UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 2017 EXAMINATION
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1 INTERNATIONAL TRADE T. J. KEHOE UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 27 EXAMINATION Please answer wo of he hree quesons. You can consul class noes, workng papers, and arcles whle you are workng on he exam, bu you are asked no o dscuss he exam wh anyone unl he exam perod s fnshed for everyone.. Consder an economy n whch here are wo ypes of goods, agrculure and manufacured goods. Agrculural goods are homogeneous and are produced usng labor accordng o he consan reurns o scale producon funcon y. Manufacured goods are dfferenaed by frm. The producon funcon for frm s y ( / b)max[ f,]. Here f s he fxed cos, n erms of labor, necessary o operae he frm and b s he un labor requremen. Suppose ha here s a represenave consumer wh preferences n c log c (/ ) log, where. There s an endowmen of uns of labor. a) Defne a monopolscally compeve equlbrum for hs economy n whch frms follow Courno prcng rules and here s free enry and ex. b) Suppose ha b 2, f 4, /2, and 36 c) Suppose now ha 36. Calculae he equlbrum.. Calculae he auarky equlbrum. d) Inerpre he equlbrum n par c as a radng equlbrum among wo counres, one 2 wh 36 and he second wh 324. Assume ha producon of he homogeneous good s dsrbued proporonally across he wo counres. Wha mpac does rade have on he number of manufacurng frms n each counry? The average oupu of frms? The oal number of producs avalable? Consumer uly and real ncome? Illusrae he effcency gans usng an average cos curve dagram.
2 2. Consder a wo-secor growh model n whch he represenave consumer has he uly funcon a a2 log( c c2 ). The nvesmen good s produced accordng o a a2 k dx x, 2 where and 2. Feasble consumpon/nvesmen plans sasfy he feasbly consrans where c x ( k, ) k c x ( k, ), k k k 2 2. The nal value of k s k. All of he varables specfed above are n per capa erms. There s a measure L of consumer/workers. a) Defne an equlbrum for hs economy. b) Wre ou a socal planner s problem for hs economy. Explan how soluon o hs socal planner s problem s relaed o ha of he one-secor socal planner s problem log c a s.. c k dk c, k k k. [You can wre done a proposon or proposons whou provdng a proof or proofs, bu be sure o carefully relae he varables n he wo-secor model o he varables n he one-secor model.] c) Solve he one-secor socal planner s problem n par b. [Recall ha he polcy funcon for nvesmen has he form ( ) a k k Adk where A s a consan ha you remember or can deermne wh a b of algebra and calculus.] d) Suppose now ha here s a world made up of n dfferen counres, all wh he same echnologes and preferences, bu wh dfferen consan populaons, L, and wh 2
3 dfferen nal capal-labor raos k. Suppose ha goods and 2 can be freely raded across counres, bu ha he nvesmen good canno be raded. Suppose oo ha here s no nernaonal borrowng. Defne an equlbrum for he world economy. a e) Le s c / y where y p k p2 dk s world GDP per capa. Transform he frs-order condons for he one-secor socal planner s problem n par b no wo dfference equaons n k and s. Use he frs-order condons for he consumer s problem of he equlbrum n par d o show ha y y s y y s y y. y s y s y f) Use he soluon o he one-secor socal planner s problem n par c o solve for s. Dscuss he economc sgnfcance of he resul ha you oban. 3
4 3. Consder an economy where he consumers have Dx-Sglz uly funcons and solve he problem m max ( ) log c log c( z) dz m s.. pc p( zczdz ) ( ) w cz ( ). Here and. Furhermore, m s he measure of frms, whch s deermned n equlbrum. Suppose ha good s produced wh he consan-reurns producon funcon y. a) Suppose ha he producer of good z akes he prces p( z ), for z z, as gven. Suppose oo ha hs producer has he producon funcon yz ( ) max xz ( ) ( z) f,. where xz ( ) s he frm s producvy level and f. Solve he frm s prof maxmzaon problem o derve an opmal prcng rule. b) Suppose ha good s produced wh he consan-reurns producon funcon y Suppose ha frm producves are dsrbued on he nerval x accordng o he Pareo dsrbuon wh dsrbuon funcon F( x) x, where 2 and /( ). Also suppose ha he measure of poenal frms s fxed a. Defne an equlbrum for hs economy. c) Suppose ha, n equlbrum no all poenal frms acually produce. Fnd an expresson for he producvy of he leas producve frm ha produces. Tha s, fnd a producvy x such ha no frm wh x( z) x produces and all frms wh x( z) x produce. Relae he measure of frms ha produce m o he measure of poenal frms and he cuoff x. d) Suppose now ha here are wo counres ha engage n rade. Each counry,, 2, has a populaon of and a measure of poenal frms of. Frms producves are agan dsrbued accordng o he Pareo dsrbuon, F( x) frm n counry faces a fxed cos of exporng o counry,, of f e where f f f. Each counry also mposes an ad valorem arff on mpors of e d dfferenaed goods from he oher counry. The revenue from hese arffs s x. A 4
5 redsrbued n lump-sum form o he consumer n ha counry. Defne an equlbrum for hs world economy. e) Suppose ha he wo counres n par d are symmerc n he sense ha 2 and 2. Explan how o characerze he equlbrum producon paerns wh a cuoff value, or values, as n par c. [You should explan carefully how o calculae any cuoff values, bu you o no acually need o calculae.] Compare hs value, or hese values, wh ha n par c. Draw a graph depcng wha happens when a closed economy opens o rade. f) Dscuss he srenghs and lmaons of hs sor of model for accounng for frmlevel daa on expors. 5
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