The Role of Land Retirement Programs for Management of Water Resources

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∣^λ = ^πijte^-ρ^t^{- λ}1^αigijt
_∂_Aijt ijt 1 i ijt

- λ2i≥ 0, λ2i≥ 0, !^λ λ2i= 0

2i 2i _∂_Aijt 2i

(13.b)

∂Λ

--- = -∏: e

∂ Lit ⁱj^t

^ρ^t + λ1αigijt

λ2i

λi- λ₄,≥ 0, λ₄,≥ 0, ^^λ λ_ti= 0

∂L_it

(13.c)

^дЛ = V (a _- L )_e-^ρ^dπj^it =

∂ G V⁽ A^j L^it ) e ∂ G

dλ₁dt

(13.d)

∂Λ

--- = λ ; =

∂Γ ^{4 i}

dλ_3idt

(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 A_ijt . 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

^-^πijt^e

^ρ^t+λ1αigijt

∂π

^{- λ}2i ^{- λ}3i ^{- λ}4i ≥ ⁰ or ^-^πijt^e⁺ 3---^e

^∂^gijt

ρtg
gijt

λλλ

^- 2i ^- 3i ^- 4i

≥ 0 . This also

implies that the land parcel with the highest benefit to cost ratio, (λ₁α_ig_ijt )/(π_ijte

^-^ρ^t ), 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 π_ijt 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

∫ V L_itdt ≥ 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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