PRELIMINARY VERSION - PLEASE DO NOT CITE
∣λ = πijte-ρt - λ1αigijt
∂Aijt ijt 1 i ijt
- λ2i≥ 0, λ2i≥ 0, !λ λ2i= 0
2i 2i ∂Aijt 2i
(13.b)
∂Λ
--- = -∏: e
∂ Lit ijt
ρt + λ1αigijt
λ2i
λi- λ4,≥ 0, λ4,≥ 0, ^λ λti= 0
∂Lit
(13.c)
дЛ = V (a - L )e-ρ dπjit =
∂ G V( Aj Lit ) e ∂ G
,j
dλ1
dt
(13.d)
∂Λ
--- = λ ; =
∂Γ 4 i
dλ3i
dt
(13.e)
Equation (12.a) defines the optimal water use for each farmer. Equation (13.a) describes
the Kuhn-Tucker conditions for the optimal land allocation Aijt . The optimal land retirement is
determined from equation (13.b). Using equations (13.a) and (13.c), we can find out the factors
affecting the choice of land parcel for retirement. Farmer i’s land
is retired if
-πijte
ρt+λ1αigijt
∂π
- λ2i - λ3i - λ4i ≥ 0 or - πijte + 3---e
∂gijt
ρtg
gijt
λλλ
- 2i - 3i - 4i
≥ 0 . This also
implies that the land parcel with the highest benefit to cost ratio, (λ1αigijt )/(πijte
-ρt ), would be
selected first for the land retirement. This model describes the optimal targeting of land
retirement to achieve the water quantity goal. It requires a rental payment of at least πijt at time t
in order to induce farmers to participate in the program.
An alternative land retirement program is to take a given number of acres ( L ) out of
production in N years. Under such a policy, the water planner’s decision problem is similar to the
one given in equations (6)-(11), with the only difference equation (11) being replaced by
N
∫ V Litdt ≥ L. The goal of this policy is to retire L acres with least cost. This policy does not
0i
consider where the land parcels to be retired are located and therefore ignore their contributions
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