Problem Set #1 - Answers

Transcription

1 Fall Term 24 Page of 7. Use indifference curves and a curved ransformaion curve o illusrae a free rade equilibrium for a counry facing an exogenous inernaional price. Then show wha happens if ha exogenous price changes in he direcion of raising he relaive price of he counry s expored good. Such a change is cusomarily called an improvemen in he counry s erms of rade. Is his erminology necessarily appropriae? As shown a he righ for a counry ha iniially expors good, an exogenous rise in he price of seepens he price line. If he counry is behaving opimally in all oher respecs, so ha i is on is communiy indifference curve afer he price change, hen he counry as a whole is definiely made beer off. This is shown by is reaching a higher indifference curve, bu i could also be inferred from he fac ha he new price line, which consiues he counry s aggregae budge line, passes ouside he iniial consumpion poin, C, making i possible o consume more of boh goods. C C P P The erminology improvemen in he erms of rade is herefore appropriae. However, i should no be hough ha any change in relaive prices in favor of he counry s expor good is necessarily beneficial for i. In he example here, he price change was exogenous. One could easily consruc a case where, if he counry were large enough in world markes o influence world prices, a change in somehing oher han prices (such as a fall in he counry s resources could cause i o supply less o he world marke. This would hen cause an increase in he world price, and while he price change alone could be hough of as beneficial, i could sill be rue ha he counry would lose from he combined effecs of he loss in resources and he induced improvemen in he erms of rade.

2 Fall Term 24 Page 2 of 7 2. The diagram below shows a free-rade equilibrium beween wo counries, A and B. Technological change now causes counry A o be able o produce exacly % more oupu of good han i could before, for any given inpu of resources. a Deermine wha his will do o he wo counries ransformaion curves, o heir offer curves, and herefore o he world equilibrium prices. The change in echnology does nohing o Counry B s ransformaion curve, bu i sreches A s o he righ by %, as shown in he broken curve a he righ. (The shif shown is somewha more han %, o make i easier o see. A iniial prices (shown by he parallel price line angen o he new ransformaion curve, oupu of rises and oupu of falls (since he expansion flaens he ransformaion curve by % a he poin where is unchanged. Consumpion moves o he new angency of he price line wih an indifference curve, bu wihou assumpions abou preferences his could enail a fall in demand for one of he goods if i is an inferior good. The case shown has demand rising for boh, in which case desired rade expands, since producion of falls while consumpion of rises. In general, if good is sufficienly inferior, is consumpion could fall by more han producion and desired rade would conrac. p p Counry A A A B p p Wha happens o he offer curves can be inferred from his change in rade a consan prices. Counry B s offer curve is unchanged, while Counry A s expands ouward from he origin if good is a normal good, as drawn, bu could conrac inward if is sufficienly inferior. This in urn causes he world price of good o change, falling in he case shown of a normal good, bu possibly rising if is sufficienly inferior for he A offer curve o conrac.

3 Fall Term 24 Page 3 of 7 b Wihou furher assumpions abou preferences, are here any of hese variables he direcion of change in which canno be deermined unambiguously? As already indicaed, he direcion of shif of counry A s offer curve is ambiguous, as is herefore he direcion of change in he world relaive price. c If you assume ha preferences are homoheic, can any of hese ambiguiies be resolved? es. Wih homoheic preferences (or even jus wih good a normal good, which is weaker han homoheiciy, counry A s offer curve mus expand as shown and he world relaive price of A s expor good,, mus fall. d Show he new equilibrium in boh counries for he case of homoheic preferences. Counry A Counry B Since we know ha he world price of falls, we can be sure ha counry B s oupu of falls and is consumpion of boh goods rises (again, due o homoheiciy. Thus B s impors of mus rise, alhough is expors of may rise or fall. The case drawn has Counry A sill reaching a higher indifference curve han i did before he expansion, bu his is no necessary. Counry A could lose from is own expansion, he case of Bhagwai s Immizerizing growh. (See Bhagwai, Jagdish "Immiserizing Growh: A Geomerical Noe," Review of Economic Sudies 25, (June, pp

4 Fall Term 24 Page 4 of 7 3. Consider a counry engaged in producion and rade of an arbirary number of goods. Assume ha here are no ranspor coss and ha producers are compeiive profi maximizers. Assuming ha rade is free, show ha if he vecor of world prices, p w, changes by a vecor Δp w, hen he vecor of he resuling changes in oupus, Δ, will be nonnegaively correlaed wih Δp w (assuming ha p w is always normalized o lie on he uni simplex. From maximizaion p w w p F and similarly where p w p w F p w p w + Δ p w + Δ Leing in he firs inequaliy and in he second, we can add hem ogeher o ge or w w w w p + p p + p p w ( - + p w ( - (p w - p w ( - Δ p w Δ If p w and p w are boh on he uni simplex (which means ha he elemens of boh vecors add up o one, hen he sample mean of he elemens in Δ p w is

5 Fall Term 24 Page 5 of 7 Mean(Δ p w n Δ w p j n (p w - p w j j # n p w - p w $ % j j & [ - ] n Therefore he correlaion beween Δ p w, and Δ has he same sign as heir inner produc: Sign[Cor(Δ p w,δ] Sign[Δ p w Δ] (See Deardorff, The Correlaion Beween Price and Oupu Changes When There Are Many Goods, Journal of Inernaional Economics, Augus 98, pp a Derive and draw he ransformaion curves of he wo economies whose endowmens and echnologies are hose described below. Each has a fixed endowmen of labor is only facor of producion and can produce wo goods, and, using he following consan amouns of labor per uni of oupu: Per-uni labor requiremen for producing Endowmen of Labor Counry A 6 2 Counry B 2 2 3

6 Fall Term 24 Page 6 of 7 Counry A Counry B b How much of goods and will be produced and consumed in auarky in hese wo counries, and wha will be heir relaive prices, assuming ha demanders always insis on consuming hem in fixed proporions of uni of for each uni of? A: p /p 2 B: p /p 2/3 c Derive and draw he world ransformaion curve.

7 Fall Term 24 Page 7 of d Derive he free rade equilibrium relaive price of and, plus he equilibrium quaniies of he goods produced, consumed, and raded. From he picure in par (c, requires producing in he upper segmen of he world ransformaion curve. Thus wih free rade p p 2 and oupus in counry B are B B, 4 World oupus: W W A A + 4 A + 2 A 6 W W + 2( W W W A , 6 A A s income in unis of 3: A A A A, A 3, 2 A A 2 A 2 A 3 2, 3 B s income in unis of 4: 3-2

8 Fall Term 24 Page 8 of 7 Trade: B B, B B B 4, B B A expors B B unis of. B expors 3 3 of. 5. In he Dornbusch, Fischer, and Samuelson Ricardian model wih ranspor coss, suppose ha here is an increase in he cos of ransporaion, and suppose also ha oher condiions happen o be such ha he wage raio, ω, remains unchanged as a resul. Deermine he effecs of his change on a he paern of rade and specializaion (which goods each counry produces, expors, and impors, b he domesic prices of goods in boh counries, and c real wages (he raio of he wage o an arbirary index of domesic prices. Hin: for he real wage, see if you can show ha he nominal wage eiher rises or falls relaive o he prices of all goods. If so, hen he exac price index does no maer.

9 Fall Term 24 Page 9 of 7 The iniial equilibrium is shown below by he solid curves for ga, (/ga, and he associaed z A and z B. The iniial wage raio is ω, wih A producing [,z A and B producing (z B,]. A expors [,z B, B expors (z A,], and (z B,z A are no raded. ( / g ʹ A ( / ga ga gʹ A ω zʹ B z B z A zʹ A a. When he cos of ransporaion increases, he fracion of each good ha survives being raded, g, falls from g o g. The curves shif o he posiions shown by he dashed curves g A and ( g A. Each counry now produces a larger range of goods, [,z A and (z B,] respecively, while each counry expors a smaller range of goods, [,z B and (z A,]. b. Wih nominal wages unchanged, he prices of domesically produced goods in each counry are unchanged, while he prices of goods ha coninue o be impored rise by he increase in ranspor coss. The prices of goods ha were previously impored bu no longer are also rise bu by less han he increase in ranspor coss. c. Since nominal wages are unchanged, and since all prices in each counry eiher remain unchanged or rise, he real wage in each counry falls.

10 Fall Term 24 Page of 7 6. In he Edgeworh Box below, poin E is one poin on he efficiency locus for he wo indusries, and, whose represenaive isoquans are as shown. Assuming ha he producion funcions for and are linearly homogeneous, derive he res of he efficiency locus. O T E O L O B A E T O L Ans: By expanding and conracing he wo isoquans radially wih respec o heir origins, you can find oher poins on he efficiency locus. Noe ha he resuling locus, O AEBO, is no concave o he diagonal. ou should check, however, ha he resuling ransformaion curve, hough piecewise linear, is concave o is origin.

11 Fall Term 24 Page of 7 7. The following are he equaions used by Jones (965 o deermine facor-price changes from commodiy-price changes: wˆ + rˆ L L T wˆ + rˆ T where Li + Ti, i,. Solve hese equaions for ŵ and rˆ in erms of and. From your soluion, show ha if good is relaively labor inensive, so ha L > L, hen a rise in p relaive o p will raise w relaive o boh prices and reduce r relaive o boh prices. Ans: or L L T wˆ wˆ T T L T T T T L T L T + L T L T ( ( ( + ( ( T T L T ( + ( T T T T T T ( + T L L T L T L T L L ( (2 If p ˆ > and L > (and hence L T >, hen T From (: wˆ > From (2: wˆ > Similarly rˆ L L L L L T T L L L L ( L L ( ( L L L L L (3

12 Fall Term 24 Page 2 of 7 or rˆ L L ( + ( L L L L L L ( + (4 If p ˆ > and L >, hen L From (3: rˆ < From (4: rˆ < 8. Use he Lerner (uni-value-isoquan diagram o work ou he effecs of a price change in he 2 2 Heckscher-Ohlin model as follows. Consider a small counry ha faces prices p and p for goods and. Suppose ha is endowmens of labor x y and land are such ha, a hese prices, i produces exacly $2 worh of each good. Work ou wha happens when he price of good rises by 2%, o p x, he price of good remaining consan. Assume ha good is he relaively labor-inensive good. Deermine, if possible, he direcion of change in he following variables: i The nominal wage. ii The raio of he nominal wage o he price of good. iii The renal price of land. iv The raio of land o labor used in producing good. v The raio of land o labor used in producing good. vi The average raio of land o labor employed in boh indusries ogeher. vii The oupu of good. viii The oupu of good.

13 Fall Term 24 Page 3 of 7 Ans: Firs draw he Lerner diagram for he iniial siuaion.(draw i big enough o see wha s going on. T ( L, T 2/ p / p 2/ p / p O L

14 Fall Term 24 Page 4 of 7 Now consruc he new equilibrium wih he price of 2% higher: p.2 p. This shifs he uni-value -isoquan approximaely 2% in oward he origin (acually by /6, hough I ve drawn i shifing more, for clariy. From ha consruc he new common angen, he rays for and, and he parallelogram showing he allocaion of facors ha will mainain full employmen of each. Isoquans hrough hese allocaions indicae he new oupus and. T ( L, T 2/ p / p 2/ p / p / p O L From his figure you can read he resuls for pars (iv-(viii. The raio of land o labor has increased in boh indusries, alhough he average raio of land o labor employed has no changed (since i mus coninue o equal he unchanged endowmen. Tha is possible because more of boh facors is employed in he indusry and less of boh in he indusry, resuling in a larger oupu of and a smaller oupu of.

15 Fall Term 24 Page 5 of 7 To ge effecs on facor prices, use he inerceps of he isocos lines o measure heir reciprocals in nominal erms ha is, in unis of he currency in which he prices have been expressed. From hese i follows immediaely ha he nominal wage has risen and he nominal renal on land has fallen. This is also a fall in he real renal, since one price is unchanged and he oher has risen. T ( L, T 2/ p /r /r / p 2/ p / p / p O /w /w ~ /w L To find he effec on he real wage, consruc a wage, w ~, which is above w by jus he percenage of he price increase. This is done by consrucing he doed line parallel o he iniial isocos line bu angen o he new uni-value -isoquan. I is hen clear ha he new wage, w is above w ~ and has herefore risen no only relaive o he consan price of bu relaive also o he increased price of. Thus he real wage of labor is increased.

16 Fall Term 24 Page 6 of 7 9. The Lerner diagram below shows an iniial equilibrium, in he 2 2 Heckscher-Ohlin model, for a small-open economy facing fixed world prices of goods and, p and p. Is iniial endowmens of he wo facors, unskilled labor U and skilled labor S, are shown by poin E. Suppose now ha some unskilled workers become skilled, moving he endowmen poin firs o E and hen o E. Deermine he effecs of hese changes on oupus of boh goods and on facor prices. S E E E / p / p O U S E /s 2 /s / p 2 E E 2 O /w 2 / p /w U

17 Fall Term 24 Page 7 of 7 Consrucing parallelograms from poins E and E, his iniial allocaion and he allocaion for endowmen E are boh found inside he diversificaion cone, i.e., beween rays and. For endowmen E, since i is ouside he cone, only good is produced using he expanded version of he isoquan hrough E. Using he disance from he origin along rays and o measure oupu, one sees ha oupu of falls from o and hen o 2. Oupu of rises from o o 2. The wage of unskilled labor, w, is iniially w and remains here when he endowmen moves o E. Bu when he endowmen moves ouside he cone o E, hen he unskilled wage rises o w 2. Likewise, he wage of skilled labor, s, remains a s for E and E, bu hen falls o s 2 a E.