GAMS Rev 236 WEX-WEI 23.6.3 x86_64/MS Windows 09/19/11 11:59:32 Page 1 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m C o m p i l a t i o n DICE 2007 after canceling extra variables and equations and simplification 4 5 SETS T Time periods /1*60/ ; 6 parameter deltat interval length of each period (number of years); 7 deltat = 10; 8 9 10 SCALARS 11 12 ** Preferences 13 B_ELASMU Elasticity of marginal utility of consumption / 2.0 / 14 B_PRSTP Initial rate of social time preference per year / .015 / 15 16 ** Population and technology 17 POP0 2005 world population millions /6514 / 18 GPOP0 Growth rate of population per year /.035 / 19 POPASYM Asymptotic population / 8600 / 20 A0 Initial level of total factor productivity /.02722 / 21 GA0 Initial growth rate for technology per year /.0092 / 22 DELA Decline rate of technol change per year /.001 / 23 DK Depreciation rate on capital per year /.100 / 24 GAMA Capital elasticity in production function /.300 / 25 K0 2005 value capital trill 2005 US dollars /137. / 26 27 ** Emissions 28 SIG0 CO2-equivalent emissions-GNP ratio 2005 /.13418 / 29 GSIGMA Initial growth of sigma per year /-.00730 / 30 DSIG Decline rate of decarbonization per year /.003 / 31 ELAND0 Carbon emissions from land 2005(GtC per year) / 1.1000 / 32 33 ** Carbon cycle 34 MAT2000 Concentration in atmosphere 2005 (GtC) /808.9 / 35 MU2000 Concentration in upper strata 2005 (GtC) /1255 / 36 ML2000 Concentration in lower strata 2005 (GtC) /18365 / 37 b12 Carbon cycle transition matrix per year /0.0189288 / 38 b23 Carbon cycle transition matrix per year /0.005 / 39 40 ** Climate model 41 T2XCO2 Equilibrium temp impact of CO2 doubling oC / 3 / 42 FEX0 Estimate of 2000 forcings of non-CO2 GHG / -.06 / 43 FEX1 Estimate of 2100 forcings of non-CO2 GHG / 0.30 / 44 TOCEAN0 2000 lower strat. temp change (C) from 1900 /.0068 / 45 TATM0 2000 atmospheric temp change (C)from 1900 /.7307 / 46 C1 Climate-equation coefficient for upper level per year /.0220 / 47 C3 Transfer coeffic upper to lower stratum per year /.300 / 48 C4 Transfer coeffic for lower level per year /.0050 / 49 FCO22X Estimated forcings of equilibrium co2 doubling /3.8 / 50 51 ** Climate damage parameters calibrated for quadratic at 2.5 C for 2105 52 A1 Damage intercept / 0.00000 / 53 A2 Damage quadratic term / 0.0028388 / 54 A3 Damage exponent / 2.00 / 55 56 ** Abatement cost 57 EXPCOST2 Exponent of control cost function /2.8 / 58 PBACK Cost of backstop 2005 000$ per tC 2005 /1.17 / 59 BACKRAT Ratio initial to final backstop cost / 2 / 60 GBACK Initial cost decline backstop pc per year /.005 / 61 LIMMIU Upper limit on control rate / 1 / 62 63 ** Participation 64 PARTFRACT1 Fraction of emissions under control regime 2005 /1 / 65 PARTFRACT2 Fraction of emissions under control regime 2015 /1 / 66 PARTFRACT21 Fraction of emissions under control regime 2205 /1 / 67 DPARTFRACT Decline rate of participation per year /0 / 68 69 ** Availability of fossil fuels 70 FOSSLIM Maximum cumulative extraction fossil fuels / 6000 / 71 ; 72 73 74 SET TLAST(T); 75 TLAST(T) = YES$(ORD(T) EQ CARD(T)); 76 77 78 79 parameters 80 bb11 Carbon cycle transition matrix 81 bb12 Carbon cycle transition matrix 82 bb21 Carbon cycle transition matrix 83 bb22 Carbon cycle transition matrix 84 bb23 Carbon cycle transition matrix 85 bb32 Carbon cycle transition matrix 86 bb33 Carbon cycle transition matrix 87 CC1 Climate-equation coefficient for upper level 88 CC3 Transfer coeffic upper to lower stratum 89 CC4 Transfer coeffic for lower level 90 GGPOP0 Growth rate of population 91 GGA0 Initial growth rate for technology 92 DDELA Decline rate of technol change 93 GGSIGMA Initial growth of sigma 94 DDSIG Decline rate of decarbonization 95 EELAND0 Carbon emissions from land 2005(GtC) 96 GGBACK Initial cost decline backstop pc 97 DDPARTFRACT Decline rate of participation 98 scale1 Scaling coefficient in the objective function; 99 100 bb12 = b12 * deltat; 101 bb23 = b23 * deltat; 102 bb11 = 1 - bb12; 103 bb21 = 587.473*bb12/1143.894; 104 bb22 = 1 - bb21 - bb23; 105 bb32 = 1143.894*bb23/18340; 106 bb33 = 1 - bb32 ; 107 108 CC1 = C1*deltat; 109 CC4 = C4*deltat; 110 CC3 = C3; 111 112 GGPOP0 = GPOP0*deltat; 113 GGA0 = GA0*deltat; 114 DDELA = DELA*deltat; 115 GGSIGMA = GSIGMA*deltat; 116 DDSIG = DSIG*deltat; 117 EELAND0 = ELAND0*deltat; 118 GGBACK = GBACK*deltat; 119 DDPARTFRACT = DPARTFRACT*deltat; 120 scale1 = POPASYM*deltat; 121 122 123 PARAMETERS 124 L(T) Level of population and labor 125 AL(T) Level of total factor productivity 126 SIGMA(T) CO2-equivalent-emissions output ratio 127 RR(T) Average utility social discount factor 128 beta one-period discount factor 129 GA(T) Growth rate of productivity from 0 to T 130 FORCOTH(T) Exogenous forcing for other greenhouse gases 131 GCOST1 Growth of cost factor 132 GSIG(T) Cumulative improvement of energy efficiency 133 ETREE(T) Emissions from deforestation 134 COST1(t) Adjusted cost for backstop 135 PARTFRACT(T) Fraction of emissions in control regime 136 LAM Climate model parameter 137 Gfacpop(T) Growth factor population ; 138 139 * Important parameters for the model 140 LAM = FCO22X/ T2XCO2; 141 Gfacpop(T) = (exp(GGPOP0*(ORD(T)-1))-1)/exp(GGPOP0*(ORD(T)-1)); 142 L(T)=POP0* (1- Gfacpop(T))+Gfacpop(T)*popasym; 143 ga(T)=GGA0*EXP(-DDELA*(ORD(T)-1)); 144 al("1") = a0; 145 LOOP(T, al(T+1)=al(T)/((1-ga(T)));); 146 gsig(T)=GGSIGMA*EXP(-DDSIG*(ORD(T)-1));sigma("1")=sig0;LOOP(T,sigma(T+1)=( sigma(T)/((1-gsig(T+1))));); 147 cost1(T) = (PBACK*SIGMA(T)/EXPCOST2)* ( (BACKRAT-1+ EXP (-GGBACK* (ORD(T)- 1) ) )/BACKRAT); 148 ETREE(T) = EELAND0*(1-0.01*deltat)**(ord(T)-1); 149 RR(t)=1/((1+B_PRSTP)**(deltat*(ord(T)-1))); 150 beta = 1 / ((1+B_PRSTP)**deltat); 151 FORCOTH(T)= FEX0+ (FEX1-FEX0)/(120/deltat-2)*(ORD(T)-1)$(ORD(T) LT 120/del tat)+ 0.36$(ORD(T) GE 120/deltat); 152 partfract(t) = partfract21; 153 PARTFRACT(T)$(ord(T)<250/deltat) = Partfract21 + (PARTFRACT2-Partfract21)* exp(-DDPARTFRACT*(ORD(T)-2)); 154 *partfract("1")= PARTFRACT1; 155 partfract("1")= 0.25372; 156 157 158 ***************************************************************** 159 160 VARIABLES 161 K(T) Capital stock trillions US dollars 162 MAT(T) Carbon concentration in atmosphere GtC 163 MU(T) Carbon concentration in shallow oceans Gtc 164 ML(T) Carbon concentration in lower oceans GtC 165 TATM(T) Temperature of atmosphere in degrees C 166 TOCEAN(T) Temperature of lower oceans degrees C 167 E(T) CO2-equivalent emissions GtC 168 C(T) Consumption trillions US dollars 169 MIU(T) Emission control rate GHGs 170 CCA total industrial carbon emissions GTC 171 UTILITY; 172 173 POSITIVE VARIABLES K, MAT, MU, ML, TATM, TOCEAN, C, MIU, E; 174 175 EQUATIONS 176 177 KK0 Initial condition for capital 178 MMAT0 Starting atmospheric concentration 179 MMU0 Initial shallow ocean concentration 180 MML0 Initial lower ocean concentration 181 TATM0EQ Initial condition for atmospheric temperature 182 TOCEAN0EQ Initial condition for lower ocean temperature 183 184 KK(T) Capital balance equation 185 MMAT(T) Atmospheric concentration equation 186 MMU(T) Shallow ocean concentration 187 MML(T) Lower ocean concentration 188 TATMEQ(T) Temperature-climate equation for atmosphere 189 TOCEANEQ(T) Temperature-climate equation for lower oceans 190 EE(T) Emissions equation 191 FIXSEQ(T) Savings rate equation 192 193 CCACCA Cumulative carbon emissions 194 KendCond(T) terminal condition for capital 195 UTIL Objective function 196 ; 197 198 ** Equations of the model 199 200 KK0.. K('1') =E= K0; 201 MMAT0.. MAT('1') =E= MAT2000; 202 MMU0.. MU('1') =E= MU2000; 203 MML0.. ML('1') =E= ML2000; 204 TATM0EQ.. TATM('1') =E= TATM0; 205 TOCEAN0EQ.. TOCEAN('1') =E= TOCEAN0; 206 207 KK(T).. K(T+1) =L= (1-DK)**deltat *K(T)+deltat*( (1-((PAR TFRACT(T)**(1-expcost2))*(cost1(t)*(MIU(T)**EXPcost2))))* 208 (AL(T)*L(T)**(1-GAMA)*K(T)**GAMA) / (1 +A1*TATM(T)+ A2*TATM(T)**A3) - C(T) ); 209 MMAT(T+1).. MAT(T+1) =E= MAT(T)*bb11+MU(T)*bb21 + E(T); 210 MML(T+1).. ML(T+1) =E= ML(T)*bb33+bb23*MU(T); 211 MMU(T+1).. MU(T+1) =E= MAT(T)*bb12+MU(T)*bb22+ML(T)*bb32; 212 TATMEQ(T+1).. TATM(T+1) =E= TATM(t)+CC1*(FCO22X*((log(((MAT(T+1)+M AT(T+2))/2+0.000001)/596.4)/log(2)))+FORCOTH(T) - 213 LAM*TATM(t)-CC3*(TATM(t)-TOCEAN(t))); 214 TOCEANEQ(T+1).. TOCEAN(T+1) =E= TOCEAN(T)+CC4*(TATM(T)-TOCEAN(T)); 215 EE(T).. E(T) =E= deltat*SIGMA(T)*(1-MIU(T))* (AL(T)*L(T )**(1-GAMA)*K(T)**GAMA) + ETREE(T); 216 FIXSEQ(T).. (1- ((PARTFRACT(T)**(1-expcost2))*(cost1(t)*(MIU(T)**EX Pcost2))))* 217 (AL(T)*L(T)**(1-GAMA)*K(T)**GAMA) / (1+A1*TATM(T)+ A2*T ATM(T)**A3) - C(T) =E= 0.22*( .001 + (1- 218 ((PARTFRACT(T)**(1-expcost2))*(cost1(t )*(MIU(T)**EXPcost2))))* 219 (AL(T)*L(T)**(1-GAMA)*K(T)**GAMA) / 220 (1+A1*TATM(T)+ A2*TATM(T)**A3) ); 221 222 CCACCA.. CCA =E= sum(T$(ord(T)