WSP02976

• File Number: 8271.300
• Description: Colorado River Basin Salinity Control Program - General Information and Publications-Reports
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 12/1/1979
• Title: An Economic Evaluation of the Salinity Impacts From Energy Development - The Case of the Upper Colorado River Basin
• Water Supply Pro - Doc Type: Report/Study

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IV. MODEL FORMULATION FOR
THE STUDY AREA

A lineal" programming (LP) approach is
employed to model the allocation of water
between agricultural and energy production.
Within the LP framework, the optimal allo-
cation of water use among water users in
the Upper Basin, from the private viewpoint,
is calculated by maximizing joint net returns
for agricultural and energy products within
appropriate constraints. The resulting
change in salinity level downstream is then
estimated through a mass-balance approach.
The model will be later modified to incorpo-
rate salinity control measures to evaluate
least-cost strategies and to identify optimal
salinity levels.

For the purpose of this analysis, the
following constraints are used:

1. Complete voluntary transfer of water
rights is allowed within each state, but
interstate transfers are not permitted due to
institutional constraints.

2. In compliance with Public Law 92-500,
aimed at elimination of waste discharges by
1985, wastewaters from energy development
will not be discharged into rivers. Energy
developers are assumed to provide total
containment of the wastewater.

3. Water available for ag"riculture and
energy sectors is the water remaining after
withdrawal for municipal and industrial
Deeds, for exports, and for wildlife conser-
vation.
t+. Both agriculture and energy sectors
are price takers in input and output markets.

The Obiective Function

Maximizing joint net returns of agri-
cultural and energy outputs can be accomp-
lished by the following approach:

Net return of agricultural outputs

The economic returns accruing to agri-
cultural crops are determined by the yield or
land productivity for the crops. The Upper
Colorado River Basin is subdivided into eight
Water Resources Subareas (WRSA) (s = l, 2,
. . .,8) along county boundaries (Figure 3).
Suppose each WRSA grows H different crops (i

= l, 2, . . ., H). If p~ is the unit price
of the ith crop and Xf is the acreage
of land used in growing the ith crop wItli
of productivity (units of the ith crop
per acre) in the sth WRSA, the gross return
to agriculture for the entire basin is

TRA '"

8
E
s=J.

(1)

H
E
i"'l

pS oS xS
i i i

The cost associated with growing crop i
comes from using various inputs such as seed,
fertilizer, labor, land, and machinery. If
cf is the unit cost of growing the ith crop
per acre, the total cost of production can
be expressed as

TeA ~

8
E
s=l

(2)

H
E
i=l

c~ x~
1 1

The difference
return and total cas t
of agricultural output

between total
yields the net
nA

gross
return

'ITA'" TRA - TeA

(3)

Net return of energy outputs

Suppose there are M raw energy outputs
(r = l, 2, . . ., M) that can be sold direct-
ly in the market after extract ion from the
gr ound and there are N final outputs (k = l,
2, ., N) from energy convers ion pro-
cesses. Let p~ and R~ be the price and
quantity, respectivell' of the rth raw
~nergy outputs, and Pk-, Q~ be the pr ice
and quantity of the kto converted product
in WRSAs. The total revenue from energy
products is written as

T'); -

8
E
s=l

8
E
s=l

(4)

M
E
r=l

N
E
k=l

s s
Pk Qk

pS RS +
r r

If C~ and C~ are the unit costs of all
factors, other than raw material, used in the
extraction and conversion process in the sth
WRSA, the total cost of producing energy
output is

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