Title Page
 Table of Contents
 Description of models and sources...
 Farm organization and water...
 Implications for economic evaluation...
 Tables I-V

Group Title: Bulletin - Colorado State University. Agricultural Experiment Station ; no. 70
Title: Marginal values of irrigation water
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00055289/00001
 Material Information
Title: Marginal values of irrigation water a linear programming analysis of farm adjustments to changes in water supply
Series Title: Technical bulletin Colorado Agricultural Experiment Station
Physical Description: 28 p. : ; 23 cm.
Language: English
Creator: Hartman, Loyal M.
Whittelsey, Norman K
Publisher: Agricultural Experiment Station, Colorado State University
Place of Publication: Fort Collins Colo
Publication Date: 1961
Subject: Irrigation water   ( lcsh )
Irrigation farming   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Includes bibliographical references.
Statement of Responsibility: L.M. Hartman and Norman Whittelsey.
General Note: Cover title.
Funding: Technical bulletin (Colorado Agricultural Experiment Station) ;
 Record Information
Bibliographic ID: UF00055289
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 23750580

Table of Contents
    Title Page
        Title Page
    Table of Contents
        Table of Contents
        Page i
        Page ii
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Description of models and sources of data
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
    Farm organization and water values
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Implications for economic evaluation of water use
        Page 22
        Page 23
        Page 24
        Page 25
    Tables I-V
        Page 26
        Page 27
        Page 28
Full Text

Peter E. Hildebrand
Agricultural Economics

Technical Bulletin 70




A Linear Programming Analysis
Of Farm Adjustments to
Changes in Water Supply

Agricultural Experiment Station
Colorado State University
Fort Collins, Colorado



Summary ---..----.- ..--.... ... ... .......... .. ..__ ...... ....------------ ii

Introduction -----__- ______ ------- --------------- 1

Description of Models and Sources of Data_....---- ---------..---.---- 6

Farm Organization and Water Values.-.__.--.._... .- -- -- 13

Implications for Economic Evaluation of Water Use ----.- 22

Appendix ----------------------------26


This study was financed by the
United States Department of
Agriculture under a Research
and Marketing Act contract ad-
ministered through the Farm
Economics Research Division of
the Agricultural Research Serv-
ice. The contract for the con-
duct of the research covered the
period July 1, 1958 to December
31, 1960. The study was super-
vised by Dr. M. L. Upchurch of
the Farm Economics Research
Division, ARS, and Dr. Rex D.
Rehnberg, Economics Section,
Colorado Agricultural Experi-
ment Station.

Dwight Blood was the prin-
cipal investigator during the
early phase of the study. He was
assisted by Norman Whittelsey
who assumed major responsibil-
ity for the data collection upon
the resignation of Mr. Blood.
The senior author assumed re-
sponsibility for completion of
the project in January 1960.

The authors wish to acknowl-
edge the many hours of time and
helpful suggestions given by Dr.
R. B. Hughes in organizing and
interpreting the results of the

Colorado State University Experiment Station
Fort Collins, Colorado

In Cooperation With

Farm Economics Research Division
Agricultural Research Service
U. S. Department of Agriculture


This study consists of a linear
programming analysis of farm
adjustments to changes in water
supply. The main effort of the
study was to estimate various in-
cremental or marginal values of
water. Several factors that affect
the value of irrigation water were
considered and their effect esti-
mated within different assump-
tions about labor supply. These
factors were land productivity,
efficiency of water use, timing
and level of water supply, and
number and kinds of enterprises.
Three farm models having dif-
ferent enterprise alternatives
were used in the analysis. Fixed
resources or limitations in the
models consisted of land, month-
ly labor, operating capital, and
monthly water supplies. Solu-
tions were programmed for three
monthly water supply situations.
Other resource limitations,
prices, and inputs per acre were
held constant throughout the
Three different output situa-
tions were considered to take
into account differing land pro-
ductivities. Water-use efficiency
levels of 40, 50, and 60 percent
were considered as they affected
water values.
Estimated marginal w a t e r
values varied from 39 cents to

approximately $41 per acre-foot
over the range in variation of the
above factors. The middle esti-
mates of marginal water values
dropped from $18.17 to $8.99 as
water supply increased from 2.18
to 3.02 to 3.67 acre-feet per acre.
The calculations from the mod-
els demonstrate the need for dif-
ferentials in supply when allo-
cating water to individual farms,
or the economic advantages of a
free market for water.
Labor use increased by ap-
proximately 35 to 50 percent for
the various models when water
supply increased from 2.18 to
3.02 acre-feet per acre. This
major change in labor use in-
dicates the need in project evalu-
ation for considering the cost and
availability of labor resources
needed to utilize supplemental
water from the project.
The farm model having a live-
stock enterprise gave the largest
estimates of water values. This
resulted because the livestock
operation provided a better mar-
ket for crops than selling on the
open market. Whether or not
the changes in the residual for
the livestock model properly re-
flect the returns to water depends
upon the assumptions regarding
the opportunity costs of the ad-
ditional capital and labor.

Marginal Values

of Irrigation Water

L. M. Hartman and Norman Whittelsey*


Economic evaluation of poten-
tial uses and development of
water resources requires esti-
mates of marginal values of
water. For example, marginal
values must be determined to
estimate benefits from potential
projects for supplying supple-
mental irrigation water. They
are also needed for judging the
relative merits of allocating exist-
ing water supplies among com-
peting uses.
The effort of the study report-
ed here is not to estimate a single
value for an increment of water,
but rather to indicate a range of
values that would apply under
different conditions. This report

presents results from a study of
individual farm adjustments to
changes in water supply and the
effect of such adjustments on
farm income.
A linear programming pro-
cedure is used to determine the
farming systems required for
maximum income on typical
farms operating under various
water supply conditions and to
estimate how water supply
changes affect income. Variations
in several factors such as manage-
ment, land productivity, effi-
ciency of water use, timing of
water deliveries, number and
kinds of enterprises, and labor
supply are considered.

Discussion of the Problem

The specific problem consid-
ered in the study involves estima-
ting the value to an individual
farm of an increased supply of
water. This problem is in con-

trast to estimating the value of
an increased supply of water to
an area, that is, to an aggregate
of farms. The latter problem in-
volves aggregation and must be

*Assistant Professor of Economics and Sociology, and former Research Assist-
ant, respectively.

considered in most decisions con-
cerning water allocation. Adjust-
ments on the individual farm
are an important aspect of this
problem, as these are the units
to be aggregated.
The effects of an area adjust-
ment on prices, both for factors
and products, may be important
in a complete study. Other con-
siderations important in a com-
plete study would be national
benefits versus individual or re-
gional benefits. These problems
ire outside the area of the study
reported here.

Valuing resources on the
individual farm
The problem of resource valu-
ation on the individual farm is
a typical one of production eco-
nomics, since it is implicit in the
allocation of resources among
competing enterprises. One way
of valuing a resource at the mar-
gin is to consider the farm at a
short-run optimum, and measure
how increasing or reducing the
resource under consideration by
desired amounts affects revenue.
Linear programming has proved
well-adapted to this type of
problem. A brief exposition of
the linear programming tech-
nique used in the study is pre-
sented here to show how the
problem of determining water
values is approached.1
Production possibilities of the
farm can be summarized symbol-

ically in matrix form as follows:
axl +X a1x2 + a11Xn:bi
a2x + a22X2 + ax. 2nXn

amixi amXX .- amnxn-bm
The b's (bi, b, b) are
quantities of various resources
which are limitational. These
would be land, water, labor,
capital, and so forth. The co-
efficients aln, a,1 am,, are the
input requirements of the enter-
prises for these resources.
The columns contain all co-
efficients for each activity; the
rows all coefficients for each re-
source. Thus an is the amount
of b, required to produce one
unit of the first activity listed in
the matrix. The x's are the un-
knowns and represent the to-be-
determined level at which each
activity will be carried on. The
inequalities indicate that no
more of a resource may be used
than is available, but some of it
may go unused.
Defining Cj as unit net revenue
above variable costs for the jth
activity, and with maximum
profit as the objective, the opti-
mum use of resources is achieved
when the quantity Cix + C2,x
+ Cnxn is at a maximum
subject to the inequality restric-
tions of the production possibili-
ties matrix. The : Cjxj is the
total net revenue or the return
to the fixed factors. Marginal
unit value of any particular
scarce resource is the amount of

1See Earl O. Heady and Wilfred Candler, "Linear Programming Methods,"
(The Iowa State College Press, Ames, Iowa, 1958), for a detailed non-mathemati-
cal exposition of the technique. Chapter 7 treats the resource valuation problem.

reduction that would occur in
the Y Cjxj from reducing avail-
ability of that resource by one
unit, with all other conditions
If the marginal unit value of
the ith resource is designated as
yi, at the optimum solution for
maximum profit the linear pro-
gramming technique assures that
bly, + b2y2 bmym is equal
to C1X1 + C2X2 + CnXn-
that is, total imputed return to
resources equals total net rev-
enue. The y's are a by-product
of the simplex procedure.2 A
complete marginal value sched-
ule for a resource may be derived
by an appropriate series of pro-
gramming steps.3

Factors affecting estimates of
marginal resource values
In the above expression of the
farm production problem, pro-
duction and profit possibilities
are expressed in terms of three
sets of coefficients: the a's, or in-
put requirements; the b's, or re-
source quantities available; and
the C's, or unit net revenues for
each enterprise. The x's are un-
knowns to be determined and
represent the activity levels. The
coefficients are given by the con-
ditions of management, market
price, resource productivity and
availability, and technology in-
herent in the problem area being
studied. These coefficients, when

estimated for a particular situa-
tion, determine the estimates to
be placed on values of resources.
Input requirements are related
to a given technology, manage-
ment level, and resource quality
situation-items that vary con-
siderably from farm to farm. The
unit net revenues, C's, are gross
unit revenue for each enterprise
minus variable costs. Thus for
crop enterprises, Cj = pjQj -
vj, where pj = the price of jth
crop, Qj = the yield per acre
and vj = the sum of the variable
cost inputs.
Past data for prices of products,
yields, and resource inputs are
readily available, although in
using these data one is restricted
to measuring resource values for
past conditions. Specifying levels
for the b's is difficult because of
possible flexibility in hiring-in
and hiring-out of resources which
makes it unrealistic to say that
resource quantities are absolute-
ly fixed during the production
period. This is particularly true
for monthly labor supplies be-
cause of use of family and sea-
sonal hired labor.
Fixity of resource supplies is
one of the more crucial variables
affected by management levels
and affecting the realized profits
of the farm.4 Flexibility in the
use of labor is allowed, to some
extent, in this study by allowing
the use of family labor during

2 Ibid., p. 471.
3 Ibid., Chapter 7.'
4 See a study by Lee Martin, Arthur J. Coutu and H. S. Singh. The Effects
of Different Levels of Management and Capital on the Incomes of Small Farmers
in the South, Journal of Farm Economics, Feb. 1960.

peak periods of labor use.
In formalizing actual condi-
tions, varying degrees of reality
may be achieved by the estimates
and assumptions built into the
computational model. The above
coefficients may be secured from
survey and secondary sources of
data, and some measure of the
range of their variability entered
quantitatively into the model.
Such factors as risk and uncer-
tainty are difficult to express
quantitatively and enter into a
model, although they are impor-
tant in determining optimum

enterprise combinations and,
consequently, resource values.
Another factor limiting the
applicability of computed results
is the assumption of profit maxi-
mizing use of resources. Farmers
may or may not be complete
"profit maximizers" and operat-
ing with incomplete knowledge
they undoubtedly never reach
the optimum regardless of their
goal. Resource values derived
from a normative study would
therefore be upper limits under
the specified conditions of the
study model.

Approach Used in This Study

As mentioned earlier, the pur-
pose of the study is not to derive
a value for water, but to estimate
the relative effect of certain fac-
tors upon water values, and, con-
sequently, to derive a range of
values. One set of input co-
efficients, prices, and variable
costs is used for enterprises exist-
ing in general irrigated farming
areas of Colorado.
Enterprise alternatives are
varied by using three models to
reflect differing ambitions of
farm operators, risk preference,
and so on. Three sets of crop
yields are used, for high, low,
and average productivity situa-
tions. Resource levels for land,
monthly labor, and operating
capital are held constant through-
out the main part of the computa-
tions. The effect of relaxing the
assumption of a fixed labor sup-
ply is estimated without using a
complete set of computations.
The description of the models

and sources of data are given in
a following section.
An illustration of the approach
used is shown in figure 1. This
is a simplified, hypothetical situ-
ation with two crop possibilities,
crop 1 and crop 2, and with three
limitational resources: land,
labor, and water. Input require-
ments, variable costs, and prices
are implied in the x's, or levels
of crop activities, and in the
slope of the iso-revenue line.
Production possibilities, with
the initial water supply, are de-
lineated by the initial water and
labor restraints. Any combina-
tion of crop 1 and crop 2 could
be realized along or below these
lines. If all of crop 1 were grown,
then production could be as high
as the point of intersection of the
initial water restraint line and
the vertical axis. At this point
water is the only limiting factor,
leaving unused land and labor.

SLabor Restraint

.--__N --__

Iso-Revenue Line-/\ {

x x

Initial Water Restraint
/- Second Water Restraint

Figure 1. A two-crop farm model showing the optimum crop acreages for
two water supply levels-land and labor supply constant.

The optimum, with prices as
reflected in the slope of the iso-
revenue line, is found by moving
the iso-revenue line to its high-
est point within the boundary of
the restraints. This occurs at
point P, for the initial water
supply. At point P, the optimum
crop combination is x,' output
for crop 2 and x,' output for
crop 1. Water and labor restrict
these crops to this level. Net
revenue is Cx,' + Cx2', where
C is used as previously defined.
If the initial water supply re-
striction is lifted to the second
level, as illustrated, then produc-
tion of crop 2 is reduced and
crop 1 production is increased.
The new optimum is at P2 with

corresponding output levels. The
change (increase) in revenue is
(CIX111 + C2x,") (ClXI' +
C2X2') which, under appropriate
conditions, is attributable to the
change in water supply from the
initial to the second level.
In imputing this change in
revenue to water it is assumed
that adequate resources of land
and labor are available to utilize
the second level of water supply.
It is further assumed that farm-
ers seek the maximum profit ad-
justment. These are assumptions
about matters of fact, and their
validity is not investigated in
this study. However, it is neces-
sary to interpret the results in
light of these assumptions.


Description of Models and Sources of Data

Alternatives for each model
Activities included in each
model are shown in table 1.
Model A is representative of a
rather intensive livestock-general
irrigated farm, typical of parts of
the South Platte Valley, Arkansas
Valley, and Western slope areas
of Colorado. Model B is identi-
cal with A except that the pos-
sibility of livestock feeding is
excluded. Model C is character-
ized by limited enterprise alter-
Three adjustments are possible
in response to a change in water
supply, namely, a change in rate
of application, a change in acre-
ages of crops with differing water
requirements, and a change in
total irrigated crop acreages. To
allow for the possibility of vary-
ing the rate of application to a
given crop three possible rates
of water application, and there-
fore three yield levels, are con-

sidered for each crop. Thus, for
crop 1 there are three yields
corresponding to three levels of
water application. In model A,
for instance, with 10 crop pos-
sibilities there are actually 3 x
10, or 30, crop activities con-

Crop yields
Actual production situations
also influence crop yields. This
is in addition to yield rates due
to varying water applications.
We allow for three yield levels
representing high, average, and
low production situations. Yields
for "normal" water applications
are shown in table 2 as compared
with the census yields (1955)
for the South Platte Valley and
for Delta and Montrose counties
in Western Colorado. The latter
two counties encompass the Bu-
reau of Reclamation's Uncom-
pahgre Project.

TABLE 1. Enterprise possibilities for three farm situations
Enterprise A B C
1. Wheat X X
2. Alfalfa X X X
3. Clover (seed) X X
4. Barley X X
5. Corn (grain) X X X
6. Corn (silage) X X X
7. Beans X X X
8. Sugar. beets X X
9. Onions X X
10. Potatoes X X X
11. Beef (fat) X
12. Hogs (1 or 2 litter) X

TABLE 2. A comparison of study yields with census yields for various crops

1954 Yields (census)


Wheat (bu.)
Alfalfa (ton)
Clover seed (cwt.)
Barley (bu.)
Corn (grain) (bu.)
Corn (silage) (ton)
Beans (cwt.)
Sugar beets (ton)
Onions (cwt.)
Potatoes (cwt.)



Delta and




Survey yields with
normal water application

Av. Low



Source: Census of Agriculture, 1955. Survey in 1959 of the Bureau of Recla-
mation Uncompahgre Project in Western Colorado.

The census figures are county
averages. Therefore, they in-
clude some dryland crops, espe-
cially in the South Platte Valley.
The average yields, which were
taken from a survey of the Un-
compahgre Project, closely ap-
proximate the 1955 census yields.
The high and low sets of yields
were derived by changing the
average estimates by a percentage
such that the optimum programs
would not be altered.

In table 1, fat beef and hogs
are shown as enterprise possibili-
ties for model A. The fat beef
enterprise consists of carrying
feeders for 180 days, starting at
700 pounds and selling at 1,050
pounds. There are two hog-rais-
ing activities, one a one-litter
enterprise that does not compete
heavily for summer labor and
the other a two-litter enterprise.
Both assume the marketing of
200-pound hogs.

Prices of Products


All crop prices used in the
study are computed as 5-year
averages of prices received by
farmers in Colorado for the years

The prices of livestock used
are a 10-year average of the per-
iod 1949-1958.6 A 10-year aver-
age was used to include one com-
plete cycle of livestock prices.

5 Colorado Agricultural Statistics, Colorado Department of Agriculture, U. S.
Department of Agriculture cooperating, Denver, Colorado, various issues.
6 Ibid., various issues.

Variable Costs of Production

Costs of production used in
this study for both crops and
livestock are only those variable
costs incurred in actual produc-
tion. Fixed costs of the farm are
not deducted from the net rev-
enue of any enterprise. Variable
costs include such items as inter-
est cost of operating capital, sea-
sonal expenses of power and
machinery repair, seasonal labor
costs, and so forth. These items
of variable costs are taken from
a study by McKains, Franklin,
and Jensen in the Columbia
River Basin of Oregon,7 with
corroboration and supplementa-
tion from other studies.8 All
costs were adjusted to 1959 prices

by the use of relative cost indexes
as published by the U. S. Depart-
ment of Agriculture.' Purchase
prices of livestock are taken from
Colorado Agricultural Statistics
for 1958.

Other costs are marketing and
feeding costs. Feed prices for
livestock rations are assumed to
be the same as the selling prices
of crops. All rations for the live-
stock enterprises are calculated
by using recommendations from
Morrison's Feeds S Feeding. A
listing of costs, prices, yields, and
corresponding net revenue is
presented in tables I and II of
the Appendix.

Input Requirements

Estimated monthly labor re-
quirements for crops are shown
in Appendix table III. Results
from a survey of farms in the
Uncompahgre Project area are
used to estimate the timing of

the various operations for each
crop.10 Secondary sources are
used to compute total monthly
labor requirements for each
Labor requirements for swine
are taken from a bulletin by
Hardin, Weigle, and Wann.2

7 P. M. McKains, E. R. Franklin, and J. E. Jensen, "Estimated Cash Costs and
Man Labor Requirements for the Production of Principal Crops, Columbia Basin
Project, Washington," (Washington State College, Department of Agricultural
Economics, Pullman Station Circular 272, June 1955).
8 A. D. Reed, "Machinery Costs and Related Data," (California University,
Agricultural Extension Service, Davis, November 1954). D. M. Stephens, "Farm
Budget Standards for Irrigated Farming," U. S. Bureau of Reclamation, Region
6, Billings, Montana. Sept. 1948. U. S. Bureau of Agricultural Economics. "Crop
Production Practices: Labor, Power, and Materials, by Operation, Mountain and
Pacific States." F. M. 92, Sec. 5. March 1953.
9 U. S. Agricultural Research Service. "The Farm Cost Situation," ARS 43-
102,- May 1959.
10 Norman Whittelsey conducted this survey in 1959.
11 See footnote 7.
12 L. S. Hardin, R. N. Weigle, and H. S. Wann, "Hogs-One- and Two-Litter
Systems Compared," (Indiana Agricultural Experiment Station, Bulletin 565,
November 1951).

The labor requirements for both
sheep and beef feeding are taken
from a study by Delwin Ste-
phens.3 For a detailed break-
down of labor requirements for
the livestock enterprises see Ap-
pendix table IV.

mentioned (see footnote 10).
Water requirement estimates
described above pertain to the
"normal" use of crops with cor-
responding "normal" yields. To
allow for varying rates of appli-
cation of water, requirements
f r I *T if .l l i rol I

Water .J,. -V, rVV,-1. yl) I lVla VVC.;
also estimated.16 It is assumed
Water requirements of each that certain irrigation during
crop are broken down to month- the season would not be made
ly consumptive use requirements the rate is varied, and that
from the first of April through water use is in increments of ap-
September as shown in Appendix pro ately 20 percent, tht
table V. The water use of each romat 0 percent, that i
from 100 to 80 to 60 percent.
crop is distributed over the grow- These water-use levels and cor-
ing season by taking the total
responding yields are shown in
consumptive use estimates sug- Appendix table V.
gested by Blaney et al.14 These
have been compared with data
from other sources.15 The final Operating capital
consumptive use estimates are Operating capital requirements
distributed over the months on are the variable cost items of in-
the basis of practices reported by terest, machinery repair, hired
farmers in the survey previously labor, etc., discussed above.

13 Delwin M. Stephens, Op. cit.
14 H. F. Blaney, H. R. Haise, and M. E. Jensen, "Monthly Consumptive Use
by Irrigated Crops in Western United States," U. S. Soil Conservation Service, a
provisional supplement to SCS-TP-96, N.d. Mimeo.
15 These figures were checked with the Extension Irrigation Specialist and the
Extension Agronomist of Colorado State University.
16 Sketchy data from the following published studies are used in making these
D. B. Archibald and J. L. Haddock, "Irrigation Practice as it Affects Fertilizer
Requirements, Quality and Yield of Sugar Beets," American Society of Sugar Beet
Technologists, Proceedings, 6:229-236, 1952.
John W. Cary, "Efficiency of Water Use by Corn Under Field Conditions,"
(Colorado State University, Master of Science Thesis, June 1958).
Colorado Agricultural Experiment Station, "Soil, Water and Plant Relation-
ships Under Irrigation," Research in the Upper Colorado River Basin, General
Series Paper 669, July 1959.
O. W. Howe and H. F. Rhoades, "Interrelation of Moisture, Plant Population
and Fertility on the Production of Red Triumph Potatoes in Western Nebraska,"
Soil Science Society of America, Proceedings, 13:539-544, 1948.
J. S. Robins and C. E. Domingo, "Moisture Deficits in Relation to the Growth
and Development of Dry Beans," Agronomy Journal, 48:67-70, 1956.
D. Stanberry, "Irrigation Practices for the Production of Alfalfa," The Year-
book of Agriculture, 1955, U. S. Department of Agriculture.
Experiment Station irrigation specialists at Colorado State University were
also consulted in making these estimates.

Resource Limitations

Acreage restrictions
For the purpose of the study,
acreage restrictions are put on
some of the high cash crops to
allow for risk. Sugar beets and
wheat are under acreage control
programs by the government so
corresponding allotments are im-
posed for these crops. It was
assumed that government plant-
ing allotments would limit wheat
to 15 acres and sugar beets to 10
acres. It was further assumed
that risk aversion would limit
potatoes, onions, and beans to
10, 8, and 40 acres, respectively.

Operating capital
The working capital supply is
assumed to be $20,000. Cost of
these yearly operating funds, if
borrowed from the Production
Credit Association, would be 6

| 5.
z 4

percent per year.. It is assumed
that because of the risk involved
a farmer will not invest this
capital in any crop or livestock
enterprise unless it returns at
least 9 percent. This restriction
is incorporated into the model
by entering an activity for cap-
ital which will return 9 percent.

Although it is necessary to use
absolute figures for resource
limitations in the study, it is the
ratio of resources to each other,
within certain limitations, that
is important. For instance, the
ratios of land to labor, land to
water, and land to capital are
crucial in determining optimum
enterprise combinations, as long
as the size of operation is suffi-
cient to justify the investment in
equipment. The land limitation

30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-109
Figure 2. Number of survey farms by acreage per man-year of labor, West-
ern Slope of Colorado.

used is 160 acres, with other re-
source limitations estimated for
this size of farm. It was found
in the survey of farms in Western
Colorado (see footnote 10) that
the modal farms of the two-
county area have approximately
one man per 65 acres. The sur-
vey area is one of general farming
with the same crop enterprises
entered as activities in this study.
Figure 2 shows the relationship
between labor and land as found
on the survey farms.
The modal quantity of labor,
2.4 man years, is used as a limita-
tion in the study. This is equiva-
lent to the full time employment
of the operator and one hired
man plus 0.4 of a man year for
family labor. Labor time is dis-
tributed over the year by months,

with most of the family labor
being utilized in the summer
months when labor requirements
are at a peak. "Stoop" labor re-
quirements of sugar beets, on-
ions, and potatoes are treated as
a variable cost and deducted
from net revenue.

Water supply
Optimum enterprise combina-
tions for the three farm models
are programmed for three water
supply levels. The overall quan-
tity and monthly distribution of
the "full supply" level for the
study closely approximates the
1958-1959 average deliveries to
the Uncompahgre Project. Ac-
tual deliveries to the project are
reported in terms of farm head-

TABLE 3. Consumptive use requirements for the optimum solutions of three
models at.three water supply levels (acre-feet/160 acres)
Model A Model B Model C
Water supply level

Months 1 2 3 1 2 3 1 2 3

April 30 37* 39 31 37 42 12 23 25
May 34 31 25 34 26 33 7 4 20
June 36 45 44 38 43 49 24 29 50
July 47* 60* 80* 47* 60* 80* 47* 60* 80*
August 20* 53* 72 20* 53* 66 20* 53* 57
September 9* 23* 26 9* 23* 23 9* 23* 27

Total 176 249 286 179 242 293 119 192 259
Change in total 73 37 63 51 73 67
Change in late
season 60 42 60 33 60 28

*Indicates the quantities for the respective months in which water supply was

TABLE 4. Average water deliveries to the Uncompahgre Project of Western
Colorado, 1958-1959

April May June July August September Total

acre deliveries .38- 1.06 1.04 .94 .80 .54 4.76
Implied consumptive
use for 160-acre
farm' 30 85 83 75 64 43 380

1Assuming 50 percent of the water delivered is used by crops, then the con-
sumptive use for a 160-acre farm would be one-half the acre-feet-per-acre deliver-
ies times 160.

gate deliveries. To convert this
to consumptive use requires an
estimate of the efficiency with
which the water is used.
A comparison of the calculated
consumptive use requirements
for the optimum programs at the
"full supply" level and the im-
plied consumptive use on the
project, assuming a 50 percent
efficiency of use, gives presump-
tive evidence that efficiency of
use may vary over the season.
Computed consumptive use re-
quirements for the three models
at the three water supply levels
are shown in table 3.
Actual acre-feet-per-acre de-
liveries to t h e Uncompahgre
Project and implied consumptive
use, assuming a 50 percent effi-
ciency, are shown in table 4. In
the programming models, the
water supply of 80 acre-feet in
July is the only limitation for

water at the third supply level,
as indicated in table 3.
A comparison of requirements
for the other months with actual
deliveries, as shown in table 4,
indicates that water would be in
excess supply for all months ex-
cept July and possibly April. For
instance, the computed require-
ments of model A for May are
25 acre-feet for 160 acres, while
the implied consumptive use for
the project is 85 acre-feet for 160
In changing the water supply
levels in the programming mod-
els, the changes are made by in-
crements in each month. How-
ever, only the monthly supplies
that become limiting are crucial
to the change. Non-limiting
monthly quantities are shown in
table 3 as consumptive use re-

Farm Organization and Water Values
Marginal Values of Limiting Resources

As discussed in the introduc-
tory section, the simplex pro-
cedure of solving a linear pro-
gramming problem results in
estimates of the marginal values
of limiting resources as a by-
product of getting an optimum
solution. These marginal re-
source val u es are simply the
amount by which total revenue
would decrease if availability of
the resource were decreased by
one unit. In most instances this
is also the value that would re-
sult from increasing the resource
by one unit or it is the marginal
value of an additional unit. The
estimates apply only to one unit,
without any indication of the
range in resource supply for
which they hold. These values
for the production models of this
study are presented in table 5.
Labor is a limit in the months
of April, June, and September,
with an additional hour of labor
worth as much as $7.04 in April
for model C at the third level of
water supply. Land is limiting
only for model B at the third
level of water supply, an addi-
tional acre being worth $12.77.
Acreage limitations on sugar
beets and onions are limiting for
all levels of water supply for the
two models for which they are
included. Value of the onion
acreage limitation for model B
at water supply level three, where
all the land is being used, is
simply the net revenue from
onions minus the net revenue

from the marginal crop that
would be displaced if onions
were increased by one acre.
The values of an acre-foot of
consumptively used water in
model A at the number one level
of water supply are $14.49,
$38.49, and $14.40 respectively
for July, August, and September.
Notice that the values are differ-
ent for each model. The reason
is that each model has different
activities and, therefore, differ-
ent timing in demand for water.
Models A and B are alike in
crop enterprises, but different in
that model A has a livestock en-
terprise. The livestock enterprise
demands for April labor results
in a different optimum crop com-
bination with different monthly
requirements and therefore, a
different demand price for water.
Table 5 shows timing of
water's availability is an impor-
tant factor in determining its
worth to a particular farm. For
a given overall level of supply
the value for different months
varies from zero to a high-for
these estimates--of $38.49 per
acre-foot. This suggests the need,
in appraising the value of addi-
tional water to a farm or farming
area, to specify timing of de-
livery and also cropping system
to which the water is applied.
How relative distribution of
water by months affects its value
is apparent. Look at the relative
change in monthly quantities

TABLE 5. The value of the marginal product of limiting resources for typical
farm models with varying water supply levels and with average yields for crops
Model A Model B Model C
Water supply levels
resources 1 2 3 1 2 3 1 2 3
March $ 0.64 $ $ $ $ $ $ $ $
April 2.94 3.05 3.62 2.34 0.20 0.57 7.04
June 6.54 1.10
Sept. .97 .97 1.75 1.75 1.60 1.75 1.75
April 12.11 11.67
July 14.49 16.50 16.05 7.74 17.04 15.96 13.44 25.35 9.18
August 38.49 8.05 36.09 9.42 23.85
Sept. 14.40 2.29 21.18 2.79 27.09 35.13
Land 12.77
Sugar beets 25.73 65.40 73.10 12.18 62.83 67.27
Potatoes 7.25 13.04 16.30 31.73 53.86
Onions 247.98 254.60 269.34 195.23 219.66 225.38
Wheat 11.42 9.80 14.09 12.95 2.74

from one supply level to another
and observe the effect on value.
Change in late season months
from supply level one to two is
28 percent for July, 165 percent
for August, and 155 percent for
September. In model B these
changes were followed by an in-
crease of 120 percent in value of
July water. Value of August
water decreased by 74 percent

and September water value de-
creased 100 percent.
The values of water listed
above apply only to an additional
acre-foot. Frequently there is
need to estimate the value for a
larger increment. This estimate
can be made by calculating
change in revenue between
water supply levels for each

Optimal Enterprise Combinations

Change in revenue between
water supply levels results from
change in the optimum farming
system. These crop combinations
are prescribed in linear program-
ming procedure within the limits
imposed by the fixed resources.
The problem is one of how to
maximize income from a given
set of resources. This is also the

problem handled by traditional
budgeting methods, but it is
brought more sharply into focus
in the procedure of linear pro-
Requirements for enterprises
vary in total use and in timing
of use of resource inputs. There-
fore, the optimum farming sys-
tem is not necessarily one that

yields the highest return to any
one factor, but one that yields
the highest total return, taking
into account the limitations im-
posed by the fixed resources.
Thus, the resulting optimum
system consists of multiple enter-
prises, when there are multiple
resource restraints, and will tend
to change as resources change in
quantity and timing of availabil-

Changes in enterprises resulting
from changes in water supply
In table 3 of the preceding
section three water supply levels
are shown for the three model
farms used in the study analysis.
Water supply level one is the
lowest, w i t h incremental in-
creases up to the third level,
which is near full supply. Full
supply is defined as the point at
which water- is no longer limit-
ing. Optimum enterprises for
these three water levels are
shown in table 6. As pointed
out previously, there are three
possible adjustments to a change
in water supply: a change in
total acreage irrigated; a change
in acreage of crops with differing
water requirements; and a
change in rate of application to
existing crops.
Total acreage irrigated in-
creases substantially from supply
level one to supply level two for
all three models. The change in
total acreage between supply
levels two and three is of a lower
order of magnitude. For model
A, the change from level one to
two is 40 acres compared to 2

acres for the change from level
two to three.
In model B most of the change
from level one to two is an in-
crease in corn acreage with a
substitution of clover for barley.
In models B and C there is some
change in rate of application of
water on corn grown for silage,
that is, the water rate on corn
grown for silage goes from two
to one. The cash crops of onions
and sugar beets do not change
from one supply level to another.
These crops are acreage restrict-
ed, so they cannot come in at any
higher level than this restriction.
Most adjustments which in-
crease revenue and, therefore,
the resulting value of water oc-
cur: (1) in substituting corn
grain, corn silage, and clover
(seed) for the small grain crops,
and (2) in increasing total acres
irrigated. W a t er application
rates do not change for the high
cash crops. These crops always
came in at the high level. This
indicates that loss in revenue
from taking an increment of
water from sugar beets, for in-
stance, would be greater than
the increase when this increment
is applied to the next best alter-
native, say corn silage.
It is disappointing to observe
that in terms of actual cropping
patterns the computed enterprise
combinations of supply level one
are more realistic than those of
supply level three. For example,
in model A at supply level three
the programming calculations in-
dicate that it is not profitable to
grow small grain crops and al-


TABLE 6. Optimum enterprise combinations for typical farms with various
water supply distributions
Model A Model B Model C
Water supply levels
Enterprises** 1 2 3 1 2 3 1 2 3

Acreage of:
Onions1 8 8 8 8 8 8 *
Sugar beets1 10 10 10 10 10 10 *
Potatoes1 10 10 4 10 10 10
Beans, 7 38
Beans, 2 16
Corn grain, 14 32 23 21 44 47
Corn grain3 7 9
Corn silage, 40 22 42 42 32
Corn silage2 1 42 10 20 31 1
Corn silage, 14
Wheat1 15 15 15 15 15 *
Barley, 41 60 *
Barley, 7 1 3 *
Clover, 20 48 51 14 42 60 *
Alfalfa, 7 1 22

Total acres 109 149 151 119 143 160 78 113 149
Beef (animals) 34 74 *
Hogs (litters) 17 *

*Enterprises excluded from these m,
**Subscripts on crops indicate the
Appendix table V.
falfa. This may be true in cer-
tain specialized areas, but one
would not think it to be gener-
ally true, since these crops are
quite widely grown in the irri-
gated valleys. One explanation
for this result is the advantages
of a crop rotation scheme, which
are not accounted for in these
Other considerations facing the
farmer are risk and uncertainty
regarding yields, prices, and
water supply. Alfalfa may be a
desirable crop to absorb the
yearly variations in water supply.
That is, in a given year of nor-

levels of water application as listed in

mal supply alfalfa can be given
a full irrigation, while in a sub-
normal year it can be irrigated
only once or twice without losing
the stand. But with crops such
as onions and sugar beets the
large cash outlay to get the
crop started would be lost in
years with an insufficient supply
of water to finish the crop.

Change in net revenue
The increase in net revenue
which comes from the changes
in enterprises resulting from
changes in water level are pre-
sented in table 7. These figures

TABLE 7. Change in net revenue for three typical farm models with three water
supply levels and with average yields
Change in net revenue
Change in water
supply level Model A Model B Model C
1-2 $3,628.90 $2,470.64 $1,891.57
2-3 645.69 935.39 649.91

indicate a definite difference in
increase in revenue for the three
different models, especially from
raising the water supply from
level one to two. Models A and
B differ only in the livestock en-
terprise, so the differences in the
changes in revenue result from
this fact. Model C, with limited
enterprise alternatives, has ap-
proximately one-half as great an
increase in revenue as model A
for the change from water sup-
ply level one to two.
However, for the change from
level two to three, model A shows
the least increase. This may fol-
low from the discreteness of the
changes in water supply and the
peculiarities of the three models,
and may not have any real sig-
nificance. That the overall
change for model C is less than
for B does suggest that the ex-
istence of many crop alternatives

increase income possibilities as-
sociated with a change in water
supply. This is to be expected
in light of the fact that, as men-
tioned earlier, multiple resource
restraints result in multiple en-
terprises at an optimum use. The
common sense of this is that
many alternatives even out the
demands on the resources of
labor and water whose avail-
ability is distributed over time.
The difference between models
B and C in the change in revenue
between different water supply
levels does not result from the
exclusion of sugar beets and
onions from model C, as one
might expect, because the acre-
ages of these crops did not change
in model B. Table 6 reveals
that less land is utilized in model
C. This indicates that model C
with its limited enterprise alter-
natives could not as effectively

TABLE 8. Use of limiting resources for each water supply level
Model A Model B Model C
Resource 1 2 3 1 2 3 1 2 3

109 149 151

119 143 160

78 113 149

(hours) 2,092 3,220 3,744 1,990 2,527 2,797 1,798 2,327 2,840

(acre-feet) 176 249 286

174 242 293 119 192 259


TABLE 9. Changes in net revenue between three water supply levels, for three
typical farm models with average yields and with labor cost deducted
Change in net revenue
Change in water
supply level Model A Model B Model C

1-2 $2,500.90 $1,933.64 $1,362.57
2-3 121.69 665.39 136.91

utilize the available water and
labor as could model B, since the
resource complement of both
models was the same.
The use of limiting resources
for each optimum enterprise
combination is shown in table 8.
These are the optimum resource
complements, given the assump-
tions and estimates of these
models. This does not imply that
farmers would actually leave
available resources unused if
they could not be combined in
these proportions. They could,
for instance, use unirrivrated land
for dryland crops. This possibil-
ity was not considered in these
models. The water supply levels
were arbitrarily changed for the
latter part of the season, while
the change in the quantities of
land, labor, and early water re-
sult from additional use of the
assumed quantities available.
As seasonal capital did not be-
come limiting, its cost was sub-
tracted out of the revenue fig-
ures, and it is not considered
here. It is obvious that the
change in revenue listed in table
7 could be attributed to the
change in amount of land, labor,
or water, depending upon which
was considered the limiting fac-

Another way to arrive at a
value for water would be to sub-
tract the opportunity cost of
land and labor from the change
in revenue. It being assumed
the quantities of land and labor
needed to use the additional
quantity of water would be hired
or bought in a block, so the cost
would not be chargeable to any
one enterprise; otherwise the op-
timum combinations of 'enter-
prises would change. Opportun-
ity cost of land in most areas of
the western slope of Colorado
would be near zero, although in
valleys of the eastern slope the
yearly cost might run around $5
or more. For estimates in this
study, the opportunity cost of
land is disregarded.
Assuming a labor cost of a
dollar an hour and subtracting
this cost from the figures in
table 7 results in the new esti-
mates presented in table 9. Note
that increases in revenue attrib-
uted to the change in water sup-
ply were reduced by approxi-
mately one-third by deducting a
labor cost.

Water values
As was suggested earlier, the
actual change in farm headgate
deliveries may vary considerably


TABLE 10. Marginal value per acre-foot of water for three typical farm models,
assuming three rates of yield for crops and three rates of water delivery efficiency
Model A Model B Model C
Water Change in water supply level
delivery Yield
efficiency rate 1-2 2-3 1-2 2-3 1-2 2-3
High $27.40 $2.62 $22.76 $10.44 $14.92 $1.56
40 percent Av. 13.70 1.31 11.38 5.22 7.46 .78
Low 6.85 .65 5.69 2.61 3.73 .39
High 34.26 3.28 28.44 13.04 18.66 2.04
50 percent Av. 17.13 1.64 14.22 6.52 9.33 1.02
Low 8.56 .82 7.11 3.26 4.66 .51
High 41.12 3.94 34.12 15.64 22.40 2.44
60 percent Av. 20.56 1.97 17.06 7.82 11.20 1.22
Low 10.28 .98 8.53 3.91 5.60 .61

among water-using situations
with the same consumptive use
requirements. This variation
results from varying efficiency
rates in water application, and
is undoubtedly an important
consideration in calculating the
value of water.
A further consideration is that
water ownership rights and de-
liveries of river flow water are
related more to conditions of
supply than to the needs of crops.
In some months supplies are in
excess of needs, especially in the
early season. Thus, a factual
problem exists in attributing the
above changes in net revenue to
a specific change in supply.
Under actual conditions, vari-
ous types of water supply changes
might be considered. For in-
stance, an area with a superflu-
ous amount of early-season water
and a shortage of late-season
water might receive more water
consequent to a diversion from

another watershed, a diversion
that would increase the supplies
in both seasons. Under these
conditions, the only changes in
supply to which the changes in
revenue may be attributed are
those in the late months, as
shown at the bottom of table 3.
Now consider a change in
water supply that occurs only
during the seasons in which
water is limiting and only to the
extent that water (rather than
other resources) is limiting.
Water values corresponding to
this assumption are shown in
table 10. These values are shown
for three levels of water-use effi-
ciency and three yield levels.
Acre-foot values range from ap-
proximately $41 for model A,
with high yields and a 60 percent
efficiency of water use, to ap-
proximately 39 cents for model
C, with low yields and a 40 per-
cent efficiency of water use.
Model A has a higher value for

TABLE 11. Consumptive use requirements for late water and returns per acre-
foot per acre of land for various crops on a hypothetical 160-acre farm
Revenue per Revenue Water req. Hypothetical Water req.
Crops* acre-foot per acre per acre acreage per crop
Acre-feet Acres Acre-feet
Onions, $154.00 $257.18 1.67 8 13.36
Wheat, 55.21 20.98 .38 15 5.70
Sugar beets, 45.53 78.32 1.72 10 17.20
Corn silage, 29.74 27.96 .94 65 61.10
Corn silage, 25.39 30.22 1.19
Barley, 23.33 6.30 .27 40 10.80
Potatoes1 22.75 40.27 1.77
BeansI 8.62 10.26 .91
Alfalfa, 7.17 2.08 .29
Alfalfa1 5.86 7.79 1.33 22 29.26

160 137.42
*Subscripts on crops indicate the levels of water application as listed in Ap-
pendix table V.

water b et w e e n water supply
levels one and two than model
B because of the livestock enter-
prise. Model A was included in
this study for comparison pur-
poses, and presentation of esti-
mates from this model are not
intended as an argument for in-
cluding livestock enterprises in
calculating water values. Further
discussion of this question is
contained in the following sec-
On a 160-acre farm the three
water supply levels would be
2.18, 3.02, and 3.67 acre-feet per
acre delivered at the farm head-
gate, assuming a 50 percent
water-use efficiency. Thus with
average yields for the farm rep-
resented by model A, the esti-
mated value of water for an in-
crease from 2.18 to 3.02 acre-feet
per acre, or 0.84 acre-feet per
acre, is $24.86; it is $18.17 for
model B and $12.96 for the
model C farm. When the change

is from 3.02 to 3.67 acre-feet per
acre the estimated values are
$6.33, $8.99, and $4.85 per acre-
foot respectively for models A,
B, and C.
Calculations displayed in table
10 are demonstrative evidence of
the need for considering mar-
ginal values in allocating water
either between areas or between
farms. They also illustrate that
a system where water rights may
be bought and sold may result
in a more efficient use of water
than a system where institutional
restrictions p r e v e n t this ex-
change. If a "free water mar-
ket" existed for the farm situa-
tions represented in the table,
there would probably not be an
equal use of water for all farms.
Farms with high yields and great-
er efficiency of water use could
afford to bid water away from
farms with lower yields and
lower efficiency.
Thus far the changes in enter-

prises resulting from changes in
water supply have been com-
puted in terms of a fixed monthly
supply of labor and a monthly
distribution of water. It is also
possible to gain some knowledge
of the value of water by simply
looking at the net return to an
acre-foot of water for each crop
In table 11 the net revenue for
each enterprise has been divided
by the total consumptive use
requirements for July, August,
and September, that is, the late-
season supply is considered as
one amount. The enterprises
have been ranked according to
their return to late water. The
net return per acre of land is
also presented for comparison
purposes to show what the choice
of enterprises would be if land
and late water were limiting.
These net revenue figures have
had labor costs taken out, where
cost of labor is assumed to be $1
per hour. Also, the net revenue
figures are computed for the
average yields above.
Hypothetical acreage figures
have been chosen so that the
acreages of onions, wheat, and
sugar beets were the same as the
restrictions of the previous mod-
els. It is supposed that alfalfa is
kept at a minimum acreage of 22
acres for rotational purposes and
that some acreage of barley is
desirable for better utilization of
labor throughout the season and
also for rotation purposes, that
is, for new seeding of alfalfa and
so on.
It is assumed that all of the
land is being irrigated, and that

the total consumptive use of late-
season water is approximately the
same as the second level in the
previous models. Several alter-
natives exist for using extra
water, namely, increasing the rate
of application on corn, substitut-
ing corn for barley, substituting
potatoes for corn, and substitut-
ing potatoes for barley. All of
these changes would increase
total net return. Beans clearly
are not a profitable alternative in
this instance from the standpoint
of its return to water or land.
Changing from corn silage2 to
corn silage, would require an
additional 0.25 acre-foot of water
per acre and would increase rev-
enue by $2.26 per acre. This
amounts to a value of $9.05 per
acre-foot of water actually con-
sumed by the crop. The return
to water delivered at the farm
headgate would depend upon the
efficiency of use, being $4.52 at
50 percent efficiency. Substitut-
ing corn silage2 for barley would
require an additional 0.67 acre-
foot per acre and would add
$21.66 to the return per acre.
This would amount to $16.16
per acre-foot of water at the head-
gate, again supposing a 50 per-
cent efficiency of water use.
The above adjustments to an
increase in water supply require
some additional amounts of labor
throughout the growing season.
The change from corn silage, to
corn silage1 requires but a slight
amount of extra labor and would
be an adjustment easily made
without changing the resource
availabilities on the farm.

-21 -

Appendix table III shows that
the substitution of potatoes for
barley would require an addi-
tional 23 hours of labor per acre.
The substitution of corn silage2
for barley would require a total
of 9 hours of additional labor;
however, corn silage requires 9.7
hours of labor per acre in Sep-.
tember while barley requires
none. The feasibility of this ad-
justment would depend upon the

Implications for Economic
The linear programming mod-
els of this study demonstrate the
effect of certain factors upon the
marginal value of water and in-
dicate the type of adjustments
that would be economic in re-
sponse to a change in water sup-
ply. The kind of adjustments
farmers can and do make to a
change in water supply deter-
mines in part the value of the
additional water. Conditions of
the market for products and for
input factors, native land char-
acteristics, and so on, also help
determine value of presently used
water and of marginal incre-

flexibility of the labor supply.
It must be concluded that the
value of an additional quantity
of water depends upon the com-
plement of other resources that
can be combined with the addi-
tional water. In the above ex-
ample the value of an additional
acre-foot of water could be $4.52
or $16.16, depending upon
whether additional labor- was

Evaluation of Water Use
Several of these factors effect-
ing water values have been con-
sidered in this study and esti-
mates of their effects presented.
It was suggested earlier that an
understanding of the quantita-
tive economic relationships with-
in the firm regarding marginal
values of water would be useful
in considering some of the ag-
gregate problems involved in the
development and use of water
resources for irrigation. It is the
purpose in this section to point
out some of the implications of
the preceding analysis for water

Timing of Water Deliveries

Marginal value products pre-
sented in table 5 are suggestive
of the monetary advantages of
flexible timing of available water
supplies. These advantages may
be gained both by having stored
water available on a demand
basis and, to some extent, by
allowing transfer of water be-
tween farms.
In model B at the first level

of supply, the value of water
would be increased by trans-
ferring Jul y and September
water to August. For example,
the transfer of one acre-foot of
water from July to August would
increase its value by $28.35
($36.09 $7.74). Also, at the
first level of water supply, July
water on the model B farm could
be traded for August water on

the model C farm with an in-
crease in value of ($13.44 -
$7.74) + ($36.09 $23.85) =
Institutional restraints in many
areas of the irrigated West dis-
courage the trading and transfer
of water between farms. The
above figures suggest costs that
may result from such restraints.
It is interesting to contemplate a
case where these restraints are
lacking. It has been reported
that in 1959 approximately 89,-
000 acre-feet of irrigation water
were transferred between farms
in the South Platte Basin.17 The
organization of the water supply
agencies in this area permits the
sale of water rights between users

and also the yearly rental of
water, and over the years trading
and exchange of water has de-
It may be inferred that the
water transfers mentioned re-
sulted from trading as pointed
out above, and also resulted from
selling water in a low-value use
to a high-value use, where the
differences in value result from
differences in overall level of
supply, differences in land pro-
ductivity, and differences in man-
agement level. This is not to say
that an optimum use of water
would occur without restraints,
but experience in the South
Platte Valley indicates there
would be a movement in this

Farm Productivity and Marginal Values of Water

Both table 5 and table 10 in-
dicate the disparity in marginal
values that may occur between
farms with different productive
capacities. Where marginal ad-
justments in farm supply are
prevented by institutional ar-
rangements we observe situations
such as exist on the Uncom-
pahgre Project. On this project,
in western Colorado, the acre-
feet-per-acre deliveries are fixed
for each farm, having been orig-
inally allocated on the basis of
consumptive u s e requirements
for soils classified on the basis of

structural characteristics rather
than productivity.18 Reported
yields for various soil classes in
the project differ considerably.
Yields on the poor soils are ap-
proximately 50 to 60 percent of
those on the best soils.'9 This is
approximately the same range as
used in this study between the
high and low productivity situa-
Institutions which prohibit ex-
change of water between farms
make it impossible to achieve an
economically efficient use of
water resources in this area.

7 Raymond L. Anderson, "Operation of the Irrigation Water Rental Market
in the South Platte Basin." Paper delivered at American Farm Economics Asso-
ciation meeting at Ames, Iowa, Aug. 1960.
s Uncompahgre Project, Colorado: Report on Ability of the Water Users to
Repay Construction Costs to the United States, U. S. Dept. of the Interior,
Bureau of Reclamation, September 30, 1948.
19 Ibid.

This discrepancy from efficiency
is sizable even when considering
only the differences in yield on
the various soil classes. The esti-
mates presented in table 10 indi-
cate that an approximate differ-
ence of 50 percent in yields be-
tween farms would result in a
difference in marginal value of
water of 75 percent. This is only
a crude approximation, since the
differences in yields are not the
same for all crops.
For a specific example from
table 10, consider model B with

a 50 percent efficiency of water
use. Water would be efficiently
allocated when farms with high
yields were receiving the quan-
tity of water at the third level
of supply, that is, 3.67 acre-feet
per acre, while the farms with
average yields were receiving the
quantity at the second level of
supply, which is 3.02 acre-feet
per acre. The marginal value
products would be approximate-
ly equal, being $14.22 and $13.04
respectively at these levels, as
shown in the table.

Project Evaluation

Two items of interest regard-
ing p r o j e c t evaluation have
evolved from this study. One of
these has to do with inclusion of
complementary enterprises in an
evaluation study; the other has
to do with estimating the cost of
the additional labor needed to
utilize additional water from a
proposed project.
The inequality of the change
in net revenue between model A
and model B when water supply
increased from supply level one
to supply level two resulted from
the increase in livestock numbers
in the budget of farm model A.
It may be argued that a change
in the residual return from the
livestock enterprise, following an
increase in water supply, is at-
tributable to the increment of
additional water in a situation
where the livestock enterprise
provides benefits that would not
occur otherwise. These benefits
would exist, for instance, if the
return from using the products

of the crop enterprise as inputs
in the livestock enterprise were
greater than the return from sell-
ing them in the market. Whether
this return was greater or less
than the return from a market
sale would depend upon several
factors, including the market
price of crops, the opportunity
cost of labor, interest cost, effi-
ciency of the feeding operation,
and so forth. These factors vary
from time to time and from place
to place, and would have to be
considered for specific situations.
As it turned out, with the
prices and costs used in this study
(and with all livestock costs
treated as variable) the residual
income attributed to water was
greater when livestock produc-
tion opportunities were assumed.
Whether or not the change in the
residual properly reflects the re-
turns to water depends upon the
assumptions regarding the oppor-
tunity costs of the additional
capital and labor.

When considering the sizable
increase in the amount of labor
needed when increasing the
water supply from level one to
two or from two to three, it is
unreasonable to treat this supply
as presently on going farms and
therefore costless. When a charge
of $1 an hour for labor required
for utilizing the additional water
at supply level two was subtract-
ed from the change in net rev-
enue, the change in revenue was
reduced by approximately one-
third. This indicates the impor-
tance of labor costs in imputing
value to increments of water.
We have also shown that some
adjustments to increases in water
supply, such as increasing the
rate of application on existing
crops, might not change the farm
organization enough to require
hiring-in additional labor. How-
ever, this is not an argument
against including additional oper-
ator or family labor as a cost in
computing the value of addition-
al water. Linear programming
procedures particularly empha-
size the idea of an opportunity
cost associated with using a re-

source in a particular activity
rather than another.
If all the possible activities in
which the farm operator and his
hired and family labor are en-
gaged were entered in a linear
programming model with their
output quantitatively expressed
in terms of revenue, the oppor-
-tunity cost for labor used by the
livestock and c r o p activities
would be determined in the
model. This can be accomplished
and made workable by enter-
ing only one unspecified oppor-
tunity cost activity.
A factual problem exists in
deciding upon a figure to use for
the net revenue of this activity.
Most farm operators would prob-
ably be reluctant to put an exact
figure on the value of the use of
all their time. However, the fact
remains that some cost is involved
in using extra quantities of labor.
The quantities of additional
labor required in the estimates
presented in this study were
sizable enough to indicate that
additional labor would have to
be hired-in, so they were charged
at a cost near the market rate for
farm labor.

TABLE I. Crop prices, average yields, costs, and net revenue for linear programming analysis

Yield per acre
Crop 1 2 3


Cost per acre

Net revenue per acre'
1 2 3

Wheat (bu.) 39
Alfalfa (ton) 3.4
Clover, hay (ton) .9
Clover, seed (cwt.) 2.7
Corn grain (bu.) 63
Corn silage (ton) 12.6
Beans (cwt.) 14.8
Sugar beets (ton) 14
Sugar beets, tops (ton) 7
Potatoes (cwt.) 171
Barley (bu.) 51
Onions (cwt.) 298



$ 1.88









26.40 23.53 21.13 22.56
385.42 356.72 312.85 285.08

two net revenue figures must be






23.67 "
37.39 c


1 Net revenue is price times yield minus cost. In the case of sugar beets and clover, the
added to get the total net revenue per acre of that crop.

TABLE II. Animal feeding costs

Beef 1-Litter hogs 2-Litter hogs

Hay S 5.89 $ 8.50 $ 11.25
Silage 10.53
Corn 51.48 120.27 217.14
Protein 8.21 64.97 119.95
Initial investment 179.34 52.20 69.60
Veterinary supplies 3.00 3.64 7.02
Marketing 5.25 1 1
Miscellaneous 6.09 11.90 22.88
Total variable cost (less feed) 201.89 132.71 219.45
Total cost 269.79 261.48 447.84
Sell gross 278.70 272.09 480.15
Net profit 8.91 10.61 32.31

1 Marketing costs are included in miscellaneous.

TABLE Ill. Labor requirements of crops (hours per acre)

Crop March April May June July Aug. Sept. Oct. Nov. Total

Wheat 1 2.45 4.88 1.95 1.95 1.95 2.62 15.80
2 2.45 4.88 1.60 2.05 1.60 2.62 15.20
3 2.45 4.88 1.60 1.60 1.60 2.40 14.53
Alfalfa 1 .75 .92 .75 3.84 4.59 .96 4.29 16.10
2 .75 .97 .80 3.89 4.14 .50 3.34 14.39
3 .75 1.02 .85 3.94 3.00 .50 10.06
Clover 1 .50 .80 .50 3.72 1.00 1.00 1.50 9.02
2 .50 .90 .60 3.60 .60 1.10 1.50 8.80
3 .50 .95 .65 3.10 1.00 1.00 1.50 8.70
Barley 1 2.10 4.23 .98 .98 1.95 2.62 12.86
2 2.10 4.33 1.08 1.08 1.20 2.62 12.41
3 2.10 4.43 1.18 1.18 .45 2.60 11.94
Corn grain 1 .50 4.14 1.07 2.74 2.19 1.47 .65 3.54 16.30
2 .50 4.19 1.07 2.75 2.29 1.02 .70 3.50 16.02
3 .50 4.24 1.07 2.80 2.39 1.07 3.45 15.52
Corn silage 1 .50 4.14 1.07 2.74 2.19 1.47 9.71 21.82
2 .50 4.19 1.07 2.75 2.29 1.02 9.60 21.42
3 .50 4.24 1.07 2.80 2.39 1.07 8.60 20.67
Beans 1 1.54 3.37 4.18 5.02 6.49 2.73 23.33
2 1.54 3.47 4.38 5.30 5.49 2.73 22.91
3 1.54 3.47 4.38 5.00 5.40 2.70 22.49
Sugar beets 1 5.63 1.55 4.41 4.04 4.04 4.45 3.47 11.63 1.00 40.22
2 5.63 1.62 4.55 4.18 4.18 3.91 2.86 11.60 1.00 39.53
3 5.63 1.69 4.69 4.32 4.32 3.30 3.00 11.00 37.95
Onions 1 3.90 2.72 3.05 4.92 6.41 4.72 2.18 27.90
2 3.90 2.92 3.25 5.22 5.51 4.02 2.28 27.10
3 3.90 3.12 3.45 5.52 5.81 3.22 2.38 27.40
Potatoes 1 1.49 6.60 6.04 6.67 5.30 1.24 9.59 36.93
2 1.49 6.70 6.14 5.97 4.60 1.34 9.59 35.83
3 1.49 6.80 6.24 6.07 4.80 .50 9.50 35.40


TABLE IV. Labor requirements for animal production (hours)

Month Beef 1-Litter hogs 2-Litter hogs

January 2.21 1.24 3.70
February 2.08 1.24 3.70
March 2.45 1.24 9.58
April .38 5.86 4.62
May .82 2.97
June .82 2.72
July 1.80 2.72
August 1.80 2.72
September 1.41 5.01
October .76 1.41 3.94
November 2.21 1.41 3.26
December 2.21 2.65 3.70
Total 12.30 21.70 48.64

TABLE V. Consumptive use water requirements of crops (acre-inches)

Crop April May June July August September

Wheat 1
Alfalfa 1
Clover 1
Barley 1
Corn grain I
Corn silage 1
Beans I
Sugar beets 1
Onions 1
Potatoes 1





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