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The selection among the remaining land-use patterns differs between the models as
described in the next sections.
3.3
The Utility Based Model (Holtz and Pahl-Wostl 2012)
This model version selects among different land-use patterns through the calculation
of a utility for each land-use pattern and selection of the one that maximizes utility.
Utility calculation is based on the four objectives identified above (profit, risk, labor,
legality), i.e. it is not limited to monetary profit (see Table 1). The parameters of the
utility function differ between farm types (cf. [10]).
Table 1.
Calculation of utility U(p
i
) of a land-use pattern p
i
(adapted from [10])
U(pi) = G(g(p
i
))*R(r(p
i
))*W(w(p
i
))*L(l(p
i
))
G
: function of the influence of gross margin
g(p
i
), R
: function of the influence of risk
r(p
i
)
W
: function of the influence of labour (work) load
w(p
i,
), L
: function of the influence of staying
legal
l(p
i
))
G (g)= g
γ
0<γ<=1. γ
is a parameter representing decreasing marginal utility of gross margin (for
γ<1
).
w
−
w
f
β
W
(
w
)
=
Max
[
0
Min
(
(
−
)
)]
κ
−
w
w is the amount of labor needed for a land-use pattern, κ sets an upper limit of the labor load that can be
handled by a farmer f and w
f
is the available family labor (it is κ≥ w
f
). Note that if w< w
f
then W(w)=1
and if w> κ then W(w)=0. W(w) (and thus utility) decreases between w
f
and κ. β determines the shape
of this decrease.
f
ρ
R
(
r
)
=
(
−
r
)
The values of risk
r
associated with a land-use pattern as calculated in the model are associated with the
standard deviation of gross margin due to short-term fluctuations of prices for products and inputs as
well as variability of yields.
r
is in [0.0,1.0].
ρ
determines the shape of utility regarding
r
.
Being legal is binary:
l e {0 = illegal,1 =legal}
. If
l=1
(legal behaviour)
L(l)=1
, thus utility is not
reduced. If
l=0
(illegal behaviour), λ varies the impact of illegal behaviour on utility.
In total the utility function is hence:
L
(
l
)
=
Max
(
l
,
0
5
λ
)
w
−
w
γ
ρ
f
β
λ
U
(
p
)
=
g
⋅
(
−
r
)
⋅
Max
(
0
,
Min
(
−
)
))
⋅
Max
(
l
,
0
.
5
)
i
κ
−
w
f
Figure 3 shows the simulation results that best fit
3
the empirical data presented in
figures 1 and 2. In the simulation results the COP
4
area rises until 1985 to a similar
level as observed empirically (cf. figure 2). The subsequent drop in irrigated COP
area after groundwater extractions have been legally limited is reproduced by the
model, but underestimated. The model does not capture the empirically observable
increase of irrigated COP area after 1995; instead a higher level of horticultural crops
3
The model was fitted manually. For a sensitivity analysis see [10].
4
COP is an abbreviation for cereals, oilseeds and proteins. In this model COP cover traditional
cereals, high-yield cereals and sunflowers.
