/
setup.lst
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setup.lst
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GAMS Rev 236 WEX-WEI 23.6.5 x86_64/MS Windows 07/26/11 20:08:12 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
1
2 SETS T Time periods /1*50/ ;
3
4 SCALARS
5
6 ** Preferences
7 B_ELASMU EFlasticity of marginal utility of consumption / 2 /
8 B_PRSTP Initial rate of social time preference per year / .015 /
9
10 * Population and technology
11 POP0 2005 world population millions /6514 /
12 GPOP0 Growth rate of population per decade /.35 /
13 POPASYM Asymptotic population / 8600 /
14 A0 Initial level of total factor productivity /.02722 /
15 GA0 Initial growth rate for technology per decade /.092 /
16 DELA Decline rate of technol change per decade /.001 /
17 DK Depreciation rate on capital per year /.100 /
18 GAMA Capital elasticity in production function /.300 /
19 Q0 2005 world gross output trill 2005 US dollars /61.1 /
20 K0 2005 value capital trill 2005 US dollars /137. /
21
22 ** Emissions
23 SIG0 CO2-equivalent emissions-GNP ratio 2005 /.13418 /
24 V0 Initial value of gnu /.13418 /
25 GSIGMA Initial growth of sigma per decade /-.0730 /
26 DSIG Decline rate of decarbonization per decade /.003 /
27 DSIG2 Quadratic term in decarbonization / .000 /
28 ELAND0 Carbon emissions from land 2005(GtC per decade) / 11.000 /
29
30 ** Carbon cycle
31 MAT2000 Concentration in atmosphere 2005 (GtC) /808.9 /
32 MU2000 Concentration in upper strata 2005 (GtC) /1255 /
33 ML2000 Concentration in lower strata 2005 (GtC) /18365 /
34 b11 Carbon cycle transition matrix /0.810712 /
35 b12 Carbon cycle transition matrix /0.189288 /
36 b21 Carbon cycle transition matrix /0.097213 /
37 b22 Carbon cycle transition matrix /0.852787 /
38 b23 Carbon cycle transition matrix /0.05 /
39 b32 Carbon cycle transition matrix /0.003119 /
40 b33 Carbon cycle transition matrix /0.996881 /
41
42 ** Climate model
43 T2XCO2 Equilibrium temp impact of CO2 doubling oC / 3 /
44 FEX0 Estimate of 2000 forcings of non-CO2 GHG / -.06 /
45 FEX1 Estimate of 2100 forcings of non-CO2 GHG / 0.30 /
46 TOCEAN0 2000 lower strat. temp change (C) from 1900 /.0068 /
47 TATM0 2000 atmospheric temp change (C)from 1900 /.7307 /
48 C1 Climate-equation coefficient for upper level /.220 /
49 C3 Transfer coeffic upper to lower stratum /.300 /
50 C4 Transfer coeffic for lower level /.050 /
51 FCO22X Estimated forcings of equilibrium co2 doubling /3.8 /
52
53 ** Climate damage parameters calibrated for quadratic at 2.5 C for 2105
54 A1 Damage intercept / 0.00000 /
55 A2 Damage quadratic term / 0.0028388 /
56 A3 Damage exponent / 2.00 /
57
58 ** Abatement cost
59 EXPCOST2 Exponent of control cost function /2.8 /
60 PBACK Cost of backstop 2005 000$ per tC 2005 /1.17 /
61 BACKRAT Ratio initial to final backstop cost / 2 /
62 GBACK Initial cost decline backstop pc per decade /.05 /
63 LIMMIU Upper limit on control rate / 1 /
64
65 ** Participation
66 PARTFRACT1 Fraction of emissions under control regime 2005 /1 /
67 PARTFRACT2 Fraction of emissions under control regime 2015 /1 /
68 PARTFRACT21 Fraction of emissions under control regime 2205 /1 /
69 DPARTFRACT Decline rate of participation /0 /
70
71 ** Availability of fossil fuels
72 FOSSLIM Maximum cumulative extraction fossil fuels / 6000 /
73
74 ** Scaling and inessential parameters
75 scale1 Scaling coefficient in the objective function /194 /
76 scale2 Scaling coefficient in the objective function /381800 / ;
77
78 * Definitions for outputs of no economic interest
79 SETS
80 TFIRST(T)
81 TLAST(T)
82 TEARLY(T)
83 TLATE(T)
84 TPENTULT(T);
85
86 PARAMETERS
87 L(T) Level of population and labor
88 AL(T) Level of total factor productivity
89 SIGMA(T) Exogenous CO2-equivalent-emissions output ratio
90 R(T) Instantaeous rate of social time preference
91 RR(T) Average utility social discount rate
92 GA(T) Growth rate of productivity from 0 to T
93 FORCOTH(T) Exogenous forcing for other greenhouse gases
94 GL(T) Growth rate of labor 0 to T
95 GCOST1 Growth of cost factor
96 GSIG(T) Cumulative improvement of energy efficiency
97 ETREE(T) Emissions from deforestation
98 PARTFRACT(T) Fraction of emissions in control regime
99 AA1 Variable A1
100 AA2 Variable A2
101 AA3 Variable A3
102 ELASMU Variable elasticity of marginal utility of consumption
103 PRSTP Variable nitial rate of social time preference per year
104 LAM Climate model parameter
105 Gfacpop(T) Growth factor population ;
106
107 * Unimportant definitions to reset runs
108 TFIRST(T) = YES$(ORD(T) EQ 1);
109 TLAST(T) = YES$(ORD(T) EQ CARD(T));
110 TEARLY(T) = YES$(ORD(T) LE 20);
111 TLATE(T) = YES$(ORD(T) GE 21);
112 AA1 = A1;
113 AA2 = A2;
114 AA3 = A3;
115 ELASMU = B_ELASMU;
116 PRSTP = B_PRSTP;
117
118 b11 = 1 - b12;
119 b21 = 587.473*B12/1143.894;
120 b22 = 1 - b21 - b23;
121 b32 = 1143.894*b23/18340;
122 b33 = 1 - b32 ;
123
124
125 * Important parameters for the model
126 LAM = FCO22X/ T2XCO2;
127 Gfacpop(T) = (exp(gpop0*(ORD(T)-1))-1)/exp(gpop0*(ORD(T)-1));
128 L(T) =POP0* (1- Gfacpop(T))+Gfacpop(T)*popasym;
129 ga(T) =ga0*EXP(-dela*10*(ORD(T)-1));
130 al("1") = a0;
131 LOOP(T, al(T+1)=al(T)/((1-ga(T))););
132 gsig(T) =gsigma*EXP(-dsig*10*(ORD(T)-1)-dsig2*10*((ord(t)-1)**2))
;
133 sigma("1") =sig0;
134 LOOP(T,sigma(T+1)=(sigma(T)/((1-gsig(T+1)))););
135 ETREE(T) = ELAND0*(1-0.1)**(ord(T)-1);
136 RR(t) =1/((1+prstp)**(10*(ord(T)-1)));
137 FORCOTH(T) = FEX0+ .1*(FEX1-FEX0)*(ORD(T)-1)$(ORD(T) LT 12)+ 0.36$(O
RD(T) GE 12);
138 partfract(t) = partfract21;
139 PARTFRACT(T)$(ord(T)<25) = Partfract21 + (PARTFRACT2-Partfract21)*exp(-DPA
RTFRACT*(ORD(T)-2));
140 partfract("1") = PARTFRACT1;
141
142
143 VARIABLES
144 MIU(T) Emission control rate GHGs
145 GNU(T) Endogenous part of CO2-equivalent-emissions output ratio
146 X(T) R&D Investment
147 SIGMA_N(T) Combined CO2-equivalent-emissions output ratio
148 FORC(T) Radiative forcing in watts per m2
149 TATM(T) Temperature of atmosphere in degrees C
150 TOCEAN(T) Temperatureof lower oceans degrees C
151 MAT(T) Carbon concentration in atmosphere GtC
152 MATAV(T) Average concentrations
153 MU(T) Carbon concentration in shallow oceans Gtc
154 ML(T) Carbon concentration in lower oceans GtC
155 E(T) CO2-equivalent emissions GtC
156 C(T) Consumption trillions US dollars
157 K(T) Capital stock trillions US dollars
158 CPC(T) Per capita consumption thousands US dollars
159 PCY(t) Per capita income thousands US dollars
160 I(T) Investment trillions US dollars
161 S(T) Gross savings rate as fraction of gross world product
162 RI(T) Real interest rate per annum
163 Y(T) Gross world product net of abatement and damages
164 YGROSS(T) Gross world product GROSS of abatement and damages
165 YNET(T) Output net of damages equation
166 DAMAGES(T) Damages
167 ABATECOST(T) Cost of emissions reductions
168 CCA(T) Cumulative industrial carbon emissions GTC
169 PERIODU(t) One period utility function
170 UTILITY
171 COST1(t) Adjusted cost for backstop ;
172
173 POSITIVE VARIABLES MIU, TATM, TOCE, E, MAT, MATAV, MU, ML, Y, YGROSS, C, K
, X,I, GNU, CCA ;
174
175 EQUATIONS
176 CCTFIRST(T) First period cumulative carbon
177 CCACCA(T) Cumulative carbon emissions
178 UTIL Objective function
179 YY(T) Output net equation
180 YNETEQ(T) Output net of damages equation
181 YGROSSEQ(T) Output gross equation
182 DAMEQ(T) Damage equation
183 ABATEEQ(T) Cost of emissions reductions equation
184 KK(T) Capital balance equation
185 KK0(T) Initial condition for capital
186 * KC(T) Terminal condition for capital
187 CPCE(t) Per capita consumption definition
188 PCYE(T) Per capita income definition
189 EE(T) Emissions equation
190 ECOST(T) Abatement cost function
191 * ETERM Terminal emmissions condition
192 SEQ(T) Savings rate equation
193 RIEQ(T) Interest rate equation
194 FORCE(T) Radiative forcing equation
195 MMAT0(T) Starting atmospheric concentration
196 MMAT(T) Atmospheric concentration equation
197 MMATAVEQ(t) Average concentrations equation
198 MMU0(T) Initial shallow ocean concentration
199 MMU(T) Shallow ocean concentration
200 MML0(T) Initial lower ocean concentration
201 MML(T) Lower ocean concentration
202 TATMEQ(T) Temperature-climate equation for atmosphere
203 TATM0EQ(T) Initial condition for atmospheric temperature
204 TOCEANEQ(T) Temperature-climate equation for lower oceans
205 TOCEAN0EQ(T) Initial condition for lower ocean temperature
206 PERIODUEQ(t) Instantaneous utility function equation ;
207
208 ** Equations of the model
209
210 CCTFIRST(TFIRST).. CCA(TFIRST)=E=0;
211 CCACCA(T+1).. CCA(T+1)=E=CCA(T)+ E(T);
212 KK(T).. K(T+1) =L= (1-DK)**10 *K(T)+10*I(T);
213 KK0(TFIRST).. K(TFIRST) =E= K0;
214 *KC(TLAST).. K(TLAST) =E= 6541;
215 EE(T).. E(T)=E=10*SIGMA_N(T)*(1-MIU(T))*YGROSS(T) + ETREE(T);
216 Ecost(T).. cost1(T) =e= (PBACK*SIGMA_N(T)/EXPCOST2)* ( (BACKRAT-1+
EXP (-gback* (ORD(T)-1) ) )/BACKRAT);
217 *ETERM.. E(40)=L= E(39);
218 FORCE(T).. FORC(T) =E= FCO22X*((log((Mat(T)+.000001)/596.4)/log(2
)))+FORCOTH(T);
219 MMAT0(TFIRST).. MAT(TFIRST) =E= MAT2000;
220 MMU0(TFIRST).. MU(TFIRST) =E= MU2000;
221 MML0(TFIRST).. ML(TFIRST) =E= ML2000;
222 MMAT(T+1).. MAT(T+1) =E= MAT(T)*b11+MU(T)*b21 + E(T);
223 MMATAVEQ(t).. MATAV(T) =e= (MAT(T)+MAT(T+1))/2 ;
224 MML(T+1).. ML(T+1) =E= ML(T)*b33+b23*MU(T);
225 MMU(T+1).. MU(T+1) =E= MAT(T)*b12+MU(T)*b22+ML(T)*b32;
226 TATM0EQ(TFIRST).. TATM(TFIRST) =E= TATM0;
227 TATMEQ(T+1).. TATM(T+1) =E= TATM(t)+C1*(FORC(t+1)-LAM*TATM(t)-C3*(TAT
M(t)-TOCEAN(t)));
228 TOCEAN0EQ(TFIRST).. TOCEAN(TFIRST) =E= TOCEAN0;
229 TOCEANEQ(T+1).. TOCEAN(T+1) =E= TOCEAN(T)+C4*(TATM(T)-TOCEAN(T));
230 YGROSSEQ(T).. YGROSS(T) =e= AL(T)*L(T)**(1-GAMA)*K(T)**GAMA;
231 DAMEQ(T).. DAMAGES(t) =E= YGROSS(T)- YGROSS(T)/(1+aa1*TATM(T)+ aa2*TA
TM(T)**aa3);
232 YNETEQ(T).. YNET(T) =E= YGROSS(T)/(1+aa1*TATM(T)+ aa2*TATM(T)**aa3);
233 ABATEEQ(T).. ABATECOST(T) =E= (PARTFRACT(T)**(1-expcost2))*YGROSS(T)*(c
ost1(t)*(MIU(T)**EXPcost2));
234 YY(T).. Y(T) =E= YGROSS(T)*((1-(PARTFRACT(T)**(1-expcost2))*cost1(
t)*(MIU(T)**EXPcost2)))/(1+aa1*TATM(T)+ aa2*TATM(T)**aa3);
235 SEQ(T).. S(T) =E= I(T)/(.001+Y(T));
236 RIEQ(T).. RI(T) =E= GAMA*Y(T)/K(T)- (1-(1-DK)**10)/10 ;
237 CPCE(T).. CPC(T) =E= C(T)*1000/L(T);
238 PCYE(T).. PCY(T) =E= Y(T)*1000/L(T);
239 PERIODUEQ(T).. PERIODU(T) =E= ((C(T)/L(T))**(1-ELASMU)-1)/(1-ELASMU);
240 UTIL.. UTILITY =E= SUM(T, (10*RR(T)F*L(T)*(PERIODU(T))/scale1))+
**** $8,409
scale2 ;
241
242
243 ** Upper and Lower Bounds: General conditions for stability
244
245 K.lo(T) = 100;
246 MAT.lo(T) = 10;
247 MU.lo(t) = 100;
248 ML.lo(t) = 1000;
249 GNU.L(T) = .05;
250 x.L(T) =.005*Q0;
251 Y.l(t) =Q0;
252 C.l(t) =.6*Q0;
253 K.L(T) =100;
254 C.lo(T) = 20;
255 y.LO(T) = 20;
256 TOCEAN.up(T) = 20;
257 TOCEAN.lo(T) = -1;
258 TATM.up(t) = 20;
259 miu.up(t) = LIMMIU;
260 partfract("1")= 0.25372;
261
262
263 ** Cumulative limits on carbon use at 6000 GtC
264 CCA.up(T) = FOSSLIM;
**** LIST OF STRAY NAMES - CHECK DECLARATIONS FOR SPURIOUS COMMAS
**** STRAY NAME TOCE OF TYPE VAR
GAMS Rev 236 WEX-WEI 23.6.5 x86_64/MS Windows 07/26/11 20:08:12 Page 2
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
Error Messages
8 ')' expected
409 Unrecognizable item - skip to find a new statement
looking for a ';' or a key word to get started again
**** 2 ERROR(S) 0 WARNING(S)
COMPILATION TIME = 0.000 SECONDS 3 Mb WEX236-236 Apr 6, 2011
USER: Initiative for Computational Economics 2011 G110725/0001AS-GEN
University of Chicago DC9139
License for teaching and research at degree granting institutions
**** FILE SUMMARY
Input C:\Users\Sonia\Documents\gamsdir\projdir\setup.gms
Output C:\Users\Sonia\Documents\gamsdir\projdir\setup.lst
**** USER ERROR(S) ENCOUNTERED