ENVIRONMENTAL QUALITY VALUATION
AND WELFARE IMPROVEMENTS FROM GREEN TAXATION
Rahimaisa Abdula
INTRODUCTION
Impact of environmental taxation has mostly been explored in literatures with pure
focus upon productivity and other macroeconomic variables. Often left in the discussion is its
positive impact upon household utility and thus upon welfare. Households derive negative
utility from pollution emission; taxing emission of pollutants from production and from input
use would then posit welfare improvements. This is often missed out in most analysis of green
taxation, which treats it akin to producer taxes with burden passed on to consumers. Welfare
analysis of green taxation could be improved by an explicit specification of pollution’s impact
upon utility.
Explicit specification of pollution into the utility of the households has rarely been done
in CGE studies. An indirect allusion is made by Robinson,S (199?), where he modeled a dirty
consumption good in the utility function together with other commodities; clean-up sector is
then incorporated into the model. Most of the studies to date on environmental quality in CGE
followed this tract. Bergman (1991) made environmental quality, which is a function of
emission affect utility in a multiplicative exponential fashion. This enables separate analysis of
pollution impacts upon utility and production and other macroeconomic variables. A green
taxation has indirect effect upon utility through the reduction of consumption bundle, but has a
direct effect of improving utility as emission which is a bad is reduced. To what extent the
direct and indirect effect of green taxation influence the direction of utility depends upon the
households’ share of the ‘dirty goods1 and upon the marginal utility responsiveness of the
households. If the share of a particular household group to dirty consumption good is high and
its marginal utility response is low, meaning it cares too little about environmental quality; then
green taxation may have negative impact upon welfare.
There is little information as to how household’s utility responds to pollution/
environmental quality. Bergman (1991) illustrated a multiplicative exponential negative effect
of total emission. This has been mostly for the ease of analysis. Other forms by which pollution
can affect utility may be explored. Responsiveness of utility may differ across income groups.
1
Consumption good that is produced by a dirty industry or is produced by a dirty factor.
The rich may care more about it than the poor who just need to meet its lowest dietary
requirements. It could be the case that middle income group respond more to it as the rich has
access to preventive or defensive expenditures. Responsiveness may differ as well with the
perceived effect they attach to it. Household may care more about a pollutant that has visible
direct short-run effect (such as PM, SOX, NOX) as they suffer through its health and
productivity effects and aesthetic and odor nuisances, than a pollutant that has a perceived
more global and long-run effect such as carbon dioxide. This can be verified by conducting
valuation studies of improved local air quality and of improved global climate scenario for
instance. Households may have higher willingness to pay for improvement of local air quality
as they see the visible impact of what they will pay for.
In this exercise, some of these above-mentioned issues will be addressed. It first models
emissions to affect utility in a multiplicative exponential fashion following Bergman model. It
looks at two pollutants with different perceived impacts and three household groups with
different marginal utility responsiveness. Households then are assumed to differ with respect to
responsiveness across income group and across pollutants. It would conclude with
comparisons of welfare effects of different policy instruments; specifically emission taxes from
production and energy use.
The Model
The model has 3 sectors, 3 factors of production: labor, capital and energy, 3
households, high, medium and low-income group and 2 pollutants C02 and SOx.
Production
Production follows a Cobb-Douglas function.
X(i)=Anek1-
for
i=agri/forestry, transpo and heavy-industries, services
Output elasticities are as follows:
L
K
E
X1
.50
0.25
0.25
X2
.20
0.35
0.45
X3
.30
0.40
0.30
Pollution
Pollution comes from emission from both production and use of energy inputs, and are
proportional to output produced and amount of energy used respectively.
EMISB(G,POL)=EMCOEF(G,POL)*QBENCH(G)
pollution from production of g for pollutant pol;
EMCOEF(G,POL)
SOX
CO2
X1
.005
.030
X2
.015
.020
X3
.020
.010
EMIFB(G,POL)=EMF(POL)*EBENCH(G)
pollution from energy use; where EMF(pol)=/SOX 0.008 ,CO2 0.025/
TEMB(POL)=SUM(G,EMISB(G,POL)+ EMIFB(G,POL))
TAX
Emission taxation is introduced in the model as an exogenous shock. Emission from
production and factor use is taxed. Different combinations of policy instruments are analyzed.
A simulation with taxes on Sox and/or carbon emission from production and/or energy is done.
Simulation of differentiated emission tax across pollutant and sectors of production is also
conducted. Budget balance is also assumed in the model. So government revenues are
redistributed back to households in a progressive manner. Low income receive 0.4%, medium
receives 0.35% and the high income group 0.25%
Demand for production factors
The cost function of the producer is given below:
c(g)=wn(g)+rk(g)+pe(energy(g))+ total tax revenue
C(G)=(((G)**(-(G)))*((G)**(-(G)))*((1-(G)-(G))**((G)+(G)-1))/AA(G))
+ SUM(POL,TPOL(G,POL)*EMISB(G,POL))+ SUM(POL,TNRG(G,POL)*EMIFB(G,POL));
where TPOL=tax on pollution from production and
TNRG=tax on emission from energy use
From this cost function, we can apply the Shepard’s lemma to derive the factor demands:
L(G)= C(G)*(G)*W**((G)-1)*R**(1-(G)-(G))*PE**((G))
C(G)=C(G)*(1-(G)-(G))*W**(G)*R**(-(G)-(G))*PE**((G))
N(G)=C(G)*(G)*W**(G)*R**(1-(G)-(G))*PE**((G)-1)
Households
Households’ utility is a function of consumption of goods from sectors 1-3 and is affected by
emission by a multiplicative exponential fashion.
U(h)=c1cc3expsum(pol,(MU(h,pol)*tem(pol))
where c(g) represent consumption of goods produced by sectors 1-3,
There are different assumptions made regarding the MU(H,POL). Below lists the different
scenarios. Impact of 10% SOX for emission from both production and factor use would be
analyzed under the different MU assumptions.
A. Impact of different marginal utility response of households upon welfare
Marginal utility response is increasing in income
MU(h,pol)=/High 0.4, Med 0.2, Low 0.1/
Marginal utility response is higher for middle income
/High 0.2, Med 0.4, Low 0.1/
B. Impact of different WTP for reducing pollutants
Marginal utility response is higher for local, increasing in income
Marginal utility response is higher for global, increasing in income
RESULTS
The impact of green taxation when pollution is incorporated in the utility is analyzed
first. Without regard for households’ valuation of environmental quality, a tax of 10% on Sox
emission from both production and energy use leaves a reduction in the utility of households
by a magnitude of –12-14%. High-income group consuming more of the goods produced by
emission-intensive sectors or by energy, emission-intensive factor of production suffers most
of the brunt of the taxation. If a positive utility response of households is incorporated, then it
can be seen that the tax has actually led to increase in welfare. And this increase is dependent
upon the magnitude of the HH utility response to emission. Assuming increasing MU in
income, improvement in welfare occurs mostly to the group valuing it the most. In this case,
the high- income group will have a 44% improvement in its utility. The poor however almost
not caring about pollution has a negligible fall in welfare. If MU of the low income is a bit
higher, that is they care a little more about it, then a 0.1 increment in MU for low income
would lead to welfare improvements. Higher utility responsiveness corresponds to higher
welfare gains.
A tax of sox when households do not care about carbon yields improvements in welfare, but if
households care only for carbon then, indirect effect of taxation, reduction in consumption
dominates and pulls utility down for middle and low income. This could be verified with
looking at utility changes when local is valued and carbon is taxed, then same negative utility
change is engendered. It is also regressive in the sense that the lowest two income brackets
suffer the negative brunt of taxation.
Comparing the improvements in utilities from sox taxation when MU is increasing in income
and when MU is higher with middle income, it can be deduced that the improvement is higher
for the high income in the first case than the improvement middle income had in the second
case. This points to the importance of the magnitude of the share of dirty consumption to
households’ consumption. The high- income class consumes less of goods from sector 2 which
has the highest sox emission compared to the middle income. Improvement then in middle
income’s utility is tempered by the reduction in the goods they consume the most.
Impact of 10% Sox tax on utility under different assumptions on MU
Increasing in income MU(H)
MU(h)=0
no tax
33,94
33,42
34,40
tax
change
29,08
-16,73
28,79
-16,09
30,16
-14,08
MU(h)=.4,.2,.1 for both
no tax
tax
change
0,61
0,89
30,78
4,49
5,03
10,64
12,61
12,60
-0,10
MU(h)=.6,.4,.3
MU(h)=.8,.5,.4
no tax
tax
change
no tax
tax
change
0,08
0,16
47,10
0,01
0,03
59,26
0,60
0,88
31,21
0,22
0,37
39,78
1,70
2,20
22,94
0,62
0,92
32,39
Mu is higher in middle income classes
MU for local is zero, global is + MU for local is +, global is 0
MU(h)=.4,.2,.1 for global
MU(h)=.4,.2,.1 for local
no tax
tax
change
no tax
tax
change
3,05
3,43
12,50
6,83
7,33
7,23
10,02
9,89
-1,29
14,99
13,75
-8,28
18,83
17,67
-6,17
23,04
19,35
-16,00
MU(H)=.2,.4,.1
no tax
tax
change
1,37
1,74
27,49
2,02
2,56
26,84
12,61
12,60
-0,10
Policy instruments
The impact of different emission tax packages is summarized in table 2.
The following can be deduced:
1. Tax on one pollutant does not only reduce the emission of that pollutant but also of the
other one. This can be seen with the impact of the sox tax to the total emission of
carbon dioxide, and a sole tax on carbon on the total emission of sox. Taxing both the
pollutants yield a greater gains in terms of reduction in total emissions. Taxing
production instead of energy use yield higher reduction in total emissions.
Differentiated tax across sectors seems to have a weaker impact in reducing total
emissions compared to emission tax on output. And the best package in terms of
reducing total emissions is a tax on both pollutants on both production and factor use.
2. Tax on emissions from input however seem to be more progressive in welfare terms.
Almost all the other tax packages reduce utility of the low income, while most raise that
of the middle and the high.
3. In terms of increase in GNP at factor prices, tax on both pollutants from emissions in
both output and input use yields the highest gains.
4. Reduction in output has been severe under the tax on both pollutants/both output and
input packages. Sector 2 which is the most pollutive had the largest production cuts.
While tax on emission from inputs alone yield the slightest reductions.
5. Consumption of goods from all sectors and across households experience reductions as
well. And again, the highest reduction is under the both pollutants/both output and input
packages.
Conclusions:
1. This exercise just sheds light on how important incorporation of direct utility impacts of
pollution in the analysis of welfare implications of pollution taxation.
2. The impact of green taxation upon utility depends upon the magnitude of households’
shares of goods produced by dirty industry or dirty inputs and upon the magnitude of
responsiveness of utility to environmental quality.
3. Policy instruments directed upon one pollutant may have effects as well on other
pollutants.
4. Survey of possible intervention should be undertaken. What is obviously ‘the way to do
it’ policy may not be the best in terms of environmental, welfare and economic
improvements. Policy instruments could produce conflicting equity and growth
implications. It is thus upon the governments to choose which package best minimize
losses from it.
5. There is a dearth on studies incorporating environmental quality in utility, there’s a
gray improvement on research frontier on this area.
IMPACT OF EMISSION FROM PRODUCTION AND ENERGY USE TAXATION
SAME MU(H,POL) INCREASING IN INCOME (L-HIGH-.4,MED.2,LOW.1, G-H-.4,M-.2,L-.1)
BASE
W
P
X1
X2
X3
Q
X1
X2
X3
CD HIGH X1
X2
X3
CD MED X1
X2
X3
CD LOW X1
X2
X3
L
X1
X2
X3
C
X1
X2
X3
E
X1
X2
X3
GNP
UTILITY HIGH
MED
LOW
TAX
TEM
SOX
CO2
EMIS
SOX X1
SOX X3
CO2 X3
EMIF
SOX X1
CO2 X1
SOX X2
CO2 X2
SOX X3
CO2 X3
OUTPUT
INPUT
BOTH OUTPUT&INPUT
S0X 10% C02 10% SOX/CO2 SOX 10% CO2 10% BOTH 10% 10% SOX 10% CO2 BOTH 10%
1.00
1.00
1.01
1.01
1.00
1.00
1.00
1.01
1.01
1.01
1.00
1.05
1.31
1.36
1.02
1.07
1.09
1.37
1.45
1.26
1.00
1.15
1.21
1.36
1.04
1.11
1.15
1.32
1.51
1.35
1.00
1.20
1.10
1.31
1.02
1.08
1.10
1.18
1.41
1.32
100.00
95.34
77.05
74.27
98.06
94.18
92.46
93.58
73.56
70.06
100.00
87.07
83.50
74.32
96.55
89.96
87.17
84.45
76.41
67.03
100.00
83.47
91.12
77.23
97.69
93.12
91.11
81.85
85.39
71.85
25.00
23.82
19.25
18.55
24.51
23.54
23.11
23.38
18.37
17.49
40.00
34.82
33.38
29.70
38.62
35.98
34.86
33.77
30.54
26.78
35.00
29.20
31.88
27.00
34.19
32.58
31.88
28.64
29.86
25.12
30.00
28.60
23.11
22.28
29.42
28.25
27.74
28.07
22.07
21.01
35.00
30.48
29.23
26.02
33.79
31.49
30.51
29.56
26.75
23.47
35.00
29.21
31.89
27.03
34.19
32.59
31.89
28.65
29.89
25.15
45.00
42.92
34.69
33.45
44.13
42.39
41.618
42.13
33.13
31.56
25.00
21.78
20.89
18.60
24.14
22.50
21.8
21.13
19.12
16.78
30.00
25.05
27.36
23.19
29.31
27.94
27.34
24.57
25.64
21.59
0.50
0.52
0.65
0.67
0.51
0.53
0.54
0.53
0.68
0.71
0.20
0.23
0.24
0.27
0.21
0.22
0.23
0.24
0.26
0.30
0.30
0.36
0.33
0.39
0.31
0.32
0.33
0.37
0.35
0.42
0.25
0.26
0.33
0.34
0.26
0.27
0.27
0.27
0.34
0.36
0.35
0.40
0.42
0.48
0.36
0.39
0.40
0.42
0.46
0.53
0.40
0.48
0.44
0.52
0.41
0.43
0.44
0.49
0.47
0.56
0.25
0.26
0.33
0.34
0.26
0.27
0.27
0.27
0.34
0.36
0.45
0.52
0.54
0.61
0.47
0.50
0.52
0.53
0.59
0.67
0.30
0.36
0.33
0.39
0.31
0.32
0.33
0.37
0.35
0.42
300.00
300.80
301.20
302.01
300.16
300.50
300.66
300.96
301.71
302.67
33.94
0.84
1.00
1.24
0.66
0.77
0.81
0.89
1.15
1.43
33.42
4.94
5.24
5.55
4.61
4.83
4.92
5.03
5.46
5.73
34.40
12.62
12.29
12.15
12.63
12.63
12.62
12.60
12.19
11.94
0.00
0.40
0.60
1.00
0.08
0.25
0.33
0.48
0.85
1.33
4.01
3.46
3.47
3.04
3.90
3.69
3.60
3.38
3.23
2.80
6.03
5.47
4.92
4.52
5.88
5.58
5.46
5.34
4.62
4.20
0.500
0.477
0.385
0.371
0.490
0.471
0.462
0.468
0.368
0.350
2.000
1.669
1.822
1.545
1.954
1.862
1.822
1.637
1.708
1.437
1.000
0.835
0.911
0.772
0.977
0.931
0.911
0.819
0.854
0.719
0.002
0.002
0.003
0.003
0.002
0.002
0.002
0.002
0.003
0.003
0.006
0.007
0.008
0.008
0.006
0.007
0.007
0.007
0.008
0.009
0.004
0.004
0.004
0.005
0.004
0.004
0.004
0.004
0.005
0.005
0.011
0.013
0.013
0.015
0.012
0.013
0.013
0.013
0.015
0.017
0.002
0.003
0.003
0.003
0.002
0.003
0.003
0.003
0.003
0.003
0.007
0.009
0.008
0.010
0.008
0.008
0.008
0.009
0.009
0.010
A. S0X 10%, C02% 5%
B. DIFFERENT ACROSS ACTIVITIES
SOX
CO2
X1
0.02
0.10
X2
0.05
0.05
X3
0.1
0.02
DIFFERENTIATED
A
B
1.01
1.01
1.39
1.39
1.26
1.26
1.27
1.27
80.11
72.82
74.73
80.29
76.52
79.71
20.01
18.19
29.87
32.09
26.76
27.87
24.03
21.84
26.16
28.10
26.78
27.90
36.08
32.79
18.70
20.09
22.98
23.93
0.62
0.69
0.27
0.25
0.39
0.38
0.32
0.35
0.47
0.44
0.53
0.51
0.31
0.34
0.60
0.56
0.39
0.38
301.82 301.78
1.17
1.17
5.45
5.47
12.31
12.11
0.91
0.89
3.06
3.17
4.70
4.62
0.401
0.364
1.530
1.594
0.765
0.797
0.002
0.003
0.008
0.009
0.005
0.004
0.015
0.014
0.003
0.003
0.010
0.009
Appendix
A. PROGRAM
$TITLE SIMPLE CGE MODEL
OPTION LIMROW = 0
OPTION LIMCOL = 0
* OPTION SOLPRINT = OFF
SETS
G GOODS
/X1 AGRI AND FORESTRY
X2 TRANSPO AND UTILITY
X3 INDUSTRY AND OTHER SERVICES/
H HOUSEHOLD
/HIGH,MED,LOW/
POL POLLUTANT
/SOX, CO2/
ALIAS (POL,POLP)
PARAMETERS
A(G)
OUTPUT ELASTICITY OF LABOR /X1 .50, X2 .20, X3 .30/
E(G)
OUTPUT ELASTICITY OF ENERGY /X1 .25, X2 .45, X3 .30/
AA(G)
SCALE FACTOR IN PRODUCTION FUNCTION
BB(H)
SCALE FACTOR IN UTILITY FUNCTION FOR HOUSEHOLD H /HIGH 1.0, MED 1.0,
LOW 1.0/
TG(G)
TAX RATE ON GOODS /X1 0.00,X2 0.00, X3 0.00/
LH(H)
LABOR ENDOWMENT OF HOUSEHOLD H /HIGH 25, MED 30,LOW 45/
CH(H)
CAPITAL ENDOWMENT OF HOUSEHOLD H /HIGH 35,MED 35,LOW 30/
EH(H)
ENERGY ENDOWMENT OF HOUSEHOLD H /HIGH 40,MED 35,LOW 25/
STRANS(H)
SHARE OF TRANSFERS ACCRUING TO HOUSEHOLD H /HIGH 0.25, MED 0.35,
LOW 0.4/
C(G)
COST FUNCTION CONSTANT
UCONST(H)
EXPENDITURE FUNCTION CONSTANT
UBENCH(H)
BENCHMARK UTILITY OF HOUSEHOLD H /HIGH 33,MED 33,LOW 34/
PGBENCH(G)
BENCHMARK PRICES OF GOODS /X1 1.0, X2 1.0,X3 1.0/
WBENCH
BENCHMARK PRICE OF LABOR
RBENCH
BERNCHMARK PRICE OF CAPITAL
PEBENCH
PRICE OF ENERGY BENCHMARK
QBENCH(G)
BENCHMARK QUANTITIES OF GOODS /X1 100,X2 100,X3 100/
LGBENCH(G)
BENCHMARK ALLOCATION OF LABOR /X1 50,X2 20,X3 30/
CGBENCH(G)
BENCHMARK ALLOCATION OF CAPITAL /X1 25,X2 35,X3 40/
EBENCH(G)
BENCHMARK ENERGY /X1 25,X2 45,X3 30/
EMF(POL)
EMISSION COEFFICIENT OF ENERGY PER POLLUTANT /SOX 0.008 ,CO2 0.025/
* EM(POL)
TOTAL EMISSION OF POLLUTANT
TPOL(G,POL)
TAX ON POLLUTANT
EMISB(G,POL) EMISSION COEF FOR SOX NOX IN OUTPUT
EMIFB(G,POL) EMISSION COEF FOR ENERGY EMISSIONS
TNRG(G,POL)
TAX ON ENERGY
STP(POL)
TEMB(POL)
;
$ontext
TABLE MU(H,POL)
SOX
RESPONSE OF UTILITY TO CHANGES IN EMISSIONS
CO2
HIGH
0.4
0.4
MED
0.2
0.2
LOW
0.1
0.1
$OffTEXT
TABLE MU(H,POL)
SOX
CO2
HIGH
0.0 0.0
MED
0.0 0.0
LOW
0.0 0.0
TABLE TPOL(G,POL) TAX ON POLLUTANT FOR ACTIVITY
SOX
;
CO2
X1
0.00
0.0
X2
0.00
0.0
X3
0.00
0.0
TABLE TNRG(G,POL)
SOX
TAX ON ENERGY
CO2
X1
0.00
0.00
X2
0.00
0.00
X3
0.00
0.00
;
TABLE DG(H,G) UTILITY ELASTICITY OF GOODS FOR HOUSEHOLD H
X1
X2
X3
LOW
.45
.25
.30
MED
.30
.35
.35
HIGH
.25
.40
.35
;
TABLE EMCOEF(G,POL)
SOX
CO2
X1
.005
.030
X2
.015
.020
X3
.020
.010
;
EMISB(G,POL)=EMCOEF(G,POL)*QBENCH(G);
EMIFB(G,POL)=EMF(POL)*EBENCH(G);
TEMB(POL)=SUM(G,EMISB(G,POL)+ EMIFB(G,POL));
STP(POL)=TEMB(POL)/SUM(POLP,TEMB(POLP));
AA(G)=A(G)**(-A(G))*E(G)**(-E(G))*(1-A(G)-E(G))**(-((1-A(G)-E(G))));
C(G)=((A(G)**(-A(G)))*(E(G)**(-E(G)))*((1-A(G)-E(G))**(E(G)+A(G)-1))/AA(G))
+ SUM(POL,TPOL(G,POL)*EMISB(G,POL))+ SUM(POL,TNRG(G,POL)*EMIFB(G,POL));
;
UCONST(H)=(PROD(G,DG(H,G)**(-DG(H,G))))/BB(H);
VARIABLES
W
PRICE OF LABOR
R
PRICE OF CAPITAL
P(G)
PRICE OF GOOD G
Q(G)
OUTPUT OF GOOD G
CD(H,G)
CONSUMPTION OF GOOD G BY HOUSEHOLD H
RL(G)
UNIT LABOR DEMAND IN SECTOR G
RC(G)
UNIT CAPITAL DEMAND IN SECTOR G
EN(G)
UNIT ENERGY DEMAND IN SECTOR G
Y
TOTAL DISPOSABLE INCOME
YH(H)
DISPOSABLE INCOME OF HOUSEHOLD H
GNP
GROSS NATIONAL INCOME AT FACTOR COST
U(H)
UTILITY OF HOUSEHOLD H
EV(H)
EQUIVALENT VARIATION FOR HOUSEHOLD H
TAX
TOTAL TAX BILL
TEM
TOTAL EMISSIONS
PE
PRICE OF ENERGY
EMIS(G,POL)
EMISSION FROM GOOD BY POLLUTANT
EMIF(G,POL)
EMISSION FROM ENERGY USE BY POLLUTANT
EQUATIONS
YDEF
DEFINITION OF TOTAL DISPOSABLE INCOME
* Associated free variable: Y
DISP(H) DEFINITION OF DISPOSABLE INCOME OF HOUSEHOLD H
* Associated free variable: YH(H)
NATIO
DEFINITION OF GNP
* Associated free variable: GNP
TAXDEF DEFINITION OF TOTAL TAX BILL
* Associated free variable: TAX
UTILITY(H) UTILITY FUNCTION OF HOUSEHOLD H
* Associated free variable: U(H)
EQUIVAR(H) DEFINITION OF EQUIVALENT VARIATION OF HOUSEHOLD H
* Associated free variable: EV(H)
DEMAND(H,G) DEMAND FOR GOODS BY HOUSEHOLD H
* Associated free variable: CD(H,G)
SUPPLY(G) UNIT LOSS FOR GOOD G
* Associated free variable: Q(G)
MARKET(G) MARKET CLEARING CONDITION FOR GOOD G
* Associated free variable: P(G)
LABDEM(G) UNIT DEMAND FOR LABOR IN SECTOR G
* Associated free variable: RL(G)
CAPDEM(G) UNIT DEMAND FOR CAPITAL IN SECTOR G
* Associated free variable: RC(G)
LABMARK MARKET EQUILIBRIUM FOR LABOR
* Associated free variable: W
CAPMARK
MARKET EQUILIBRIUM FOR CAPITAL
* Associated free variable: R
TEMEQ(POL) TOTAL EMISSION
ENDEM
ENERGY DEMAND
*ASSOCIATED FREE VARIABLE: EN(G)
EMARK
ENERGY MARKET EQUILIBRIUM
*ASSOC FREE VARIABLE EH(H)
EMIDEMG(G,POL) EMISSION DEMAND FOR ACTIVITY
*ASSOC FREE VARIABLE EMIS(G,POL)
EMIDEMF(G,POL) EMISSION DEMAND FOR ENERGY USE
*ASSOC FREE VARIABLE EMIF(G,POL)
;
YDEF..
Y=E=SUM(H,YH(H));
DISP(H)..
YH(H)=E=W*LH(H)+R*CH(H)+PE*EH(H)+STRANS(H)*TAX;
NATIO..
GNP=E=SUM(H,W*LH(H)+R*CH(H)+PE*EH(H));
TAXDEF..
TAX=E=SUM(G,TG(G)*P(G)*Q(G))+
SUM(G,SUM(POL,TPOL(G,POL)*EMISB(G,POL)))+
SUM(G,SUM(POL,TNRG(G,POL)*EMIFB(G,POL)));
UTILITY(H)..
U(H)=E=PROD(G,CD(H,G)**DG(H,G))*EXP(-
(SUM(POL,(TEM(POL)*MU(H,POL)))));
EQUIVAR(H)..
DEMAND(H,G)..
EV(H)=E=UCONST(H)*(PROD(G,PGBENCH(G)**DG(H,G)))*(UBENCH(H)-U(H));
(1+TG(G))*P(G)*CD(H,G)=E=DG(H,G)*YH(H);
SUPPLY(G)..
C(G)*W**A(G)*R**(1-A(G)-E(G))*PE**(E(G))=E= P(G);
MARKET(G)..
Q(G)=E=SUM(H,CD(H,G));
LABDEM(G)..
RL(G)=E=C(G)*A(G)*W**(A(G)-1)*R**(1-E(G)-A(G))*PE**(E(G));
CAPDEM(G)..
RC(G)=E=C(G)*(1-A(G)-E(G))*W**A(G)*R**(-A(G)-E(G))*PE**(E(G));
ENDEM(G)..
EN(G)=E=C(G)*E(G)*W**A(G)*R**(1-E(G)-A(G))*PE**(E(G)-1);
LABMARK..
SUM(H,LH(H))=E=SUM(G,RL(G)*Q(G));
CAPMARK..
SUM(H,CH(H))=E=SUM(G,RC(G)*Q(G));
EMARK..
SUM(H,EH(H))=E=SUM(G,EN(G)*Q(G));
TEMEQ(POL)..
TEM(POL)=E=SUM(G,EMIS(G,POL)+ EMIF(G,POL));
EMIDEMG(G,POL)..
EMIS(G,POL)=E=EMCOEF(G,POL)*Q(G);
EMIDEMF(G,POL)..
EMIF(G,POL)=E=EMF(POL)*EN(G);
MODEL OPEN SIMPLE OPEN-ECONOMY CGE MODEL
/ UTILITY.U, EQUIVAR.EV, NATIO.GNP, DISP.YH, TAXDEF.TAX, DEMAND.CD, SUPPLY.Q,
MARKET.P,
LABDEM.RL, CAPDEM.RC, LABMARK.W, CAPMARK.R, TEMEQ.TEM,
ENDEM.EN,EMARK.PE,EMIDEMG.EMIS,
EMIDEMF.EMIF/ ;
* NUMERAIRE
R.FX=1.000 ;
* BOUNDS ON VARIABLES
W.LO=0.01;
CD.LO(H,G)=0.01;
* INITIAL VALUES
W.L=1.00;
Y.L=300;
YH.L(H)=300;
Q.L(G)=QBENCH(G);
* TEM.L= TEM;
PE.L= 1.00;
P.L(G) =PGBENCH(G);
EMIS.LO(G,POL)=0;
EMIF.LO(G,POL)=0;
SOLVE OPEN USING MCP;
DISPLAY GNP.L, Y.L, YH.L, U.L, EV.L, Q.L, CD.L, P.L, W.L, PE.L, R.L, RL.L,
RC.L,EMIS.L,EMIF.L,TEM.L,EN.L;