T. Chen r Energy Economics 23 2001 141᎐151 143
Ž .
jective being a trade-off itself. Hafkamp and Nijkamp 1982 presented a multi- objective programming approach and applied it to the issue of integrated resource
planning. They argued that a single-objective model cannot assess social welfare Ž
. changes accurately. Nijkamp 1986 employed multi-objective approach to evaluate
Ž .
the policy impact of resource allocation. Nordhous 1992 and Morrison and Brink Ž
. 1993 conducted two surveys to present the economic costs of mitigating climate
change. Among the programming model on the mitigation of CO emissions, four papers
2
Ž .
are reviewed here. Manne and Richels 1991 established a Global 2100 model, which is a programming analysis, to evaluate the costs and benefits of controlling
Ž .
CO emissions for the US. Rose and Steven 1993 presented a non-linear
2
programming model to simulate the net welfare changes of various strategies for Ž
. the mitigation of CO emissions for eight countries. Fells and Woolhouse 1994
2
provided an optimization model to estimate the impact of mitigating CO emis-
2
Ž .
sions on economic growth in the UK. Finally, Rose 1995 provided a linear-pro- gramming model to evaluate reduction in GDP resulting from five proposed CO
2
emissions mitigation programs in Mainland China.
3. The multi-objective programming model
In this section, a multi-objective programming combined with an input-output model is employed to determine the trade-off between GDP growth and CO
2
emissions on Taiwan’s economy. There are three reasons. First, the multi-objective approach is superior to the single-objective method, in that it focuses on the range
of choices associated with a decision. The decision-maker can judge the relative values of objectives and find the ‘best’ possible values under the given conditions
Ž
. Zeleny, 1982 . Second, multi-objective programming emphasizes resource alloca-
tion, i.e. it determines what the economy should ideally be like. Multi-objective analysis can derive trade-off between economic and environmental objectives
subject to constraints. Third, the multi-objective approach can avoid some issues of econometric modeling, such as heteroscedasticity, autocorrelation, multicollinear-
ity, etc. The model for the problem to be solved in the present paper is stated as:
Ž .
Ž Ž
. Ž
.. Ž
. MaxU s GDP,CO emissions s G X ,y C X
s VX
,y CX
2
subject to
d
Ž .
d
F F
1 y A q M X s F
1994 2000
X F X
u
X G X
L
LX F L
max
WX F W
max
T. Chen r Energy Economics 23 2001 141᎐151 144
where GDP presents gross domestic product. X represents the n = 1 vector of sector output, i.e. the dependent variables of this model. V is the 1 = n vector of
direct income coefficients, i.e. the ratio of sectional value-added to total sales for each sector, and n represents 33 industrial sectors. C is the 1 = n vector of CO
2
emission coefficients, i.e. the ratio of total CO emissions of energy in each sector.
2
F
d
and F
d
are, respectively, the n = 1 vectors of the 2000 and 1994 levels of
2000 1994
final demand. I is the n = n unit matrix, A is the n = n matrix of technical coefficients and M represents the n = n diagonal matrix of import coefficients.
Furthermore, X and X present the n = 1 vectors of the projected upper and
u L
lower limits, respectively, of the production level of each sector in the year 2000. L represents the 2 = n matrix of labor input coefficients, i.e. the ratio of labor
Ž employed to total sales for each sector two types of labor were measured, i.e.
. technical and non-technical labor , and L
is the 2 = 1 vector of the two-types of
max
labor employed. W is the 1 = n vector of water utilization coefficients, is the ratio of water utilization to total water supply for each sector, and W
means the
max
maximum resource limit of the water supply. Ž
. Ž
. In this model, G X has the objective of maximizing GDP and C X has the
Ž .
objective of minimizing CO emissions. C X is multiplied by y1 because CO
2 2
emissions are to be minimized. The first constraint set is derived from the relationship X y AX q M s F, which indicates that the sum of domestic output
Ž .
and importation in each industry sector which is total supply must be equal to the Ž
intermediate requirement of other sectors and the final demand sector which is .
total demand . Also, the level of each final demand sector in year 2000 cannot be less than in the year 1994. This is a general equilibrium restriction. The second and
third constraint sets limit each sector to a specified upper bound of capacity expansion and to a lower bound of depressed scale. The last two constraints are the
labor and water supply conditions, respectively.
4. Empirical results
