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dice_main.lst
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dice_main.lst
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GAMS Rev 236 WEX-WEI 23.6.5 x86_64/MS Windows 07/24/11 21:44:50 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
changes to test the stern run
DICE delta version 8
July 17, 2008
This is for the revised model with climate and emissions modules changed.
This version is used for the 2007 book.
8
9 SETS T Time periods /1*60/ ;
10
11 SCALARS
12
13 ** Preferences
14 B_ELASMU Elasticity of marginal utility of consumption / 2.0 /
15 B_PRSTP Initial rate of social time preference per year / .015 /
16
17 ** Population and technology
18 POP0 2005 world population millions /6514 /
19 GPOP0 Growth rate of population per decade /.35 /
20 POPASYM Asymptotic population / 8600 /
21 A0 Initial level of total factor productivity /.02722 /
22 GA0 Initial growth rate for technology per decade /.092 /
23 DELA Decline rate of technol change per decade /.001 /
24 DK Depreciation rate on capital per year /.100 /
25 GAMA Capital elasticity in production function /.300 /
26 Q0 2005 world gross output trill 2005 US dollars /61.1 /
27 K0 2005 value capital trill 2005 US dollars /137. /
28
29 ** Emissions
30 SIG0 CO2-equivalent emissions-GNP ratio 2005 /.13418 /
31 GSIGMA Initial growth of sigma per decade /-.0730 /
32 DSIG Decline rate of decarbonization per decade /.003 /
33 DSIG2 Quadratic term in decarbonization / .000 /
34 ELAND0 Carbon emissions from land 2005(GtC per decade) / 11.000 /
35
36 ** Carbon cycle
37 MAT2000 Concentration in atmosphere 2005 (GtC) /808.9 /
38 MU2000 Concentration in upper strata 2005 (GtC) /1255 /
39 ML2000 Concentration in lower strata 2005 (GtC) /18365 /
40 b11 Carbon cycle transition matrix /0.810712 /
41 b12 Carbon cycle transition matrix /0.189288 /
42 b21 Carbon cycle transition matrix /0.097213 /
43 b22 Carbon cycle transition matrix /0.852787 /
44 b23 Carbon cycle transition matrix /0.05 /
45 b32 Carbon cycle transition matrix /0.003119 /
46 b33 Carbon cycle transition matrix /0.996881 /
47
48 ** Climate model
49 T2XCO2 Equilibrium temp impact of CO2 doubling oC / 3 /
50 FEX0 Estimate of 2000 forcings of non-CO2 GHG / -.06 /
51 FEX1 Estimate of 2100 forcings of non-CO2 GHG / 0.30 /
52 TOCEAN0 2000 lower strat. temp change (C) from 1900 /.0068 /
53 TATM0 2000 atmospheric temp change (C)from 1900 /.7307 /
54 C1 Climate-equation coefficient for upper level /.220 /
55 C3 Transfer coeffic upper to lower stratum /.300 /
56 C4 Transfer coeffic for lower level /.050 /
57 FCO22X Estimated forcings of equilibrium co2 doubling /3.8 /
58
59 ** Climate damage parameters calibrated for quadratic at 2.5 C for 2105
60 A1 Damage intercept / 0.00000 /
61 A2 Damage quadratic term / 0.0028388 /
62 A3 Damage exponent / 2.00 /
63
64 ** Abatement cost
65 EXPCOST2 Exponent of control cost function /2.8 /
66 PBACK Cost of backstop 2005 000$ per tC 2005 /1.17 /
67 BACKRAT Ratio initial to final backstop cost / 2 /
68 GBACK Initial cost decline backstop pc per decade /.05 /
69 LIMMIU Upper limit on control rate / 1 /
70
71 ** Participation
72 PARTFRACT1 Fraction of emissions under control regime 2005 /1 /
73 PARTFRACT2 Fraction of emissions under control regime 2015 /1 /
74 PARTFRACT21 Fraction of emissions under control regime 2205 /1 /
75 DPARTFRACT Decline rate of participation /0 /
76
77 ** Availability of fossil fuels
78 FOSSLIM Maximum cumulative extraction fossil fuels / 6000 /
79
80 ** Scaling and inessential parameters
81 scale1 Scaling coefficient in the objective function /194 /
82 scale2 Scaling coefficient in the objective function /381800 / ;
83
84 * Definitions for outputs of no economic interest
85 SETS
86 TFIRST(T)
87 TLAST(T)
88 TEARLY(T)
89 TLATE(T);
90
91 PARAMETERS
92 L(T) Level of population and labor
93 AL(T) Level of total factor productivity
94 SIGMA(T) CO2-equivalent-emissions output ratio
95 R(T) Instantaeous rate of social time preference
96 RR(T) Average utility social discount rate
97 GA(T) Growth rate of productivity from 0 to T
98 FORCOTH(T) Exogenous forcing for other greenhouse gases
99 GL(T) Growth rate of labor 0 to T
100 GCOST1 Growth of cost factor
101 GSIG(T) Cumulative improvement of energy efficiency
102 ETREE(T) Emissions from deforestation
103 COST1(t) Adjusted cost for backstop
104 PARTFRACT(T) Fraction of emissions in control regime
105 AA1 Variable A1
106 AA2 Variable A2
107 AA3 Variable A3
108 ELASMU Variable elasticity of marginal utility of consumption
109 PRSTP Variable nitial rate of social time preference per year
110 LAM Climate model parameter
111 Gfacpop(T) Growth factor population ;
112
113 PARAMETERS
114 L(T) Level of population and labor
115 AL(T) Level of total factor productivity
116 SIGMA(T) CO2-equivalent-emissions output ratio
117 RR(T) Average utility social discount factor
118 GA(T) Growth rate of productivity from 0 to T
119 FORCOTH(T) Exogenous forcing for other greenhouse gases
120 GL(T) Growth rate of labor 0 to T
121 GCOST1 Growth of cost factor
122 GSIG(T) Cumulative improvement of energy efficiency
123 ETREE(T) Emissions from deforestation
124 COST1(t) Adjusted cost for backstop
125 PARTFRACT(T) Fraction of emissions in control regime
126 AA1 Variable A1
127 AA2 Variable A2
128 AA3 Variable A3
129 ELASMU Variable elasticity of marginal utility of consumption
130 PRSTP Variable nitial rate of social time preference per year
131 LAM Climate model parameter
132 Gfacpop(T) Growth factor population ;
133
134 * Unimportant definitions to reset runs
135 TFIRST(T) = YES$(ORD(T) EQ 1);
136 TLAST(T) = YES$(ORD(T) EQ CARD(T));
137 TEARLY(T) = YES$(ORD(T) LE 20);
138 TLATE(T) = YES$(ORD(T) GE 21);
139 AA1 = A1;
140 AA2 = A2;
141 AA3 = A3;
142 ELASMU = B_ELASMU;
143 PRSTP = B_PRSTP;
144
145 b11 = 1 - b12;
146 b21 = 587.473*B12/1143.894;
147 b22 = 1 - b21 - b23;
148 b32 = 1143.894*b23/18340;
149 b33 = 1 - b32 ;
150
151
152 * Important parameters for the model
153 LAM = FCO22X/ T2XCO2;
154 Gfacpop(T) = (exp(gpop0*(ORD(T)-1))-1)/exp(gpop0*(ORD(T)-1));
155 L(T)=POP0* (1- Gfacpop(T))+Gfacpop(T)*popasym;
156 ga(T)=ga0*EXP(-dela*10*(ORD(T)-1));
157 al("1") = a0;
158 LOOP(T, al(T+1)=al(T)/((1-ga(T))););
159 gsig(T)=gsigma*EXP(-dsig*10*(ORD(T)-1)-dsig2*10*((ord(t)-1)**2));
160 sigma("1")=sig0;
161 LOOP(T,sigma(T+1)=(sigma(T)/((1-gsig(T+1)))); );
162 cost1(T) = (PBACK*SIGMA(T)/EXPCOST2)* ( (BACKRAT-1+ EXP (-gback* (ORD(T)-1
) ) )/BACKRAT);
163 ETREE(T) = ELAND0*(1-0.1)**(ord(T)-1);
164 RR(t)=1/((1+prstp)**(10*(ord(T)-1)));
165 FORCOTH(T)= FEX0+ .1*(FEX1-FEX0)*(ORD(T)-1)$(ORD(T) LT 12)+ 0.36$(ORD(T) G
E 12);
166 partfract(t) = partfract21;
167 PARTFRACT(T)$(ord(T)<25) = Partfract21 + (PARTFRACT2-Partfract21)*exp(-DPA
RTFRACT*(ORD(T)-2));
168 partfract("1")= PARTFRACT1;
169
170
171 VARIABLES
172 MIU(T) Emission control rate GHGs
173 FORC(T) Radiative forcing in watts per m2
174 TATM(T) Temperature of atmosphere in degrees C
175 TOCEAN(T) Temperatureof lower oceans degrees C
176 MAT(T) Carbon concentration in atmosphere GtC
177 MATAV(T) Average concentrations
178 MU(T) Carbon concentration in shallow oceans Gtc
179 ML(T) Carbon concentration in lower oceans GtC
180 E(T) CO2-equivalent emissions GtC
181 C(T) Consumption trillions US dollars
182 K(T) Capital stock trillions US dollars
183 CPC(T) Per capita consumption thousands US dollars
184 PCY(t) Per capita income thousands US dollars
185 I(T) Investment trillions US dollars
186 S(T) Gross savings rate as fraction of gross world product
187 RI(T) Real interest rate per annum
188 Y(T) Gross world product net of abatement and damages
189 YGROSS(T) Gross world product GROSS of abatement and damages
190 YNET(T) Output net of damages equation
191 DAMAGES(T) Damages
192 ABATECOST(T) Cost of emissions reductions
193 CCA(T) Cumulative industrial carbon emissions GTC
194 PERIODU(t) One period utility function
195 UTILITY;
196
197 POSITIVE VARIABLES MIU, TATM, TOCE, E, MAT, MATAV, MU, ML, Y, YGROSS, C, K
, I, CCA ;
198
199 EQUATIONS
200
201 CCTFIRST(T) First period cumulative carbon
202 CCACCA(T) Cumulative carbon emissions
203 UTIL Objective function
204 YY(T) Output net equation
205 YNETEQ(T) Output net of damages equation
206 YGROSSEQ(T) Output gross equation
207 DAMEQ(T) Damage equation
208 ABATEEQ(T) Cost of emissions reductions equation
209 CC(T) Consumption equation
210 KK(T) Capital balance equation
211 KK0(T) Initial condition for capital
212 KC(T) Terminal condition for capital
213 CPCE(t) Per capita consumption definition
214 PCYE(T) Per capita income definition
215 EE(T) Emissions equation
216 SEQ(T) Savings rate equation
217 RIEQ(T) Interest rate equation
218 FORCE(T) Radiative forcing equation
219 MMAT0(T) Starting atmospheric concentration
220 MMAT(T) Atmospheric concentration equation
221 MMATAVEQ(t) Average concentrations equation
222 MMU0(T) Initial shallow ocean concentration
223 MMU(T) Shallow ocean concentration
224 MML0(T) Initial lower ocean concentration
225 MML(T) Lower ocean concentration
226 TATMEQ(T) Temperature-climate equation for atmosphere
227 TATM0EQ(T) Initial condition for atmospheric temperature
228 TOCEANEQ(T) Temperature-climate equation for lower oceans
229 TOCEAN0EQ(T) Initial condition for lower ocean temperature
230 PERIODUEQ(t) Instantaneous utility function equation ;
231
232 ** Equations of the model
233
234 CCTFIRST(TFIRST).. CCA(TFIRST)=E=0;
235 CCACCA(T+1).. CCA(T+1)=E=CCA(T)+ E(T);
236 KK(T).. K(T+1) =L= (1-DK)**10 *K(T)+10*I(T);
237 KK0(TFIRST).. K(TFIRST) =E= K0;
238 KC(TLAST).. .02*K(TLAST) =L= I(TLAST);
239 EE(T).. E(T)=E=10*SIGMA(T)*(1-MIU(T))*AL(T)*L(T)**(1-GAMA)*K(T)
**GAMA + ETREE(T);
240 FORCE(T).. FORC(T) =E= FCO22X*((log((Matav(T)+.000001)/596.4)/log
(2)))+FORCOTH(T);
241 MMAT0(TFIRST).. MAT(TFIRST) =E= MAT2000;
242 MMU0(TFIRST).. MU(TFIRST) =E= MU2000;
243 MML0(TFIRST).. ML(TFIRST) =E= ML2000;
244 MMAT(T+1).. MAT(T+1) =E= MAT(T)*b11+MU(T)*b21 + E(T);
245 MMATAVEQ(t).. MATAV(T) =e= (MAT(T)+MAT(T+1))/2 ;
246 MML(T+1).. ML(T+1) =E= ML(T)*b33+b23*MU(T);
247 MMU(T+1).. MU(T+1) =E= MAT(T)*b12+MU(T)*b22+ML(T)*b32;
248 TATM0EQ(TFIRST).. TATM(TFIRST) =E= TATM0;
249 TATMEQ(T+1).. TATM(T+1) =E= TATM(t)+C1*(FORC(t+1)-LAM*TATM(t)-C3*(TAT
M(t)-TOCEAN(t)));
250 TOCEAN0EQ(TFIRST).. TOCEAN(TFIRST) =E= TOCEAN0;
251 TOCEANEQ(T+1).. TOCEAN(T+1) =E= TOCEAN(T)+C4*(TATM(T)-TOCEAN(T));
252 YGROSSEQ(T).. YGROSS(T) =e= AL(T)*L(T)**(1-GAMA)*K(T)**GAMA;
253 DAMEQ(T).. DAMAGES(t) =E= YGROSS(T)- YGROSS(T)/(1+aa1*TATM(T)+ aa2*TA
TM(T)**aa3);
254 YNETEQ(T).. YNET(T) =E= YGROSS(T)/(1+aa1*TATM(T)+ aa2*TATM(T)**aa3);
255 ABATEEQ(T).. ABATECOST(T) =E= (PARTFRACT(T)**(1-expcost2))*YGROSS(T)*(c
ost1(t)*(MIU(T)**EXPcost2));
256 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);
257 SEQ(T).. S(T) =E= I(T)/(.001+Y(T));
258 RIEQ(T).. RI(T) =E= GAMA*Y(T)/K(T)- (1-(1-DK)**10)/10 ;
259 CC(T).. C(T) =E= Y(T)-I(T);
260 CPCE(T).. CPC(T) =E= C(T)*1000/L(T);
261 PCYE(T).. PCY(T) =E= Y(T)*1000/L(T);
262 PERIODUEQ(T).. PERIODU(T) =E= ((C(T)/L(T))**(1-ELASMU)-1)/(1-ELASMU);
263 UTIL.. UTILITY =E= SUM(T, 10 *RR(T)*L(T)*(PERIODU(T))/scale1)+ sc
ale2 ;
264
265 ** Upper and Lower Bounds: General conditions for stability
266
267 K.lo(T) = 100;
268 MAT.lo(T) = 10;
269 MU.lo(t) = 100;
270 ML.lo(t) = 1000;
271 C.lo(T) = 20;
272 TOCEAN.up(T) = 20;
273 TOCEAN.lo(T) = -1;
274 TATM.up(t) = 20;
275 miu.up(t) = LIMMIU;
276 partfract("1")= 0.25372;
277
278 * First period predetermined by Kyoto Protocol
279 miu.fx("1") = 0.005;
280
281 ** Fix savings assumption for standardization if needed
282 *s.fx(t)=.22;
283
284 ** Cumulative limits on carbon use at 6000 GtC
285 CCA.up(T) = FOSSLIM;
286
287 ** Solution options
288 option iterlim = 99900;
289 option reslim = 99999;
290 option solprint = on;
291 option limrow = 0;
292 option limcol = 0;
293 model CO2 /all/;
294
295 * Optimal run
INCLUDE C:\Users\Sonia\Documents\gamsdir\projdir\def_opt.gms
297 * Solution for optimal run
298
299 solve CO2 maximizing UTILITY using nlp ;
300
301
302 * Definition of opt results
303
304 Parameters
305 Year(t) Date
306 opt_y(t)
307 opt_cpc(t)
308 opt_s(t)
309 opt_indem(t)
310 opt_sigma(t)
311 opt_tatm(t)
312 opt_mat(t)
313 opt_tax(t)
314 opt_ri(t)
315 opt_rr(t)
316 opt_al(t)
317 opt_forcoth(t)
318 opt_l(t)
319 opt_etree(t)
320 opt_yy(t)
321 opt_cc(t)
322 opt_miu(t)
323 opt_wem(t)
324 opt_ri(t)
325 opt_dam(t)
326 opt_abate(t)
327 opt_mcemis(t)
328 opt_utility ;
329
330 Year(t) = 2005 +10*(ord(t)-1);
331 opt_y(t)=y.l(t);
332 opt_cpc(t)=cpc.l(t);
333 opt_s(t)=s.l(t) ;
334 opt_indem(t)= e.l(t)-etree(t);;
335 opt_sigma(t)=sigma(t) ;
336 opt_tatm(t)=tatm.l(t) ;
337 opt_mat(t)=mat.l(t) ;
338 opt_tax(t)=-1*ee.m(t)*1000/(kk.m(t)+.00000000001) ;
339 opt_ri(t)=ri.l(t);
340 opt_rr(t)=rr(t) ;
341 opt_al(t)=al(t) ;
342 opt_forcoth(t)=forcoth(t);
343 opt_l(t)=l(t);
344 opt_etree(t)=etree(t);
345 opt_yy(t)=yy.m(t) ;
346 opt_cc(t)=cc.m(t) ;
347 opt_miu(t)=miu.l(t) ;
348 opt_wem(t)= e.l(t);
349 opt_ri(t)=ri.l(t) ;
350 opt_dam(t)= damages.l(t);
351 opt_abate(t) = abatecost.l(t);
352 opt_mcemis(t)= expcost2*cost1(t)*miu.l(t)**(expcost2-1)/sigma(t)*1000;
353 opt_utility=utility.l ;
INCLUDE C:\Users\Sonia\Documents\gamsdir\projdir\sigmaput.gms
355 *This file prints output from DICE
356
357 FILE csv Report File /sigma.csv/;
358 csv.pc=5;
359 PUT csv;
360 *DICEModOutput.pc=5;
361 *DICEModOutput.pw=250;
362 *PUT DICEModOutput;
363 LOOP (T, put opt_sigma(t)::3);
364 PUTCLOSE csv;
365
$include def_reset.gms
* Estimate of geoengineering
$include def_geoeng.gms
$include def_reset.gms
* Estimate Hoteling rents
$ include def_hotel.gms
$include def_reset.gms
* Base-5per defined as 50 years of no action with miu at Hotelling control
rates
$include def_base_5per.gms
$include def_reset.gms
* Base-25per defined as 250 years of no action with miu at Hotelling contr
ol rates
$include def_base_25per.gms
$include def_reset.gms
* Stern run
$include def_stern_v2.gms
$include def_reset.gms
* Original specification of damage function
$include def_orig_dam.gms
$include def_reset.gms
* Limit to 1.5, 2.0, 2.5, 3.0 degrees temperature increase
$include def_limt15deg.gms
$include def_reset.gms
$include def_limt2deg.gms
$include def_reset.gms
$include def_limt25deg.gms
$include def_reset.gms
$include def_limt3deg.gms
$include def_reset.gms
* Limit to 1.5 2 and 2.5 preindustrial co2
$include def_lim15xco2.gms
$include def_reset.gms
$include def_lim2xco2.gms
$include def_reset.gms
$include def_lim25xco2.gms
$include def_reset.gms
* Limited participation in emissions reductions from 20% to 50%
$include def_limpart.gms
$include def_reset.gms
* Estimate of run with Kyoto without US and full trading
$include def_kyoto_nous.gms
$include def_reset.gms
* Estimate of run with Kyoto with US and full trading
$include def_kyoto_withus.gms
$include def_reset.gms
* Estimate of strengthened Kyoto
$include def_kyoto_strong.gms
$include def_reset.gms
$include def_gore.gms
$include def_reset.gms
$include def_limpart.gms
$include def_reset.gms
$include def_base_35per.gms
$include def_reset.gms
* Output of all runs in one put file
$include put_dice_delta_runs_050807.gms
display b11, b12, b21, b22, b23, b32, b33;
**** 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 07/24/11 21:44:50 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
Include File Summary
SEQ GLOBAL TYPE PARENT LOCAL FILENAME
1 1 INPUT 0 0 C:\Users\Sonia\Documents\gamsdir\projd
ir\dice_main.gms
2 296 INCLUDE 1 296 .C:\Users\Sonia\Documents\gamsdir\proj
dir\def_opt.gms
3 354 INCLUDE 1 297 .C:\Users\Sonia\Documents\gamsdir\proj
dir\sigmaput.gms
COMPILATION TIME = 0.000 SECONDS 3 Mb WEX236-236 Apr 6, 2011
GAMS Rev 236 WEX-WEI 23.6.5 x86_64/MS Windows 07/24/11 21:44:50 Page 3
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
Model Statistics SOLVE CO2 Using NLP From line 299
MODEL STATISTICS
BLOCKS OF EQUATIONS 30 SINGLE EQUATIONS 1,263
BLOCKS OF VARIABLES 24 SINGLE VARIABLES 1,381 300 projected
NON ZERO ELEMENTS 3,767 NON LINEAR N-Z 1,080
DERIVATIVE POOL 6 CONSTANT POOL 327
CODE LENGTH 5,643
GENERATION TIME = 0.016 SECONDS 4 Mb WEX236-236 Apr 6, 2011
EXECUTION TIME = 0.016 SECONDS 4 Mb WEX236-236 Apr 6, 2011
GAMS Rev 236 WEX-WEI 23.6.5 x86_64/MS Windows 07/24/11 21:44:50 Page 4
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
Solution Report SOLVE CO2 Using NLP From line 299
S O L V E S U M M A R Y
MODEL CO2 OBJECTIVE UTILITY
TYPE NLP DIRECTION MAXIMIZE
SOLVER CONOPT FROM LINE 299
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 2 Locally Optimal
**** OBJECTIVE VALUE 150238.1471
RESOURCE USAGE, LIMIT 2.559 99999.000
ITERATION COUNT, LIMIT 539 99900
EVALUATION ERRORS 0 0
CONOPTD 0.1 Dec 13, 2010 23.6.5 WEX 24181.24195 WEI x86_64/MS Windows
C O N O P T 3 version 3.14W
Copyright (C) ARKI Consulting and Development A/S
Bagsvaerdvej 246 A
DK-2880 Bagsvaerd, Denmark
The model has 1381 variables and 1263 constraints
with 3767 Jacobian elements, 1080 of which are nonlinear.
The Hessian of the Lagrangian has 360 elements on the diagonal,
360 elements below the diagonal, and 480 nonlinear variables.
** Optimal solution. Reduced gradient less than tolerance.
CONOPT time Total 2.550 seconds
of which: Function evaluations 0.511 = 20.0%
1st Derivative evaluations 0.184 = 7.2%
2nd Derivative evaluations 0.072 = 2.8%
Directional 2nd Derivative 0.198 = 7.8%
---- EQU CCTFIRST First period cumulative carbon
LOWER LEVEL UPPER MARGINAL
1 . . . EPS
---- EQU CCACCA Cumulative carbon emissions
LOWER LEVEL UPPER MARGINAL
2 . . . EPS
3 . . . EPS
4 . . . EPS
5 . . . EPS
6 . . . EPS
7 . . . EPS
8 . . . EPS
9 . . . EPS
10 . . . EPS
11 . . . EPS
12 . . . EPS
13 . . . EPS
14 . . . EPS
15 . . . EPS
16 . . . EPS
17 . . . EPS
18 . . . EPS
19 . . . EPS
20 . . . EPS
21 . . . EPS
22 . . . EPS
23 . . . EPS
24 . . . EPS
25 . . . EPS
26 . . . EPS
27 . . . EPS
28 . . . EPS
29 . . . EPS
30 . . . EPS
31 . . . EPS
32 . . . EPS
33 . . . EPS
34 . . . EPS
35 . . . EPS
36 . . . EPS
37 . . . EPS
38 . . . EPS
39 . . . EPS
40 . . . EPS
41 . . . EPS
42 . . . EPS
43 . . . EPS
44 . . . EPS
45 . . . EPS
46 . . . EPS
47 . . . EPS
48 . . . EPS
49 . . . EPS
50 . . . EPS
51 . . . EPS
52 . . . EPS
53 . . . EPS
54 . . . EPS
55 . . . EPS
56 . . . EPS
57 . . . EPS
58 . . . EPS
59 . . . EPS
60 . . . EPS
LOWER LEVEL UPPER MARGINAL
---- EQU UTIL 3.8180E+5 3.8180E+5 3.8180E+5 1.000
UTIL Objective function
---- EQU YY Output net equation
LOWER LEVEL UPPER MARGINAL
1 . . . 1177.503
2 . . . 756.535
3 . . . 489.319
4 . . . 318.768
5 . . . 209.043
6 . . . 137.892
7 . . . 91.427
8 . . . 60.896
9 . . . 40.726
10 . . . 27.339
11 . . . 18.415
12 . . . 12.442
13 . . . 8.430
14 . . . 5.727
15 . . . 3.900
16 . . . 2.663
17 . . . 1.822
18 . . . 1.249
19 . . . 0.858
20 . . . 0.590
21 . . . 0.406
22 . . . 0.278
23 . . . 0.191
24 . . . 0.132
25 . . . 0.091
26 . . . 0.063
27 . . . 0.043
28 . . . 0.030
29 . . . 0.021
30 . . . 0.015
31 . . . 0.010
32 . . . 0.007
33 . . . 0.005
34 . . . 0.004
35 . . . 0.002
36 . . . 0.002
37 . . . 0.001
38 . . . 8.8858E-4
39 . . . 6.3226E-4
40 . . . 4.5079E-4
41 . . . 3.2205E-4
42 . . . 2.3053E-4
43 . . . 1.6535E-4
44 . . . 1.1882E-4
45 . . . 8.5552E-5
46 . . . 6.1714E-5
47 . . . 4.4601E-5
48 . . . 3.2293E-5
49 . . . 2.3424E-5
50 . . . 1.7021E-5
51 . . . 1.2390E-5
52 . . . 9.0335E-6
53 . . . 6.5961E-6
54 . . . 4.8215E-6
55 . . . 3.5249E-6
56 . . . 2.5717E-6
57 . . . 1.8629E-6
58 . . . 1.3222E-6
59 . . . 8.8651E-7
60 . . . 6.9058E-7
---- EQU YNETEQ Output net of damages equation
LOWER LEVEL UPPER MARGINAL
1 . . . EPS
2 . . . EPS
3 . . . EPS
4 . . . EPS
5 . . . EPS
6 . . . EPS
7 . . . EPS
8 . . . EPS
9 . . . EPS
10 . . . EPS
11 . . . EPS
12 . . . EPS
13 . . . EPS
14 . . . EPS
15 . . . EPS
16 . . . EPS
17 . . . EPS
18 . . . EPS
19 . . . EPS
20 . . . EPS
21 . . . EPS
22 . . . EPS
23 . . . EPS
24 . . . EPS
25 . . . EPS
26 . . . EPS
27 . . . EPS
28 . . . EPS
29 . . . EPS
30 . . . EPS
31 . . . EPS
32 . . . EPS
33 . . . EPS
34 . . . EPS
35 . . . EPS
36 . . . EPS
37 . . . EPS
38 . . . EPS
39 . . . EPS
40 . . . EPS
41 . . . EPS
42 . . . EPS
43 . . . EPS
44 . . . EPS
45 . . . EPS
46 . . . EPS
47 . . . EPS
48 . . . EPS
49 . . . EPS
50 . . . EPS
51 . . . EPS
52 . . . EPS
53 . . . EPS
54 . . . EPS
55 . . . EPS
56 . . . EPS
57 . . . EPS
58 . . . EPS
59 . . . EPS
60 . . . EPS
---- EQU YGROSSEQ Output gross equation
LOWER LEVEL UPPER MARGINAL
1 . . . 1175.720
2 . . . 754.374
3 . . . 487.238
4 . . . 316.888
5 . . . 207.419
6 . . . 136.534
7 . . . 90.319
8 . . . 60.010
9 . . . 40.029
10 . . . 26.797
11 . . . 17.999
12 . . . 12.127
13 . . . 8.194
14 . . . 5.551
15 . . . 3.770
16 . . . 2.567
17 . . . 1.752
18 . . . 1.198
19 . . . 0.821
20 . . . 0.564
21 . . . 0.387
22 . . . 0.266
23 . . . 0.183
24 . . . 0.126
25 . . . 0.087
26 . . . 0.060
27 . . . 0.042
28 . . . 0.029
29 . . . 0.020
30 . . . 0.014
31 . . . 0.010
32 . . . 0.007
33 . . . 0.005
34 . . . 0.003
35 . . . 0.002
36 . . . 0.002
37 . . . 0.001
38 . . . 8.6717E-4
39 . . . 6.1748E-4
40 . . . 4.4057E-4
41 . . . 3.1497E-4
42 . . . 2.2562E-4
43 . . . 1.6193E-4
44 . . . 1.1644E-4
45 . . . 8.3886E-5
46 . . . 6.0547E-5
47 . . . 4.3783E-5
48 . . . 3.1718E-5
49 . . . 2.3019E-5
50 . . . 1.6735E-5
51 . . . 1.2187E-5
52 . . . 8.8902E-6
53 . . . 6.4944E-6
54 . . . 4.7492E-6
55 . . . 3.4734E-6
56 . . . 2.5353E-6
57 . . . 1.8371E-6
58 . . . 1.3045E-6
59 . . . 8.7491E-7
60 . . . 6.8895E-7
---- EQU DAMEQ Damage equation
LOWER LEVEL UPPER MARGINAL
1 . . . EPS
2 . . . EPS
3 . . . EPS
4 . . . EPS
5 . . . EPS
6 . . . EPS
7 . . . EPS
8 . . . EPS
9 . . . EPS
10 . . . EPS
11 . . . EPS
12 . . . EPS
13 . . . EPS
14 . . . EPS
15 . . . EPS
16 . . . EPS
17 . . . EPS
18 . . . EPS
19 . . . EPS
20 . . . EPS
21 . . . EPS
22 . . . EPS
23 . . . EPS
24 . . . EPS
25 . . . EPS
26 . . . EPS
27 . . . EPS
28 . . . EPS
29 . . . EPS
30 . . . EPS
31 . . . EPS
32 . . . EPS
33 . . . EPS
34 . . . EPS
35 . . . EPS
36 . . . EPS
37 . . . EPS
38 . . . EPS
39 . . . EPS
40 . . . EPS
41 . . . EPS
42 . . . EPS
43 . . . EPS
44 . . . EPS
45 . . . EPS
46 . . . EPS
47 . . . EPS
48 . . . EPS
49 . . . EPS
50 . . . EPS
51 . . . EPS
52 . . . EPS
53 . . . EPS
54 . . . EPS
55 . . . EPS
56 . . . EPS
57 . . . EPS
58 . . . EPS
59 . . . EPS
60 . . . EPS
---- EQU ABATEEQ Cost of emissions reductions equation
LOWER LEVEL UPPER MARGINAL
1 . . . EPS
2 . . . EPS
3 . . . EPS
4 . . . EPS
5 . . . EPS
6 . . . EPS
7 . . . EPS
8 . . . EPS
9 . . . EPS
10 . . . EPS
11 . . . EPS
12 . . . EPS
13 . . . EPS
14 . . . EPS
15 . . . EPS
16 . . . EPS
17 . . . EPS
18 . . . EPS
19 . . . EPS
20 . . . EPS
21 . . . EPS
22 . . . EPS
23 . . . EPS
24 . . . EPS
25 . . . EPS
26 . . . EPS
27 . . . EPS
28 . . . EPS
29 . . . EPS
30 . . . EPS
31 . . . EPS
32 . . . EPS
33 . . . EPS
34 . . . EPS
35 . . . EPS
36 . . . EPS
37 . . . EPS
38 . . . EPS
39 . . . EPS
40 . . . EPS
41 . . . EPS
42 . . . EPS
43 . . . EPS
44 . . . EPS
45 . . . EPS
46 . . . EPS
47 . . . EPS
48 . . . EPS
49 . . . EPS
50 . . . EPS
51 . . . EPS
52 . . . EPS
53 . . . EPS
54 . . . EPS
55 . . . EPS
56 . . . EPS
57 . . . EPS
58 . . . EPS
59 . . . EPS
60 . . . EPS
---- EQU CC Consumption equation
LOWER LEVEL UPPER MARGINAL
1 . . . 1177.503
2 . . . 756.535
3 . . . 489.319
4 . . . 318.768
5 . . . 209.043
6 . . . 137.892
7 . . . 91.427
8 . . . 60.896
9 . . . 40.726
10 . . . 27.339
11 . . . 18.415
12 . . . 12.442
13 . . . 8.430
14 . . . 5.727
15 . . . 3.900
16 . . . 2.663
17 . . . 1.822
18 . . . 1.249
19 . . . 0.858
20 . . . 0.590
21 . . . 0.406
22 . . . 0.278
23 . . . 0.191
24 . . . 0.132
25 . . . 0.091
26 . . . 0.063
27 . . . 0.043
28 . . . 0.030
29 . . . 0.021
30 . . . 0.015
31 . . . 0.010
32 . . . 0.007
33 . . . 0.005
34 . . . 0.004
35 . . . 0.002
36 . . . 0.002
37 . . . 0.001
38 . . . 8.8858E-4
39 . . . 6.3226E-4
40 . . . 4.5079E-4
41 . . . 3.2205E-4
42 . . . 2.3053E-4
43 . . . 1.6535E-4
44 . . . 1.1882E-4
45 . . . 8.5552E-5
46 . . . 6.1714E-5
47 . . . 4.4601E-5
48 . . . 3.2293E-5
49 . . . 2.3424E-5
50 . . . 1.7021E-5
51 . . . 1.2390E-5
52 . . . 9.0335E-6
53 . . . 6.5961E-6
54 . . . 4.8215E-6
55 . . . 3.5249E-6
56 . . . 2.5717E-6