Climate change and water resources in the Murray Darling Basin ...

ABARE CONFERENCE PAPER 02.11
subject to constraints on the overall availability of irrigation water from rivers, sw*, and
from ground water sources, gw*, and suitable land, L*:
(4)
subject to
(5)
where x j is output of activity j, L j is land used in activity j, sw j is surface water and gw j is
ground water used for irrigation of activity j, r is the discount rate, and csw is the unit cost
of surface water used for irrigation and cgw is the unit cost of ground water used for irrigation.
The net return to output for each activity is given by p j and is defined as the revenue
from output less the cost of inputs, other than land and water, per unit of output.
For each activity, the volume of output depends on land and water use (or on a subset of
these inputs) according to a Cobb-Douglas production function:
(6)
where A j , α Lj , α swj and α gwj are technical coefficients in the production function. Note, the
technical coefficients on surface irrigation water are time dependent, to capture the impact
of changes in salt concentration in the Murray River.
The costs to irrigated agriculture and horticulture resulting from yield reductions caused by
increased river salinity are modeled explicitly. The impact of saline water on the productivity
of plants is assumed to occur as plants extract saline water from the soil. The electroconductivity,
EC, of the soil reflects the concentration of salt in the soil water and reduces
the level of output per unit of land input (land yield) and per unit of water input (water
yield). This is represented by modifying the appropriate technical coefficients, α swj , in the
production function for each activity from the level of those coefficients in the absence of
salinity impacts. That is:
(7)
x
j
1
max ∑ p x ( L , sw , gw )−csw∑ sw −cgw∑ gw
r
j
j j j j j j j
j
j
∑ j ∑ j ∑
j
j
j
sw ≤ sw*, gw ≤ gw * and L ≤ L *
αLj αswj () t αgwj
⎧
⎪AjLj
swj gwj 0< αLj + αswj + αgwj
< 1for j = 12 , , 3
= ⎨ α Lj
⎩⎪ AL j j 0< α Lj < 1 for j=
4, 5
α
swj
max
α swj
() t =
+ exp µ + µ
1 ( 0j 1jEC)
where µ 0j and µ 1j are productivity impact coefficients determined for each activity and
α swj max is the level of the technical coefficient in the absence of salinity.
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