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

dealing with only one of these two variables
are in ~eneral economically inefficient.
Controlling salinity by reducin~ waste
discharges has been discussed and low-flow
augmentation and desalting alternatives need
to be integrated into the analysis.

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Economic Implications of Dilution

To illustrate this point, two groups of
water users will be assumed in a river basin.
Allocation of a given quantity of water by
maximizing combined profits for the two users
is economically efficient. In the absence of
externalities, market mechanisms will lead to
optimal allocations. When externalities
resulting from water pollution are present,
voluntary transfer of consumptive use por-
tions of water rights will no longer result
in optimal allocation. .

The two user groups, firms I and 2, use
water as an input in their production pro-
cesses. Firm 1 discharges salt load in
proportion to the amount of water used. No
salt is discharged by firm 2. Line WOWO
represents the maximum quantity of water
available for use by the two firms (Figure
1). The slope of WOWO reflects the ratio of
the marginal value of water to firms land 2.
Firms land 2 are price takers in input and
output markets. Let 'lT1 be an isoprofit curve
whose propert ies are der ived in Append ix
A. Every po int on 1Tl represent s a comb ina.-
t ion of water used in firm 1 (WI) and water
used in firm Z (WZ) that yields a specified

level of joint profits. The slope of the
tangent at a point on an isoprofit is the
ratio of the marginal profit of firm I to
marginal profit of firm 2 from using water in
their production. If water is assumed to be
fixed in supply, the marginal profit of each
firm is the value of the marginal product of
water to that firm. The highest combined
profits of firms 1 and 2 depend on the

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Z
Q:
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0-
w-
..J'O
II) Q) ,0
ct ~ W,
..J "
Ci '5 II
~:S w2
Q:=
w 5/
tt 0 I
3= ~ w2

Wc

W,

11'1> '11'2>11'3>""4

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: : 11'1
-------~-~---,
I , ,I
I I H

WI W;11 wfwll Wo wr WO
WATER AVAILABLE TO FIRM I
($GII:d"cha,ged al conslanl concent,allon)

Figure 1.

Allocation of water under quantity
and quality constraints. ,

availability of water dnd its marginal
productivity. Any combination of WI and VJ2
cannot exceed the available quantity WOWO
Therefore., WOWO is the resource constraint.
The tangency of 1fl at}d WoVb shows the opt ima 1
allocation of resources under free trade. At
A, the point of tangency, firm 1 consumes OWl
units of water, and firm 2 consumes OW~. The
sum of the highest net profits attainable bX
the firms is 1TI' The quantities OW~ and OW~
are the optimal allocation of water resources
from the private pointoof view. If the
amount of water used, OWL plus OW~, imposes
substantial economic losses on downstreau\
water users, the river basin authorities may
desire to maintain a higher level of water
quality to reduce downstream dama~es.
Lil)e We WoG. is the bou,ndary of a maximum
allocatIon of WI and W2 whlch meets a certaIn
qualIty standard, C*. The properties of We
Wc are derived in Appendix B. The joint
prof its 1Tl, are no longer attainable since
consumpt ion of OW~ and OW~ by firms 1 and 2
will violate standard C*.

If the river basin authority dealt with
the problem only by reducing waste dis-
charges6 it wo~ld reduce water use "by firm 1
from OWl to OW;!. but the amount of water used
by firm Z (OW~) would be unaffected. The
jo int prof its would be TTJ. The allocat ion of
water at B, however, IS nonoptimal because
the slope of 1f3 curve is steeper than the
slope of the curve Wc Wc. The ratio of the
value of the marginal product of an addi-
,tional unit of water to firm 1 (VMP1) to firm
2 (VMP2) is greater than the marginal rate of
substitution in concentration of WI for W2

ac ac ,
( YVJIYVJ ). ThiS can be interpreted as firm
1 Z
lis sacrifice of marginal profit from water
use being greater than firm 2's. Firm 1 will
experience a reduction in its profit.

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On the other hand, if the authorities
choose to deal with the problem by reducin~
wa ter use, both firms 1 and 2 mu s t decrease
their production. If it were decided to
reduce total water use to that represented by
line WrWr, the maximum joint profits attain-
able to the two firms fall from 1TI to TT4' At
C where WrWr passes through Wc We and the
7T4 curve, the allocation of water OWl to
fIrm 1 and OWZ to firm 2 is also nonoptImal.
Thus, reducing the amount of water supplied
to users in a basin is also an inefficient
method for improving water quality.
Since controlling either one of the two
variables alone is economically inefficient,
policies to deal jointly with the two control
variables should be devised. The optimal
policy must involve both reducing salt
loading and reducing the volume of water
consumption upstream: Only the allocation at
point 0 where the joint p~of its curve TT2 IS
tangent to the water qualIty standard curve
WcWc is optimal. This implIes an equalIty In
, the rates of sacrificing water by firms 1 and
2 to maintain water quality. Firm 1 will

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