Lecture 8. Introduction to New Trade Theory: Intra-industry trade

Transcription

1 eture 8. Introduton to e Trade Theory: Intra-ndustry trade The lassal and neolassal trade theores resented establshed a lnk beteen ross-ountry dfferenes n ether effeny or fator endoments and the dreton and omoston of trade. They dd not, hoever, exlan to key stylzed fats that haraterze ontemorary nternatonal trade atterns:. Dsroortonately large volume of trade takes lae beteen the develoed ountres (orth-orth trade.. Most trade beteen develoed ountres s ntra-ndustry trade n smlar roduts. o t s tme to relax unrealst assumtons of the neolassal trade theory regardng market struture and ondtons of roduton. In artular, e ll fous on the roles of merfet ometton and eonomes of sale. The lassal and neolassal models of omaratve advantage assumed onstant returns to sale (CRS. That s, f nuts to an ndustry ere doubled, ndustry outut ould double as ell. Hoever, n many ndustres e have nreasng returns to sale (IRS,.e. doublng the nuts to an ndustry ll more than double the ndustry s outut.

2 A smle examle an be used to llustrate the mortane of eonomes of sale for nternatonal trade. Total outut Total labor nut Unt labor requrement Soure: Krugman, Meltz and Obstfeld textbook (05. For examle, n to ountres searately you emloy 30 (x5 unt of labor to rodue 0 unts of outut, hoever, f you onentrate roduton n only one ountry you an get 5 unts nstead of 0 unts due to eonomes of sale (loer average osts of roduton. In ths lass e dsuss to ossble aroahes to modelng eonomes of sale and merfet ometton: The reroal dumng olgoolst ometton model of Brander (98. (strong eonomes of sale, lmted number of frms n the market a small grou ase, rodut homogenety The monoolst ometton model of Krugman (979. (eak eonomes of sale, relatvely large number of frms n the market a large grou ase, rodut dfferentaton

3 xx Brander model of nternatonal Cournot olgooly (smlfed verson Model Setu: ountres: ountry (Home and ountry (Foregn ndustry: th frm rodung a homogenous good n eah ountry ( natonal monoolsts fator of roduton (labor Man ontrbuton: Introduton of the frm strategy nto the study of nternatonal trade. Demonstraton of gans from nreased outut (suly sde market sze In neolassal eonoms the most frequently assumed frm strategy s the omettve strategy,.e. frms are assumed to beleve that they an sell as muh outut as they lke at the gong re (thout affetng t. Brander (98 argues that ths strategy s hghly narorate for many ndustres hh are haraterzed by olgoolst ometton here frms have monooly oer and an affet the re. In Brander s model frms emloy a Cournot strategy. Frms lay an outut game (ometton n quanttes. Eah frm maxmzes ts roft assumng the outut of other frms n eah market remans the same. 3

4 Key Model Assumtons Produton Inreasng returns to sale at the frm level are modeled n a very smle ay assumng that the total ost funton s: TC(x F x here F s the fxed ost, s the onstant margnal ost of roduton and x s outut. We an mmedately see that the average ost of roduton delnes th outut as the fxed ost s sread over a larger number of unts: AC(x F/x Transort osts Samuelson eberg assumton. Transort osts are borne by roduers. Thnk of transort osts as shrnkage of the rodut. If the quantty x s shed from ountry to ountry only gx arrves at the lae of destnaton, th 0<g<. Sent Arrved Transort ost x gx (-gx x/g x [(-g/g]x 4

5 Eah frm must dede ho muh to rodue for domest market and ho muh to exort. x j outut delvered by roduer to market j x x total amount delvered to the home market (ountry x x total amount delvered to the foregn market (ountry Demand funton s exatly the same n both ountres. For onvenene, e ll use lnear nverse demand funtons that relate re to outut: P ( a b P ( a b For smlty, e assume that markets are segmented. (o arbtrage an take lae beteen markets Total rofts of the home frm from sales n both markets an be rtten as: Π a b( x x ] x [ a b( x x ] x ( x x / g F [ Total rofts of the foregn frm from sales n both markets an be rtten as: Π a b( x x ] x [ a b( x x ] x ( x x / g F [ 5

6 Frst order ondtons for the home frm an be rtten as: Π x a b( x x bx a bx bx Ths ondton desrbes the otmal behavor of frm n market gven the behavor of frm,.e.: 0 x a bx b Π x a b( x x bx / g a bx bx / g Ths ondton desrbes the otmal behavor of frm n market gven the behavor of frm,.e.: x a g bx b / 0 6

7 Frst order ondtons for the foregn frm an be rtten as: Π a b( x x bx / g a bx bx / g 0 x Ths ondton desrbes the otmal behavor of frm n market gven the behavor of frm,.e.: x a g bx / b Π x a b( x x bx a bx bx Ths ondton desrbes the otmal behavor of frm n market gven the behavor of frm,.e.: 0 x a bx b We have obtaned a system of four equatons n four unknons. Fortunately, ths system an be slt nto to subsystems that desrbe eah market. These to subsystems are erfetly symmetr, so the set of solutons to the frst s also the set of solutons to the seond th x x and x x. Therefore, let s onentrate on the market n the home ountry only. 7

8 8 Rearrangng the set of frst order ondtons for the home and the foregn frms n the frst market e obtan: g a bx bx a bx bx / Wrtng t n the matrx form e obtan: g a a x x b b b b / Det B 4b b 3b 3 / ( ( 3 / ( 3 / 3 ( / ( ( 3 / ( 3 ] / ( [ g a b a P b g a x x b a g b b a a g b x b g a b g a b x Man onluson: Trade an be seen as an nstrument of the anttrust oly. Oenng to nternatonal trade leads to loer res and hgher outut and onsumton (omared to the natonal monooly.

9 Grahal llustraton of the tradng equlbrum x HOME FIRM reaton funton Equal market shares for both frms E E FOREIG FIRM reaton funton a x m x b Fgure. Equlbrum n the Brander model. 9

10 Krugman (979 monoolst ometton model (smlfed verson Model Setu: ountres: ountry (Home and ountry (Foregn ndustry: th many frms rodung a (horzontally dfferentated good n eah ountry fator of roduton (labor Man ontrbuton: Introduton of rodut dfferentaton and monoolst ometton nto the study of nternatonal trade Demonstraton of gans from nreased dversty of roduts (demand sde nreased market effet ke n the Brander (98 model trade s aused by eonomes of sale (and not by dfferenes n fator endoments or dfferenes n tehnology lke n the neolassal trade models. Eonomes are nternal to the frm due to the resene of fxed osts (hoever, they are not as large as n the Brander model!. Hoever, n ontrast to the Brander model the market struture s desrbed by erfet Chamberlnan monoolst ometton and bulds on the Dxt-Stgltz (977 love of varety model for the losed eonomy th many small frms rodung dfferent varetes of rodut. Eah frm rodues only one varety. 0

11 Man assumtons: There s one fator of roduton only labor. The eonomy s able to rodue any of a large number of goods rangng from to, here s determned endogenously thn the model. All resdents have the same utlty funton nto hh all varetes enter symmetrally (the so-alled eream model U ( 0 < < Eah varety yelds dmnshng margnal utlty, so the onsumer alays ants to have one unt of eah rodut, say and, nstead of to unts of ether. s the fxed arameter that has three nterretatons. It determnes: the elastty of substtuton beteen dfferent varetes, the re elastty of demand and the degree of eonomes of sale.

12 The outut of eah varety must equal the sum of ndvdual onsumton: Consumers are at the same tme orkers. The eonomy-de budget onstrant s labor nome sent on rodut. We assume for smlty the same ost funton for all varetes (no frm heterogenety. The labor used n rodung eah good s a lnear funton of outut: l α α, > 0 α - the fxed ost exressed n terms of labor the onstant margnal ost (ndeendent of the volume of outut The total roduton ost an be obtaned multlyng the total labor requrement l by the age rate : TC l α

13 Moreover, e assume full emloyment n the eonomy: l ( α (total labor suly total demand for labor To solve the model e need to determne: Pre-age rato (or ts nverse real ages Outut of eah varety The number of varetes atually rodued We ll onsder a symmetr equlbrum n hh e ll sho that: Symmetr referenes lead to symmetr res Symmetr tehnologes (osts lead to symmetr oututs x x Frst, e need to derve the demand urve fang an ndvdual frm. To do ths e need to solve a deson roblem of a reresentatve onsumer: 3

14 4 s t U.. ( max To solve the onsumer otmzaton roblem e an alays set u a agrangan: λ λ the shado re (margnal utlty of nome. Frst order ondtons (FOC: ( λ λ λ Usng the relatonsh beteen ndvdual onsumton and outut e an turn our FOC nto the exresson for the nverse demand fang an ndvdual frm:

15 5 λ If the number of varetes s large, then eah frm s rng strategy ll have a neglgble effet on the margnal utlty of nome so e an take λ as fxed. In ths ase the demand elastty fang an ndvdual frm ll be onstant and ndeendent of the number of frms. To sho ths substtute the FOC nto the budget onstrant to obtan: ( λ ( λ λ Substtute ths bak nto the FOC to elmnate λ and obtan the ndvdual demand funton:

16 The total demand funton for -th varety s: If the number of frms (varetes s large then the aggregate re ndex s treated by frms as a onstant term. The re elastty of demand n the symmetr ase an be alulated as: ε Hoever, f the number of frm s large, e obtan: lm ε 6

17 7 o let s onsder the roft maxmzaton roblem of a reresentatve frm: ( ( max α Π Calulate the frst order ondton: ε ε ε Π 0 ( ( Knong that f the number of frms s large the re elastty of demand an be treated as a onstant, hene the otmal rng strategy s: ] [/( /( The roft maxmzng re deends on the margnal ost and the elastty of demand. In ths seal ase of the model the re elastty does not deend on outut! (t ll deend n a more general ase.

18 8 Moreover, f the frms have the same roduton tehnology t an be noted that all frms harge the same re: (onstant re-age rato or real age ext, e need to fnd the volume of outut of eah varety (gven the rng strategy. For ths e an use the free entry assumton that drves the roft to zero: α α α α α ( (/ ( 0 ( Π AC

19 We an note that all frms suly the same amount of eah varety: α ( Interestngly, the equlbrum level of outut n ths model s ndeendent of the sze of the eonomy! Hoever, ndvdual onsumton (er orker s not and dereases n the market sze: α ( The equlbrum outut n ths model an be reresented grahally by lookng at the revenue and ost funtons. 9

20 Revenue, ost Revenue funton P Cost funton (α Fxed ost α mn Fgure. Determnaton of the equlbrum level of outut 0

21 The number of varetes rodued an be determned from the full emloyment ondton: α ( α The number of varetes rodued deends on the sze of the eonomy. A bgger eonomy ll enjoy a hgher utlty of onsumers (more varetes avalable for onsumton. The equlbrum n the losed eonomy an be llustrated grahally usng the PP and ZZ urves. The PP urve s derved from the otmal rng ondton: The ZZ urve s derved from the free entry ondton: α α

22 PP ZZ α ( Fgure 3. Equlbrum n the losed eonomy

23 o e are ready to nvestgate the effets of nternatonal trade and nreased market sze. If nreases the onsumton of a reresentatve varety falls and the re-age rato (nverse of real age remans unhanged. Moreover, the total outut of eah varety remans unhanged as t s ndeendent of! The OY gan from trade n ths smlfed model s through nreased dversty of roduts (n the orgnal verson of Krugman s model there s also outut exanson. Assume that there s a foregn ountry th the same tastes and tehnology and oulaton equal. Hene, the number of goods rodued n ths ountry ll be: α ( α The utlty of onsumers n the oen eonomy an be rtten as the sum of utltes derved from onsumton of domestally- and foregn-made varetes: U ( To see gans from trade omare utlty levels under autarky and free trade. Under autarky the onsumton of a reresentatve varety equals: 3

24 A α ( Under free trade the onsumton of a reresentatve varety equals: T α ( ( Substtutng the exressons for onsumton nto the utlty funton e obtan, resetvely: U T U A ( α ( α ( ( To make an easy omarson onsder a erfetly symmetr ase th, then and e have: U T α ( α ( U A > Hene, e an easly note that under free trade utlty of onsumers s hgher omared to autarky. 4

25 The Volume of Trade Fator reards (nome must equal exendture (n eah ountry as trade s balaned (n one-erod model there s no ntertemoral trade: ( home ountry nome total (orld exendture the share of varetes rodued n the home ountry Alternatve nterretaton: Balaned Trade Condton (BTC Home ountry morts Foregn ountry morts (Home ountry exorts 5

26 6 Knong that: Free trade brngs age equalzaton (n the absene of trade osts. The volume of trade s defned as the sum of our exorts and morts: E IM VT

27 Assume that the total labor endoment n the orld eonomy s fxed: Then, ( VT VT ( 0 0 The volume of trade s maxmzed hen ountres are of equal sze. Man onluson: The mortant message from ths model s that eonomes of sale (nreasng returns due to exstene of fxed osts n roduton gve rse to nternatonal trade even hen there are no nternatonal dfferenes n tastes, tehnologes or fator endoments. 7

28 Monoolst ometton model and nternatonal labor moblty Suosng that there s no trade beteen ountres labor but there s ossblty of mgraton labor ll move from a small ountry to a bg ountry (agglomeraton and eventually a small ountry ll dsaear (due to deoulaton. If ountres are of equal sze and roduton tehnologes are the same everyhere then there s no fator moblty beause eah ountry rodues the same number of varetes so the utlty levels n both ountres are exatly the same. Hoever, f tehnologes are not the same,.e. one ountry has hgher roduton osts (both fxed and margnal and the same a larger oulaton, mgraton mght lead to an undesrable outome as orkers mght agglomerate n an neffent regon (nferor soluton, for examle n Calforna (earthquake regon. What f e have both trade and fator moblty? These are erfet substtutes! othng ll haen. As a result of nternatonal trade the number of varetes onsumed ll be the same everyhere, so f there s free trade no labor moblty ours. Hoever, f there are tarffs or transortaton osts quanttes onsumed ll not be the same everyhere. Consumers loated lose to a larger market ll enjoy hgher utlty levels and there ll be an nentve for labor moblty. 8