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1MelitzModel1.1DemandU=(R!q(!)d!)1s.t.R!p(!)q(!)d!=R;de ne=11 ;= 1;note2(0;1);2(1;1)FOC:q(!) 1(R!q(!)d!)1 =p(!))q(!) 1(R!q(!)d!)1 1=p(!))p(!)q(!)=(R!q(!)d!) 1 p(!)1 )R=(R!q(!)d!) 1 R!p(!)1 d!becausewehaveq(!) 1(R!q(!)d!) 1=p(!);de neP=(R!p(!)1 d!)11 thenwecangetq(!) 1RP1 =p(!))q(!)=RP(p(!)P) 1.2SupplyTC=f+q(')'becausep(!)=q(!) 1(R!q(!)d!)1 1=q(')(R!q(!)d!)1 1 f q'FOC:q(') 1(R!q(!)d!)1 1=1')p(')=1')p(')=1'(Thetrickhereis,actuallyp(');q(')shouldbewriteasp(';!);q(';!);however,since!issymmtric,thereisnoneedtowritethemout.)q(')=RP(p(')P) =RP(1P') =RP 1(')r(')=q(')p(')=RP 1(') 11(')=r(') TC=RP 1(') 1 f RP 1(')'=r(') f r(')=(1 )r(') f=r(') f1.3IndustryEquilibrium1.3.1De nitionsandAggregationde ne~'=(R10' 1(')d')1 1here(')=fg(')1 G(')if''0otherwisethen~'(')=(11 G(')R1'' 1g(')d')1 1(intuitively,~' 1istheaverage'ofalltheexisting rms)ActuallywecanrelatetheaggregatevariableswithMand~'U=[R10q(')M(')d']1=[R10q(~')('~')M(')d']1=M1q(~');hereusingq('1)q('2)=('1'2) 1R=R10r(')M(')d'=R10r(~')('~') 1M(')d'=Mr(~')=R10(')M(')d'=1R10r(')M(')d' Mf=M(r(~') f)=M(~')1.3.2DeriveZeroCuto¤Pro tConditionsincer('1)r('2)=('1'2) 1and~=r(~') fthenwehave~=(~'(')') 1r(') fsincer(')=f;then~=f[(~'(')') 1 1](ZCP)zerocuto¤pro tNote,inthismodel, rmneedtopaytwokindsof xedcost,fe,theentrycost,andf,the xedcostinoperation.21.3.3DeriveFreeEntryConditionR10(')g(')d'=fe)1 G(')R10(')(')d'=fe)~=fe1 G(')1.3.4NumberofFirmsP1 =R!p(!)1 d!=R10(') 1(')d'=M(~') 1(Here,Mcomesfromthesym-metryofallthe rms,sotheintegraljustaddsthemup)~=r f=RM(~') 1(~') 1 f=RM fAlso,giventhefullemploymentcondition,wecanderiveR=Lasfollowing,R=+Lp(revenueisdividedbycapitalandlabor)=M~+Lp=M1 G(')fe+LpsinceM=[1 G(')]Me(numberofexit=numberofsuccessfulentry)wehaveR=Mefe+Lp=Le+Lp=L3Subsitutein~;wehave~=LM f)M=L(~+f)1.3.5WelfareU=(R!q(!)d!)1=(MR10(LM(~') 1('))(')d')1=LM1 1~'1.4OpenEconomyModelKeyfeatureoftheclosedmodelis~'isindependantofL,soiftradeonlyincreasesthesizeoftheeconomy,itwilla¤ecttheaverageproductivity.SoMelitzintroducestwokindsoftradecost:1)icebergcost, ;itlookslike rmsmarginalcostnowbecomes '2)a xedcosttostartexport,fex;weusefxtodenotetheamortizedperperiodportionoftheinitial xedcostNow,revenuefromdomesticsalesarerd=R(P') 1;whilerevenuefromexportisrx= 1 R(P') 1sowehaver(')=8:rd(')ifthe rmdoesntexport(1+n 1 )rd(')ifthe rmexportstoallcountries(1)Note,wewanttoreplicatethefactthatcuto¤productivitytoexportishigherthandomesticsale,or'x';sincewehaverd(')=f;then 1 f=fxif'x=';soweneed 1fxf:Thatswhyweneedthetradecost.Melitzstrickistowrite'xintermsof':40= 1 rd('x) fx= 1 ('x) 1rd(')(') 1f fx;or'x=' (fxf)1 1(2)Nowexanteprobabilityofthatoneofthesuccessful rmswillexportpx=(1 G('x))(1 G('))Letthemassofexporting rmsisMx=pxMthenthetotalmassofvarietiesisMt=M+nMx(here,onecanthinkthatifa rmsuppliesavarietytoonecountry,itslikeapointintheline.Thesamevarietysuppliedtohomecountryandtooneofforeigncountriesiscountedastwopoints.)Thentheaverageproductivityoftheeconomycanbewrittenas,~'t=f1Mt[M~' 1+nMx 1 ~' 1x]g1 1(3)Nowtheaverageexpectedpro tsis_=d(~')+pxnx(~'x)=f((~'(')') 1 1)+pxnfx((~'(')'x(')) 1 1)ZCP(4)FEis_=fe1 G(');whichisunchangedasbeforeTogetM;Mx;Mt;notethat_r=(_+f+pxnfx);wehaveM=R_r=L(_+f+pxnfx)1.5ImpactofTradeNote,thenewZCPtellsusthat,given~';wewillgetahigher_;soexposuretotradewillforcetheleastproductive rmstoexitorshutdown.5Inautarky,M=L(~+f);inopeneconomy,M=R_r=L(_+f+pxnfx);sothenumberof rmsbecomessmallafteropenning.Recallthataveragepro tishigherthanautarky.Thevarietyconsumersenjoywillincrease,(1+npx)MMa:Thisisbecauseofthetradebalance.Theamountofexportequalstotheamountofimport.Forwelfare,noteW=LM1 1~';thenWa=LM1 1a~'a;itsmoreconvenienttoexpress'initscuto¤value,since(~'t') 1=rd(~'t)rd(');andrd(~'t)=RMt;rd(')=f;thenWa=L(R=Maf)1 1'aM1 1a=L(Lf)1 1'a(5)Forthesamereason,Wx=L(Lf)1 1'xsowelfareintheopeneconomyislargerthancloseeconomy.1.5.1Thereallocationofmarketsharesandpro tsacross rmsConsidera rmwithproductivity';inautarky,ra(')=(''a) 1r('a)=(''a) 1f;inopeneconomy,domesticsaleisrd(')=('') 1f;thenwehaverd(')ra(');also,therevenueforexporting rmisrd(')+nrx(')=(1+n 1 )rd(');weknowthatwhen !1;ra(')=rd(')=(1+n 1 )rd(');sofora nite ;wehave(1+n 1 )rd(')ra(');sincethemarketisR,thenaexporting rmincreasesitsmarketrevenuewhilenonexporting rmlosesitsmarketshare.Considerthechangeinpro t.4(')=(') a(')=1(rd(')+nrx(') ra(')) nfx=' 1f(1+n 1 (') 1 1('a) 1) nfx;since(1+n 1 )rd(')ra(');then(1+n 1 )('') 1f(''a) 1f;6or(1+n 1 )(1') 1(1'a) 1;thentheiteminbracketispositive,sothechangeofpro tisanincreasingfunctionof rmsproductivity';inaddition,the rmwithcuto¤productivity'xwilllosesinceitschangeofpro tis1(rd(') ra('))0;soonlyexporting rmsgainfromtrade.1.5.2Whydoestheleastproductive rmexit?Note,sinceq(!)=RP(p(!)P) ;theelasticity