$TITLE M9_1.GMS: Two-Country Oligopoly, free entry, segmented markets * $ONTEXT YI YJ XI XJ NI NJ PUI PUJ CONI CONJ EHTI ENTJ PYI 100 -100 PYJ 100 -100 PXI 100 -50 -50 PXJ 100 -50 -50 FCI 20 -20 FCJ 20 -20 PSI -40 -48 -12 100 PSJ -40 -48 -12 100 PUI -60 -32 -8 100 PUJ -60 -32 -8 100 PWI 200 -200 PWI 200 -200 MKI -10 -10 10 10 MKJ -10 -10 10 10 $OFFTEXT PARAMETERS TC trade costs on a gross basis (TC = 1 is costless trade) FC fixed costs ENDOWIS endowment of skilled labor in country i ENDOWIL endowment of unskilled labor in country i ENDOWJS endowment of skilled labor in country j ENDOWJL endowment of unskilled labor in country j SUBSIDY subsidy to X productioni in country i MODELSTAT indicator whether or not model solved REALPUI real price of unskilled labor in i REALPUJ real price of unskilled labor in j REALPSI real price of skilled labor in i REALPSJ real price of skilled labor in j XOPFI X output per firm in country i XOPFJ X output per firm in country j; ENDOWIL = 1; ENDOWIS = 1; ENDOWJL = 1; ENDOWJS = 1; TC = 1; FC = 8; SUBSIDY = 0; POSITIVE VARIABLES WFI welfare in country i WFJ welfare in country j YI production of Y in i YJ production of Y in j XI production of X in i XII supply of XI to market i XIJ supply of XI to market j (XIJ shipped XIJ over TC recieved) XJ production of X in j XJJ supply of XJ to market j XJI supply of XJ to market j (XIJ shipped XIJ over TC recieved) NI number of firms in (headquartered in) i NJ number of firms in (headquartered in) j PY domestic and world price of Y (no trade costs) PWI real consumer price index in i PWJ real consumer price index in j PUI price of unskilled labor in i PUJ price of unskilled labor in j PSI price of skilled labor in i PSJ price of skilled labor in j PXI price of X in i PXJ price of X in j PXDI producer marginal cost of X in i PXDJ producer marginal cost of X in j PFI price of fixed costs in i PFJ price of fixed costs in j CONSI consumer income in i CONSJ consumer income in j ENTI entrepreneurs' markup revenues in i ENTJ entrepreneurs' markup revenues in j MARKII markup on a firm from i's sales in i MARKIJ markup on a firm from i's sales in j MARKJI markup on a firm from j's sales in i MARKJJ markup on a firm from j's sales in j; EQUATIONS PRWI Zero profits for WFI PRWJ Zero profits for WFJ PRXDI Marginal cost of X in i PRXII MR = MC for XII PRXIJ MR = MC for XIJ PRXDJ Marginal cost of X in j PRXJJ MR = MC for XJJ PRXJI MR = MC for XJI PRYI Zero profits for YI PRYJ Zero profits for YJ PRFI Zero profits for FI PRFJ Zero profits for FJ DXDI X output in country i DXI Demand for X in country i DXDJ X output in country j DXJ Demand for X in country j DY Demand for Y DWI Demand for welfare in country i DWJ Demand for welfare in country j DFI Demand for fixed costs in i (markup revenues = fixed costs) DFJ Demand for fixed costs in j (markup revenues = fixed costs) SKLABI Market clearing for SI SKLABJ Market clearing for SJ UNLABI Market clearing for LI UNLABJ Market clearing for LJ ICONSI Consumer income in i ICONSJ Consumer income in j IENTREI Entreprenuer's income (markups) in i IENTREJ Entrepreneur's income (markups) in j MKII Markup ii MKIJ Markup ij MKJJ Markup jj MKJI Markup ji; PRXDI.. (PUI**0.40)*(PSI**0.60)*(1-SUBSIDY) =G= PXDI; PRXII.. PXDI =G= PXI*(1 - MARKII); PRXIJ.. PXDI*TC =G= PXJ*(1 - MARKIJ); PRXDJ.. (PUJ**0.40)*(PSJ**0.60) =G= PXDJ; PRXJJ.. PXDJ =G= PXJ*(1 - MARKJJ); PRXJI.. PXDJ*TC =G= PXI*(1 - MARKJI); PRYI.. (PUI**0.60)*(PSI**0.40) =G= PY; PRYJ.. (PUJ**0.60)*(PSJ**0.40) =G= PY; PRWI.. ((PXI/1.25)**0.5)*(PY**0.5) =G= PWI; PRWJ.. ((PXJ/1.25)**0.5)*(PY**0.5) =G= PWJ; PRFI.. (PUI**0.40)*(PSI**0.60) =G= PFI; PRFJ.. (PUJ**0.40)*(PSJ**0.60) =G= PFJ; DXDI.. XII*40 + XIJ*40 =E= XI*80; DXDJ.. XJJ*40 + XJI*40 =E= XJ*80; DXI.. (XII*40 + XJI*40/TC) =E= 0.5*CONSI/PXI; DXJ.. (XJJ*40 + XIJ*40/TC) =E= 0.5*CONSJ/PXJ; DY.. (YI + YJ)*100 =E= 0.5*(CONSI + CONSJ)/PY; DWI.. WFI*200 =E= CONSI/PWI; DWJ.. WFJ*200 =E= CONSJ/PWJ; DFI.. NI*FC =G= ENTI/PFI; DFJ.. NJ*FC =G= ENTJ/PFJ; SKLABI.. 100*ENDOWIS =E= 0.40*YI*100*PY/PSI + 0.60*(XII+XIJ)*40*(PXDI/(1-SUBSIDY))/PSI + 0.60*NI*FC*PFI/PSI; SKLABJ.. 100*ENDOWJS =E= 0.40*YJ*100*PY/PSJ + 0.60*(XJJ+XJI)*40*PXDJ/PSJ + 0.60*NJ*FC*PFJ/PSJ; UNLABI.. 100*ENDOWIL =E= 0.60*YI*100*PY/PUI + 0.40*(XII+XIJ)*40*(PXDI/(1-SUBSIDY))/PUI + 0.40*NI*FC*PFI/PUI; UNLABJ.. 100*ENDOWJL =E= 0.60*YJ*100*PY/PUJ + 0.40*(XJJ+XJI)*40*PXDJ/PUJ + 0.40*NJ*FC*PFJ/PUJ; ICONSI.. CONSI =E= PSI*100*ENDOWIS + PUI*100*ENDOWIL -(PUI**0.40)*(PSI**0.60)*SUBSIDY*XI*80; ICONSJ.. CONSJ =E= PSJ*100*ENDOWJS + PUJ*100*ENDOWJL; IENTREI.. ENTI =G= MARKII*PXI*XII*40 + MARKIJ*PXJ*(XIJ/TC)*40; IENTREJ.. ENTJ =G= MARKJJ*PXJ*XJJ*40 + MARKJI*PXI*(XJI/TC)*40; MKII.. MARKII =E= (XII/NI)/(XII + XJI/TC); MKIJ.. MARKIJ =E= (XIJ/TC/NI)/(XIJ/TC + XJJ); MKJJ.. MARKJJ =E= (XJJ/NJ)/(XIJ/TC + XJJ); MKJI.. MARKJI =E= (XJI/TC/NJ)/(XII + XJI/TC); MODEL M9_1 /DXDI.PXDI, DXDJ.PXDJ, DXI.PXI, DXJ.PXJ, DY.PY, DWI.PWI, DWJ.PWJ, DFI.PFI, DFJ.PFJ, PRXDI.XI, PRXII.XII, PRXIJ.XIJ, PRXDJ.XJ, PRXJJ.XJJ, PRXJI.XJI, PRYI.YI, PRYJ.YJ, PRWI.WFI, PRWJ.WFJ, PRFI.NI, PRFJ.NJ, SKLABI.PSI, SKLABJ.PSJ, UNLABI.PUI, UNLABJ.PUJ, ICONSI.CONSI, ICONSJ.CONSJ, IENTREI.ENTI, IENTREJ.ENTJ, MKII.MARKII, MKIJ.MARKIJ, MKJJ.MARKJJ, MKJI.MARKJI/; CONSI.L = 200; CONSJ.L = 200; ENTI.L = 20; ENTJ.L = 20; XI.L = 1; XJ.L = 1; XII.L = 1; XIJ.L = 1; XJJ.L = 1; XJI.L = 1; YI.L = 1; YJ.L = 1; WFI.L = 1; WFJ.L = 1; NI.L = 2.5; NJ.L = 2.5; PXDI.L = 1; PXDJ.L = 1; PXI.L = 1.25; PXJ.L = 1.25; PY.L = 1; PSI.L = 1; PSJ.L = 1; PUI.L = 1; PUJ.L = 1; PWI.L = 1; PWJ.L = 1; PFI.L = 1; PFJ.L = 1; MARKII.L = 0.20; MARKIJ.L = 0.20; MARKJJ.L = 0.20; MARKJI.L = 0.20; PY.FX = 1; *M9_1.ITERLIM = 0; SOLVE M9_1 USING MCP; MODELSTAT = M9_1.MODELSTAT - 1.; * counterfactual: trade costs of 10% TC = 1.1; SOLVE M9_1 USING MCP; REALPUI = PUI.L/PWI.L; REALPUJ = PUJ.L/PWJ.L; REALPSI = PSI.L/PWI.L; REALPSJ = PSJ.L/PWJ.L; XOPFI = XI.L/(NI.L/2.5); XOPFJ = XJ.L/(NJ.L/2.5); DISPLAY REALPUI, REALPUJ, REALPSI, REALPSJ, XOPFI, XOPFJ; * counterfactual: country's identical except for size, * positive trade costs (home market advantage) TC = 1.1; ENDOWIL = 1.5; ENDOWIS = 1.5; ENDOWJL = 0.5; ENDOWJS = 0.5; SOLVE M9_1 USING MCP; REALPUI = PUI.L/PWI.L; REALPUJ = PUJ.L/PWJ.L; REALPSI = PSI.L/PWI.L; REALPSJ = PSJ.L/PWJ.L; XOPFI = XI.L/(NI.L/2.5); XOPFJ = XJ.L/(NJ.L/2.5); DISPLAY REALPUI, REALPUJ, REALPSI, REALPSJ, XOPFI, XOPFJ; * counterfactual: country h has a comparative advantage in X TC = 1.1; ENDOWIL = 0.8; ENDOWIS = 1.2; ENDOWJL = 1.2; ENDOWJS = 0.8; SOLVE M9_1 USING MCP; REALPUI = PUI.L/PWI.L; REALPUJ = PUJ.L/PWJ.L; REALPSI = PSI.L/PWI.L; REALPSJ = PSJ.L/PWJ.L; XOPFI = XI.L/(NI.L/2.5); XOPFJ = XJ.L/(NJ.L/2.5); DISPLAY REALPUI, REALPUJ, REALPSI, REALPSJ, XOPFI, XOPFJ; * counterfactual: country h has a comparative advantage in X * no trade costs TC = 1.; ENDOWIL = 0.80; ENDOWIS = 1.20; ENDOWJL = 1.20; ENDOWJS = 0.80; SOLVE M9_1 USING MCP; REALPUI = PUI.L/PWI.L; REALPUJ = PUJ.L/PWJ.L; REALPSI = PSI.L/PWI.L; REALPSJ = PSJ.L/PWJ.L; XOPFI = XI.L/(NI.L/2.5); XOPFJ = XJ.L/(NJ.L/2.5); DISPLAY REALPUI, REALPUJ, REALPSI, REALPSJ, XOPFI, XOPFJ;