HAL Id: hal-00704970
https://hal.archives-ouvertes.fr/hal-00704970
Submitted on 6 Jun 2012
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S. Foudi, K. Erdlenbruch. The role of irrigation in farmer’s risk management strategies in France.
European Review of Agricultural Economics, Oxford University Press (OUP), 2011, 39 (3), p. 439
-p. 457. �10.1093/erae/jbr024�. �hal-00704970�
† ∗,‡ †
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2
e
e
∗e
e
∗∗e
e
∗∗∗e
e
%
∗ ∗∗ ∗∗∗Y
Y = f(X) + g(X)ε.
f
X
g
ε
E(ε) = 0
V ar(ε) = 1
Π = pY − r
X,
p
r
X
max
XEU[Π] = max
XEU
p (f(X) + g(X)ε) − r
X
.
x
j∈ X
∂f
∂x
j=
r
jp −
∂g
∂x
jE[εU
]
E[U
]
.
E[εU] E[U]≡ θ
U
∂g ∂xjx
j ∂x∂gj< 0
∂x∂gj> 0
θ
AR
σ
2 πDR
AR
DR
i ∂AR/∂μπ = δ1 + δ2μπx
w∈ X
x
j∈ X
Y =
f(x
j, x
w) + g(x
j, x
w)ε
x
w> 0,
f(x
j) + g(x
j)ε
x
w∂f
∂x
w−
r
wp +
∂g
∂x
wθ = 0,
x
w> 0
x
w= 0
x
wθ < 0
∂x∂gj> 0
∂g ∂xj< 0
θ > 0
i = 1, ..., N
i = 1, ..., N1
,
N
1⊂ N
P rob(x
∗ iw> 0|x
ij, Z
i, D, z
i)
Z
iD
z
ix
∗ wi= α
1x
ji+ α
2Z
i+ α
3z
i+ α
4D + εwiz
∗ i= β
1x
ji+ β
2Z
i+ β
3D + ε
zi,
Zi D zix
wi=
1
x
∗ wi> 0
0
z
wi=
1
z
∗ wi> 0
0
x
∗ wiz
i∗(ε
w, ε
z)
V ar(ε
wi) = V ar(ε
zi) = 1
ˆ
Mσ
u=
φ()Φ()σ
uφ
Φ
P rob(x
∗ iw> 0|x
ij, Z
i, D, z
i)
σ
uk = w, f, l
y
g(X)
=
f(X)
g(X)
+ .
f(x
w, x
f, x
l) =
kα
kx
k+
1
2
k kα
kkx
kx
k+ σ
uM,
ˆ
g(x
w, x
f, x
l) = x
wβwx
βffx
βll.
k = w, f, l
α
k+ α
kkx
k+
k=kα
kkx
k−
r
kp +
θ(.)
g(.)
x
kβ
k= u
k.
θ =
−ARσ
1 + 0.5DRσ
π+ 0.5DRσ
2 π2γ
π.
μ
πAR = δ
0+ δ
1μ
π+ 0.5δ
2μ
2π,
DR =
−∂AR
∂μ
π+ AR
2.
f(.)
p
s
μ
π= pf(.) −
kr
kx
k+ s,
k = w, f, l
g(.)
σ
π2= p
2g(.)
2.
∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗ ∗ ∗∗ ∗
10%
10%
5%
§
α
w ∗∗α
ww ∗∗α
f ∗∗α
ff ∗∗α
l ∗∗α
ll ∗∗α
wf ∗α
wl ∗∗α
fl ∗∗σ
u ∗∗β
w ∗∗β
f ∗∗β
l ∗∗δ
0δ
1 ∗∗δ
2 ∗γ
∗∗ § ∗ ∗ ∗ ∗∗ ∗μ
πσ
μπξ
xwξ
xfξ
xlθ
x
f
ξ
x≡
∂f ∂xfx%
%
R isk A ver si o n (A R ) Expected Profit
θ
μ
π> 2600
μ
π< 200
e
0.34
0.072
−2
+2
profit (€)