Environmental Engineering Reference
In-Depth Information
Subject to: Ax ≤ B; x ≥ 0
(5.2)
Where: U is the variable to be maximised (i.e. utility), Z is the expected income (i.e.
the average annual income), x is a (n × 1) vector of agricultural activity levels, A is
a (m × n) matrix of technical coefficients, B is a (m × 1) vector of available resource
levels, f is a scalar for the risk aversion coefficient and s is the standard deviation
of income according to states of nature defined under two different sources of
variation: yield (due to climatic conditions) and prices.
The expected income (Z) is a non-linear profit function. Using matrix denotation,
this gives:
x
( )
∑∑ ∑
a
a
Z
=
pq
+
p q
+
s c
−
i
j
j
j, l
j, l
i, t
i, t
h
j
j, l
i, t
i
y
x
x
∑
i, t
i
i
+
d
+
−ϖ
L
i, t
2
h
i, t
(5.3)
i
Where: i indexes agricultural activities, j indexes crop products, l indexes quota
types (e.g. for sugar beet A and B quota exist), t indexes number of years in a rotation,
p is a vector of average product prices, q is a vector of sold production, p
a
is a vector
of additional price that the farmer gets when selling within quota l, q
a
is a vector of
sold production within quota l, s is a vector of subsidies per crop within agricultural
activity
i
(depending on the Common Market Organisations [CMOs]), c is a vector
to account for variable cost per crop within agricultural activity
i,
d is a vector of
linear terms used to calibrate the model (depending on the calibration approach),
Y is a symmetric, positive (semi-) definite matrix of quadratic terms used to
calibrate the model (depending on the calibration approaches), h is a vector
representing the length of a rotation within each agricultural activity, v is a scalar
for the labour cost and L is the number of hours of rented labour.
An agricultural activity is defined in FSSIM as a way of growing a rotation
(including mono-crop rotations) taking into account the agri-environmental zone
(or soil type), the management practice, and the production orientation. It consists
of a combination of one crop rotation, one agri-environmental zone, one production
technique (i.e. management type) and one production orientation. Let R denote the
set of crop rotations (including mono-crop rotations), S the set of agri-environmental
zones, T the set of production techniques and Sys the set of production orientations.
The set of agricultural activities i can be defined as follows:
i
= {i
1
, i
2
,…} = {(R
1
,S
1
,T
1
,Sys
1
), (R
2
,S
1
,T
1
,Sys
1
),…} ⊆ R × S × T × Sys.
Agricultural activities can be based on individual crops if data on crop rotations are
not available.
The principal technical and socio-economic constraints that are implemented in
FSSIM-MP are: arable land per soil type (or agri-environmental zone), irrigable
land per soil type, labour and water constraints. The same rule was applied for all
