*This holistic economic growth model consists of the economic *sub-system with the aid equations, the carbon cycle model, *the global surface temperature model, and the feedback equations. *This model was developed by Anantha K. Duraiappah of the Economics *Department, University of Texas at Austin, Texas, 1991. $OFFSYMXREF OFFSYMLIST OFFUELLIST OFFUELXREF SETS R REGIONS /Deved,Deveing / * Deved represents the developed countries * Deveing represents the developing countries RD(R) Region which provides aid /Deved / RR(R) Region which receives aid /Deveing / S SECTORS /Industry, Agri, Services/ * Agri stands for the agriculture sector. * Industry represents manufacturing, construction, and other * heavy industries. * Services represents communications, transport, and other * light industries. SR(S) Energy Dependent sectors /Industry, Services / P PROCESS /Abat, Inter, Intens / * Abat represents pollution abatement processes. * Inter represents pollution technique that falls in between * Abat and Intens. * Intens represents pollution intensive techniques. * These numbers represent the natural carbon reservoirs. RI NUMBERS /1*4 / T TIME /1985,1990,1995,2000,2005,2010,2015,2020,2025,2030, 2035 / TE(T) SUBSET /1985,1990,1995,2000,2005,2010,2015,2020,2025,2030/ TB(T) BASE YEAR TT(T) TERMINAL YEAR ; TB(T) =YES$(ORD(T) EQ 1) ; TT(T) =YES$(ORD(T) EQ CARD(T)) ; ALIAS (S,SP) ; ALIAS (R,RP) ; TABLE Alphar(R,S,SP) INPUT-OUTPUT MATRIX Industry Agri Services Deved.Industry 0.33 0.08 0.11 Deved.Agri 0.05 0.34 0.03 Deved.Services 0.14 0.12 0.20 Deveing.Industry 0.30 0.07 0.07 Deveing.Agri 0.10 0.17 0.01 Deveing.Services 0.18 0.14 0.14 TABLE Delta(R,S) DEPRECIATION RATES Industry Agri Services Deved 0.02 0.02 0.02 Deveing 0.02 0.02 0.02 TABLE Beta(S,SP) CAPITAL-OUTPUT RATIO Industry Agri Services Industry 1.39 0.69 0.35 Agri 0.00 0.00 0.00 Services 0.00 0.00 0.00 * The parameter Betar assigns the same values of beta for * both regions. PARAMETER Betar(R,S,SP) ; Betar(R,S,SP) = Beta(S,SP) ; TABLE Zeta(R,S,*) Energy units (exajoules) to produce unit output in base year 1985 Deved.Industry 0.016 Deved.Agri 0.0 Deved.Services 0.009 Deveing.Industry 0.034 Deveing.Agri 0.0 Deveing.Services 0.016 SCALAR EFF Efficiency parameter for energy use in sectors /0.99/ ; SCALAR TAU YEARS PER TIME PERIOD /5/ ; PARAMETER ZETAT(R,S,T) Energy units (exajoules) in each subsequent time period; ZETAT(R,S,T) = ZETA(R,S,"1985")* (EFF**(TAU*(ORD(T)-1))) ; DISPLAY ZETAT ; TABLE ZETACO2 (S,P) CO2 emission coefficienys for each process Abat Inter Intens Industry 0.00 0.0177 0.0238 Agri 0.00 0.000 0.000 Services 0.00 0.0177 0.0238 PARAMETER Zetaf(R) CO2 emissions from deforestation /Deved 0.06 Deveing 0.12 / ; PARAMETER Theta(RI) Transfer rates of CO2 from natural reservoirs /1 0.049 2 0.136 3 0.123 4 0.09 / ; TABLE zsini(R,S,*) Initial values for each region sectorial GDP levels in 1980 billion dollars 1985 Deved.Industry 3500 Deved.Agri 1000 Deved.Services 5500 Deveing.Industry 816 Deveing.Agri 840 Deveing.Services 696 TABLE ZSGROWTH(R,S) Sectorial growth rate in each region Industry Agri Services Deved 1.03 1.03 1.03 Deveing 1.07 1.04 1.02 PARAMETER zstilde(R,S,T) DESIRED PATH FOR Sectorial GDP ; zstilde(R,S,T) = zsini(R,S,"1985") *(ZSGROWTH(R,S)**(TAU*(ORD(T)-1))); TABLE qsini(R,S,*) Initial values for sectorial output in base year in 1980 billion dollars 1985 Deved.Industry 6900 Deved.Agri 2420 Deved.Services 8440 Deveing.Industry 1415 Deveing.Agri 1200 Deveing.Services 1300 TABLE QSGROWTH(R,S) Growth rate for sectorial output Industry Agri Services Deved 1.03 1.03 1.03 Deveing 1.07 1.04 1.02 PARAMETER QSTILDE(R,SP,T) Desired path for sectorial output ; qstilde(R,S,T) = qsini(R,S,"1985") *(QSGROWTH(R,S)**(TAU*(ORD(T)-1))); TABLE Wzs(R,S,T) PENALTY MATRIX FOR PRODUCTION 1985 1990 1995 2000 2005 2010 2015 2020 Deved.Industry 30 30 30 30 30 30 30 30 Deved.Agri 300 300 300 300 300 300 300 300 Deved.Services 50 50 50 50 50 50 50 50 Deveing.Industry 460 460 460 460 460 460 460 460 Deveing.Agri 430 430 430 430 430 430 430 430 Deveing.Services 620 620 620 620 620 620 620 620 + 2025 2030 2035 Deved.Industry 30 30 30 Deved.Agri 300 300 300 Deved.Services 50 50 50 Deveing.Industry 460 460 460 Deveing.Agri 430 430 430 Deveing.Services 620 620 620 TABLE MPC(R,S) MARGINAL PROPENSITY TO CONSUME Industry Agri Services Deved 0.40 0.35 0.6 Deveing 0.30 0.50 0.50 TABLE CGROWTH(R,*) Growth rate for consumption in agriculture sector AGRI DEVED 1.005 DEVEING 1.04 PARAMETER ctilde(R,S,T) Desired path for sectorial consumption ; ctilde(R,SR,T) = MPC(R,SR) * qstilde(R,SR,T) ; CTILDE(R,"AGRI","1985") = MPC(R,"AGRI")*QSTILDE(R,"AGRI","1985") ; CTILDE(R,"AGRI",T) = CTILDE(R,"AGRI","1985")* (CGROWTH(R,"AGRI")**(TAU*(ORD(T)-1))) ; TABLE Wc(R,S,T) PRIORITY MATRIX FOR CONSUMPTION VARIABLE 1985 1990 1995 2000 2005 2010 Deved.Industry 40 40 40 40 40 40 Deved.Agri 121 121 121 121 121 121 Deved.Services 4 4 4 4 4 4 Deveing.Industry 2000 2000 2000 2000 2000 2000 Deveing.Agri 170 170 170 170 170 170 Deveing.Services 250 250 250 250 250 250 + 2015 2020 2025 2030 2035 Deved.Industry 40 40 40 40 40 Deved.Agri 121 121 121 121 121 Deved.Services 4 4 4 4 4 Deveing.Industry 2000 2000 2000 2000 2000 Deveing.Agri 170 170 170 170 170 Deveing.Services 250 250 250 250 250 PARAMETER BO(R) Base level of forest land in million hectares /Deved 1824 Deveing 2265 / ; TABLE DO(*,R) Initial conditions for agriculture land in million hectares Deved Deveing 1985 670 800 TABLE IO(R,S,*) Initial values for sectorial investment in 1980 billion dollars 1985 Deved.Industry 500 Deved.Agri 300 Deved.Services 500 Deveing.Industry 340 Deveing.Agri 150 Deveing.Services 250 parameter dtilde(R,T) Desired path for agriculture land usage ; PARAMETER LU(R) Land usage growth rate /Deved 1.0032 Deveing 1.012 / ; dtilde(R,T) = DO("1985",R)*( LU(R) **(TAU*(ORD(T)-1))) ; TABLE Wd(R,T) PRIORITY MATRIX FOR LAND 1985 1990 1995 2000 2005 2010 Deved 3E+4 3E+4 3E+4 3E+4 3E+4 3E+4 Deveing 2E+5 2E+5 2E+5 2E+5 2E+5 2E+5 + 2015 2020 2025 2030 2035 Deved 3E+4 3E+4 3E+4 3E+4 3E+4 Deveing 2E+5 2E+5 2E+5 2E+5 2E+5 PARAMETER natilde(R,T) Desired path for regional CO2 emissions in carbon Gt per year ; natilde("Deved",T) = 1.5 ; natilde("Deveing",T) = 1.5 ; TABLE Wna(R,T) PENALTY MATRIX FOR CARBON CONCENTRATIONS 1985 1990 1995 2000 2005 2010 Deved 7E-8 7E-8 7E-8 7E-8 7E-8 7E-8 Deveing 7E-8 7E-8 7E-8 7E-8 7E-8 7E-8 + 2015 2020 2025 2030 2035 Deved 7E-8 7E-8 7E-8 7E-8 7E-8 Deveing 7E-8 7E-8 7E-8 7E-8 7E-8 TABLE IGROWTH(R,S) Growth rates for sectorial investment Industry Agri Services Deved 1.02 1.03 1.03 Deveing 1.04 1.03 1.02 PARAMETER itilde(R,S,T) DESIRED PATH FOR INVESTMENT ; itilde(R,S,T) = io(R,S,"1985") *(iGROWTH(R,S)**(TAU*(ORD(T)-1))); TABLE Lambdai(R,S,T) PENALTY MATRIX FOR INVESTMENT 1985 1990 1995 2000 2005 2010 Deved.Industry 120 120 120 120 120 120 Deved.Agri 340 340 340 340 340 340 Deved.Services 120 120 120 120 120 120 Deveing.Industry 260 260 260 260 260 260 Deveing.Agri 1300 1300 1300 1300 1300 1300 Deveing.Services 500 500 500 500 500 500 + 2015 2020 2025 2030 2035 Deved.Industry 120 120 120 120 120 Deved.Agri 340 340 340 340 340 Deved.Services 120 120 120 120 120 Deveing.Industry 260 260 260 260 260 Deveing.Agri 1300 1300 1300 1300 1300 Deveing.Services 500 500 500 500 500 PARAMETER ftilde(R,T) DESIRED PATH FOR DEFORESTATION ; PARAMETER DF(R) DESIRED RATE OF DEFORESTATION PER YEAR /Deved 1 Deveing 11 / ; ftilde(R,T) =DF(R) ; TABLE Lambdaf(R,T) PENALTY MATRIX FOR DEFORESTATION 1985 1990 1995 2000 2005 2010 Deved 3.5E+3 3.5E+3 3.5E+3 3.5E+3 3.5E+3 3.5E+3 Deveing 3.0E+8 3.0E+8 3.0E+3 3.0E+3 3.0E+3 3.0E+3 + 2015 2020 2025 2030 2035 Deved 3.5E+3 3.5E+3 3.5E+3 3.5E+3 3.5E+3 Deveing 3.0E+3 3.0E+3 3.0E+3 3.0E+3 3.0E+3 TABLE MUK(R,S,P) Constant term in capital-output coefficient Abat Inter Intens Deved.Industry 3.0 1.68 1.40 Deved.Agri 1.08 1.20 1.32 Deved.Services 2.50 1.50 1.25 Deveing.Industry 4.87 2.74 2.11 Deveing.Agri 1.20 1.33 1.46 Deveing.Services 3.59 2.15 1.65 TABLE TECK(R,S,P) Technical innovation factor for constant term in capital-output coefficient Abat Inter Intens Deved.Industry 0.99 1.00 1.00 Deved.Agri 1.00 1.00 1.00 Deved.Services 0.99 1.00 1.00 Deveing.Industry 0.99 1.00 1.00 Deveing.Agri 1.00 1.00 1.00 Deveing.Services 0.99 1.00 1.00 PARAMETER MUKT(R,S,P,T) Capital-output coefficients reflecting technical innovation ; MUKT(R,S,P,T) = MUK(R,S,P)* (TECK(R,S,P)**(TAU*(ORD(T)-1))); DISPLAY MUKT ; TABLE NUK(R,S,P) temperature feedback effect on capital-output coefficient Abat Inter Intens Deved.Industry 0 0 0 Deved.Agri 0.36 0.40 0.44 Deved.Services 0 0 0 Deveing.Industry 0 0 0 Deveing.Agri 0.40 0.44 0.48 Deveing.Services 0 0 0 TABLE SIGMAK(R,S,P) CO2 fertilization effect on capital-output coefficient Abat Inter Intens Deved.Industry 0 0 0 Deved.Agri -0.0009 -0.001 -0.001 Deved.Services 0 0 0 Deveing.Industry 0 0 0 Deveing.Agri -0.0004 -0.0004 -0.0005 Deveing.Services 0 0 0 TABLE MUD(R,S,P) Constant term in land-output coefficient Abat Inter Intens Deved.Industry 0.00 0.00 0.00 Deved.Agri 1.00 0.67 0.28 Deved.Services 0.00 0.00 0.00 Deveing.Industry 0.00 0.00 0.00 Deveing.Agri 0.95 0.67 0.28 Deveing.Services 0.00 0.00 0.00 TABLE TECD(R,S,P) Technical innovation factor for constant term in land-output coefficient Abat Inter Intens Deved.Industry 1.00 1.00 1.00 Deved.Agri 0.99 0.99 0.99 Deved.Services 1.00 1.00 1.00 Deveing.Industry 1.00 1.00 1.00 Deveing.Agri 0.99 0.99 0.99 Deveing.Services 1.00 1.00 1.00 PARAMETER MUDT(R,S,P,T) Land-output coefficients reflecting technical innovation ; MUDT(R,S,P,T) = MUD(R,S,P)*(TECD(R,S,P)**(TAU*(ORD(T)-1))) ; DISPLAY MUDT ; TABLE NUD(R,S,P) Temperature feedback effect on land-output coefficient Abat Inter Intens Deved.Industry 0 0 0 Deved.Agri 0.33 0.22 0.09 Deved.Services 0 0 0 Deveing.Industry 0 0 0 Deveing.Agri 0.32 0.22 0.09 Deveing.Services 0 0 0 TABLE SIGMAD(R,S,P) CO2 fertilization effect on land-output coefficient Abat Inter Intens Deved.Industry 0 0 0 Deved.Agri -0.0008 -0.0005 -0.0002 Deved.Services 0 0 0 Deveing.Industry 0 0 0 Deveing.Agri -0.0003 -0.0002 -0.0001 Deveing.Services 0 0 0 VARIABLES k(T,R,S) CAPITAL STOCKS d(T,R) LAND SUPPLY i(T,R,S) Investment levels c(T,R,S) Consumption levels hr(t,rr,s) Sectorial foreign aid received by recipient region hd(t,rd,s) Sectorial foreign aid sent by donor region faid(t,r) Regional foreign aid f(T,R) Deforestation rate qp(T,R,S,P) Output at process level qs(T,R,S) Output at sectorial level zs(t,r,s) Sectorial gross domestic product zr(t,r) Regional gross domestic product qj(t,r,s,p) Energy units used at process level e(t,r,s,p) CO2 emissions in Gt at the process level er(t,r) CO2 emissions in Gt by regions eg(t) Global CO2 emission in Gt J CRITERION POSITIVE VARIABLES i,c,k,d,f,qp,qs,qj,e,er,eg,zs,zr,hd,hr ; EQUATIONS CRITERION OBJECTIVE FUNCTION MATBALD(T,RD,S) MATERIAL BALANCE FOR DONAR REGION MATBALR(T,RR,S) MATERIAL BALANCE FOR RECIPENT REGION CAPITAL(T,R,S) CAPITAL ACCUMULATION SECTORAL(T,R,S) OUTPUT AT SECTOR LEVEL GDPS(T,R,S) SECTORIAL GDP GDP(T,R) REGIONAL GDP CAPSTOCK(T,R,S) CAPITAL STOCK CONSTRAINT BTUC(t,r,s,p) ENERGY DEMAND BY PROCESSES POLLUTION(t,r,s,p) CO2 EMISSIONS BY PROCESSES (FOSSIL FUELS) RPOLL(t,r) CO2 EMISSIONS BY REGIONS (FOSSIL FUELS AND DEFORESTATION) GLOBPOLL(t) GLOBAL CO2 EMISSIONS TAID(T) TOTAL AID BALANCE UAID(T) UPPER BOUND ON AID FROM DONOR REGION AIDC(T,RR,S) FOREIGN AID CONDITION UPPERF(T,R) DEFORESTATION CONSTRAINT IN EACH TIME PERIOD LOWERP(T,R,S,P) LOWER BOUND ON OUTPUT BY POLLUTION INTERMEDIATE PROCESS LAND(T,R) LAND CONSTRAINT LANDSUPP(T,R) LAND SUPPLY DEFOREST(R) DEFORESTATION CONSTRAINT OVER PLANNING PERIOD ; * OBJECTIVE FUNCTION CRITERION.. J =E= 0.5*SUM((T,R,S), (zs(T,R,S)-zstilde(R,S,T)) *Wzs(R,S,T) *(zs(T,R,S)-zstilde(R,S,T))) + 0.5* SUM((T,R,S), (c(T,R,S)-ctilde(R,S,T)) *Wc(R,S,T) *(c(T,R,S)-ctilde(R,S,T))) + 0.5*SUM((T,R), (d(T,R)-dtilde(R,T)) *wd(R,T) *(d(T,R)-dtilde(R,T))) + 0.5*SUM((T,R,S), (i(T,R,S)-itilde(R,S,T)) *Lambdai(R,S,T) *(i(T,R,S)-itilde(R,S,T))) ; * MATERIAL BALANCE FOR THE DONOR REGION MATBALD(T,RD,S).. qs(T,RD,S) =E= SUM(SP,Alphar(RD,S,SP)* qs(T,RD,SP)) + SUM(SP,Betar(RD,S,SP)*i(T,RD,SP)) + c(T,RD,S)+ hd(T,RD,S) ; * MATERIAL BALANCE FOR THE RECIPIENT REGION MATBALR(T,RR,S).. qs(T,RR,S) =E= SUM(SP,Alphar(RR,S,SP)* qs(T,RR,SP)) + SUM(SP,Betar(RR,S,SP)*i(T,RR,SP)) + c(T,RR,S) -hr(T,RR,S) ; * CAPITAL ACCUMULATION CAPITAL(T+1,R,S).. k(T+1,R,S) =E=(1-DELTA(R,S))** TAU * k(T,R,S) + TAU * i(T,R,S) ; * OUTPUT AT SECTOR LEVEL SECTORAL(T,R,S).. qs(T,R,S) =E= SUM(P,qp(T,R,S,P)) ; * SETORIAL GDP GDPS(T,R,S).. zs(T,R,S) =E= qs(T,R,S) - SUM(SP, ALPHAR(R,S,SP)*qs(T,R,SP)); * REGIONAL GDP GDP(T,R).. zr(T,R) =E= SUM(S,zs(T,R,S)) ; * CAPITAL STOCK CONSTRAINT CAPSTOCK(T,R,S).. SUM(P, MUKT(R,S,P,T)*qp(T,R,S,P)) =L= k(T,R,S) ; * ENERGY DEMAND BY PROCESSES BTUC(T,R,S,P).. qj(T,R,S,P) =E= qp(T,R,S,P)*ZETAT(R,S,T) ; * CO2 EMISSIONS BY PROCESSES (FOSSIL FUELS) POLLUTION(T,R,S,P).. e(T,R,S,P) =E= (qj(T,R,S,P) * ZETACO2(S,P)); * CO2 EMISSIONS AT REGIONAL LEVEL (DEFORESTATION AND FOSSIL FUELS) RPOLL(t,r).. er(T,R) =E= SUM((S,P),e(T,R,S,P)) + ZETAF(R)*f(T,R) ; * GLOBAL CO2 EMISSIONS GLOBPOLL(T).. eg(T) =E= SUM(R,er(T,R)) ; * TOTAL AID BALANCE TAID(T).. SUM((RD,S),HD(T,RD,S)) =E= SUM((RR,SR),HR(T,RR,SR)) ; * UPPER BOUND ON AID FROM DONOR REGION UAID(T).. SUM((RD,S),HD(T,RD,S)) =L= 0.15* SUM(RD,zr(T,RD)) ; * FOREIGN AID CONDITION AIDC(T,RR,SR).. hr(T,RR,SR) =L= (MUKT(RR,SR,"ABAT",T)- MUKT(RR,SR,"INTENS",T))*qp(T,RR,SR,"ABAT") + (MUKT(RR,SR,"INTER",T)-MUKT(RR,SR,"INTENS",T))*qp(T,RR,SR,"INTER"); * DEFORESTATION CONSTRAINT IN EACH TIME PERIOD UPPERF(T,R).. f(t,r) =L= 20 ; * LOWER BOUND ON OUTPUT BY POLLUTION INTERMEDIATE PROCESS LOWERP(T,R,SR,"INTER").. QP(T,R,SR,"INTER") =G= 0.5*QS(T,R,SR); * LAND CONSTRAINT LAND(T,R).. SUM((S,P), MUD(R,S,P)*qp(T,R,S,P)) =L= d(t,r) ; * LAND SUPPLY LANDSUPP(T+1,R).. d(T+1,R) =E= d(T,R) + TAU*f(T,R) ; * DEFORESTATION CONSTRAINT OVER PLANNING PERIOD DEFOREST(R).. SUM(T, TAU*f(T,R)) =L= BO(R) ; * The following option statement are used to solve the model OPTION ITERLIM = 50000; OPTION NLP=MINOS5 ; OPTION LIMCOL = 0 ; OPTION LIMROW = 0 ; OPTION SOLPRINT = Off ; OPTION DECIMALS = 5 ; OPTION RESLIM = 10000 ; * These are fixed initial values for capital stock in base year k.FX ("1985","Deved","Industry") = 10916; k.FX ("1985","Deved","Agri") = 3195 ; k.FX ("1985","Deved","Services") = 11922 ; k.FX ("1985","Deveing","Industry") = 3458 ; k.FX ("1985","Deveing","Agri") =1440; k.FX ("1985","Deveing","Services") =2489 ; * These are initial vlues for sectorial GDP in base year zs.L("1985","Deved","Industry") = 3500 ; zs.L("1985","Deved","Agri") = 1000 ; zs.L("1985","Deved","Services") = 5500 ; zs.L("1985","Deveing","Industry") = 816 ; zs.L("1985","Deveing","Agri") = 840 ; zs.L("1985","Deveing","Services") = 696 ; * This is fixed initial value for agricultural land in base year d.FX ("1985",R) = DO("1985",R) ; * Foerign aid is only used by the industry and services sectors in the * recipient region hr.FX(T,RR,"Agri") = 0.0 ; * The results from the first solve statement are used as reference * points to help find feasible solutions for the non-linear * Holistic Base model MODEL ENVIRO /ALL / ; SOLVE ENVIRO MINIMIZING J USING NLP ; * The following parameters represent the desired paths for the state * and control variables in the criterion function PARAMETER zstildep(T,R,S) ; zstildep(T,R,S) = zstilde(R,S,T) ; OPTION zstildep:3:1:2; DISPLAY zstildep ; PARAMETER ctildep(T,R,S) ; ctildep(T,R,S) = ctilde(R,S,T) ; OPTION ctildep:3:1:2; DISPLAY ctildep; PARAMETER dtildep(T,R); dtildep(T,R) = dtilde(R,T) OPTION dtildep:5:1:1; DISPLAY dtildep; PARAMETER itildep(T,R,S); itildep(T,R,S) = itilde(R,S,T); OPTION itildep:5:1:2; DISPLAY itildep; PARAMETER ftildep(T,R) ; ftildep(T,R) = ftilde(R,T) ; OPTION ftildep:5:1:1; DISPLAY ftildep; PARAMETER qstildep(t,r,sp); qstildep(t,r,sp) = qstilde(r,sp,t); OPTION qstildep:3:1:2; DISPLAY qstildep ; * THIS IS THE SECOND MODEL WITH THE CARBON CYCLE AND TEMPERATURE * MODEL ADDED TO THE ECONOMIC MODEL VARIABLES nat(t) Carbon mass in Gt in atmosphere nbt(T) Carbon mass in Gt in land nmt(T) Carbon mass in Gt in surface ocean erpmv(t) Concentration of CO2 in atmosphere in ppmv tg(t) Global surface temperature J1 Criterion POSITIVE VARIABLES nat,mbt,nmt,erpmv,tg ; EQUATIONS CRITERION1 OBJECTIVE FUNCTION AB(T) CARBON FLUX BETWEEN LAND AND THE OTHER RESERVOIRS ABSO(T) CARBON FLUX BETWEEN ATMOSPHERE AND THE OTHER RESERVOIRS ASODO(T) CARBON FLUX BETWEEN SURFACE OCEAN AND THE OTHER RESERVOIRS CONE (T) CONVERSION FORMULA FROM MASS TO CONCENTRATION IN ATMOSPHERE TEMP(T) GLOBAL SURFACE TEMPERATURE CHANGE ; * OBJECTIVE FUNCTION CRITERION1.. J1 =E= 0.5*SUM((T,R,S), (zs(T,R,S)-zstilde(R,S,T)) *Wzs(R,S,T) *(zs(T,R,S)-zstilde(R,S,T))) + 0.5* SUM((T,R,S), (c(T,R,S)-ctilde(R,S,T)) *Wc(R,S,T) *(c(T,R,S)-ctilde(R,S,T))) + 0.5*SUM((T,R), (d(T,R)-dtilde(R,T)) *wd(R,T) *(d(T,R)-dtilde(R,T))) +0.5*SUM((T,R,S), (i(t,r,s)-itilde(R,S,T)) *Lambdai(R,S,T) *(i(t,r,s)-itilde(R,S,T))) +0.5*SUM((T,R), (er(T,R)-natilde(R,T)) *Wna(R,T) *(er(T,R)-natilde(R,T))); * CARBON FLUX BETWEEN LAND AND THE OTHER RESERVOIRS AB(T+1).. nbt(T+1) =E= Theta("2") * nat(T) +(1-theta("1"))* nbt(T) ; * CARBON FLUX BETWEEN ATMOSPHERE AND THE OTHER RESERVOIRS ABSO(T+1).. nat(T+1) =E= TAU* eg(T) + (1-Theta("2")-Theta("3"))*nat(T) +Theta("1")*nbt(T) +Theta("4")*nmt(T) ; * CARBON FLUX BETWEEN SURFACE OCEAN AND THE OTHER RESERVOIRS ASODO(T+1).. nmt(T+1) =E= Theta("3")*nat(T) +(1-Theta("4"))* nmt(T) ; * CONVERSION FORMULA FOR CONVERTING FROM MASS TO CONCENTRATION * FOR CO2 IN ATMOSPHERE CONE (T).. erpmv (T) =E= nat(T) /2.12; * GLOBAL SURFACE TEMPERATURE CHANGE TEMP(T).. tg(T) =E= 3*(LOG(ERPMV(T))-LOG(270))/0.6931 ; * The initial values for the mass in each reservoir are fixed * in Gt carbon for the base year nat.fx("1985") = 760 ; nbt.fx("1985") = 2060; nmt.FX("1985") = 1005; * lower bound is assigned to atmospheric CO2 concentration to avoid * infeasibility problems erpmv.LO(t) = 0.001 ; OPTION BRATIO= 1 ; option solprint = off; OPTION LIMROW = 0; MODEL BASE /CRITERION1,MATBALD,CAPITAL,SECTORAL,CAPSTOCK, POLLUTION,GLOBPOLL,LAND,LANDSUPP,DEFOREST,AB,RPOLL,ABSO,ASODO, TEMP,UPPERF,MATBALR,GDPS,GDP,LOWERP,BTUC,CONE,TAID,UAID,AIDC/; SOLVE BASE MINIMIZING J1 USING NLP ; * The following parameters represent the optimal values for the * variables in the model. The 0.00001 is added to ensure that * variables which have a value of zero are displayed in the output * file. GAMS display option does not show variables which have * zero values. PARAMETER kp1(T,R,S) ; kp1(t,r,s) = k.L(t,r,s) + 0.00001 ; OPTION kp1:5:1:2; DISPLAY kp1 ; PARAMETER dp1(t,r) ; dp1(t,r) = d.L(t,r) + 0.00001 ; OPTION dp1:5:1:1; DISPLAY dp1 ; PARAMETER ip1(t,r,s) ; ip1(t,r,s) = i.L(t,r,s) + 0.00001 ; OPTION ip1:5:1:2; DISPLAY ip1 ; PARAMETER hrp1(t,rr,s) ; hrp1(t,rr,s) = hr.L(t,rr,s) + 0.00001 ; OPTION hrp1:5:1:2; DISPLAY hrp1 ; PARAMETER hdp1(t,rd,s) ; hdp1(t,rd,s) = hd.L(t,rd,s) + 0.00001 ; OPTION hdp1:5:1:2; DISPLAY hdp1 ; PARAMETER fp1(t,r) ; fp1(t,r) = f.L(t,r) + 0.00001 ; OPTION fp1:5:1:1; DISPLAY fp1; PARAMETER qpp1(t,r,s,p) ; qpp1(t,r,s,p) = qp.L(t,r,s,p) + 0.00001 ; OPTION qpp1:5:1:3; DISPLAY qpp1 ; PARAMETER qsp1(t,r,s) ; qsp1(t,r,s) = qs.L(t,r,s) + 0.00001 ; OPTION qsp1:5:1:2; DISPLAY qsp1 ; PARAMETER zsp1(t,r,s) ; zsp1(t,r,s) = zs.L(t,r,s) + 0.00001 ; OPTION zsp1:5:1:2; DISPLAY zsp1 ; PARAMETER cp1(t,r,s) ; cp1(t,r,s) = c.L(t,r,s) + 0.00001 ; OPTION cp1:5:1:2; DISPLAY cp1 ; PARAMETER ep1(t,r,s,p) ; ep1(t,r,s,p) = e.L(t,r,s,p) + 0.00001 ; OPTION ep1:5:1:3; DISPLAY ep1 ; PARAMETER erp1(t,r) ; erp1(t,r) =er.L(t,r) + 0.00001 ; OPTION erp1:5:1:1; DISPLAY erp1; PARAMETER egp1(T) ; egp1(T) = eg.L(T) + 0.00001 ; DISPLAY egp1 ; PARAMETER erpmvp1(T) ; erpmvp1(T) = erpmv.L(T) + 0.00001 ; DISPLAY erpmvp1; PARAMETER nap1(T) ; nap1(T) = nat.L(T) + 0.00001 ; OPTION nap1:5:0:1; DISPLAY nap1 ; PARAMETER tgp1(T) ; tgp1(T) = tg.L(T) + 0.00001 ; OPTION tgp1:5:0:1; DISPLAY tgp1 ; PARAMETER zrp1(T,R) ; zrp1(T,R) = zr.L(T,R) + 0.00001 ; OPTION zrp1:5:1:1; DISPLAY zrp1 ; * THE FEEDBACK EFFECTS ARE ADDED AT THIS POINT. THIS FINAL * VERSION CONSTITUTES THE HOLISTIC MODEL VARIABLE J2 ; POSITIVE VARIABLES kappa, phi ; EQUATIONS CRITERION2 Objective function INIC(*,R,S,P) Initial condition for capital-output variable INID(*,R,*,P) Initial condition for land-output variable LANDDEF(t,r,*,p) Land-output variable definition CAPDEF(t,r,s,p) Capital-output variable definition CAPSTOCK1(t,r,s) Capital stock constraint LAND2(t,r) Land constraint ; * OBJEVTIVE FUNCTION CRITERION2.. J2 =E= 0.5*SUM((T,R,S), (zs(T,R,S)-zstilde(R,S,T)) *Wzs(R,S,T) *(zs(T,R,S)-zstilde(R,S,T))) + 0.5* SUM((T,R,S), (c(T,R,S)-ctilde(R,S,T)) *Wc(R,S,T) *(c(T,R,S)-ctilde(R,S,T))) + 0.5*SUM((T,R), (d(T,R)-dtilde(R,T)) *wd(R,T) *(d(T,R)-dtilde(R,T))) + 0.5*SUM((T,R,S), (i(t,r,s)-itilde(R,S,T)) *Lambdai(R,S,T) *(i(t,r,s)-itilde(R,S,T))) + 0.5*SUM((T,R), (er(T,R)-natilde(R,T)) *Wna(R,T) *(er(T,R)-natilde(R,T))); * LAND-OUTPUT VARIABLE DEFINITION LANDDEF(t+1,r,"Agri",p).. phi(t+1,r,"Agri",p) =E= MUD(R,"Agri",P)+ NUD(R,"Agri",P)* (tg(T+1)-tg("1985")) + SIGMAD(R,"Agri",P)*(erpmv(T+1)-erpmv("1985")) ; * CAPITAL-OUTPUT VARIABLE DEFINITION CAPDEF(t+1,r,s,p).. kappa(t+1,r,s,p) =E= MUKT(R,S,P,T) + NUK(R,S,P)* (tg(T+1)-tg("1985")) + SIGMAK(R,S,P)*(erpmv(T)-erpmv("1985")) ; * INITIAL CONDITION FOR CAPITAL-OUTPUT VARIABLE INIC("1990",R,S,P).. kappa("1985",r,s,p) =E= MUK(R,S,P) ; * INITIAL CONDITION FOR LAND-OUTPUT VARIABLE INID("1990",R,"Agri",P).. phi("1985",R,"Agri",P) =E= MUD(R,"Agri",P) ; * CAPITAL STOCK CONSTRAINT CAPSTOCK1(t,r,s).. sum(p, kappa(t,r,s,p)*qp(t,r,s,p)) =L= k(t,r,s) ; * LAND CONSTRAINT LAND2(t,r).. SUM(P, phi(t,r,"Agri",p)*qp(t,r,"Agri",p)) =L= d(t,r) ; OPTION BRATIO= 1 ; option solprint = oFF; option limrow = 0 ; MODEL HOLISTIC /CRITERION2,MATBALD,CAPITAL,SECTORAL,CAPSTOCK1, POLLUTION,GLOBPOLL,LAND2,LANDSUPP,DEFOREST,AB,RPOLL, ABSO,ASODO,TEMP,UPPERF,MATBALR,CAPDEF,LANDDEF,INID, BTUC,CONE,INIC,GDPS,GDP,TAID,UAID,AIDC / ; SOLVE HOLISTIC MINIMIZING J2 USING NLP ; PARAMETER kp2(T,R,S) ; kp2(T,R,S) = k.L(T,R,S) + 0.00001 ; OPTION kp2:5:1:2 ; DISPLAY kp2 ; PARAMETER dp2(T,R) ; dp2(T,R) = d.L(T,R) + 0.00001 ; OPTION dp2:5:1:1; DISPLAY dp2 ; PARAMETER ip2(T,R,S) ; ip2(T,R,S) = i.L(T,R,S) + 0.00001 ; OPTION ip2:5:1:2 ; DISPLAY ip2 ; PARAMETER fp2(T,R) ; fp2(T,R) = f.L(T,R) + 0.00001 ; OPTION fp2:5:1:1 ; DISPLAY fp2 ; PARAMETER qpp2(T,R,S,P) ; qpp2(T,R,S,P) = qp.L(T,R,S,P) + 0.00001 ; OPTION qpp2:5:1:3 ; DISPLAY qpp2 ; PARAMETER qsp2(T,R,S) ; qsp2(T,R,S) = qs.L(T,R,S) + 0.00001 ; OPTION qsp2:5:1:2 ; DISPLAY qsp2 ; PARAMETER zsp2(t,r,s) ; zsp2(t,r,s) = zs.L(t,r,s) + 0.00001 ; OPTION zsp2:5:1:2; DISPLAY zsp2 ; PARAMETER cp2(T,R,S) ; cp2(T,R,S) = c.L(T,R,S) + 0.00001 ; OPTION cp2:5:1:2 ; DISPLAY cp2 ; PARAMETER hrp2(t,rr,s) ; hrp2(t,rr,s) = hr.L(t,rr,s) + 0.00001 ; OPTION hrp2:5:1:2; DISPLAY hrp2 ; PARAMETER hdp2(t,rd,s) ; hdp2(t,rd,s) = hd.L(t,rd,s) + 0.00001 ; OPTION hdp2:5:1:2; DISPLAY hdp2 ; PARAMETER ep2(T,R,S,P) ; ep2(T,R,S,P) = e.L(T,R,S,P) + 0.00001 ; OPTION ep2:5:1:3 ; DISPLAY ep2 ; PARAMETER erp2(t,r) ; erp2(t,r) =er.L(t,r) + 0.00001 ; OPTION erp2:5:1:1; DISPLAY erp2; PARAMETER egp2(T) ; egp2(T) = eg.L(T) + 0.00001 ; OPTION egp2:5:0:1; DISPLAY egp2 ; PARAMETER nap2(T) ; nap2(T) = nat.L(T) + 0.00001 ; DISPLAY nap2 ; PARAMETER erpmvp2(T) ; erpmvp2(T) = erpmv.L(T) + 0.00001 ; OPTION erpmvp2:5:0:1; DISPLAY erpmvp2; PARAMETER tgp2(T) ; tgp2(T) = tg.L(T) + 0.00001 ; OPTION tgp2:5:0:1; DISPLAY tgp2 ; PARAMETER KAPPAP(T,R,S,P) ; KAPPAP(T,R,S,P) = KAPPA.L(T,R,S,P) + 0.00001; OPTION KAPPAP:5:3:1; DISPLAY KAPPAP ; PARAMETER PHIP(T,R,S,P) ; PHIP(T,R,S,P) = PHI.L(T,R,S,P) + 0.00001; OPTION PHIP:5:3:1; DISPLAY PHIP;