? Ptterns of production nd speciliztion re unltered, i.e. both countries re specilized in their comprtive dvntge good. However, now commodity prices re not equl, but re relted s 3/2. Thus the reltive wge, w/w* = 15/8. 4. Compring models: Define n increse in demnd for clothing s shift in the indifference curves towrd the clothing xis. This is illustrted below s shift from curve A to curve B.. Consider first n endowment economy with n lloction fo food nd clothing shown by point E nd the indifference curve A. Given our definition of demnd shock, suppose there is n increse in demnd for clothing. ht hppens to the reltive (utrky price of clothing)? ht hppens to the supply of clothing.
11 From the bove digrm it is esy to see tht t tstes given by B the reltive price of food (determined by the MRS t E) is greter thn when the tstes re given by A. Becuse this is n endowment economy, there is no chnge in supply. b. Now suppose the economy hs bowed out production possibilities frontier. ht hppens to the reltive price of clothing when demnd for clothing increses? ht hppens to the supply of clothing? Now the finl price is determined by the tngency between n indifference curve nd the PPF t the point where MRS = MRT. At this new equilibrium point the reltive price of food hs incresed, but so hs the output of food. The output of clothing hs, of course,
12 fllen. c. Finlly consider Ricrdin model of production. Now wht hppens to the reltive price of clothing when the demnd for clothing increses? ht hppens to the supply of clothing? In this cse, becuse we re t n interior equilibrium both before nd fter the chnge in tstes (i.e. both goods re produced in both equilibri), the reltive price is unchnged. Recll tht in the Ricrdin model, reltive price t interior equilibri is completely determined by technologicl conditions. Adjustment occurs only on the output mrgin, with output of food rising nd output of food flling. d. Since we know tht utrky prices determine the pttern of trde (i.e. vi the lw of comprtive dvntge), in wht sense re the endowment model nd the Ricrdin model extreme cses? (Hint: Think bout the role of supply nd demnd in determining utrky prices.) In the endowment model utrky prices re determined completely by the MRS, while in the Ricrdin model they re determined completely by the MRT. Tht is, demnd conditions determine utrky reltive price in the first cse nd supply conditions determine utrky reltive price in the ltter cse. In the stndrd neoclssicl cse, the interction of these two forces determine the utrky reltive price. 8. Interntionl wge comprisons: The following tble of wge rtes in different countries ws published in the ll Street Journl. Hourly Py Levels (For production workers in US Dollrs)
13 United Sttes $12.96 $13.19 $13.44 $13.62 Jpn $6.47 $9.47 $11.44 $13.80 est Germny $9.56 $13.35 $16.87 $20.19 Itly $7.40 $10.01 $12.33 $14.77 Frnce $7.52 $10.27 $12.42 $14.03 Britin $6.19 $7.50 $8.96 $11.06 In view of wht you hve lerned from the Ricrdin model of production, how would you respond to the following comments?. The high cost of hiring production workers in the US hs undermined its competitive position in world mrkets. No. US workers re pid more becuse they re more productive. b. The high wges in the US compred to those found brod re due to lbor unions forcing their levels bove wht would be implied by lbor s productivity in competitive Ricrdin world. Possible, but not likely. If wges were held bove competitive levels, US goods would be unble to compete interntionlly, cusing the eventul shutdown of industries supporting such wges. Also, note tht this might explin the reltively high wges in 1985, but if this explntion is correct, the dt show wekening of unions in the US reltive to the other countries, where much stronger wge growth is seen. c. The increse in Jpn s wges implies tht Jpn is losing its competitive edge in world mrkets. No. It implies tht the productivity of Jpnese workers is incresing. d. The low wges in Britin re n indiction tht British workers re being underpid. No. Their productivity is lower. e. Allowing importtion of goods from workers with lower wges is unfir to Americn workers. No. The lower pid worker is lso the less productive one.
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