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

24 3 MODEL DEVELOPMENT AND ANALYSIS
Figure 3: Game theoretic structure of the basemodel
3.1 Description of the Basemodel
The basemodel as introduced in this section is subject to later extensive analytical
and numerical analysis. In order to highlight the theoretic structure of the
Stackelberg game, Fig. 3 shows the players and their strategical variables subject
to payoff maximization. As every economic sector maximizes intertemporal
payoff given the optimal strategies of the other sectors, the market economic
outcome is a Nash equilibrium. Imposed taxes of the government as Stackelberg
leader who anticipates the reaction functions of the followers can influence the
optimization behavior of economic sectors.
3.1.1 Households
Description of the Household Sector Utility u of the households depends
for each point of time on consumption C and labor time L such that increasing
consumption and decreasing labor time causes higher utility 23 but marginal
utility declines over time.That is formally:
u ′ C > 0 , u′′ C < 0 (4)
u ′ L < 0 , u ′′ L < 0 (5)
To consider utility for a whole space of time instead of a single point of time an
intertemporal utility function J H is used that depends on all time-point utilities.
Usually the utility of each time weighted by a discount factor f(t) is integrated
to:
J H =
∫ T
t 0
u(C, L) f(t) dt
23 Consumption C and leisure L max−L are goods in the meaning that they are always preferable
and more of them is always better than less. However this on the first view plausible
assumption is indeed very disputable. The economy of happiness looks for a better understanding
of the factors of well-being that are more sophisticated than the standard approach
presented here. Thus, Layard (2006) shows that increasing income does not necessarily lead
to a higher level of happines.