Modeling Climate Policy Instruments in a Stackelberg Game with ...

32 3 MODEL DEVELOPMENT AND ANALYSIS
The mitigation goal (in terms of a carbon budget) is formulated as constraint
for the government. Furthermore, by setting single taxes and tax combinations
equal to zero, a detailed study of selected policy instruments is possible.
The applied utility function of the government is the same like the one of
the households (12) – except for the social time preference rate ρ G . This allows
for the possibility to change the social time preference rate and to distinguish
between personal impatience of someone’s own future utility and the weighting
of future well-being of following generations. 40
The Optimization Problem of the government to maximize welfare is the
following:
max
{{τ i},ς R,Γ,R L,R E,R E2 }
∫ ∞
0
u(C, L)e −ρGt dt
with i ∈ {K, K Y , K E , K R , E, R, E 2 , L}
subject to:
S ≥S (58)
C gov =Γ + τ K rK + τ L wL + τ E p E E + τ R p R R + τ Eren p E E ren (59)
+ τ KY rK Y + τ KR rK R + τ KR rK R + ς R R
− R L − R E − R E2
¯r =r(1 − τ K ) (60)
¯w =w(1 + τ L ) (61)
¯p E =p E (1 + τ E ) (62)
¯p R =p R (1 + τ R ) (63)
A full description of the Stackelberg leader problem with all constraints (including
the model extensions of the following subsections) is listed in Appendix
C.
40 While ρ H is a positive paremeter about the personal intertemporal distribution of wellbeing
and occurs like a individual preference parameter, ρ G is a normative parameter who
touches questions of intergenerational justice and hence is a matter of social and political
discussion (Schelling, 1995, 1999). An approach of combining the impatience character of
ρ H and the intergenerational justice aspect of ρ G present Sumaila and Walters (2005) by
derivating a hyperbolic discount formula.