Marginal values of irrigation water

Material Information

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
Hartman, Loyal M.
Whittelsey, Norman K
Place of Publication:
Fort Collins Colo
Agricultural Experiment Station, Colorado State University
Publication Date:
Physical Description:
28 p. : ; 23 cm.


Subjects / Keywords:
Irrigation water ( lcsh )
Irrigation farming ( lcsh )
bibliography ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references.
General Note:
Cover title.
Technical bulletin (Colorado Agricultural Experiment Station) ;
Statement of Responsibility:
[L.M. Hartman and Norman Whittelsey].

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact Digital Services ( with any additional information they can provide.
Resource Identifier:
23750580 ( OCLC )

Full Text

Peter E. Hildebrand Agricultural Economic , 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 ----------------------------- - ---------------------------------- - ------------------------------------- - -------------Introduction -------------------- ------- - ------------ - ------------------------------------------------ -- -------- ------Description of M odels and Sources of Data ---------------------------------------------------- - ------ 6

Farm Organization and W ater Values --------------------- - -------- - ------------------------------------- 13

Implications for Economic Evaluation of W ater Use ---------------------------------------- - 22

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

Dwight Blood was the principal investigator during the early phase of the study. He was assisted by Norman Whittelsey who assumed major responsibility for the data collection upon the resignation of Mr. Blood. The senior author assumed responsibility for completion of the project in January 1960.

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

This study was financed by the United States Department of Agriculture under a Research and Marketing Act contract administered through the Farm Economics Research Division of the Agricultural Research Service. The contract for the conduct of the research covered the period July 1, 1958 to December 31, 1960. The study was supervised by Dr. M. L. Upchurch of the Farm Economics Research Division, ARS, and Dr. Rex D. Rehnberg, Economics Section, Colorado Agricultural Experiment Station.

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 incremental or marginal values of water. Several factors that affect the value of irrigation water were considered and their effect estimated within different assumptions 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 different enterprise alternatives were used in the analysis. Fixed resources or limitations in the models consisted of land, monthly labor, operating capital, and monthly water supplies. Solutions were programmed for three monthly water supply situations. Other resource limitations, prices, and inputs per acre were held constant throughout the analysis.
Three different output situations were considered to take into account differing land productivities. 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 estimates 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 models demonstrate the need for differentials in supply when allocating water to individual farms, or the economic advantages of a free market for water.
Labor use increased by approximately 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 indicates the need in project evaluation for considering the cost and availability of labor resources needed to utilize supplemental water from the project.
The farm model having, a livestock enterprise gave the largest estimates of water values. This resulted because the livestock operation provided a better market for crops than selling on the open market. Whether or not the changes in the residual for the livestock model properly reflect the returns to water depends upon the assumptions regarding the opportunity costs of the additional capital and labor.


Economic evaluation of potential uses and development of water resources requires estimates of marginal values of water. For example, marginal values must be determined to estimate benefits from potential projects for supplying supplemental irrigation water. They are also needed for judging the relative merits of allocating existing water supplies among competing uses.
The effort of the study reported 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 procedure 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 management, land productivity, efficiency of water use, timing of water deliveries, number and kinds of enterprises, and labor supply are considered.

Discussion of the Problem

The specific problem considered in the study involves estimating 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 involves aggregation and must be

*Assistant Professor of Economics and Sociolo- , and former Research Assistant, respectively. Oy

Marginal Values of Irrigation Water

L. M. Hartman and Norman Whittelsey* Introduction

considered in most decisions concerning water allocation. Adjustments on the individual farm are an important aspect of this problem, as these are the units to be aggregated.
The effects of an area adjustment on prices, both for factors and products, may be important in a complete study. Other considerations important in a complete study would be national benefits versus individual or regional benefits. These problems sire outside the area of the study reported here.

Valuing resources on the individual farm
The problem of resource valuation on the individual farm is a typical one of production economics, since it is implicit in the allocation of resources among competing enterprises. One way of valuing a resource at the miargin 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 technique used in the study is presented here to show how the problem of determining water values is approached.'
Production possibilities of the farm can be summarized symbol-

ically in matrix form as follows:
a11x1 + a12X2 .+ a111Xn bi a21xl + a22x2 + a.,x,:! b2

amixi + am, x. . . +- arnxn_ b m
The b's (b1, b2. b .i) are
quantities of various resources which are limitational. These would be land, water, labor, capital, and so forth. The coefficients all, a,, . . . a.,, are the input requirements of the enterprises for these resources.
The columns contain all coefficients for each activity; the rows all coefficients for each resource. Thus a.1 is the amount of b, required to produce one unit of the first activity listed in the matrix. The x's are the unknowns and represent the to-bedetermined 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 Q~ as unit net revenue above variable costs for the jth activity, and with maximum profit as the objective, the optimum use of resources is achieved when the quantity Cix1 + C2X2
.+ Cnxl is at a maximum subject to the inequality restrictions of the production possibilities 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

See Earl 0. Heady and Wilfred Candler, "Linear Programming Methods," (The Iowa State College Press, Ames, Iowa, 1938), for a detailed non-mathematical exposition of the technique. Chapter 7 treats the resource valuation problem.

reduction that would occur in the Y. Cjxj from reducing availability of that resource by one unit, with all other conditions constant.
If the marginal unit value of the ith resource is designated as yi, at the optimum solution for maximum profit the linear programming technique assures that bly, + b2Y2 . . . + by. is equal
to CIXI + C2X1 - - - + C11X11that is, total imputed return to resources equals total net revenue. The y's are a by-product of the simplex procedure .2 A complete marginal value schedtile for a resource may be derived by an appropriate series of programming steps.3

Factors affecting estimates of marginal resource values
In the above expression of the farm production problem, production and profit possibilities are expressed in terms of three sets of coefficients: the a's,, or input requirements; the Us, or resource quantities available; and the C's, or unit net revenues for each enterprise. The x's are unknowns to be determined and represent the activity levels. The coefficients are given by the conditions of management, market price, resource productivity and availability, and technology inherent in the problem area being studied. These coefficients, when

estimated for a particular situation, determine the estimates to be placed on values of resources.
Input requirements are related to a given technology, management level, and resource quality situation-items that vary considerably 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 absolutely fixed during the production period. This is particularly true for monthly labor supplies because of use of family and seasonal 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. 47 1.
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 conditions, 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 uncertainty are difficult to express quantitatively and enter into a model, although they are important in determining optimum

enterprise co mbinations and, consequently, resource values.
Another factor limiting the applicability of computed results is the assumption of profit maximizing use of resources. Farmers may or may not be complete "profit maximizers" and operating 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.

As mentioned earlier, the purpose of the study is not to derive a value for water, but to estimate the relative effect of certain factors upon water values, and, consequently, to derive a range of values. One set of input coefficients, prices, and variable costs is used for enterprises existing 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 situations. Resource levels for land, monthly labor, and operating capital are held constant throughout the main part of the computations. The effect of relaxing the assumption of a fixed labor supply 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 situation with two crop possibilities, crop I and crop 2, and with three limitational resources: land, labor, and water. Input requirements, 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 delineated by the initial water and labor restraints. Any combination of crop I and crop 2 could be realized along or below these lines. If all of crop I 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.

Approach Used in This Study

.Labor Restraint

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 isorevenue line, is found by moving the iso-revenue line to its highest 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 X2' Output for crop 2 and x,' output for crop 1. Water and labor restrict these crops to this level. Net revenue is C~x,' + C~x,', where C is used as previously defined.
If the initial water supply restriction is lifted to the second level, as illustrated, then production 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 (CIXIt' + C2X2tt) - (CIX1' -+ C22) 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 farmers seek the maximum profit adjustment. These are assumptions about matters of fact, and their validity is not investigated in this study. However, it is necessary to interpret the results in light of these assumptions.


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 (I or 2 litter) X

Description of Models and Sources of Data Enterprises

sidered for each crop. Thus, for crop I there are three yields corresponding to three levels of water application. In model A, for instance, with 10 crop possibilities there are actually 3 x 10, or 30, crop activities considered.

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 Bureau of Reclamation's Uncompahgre Project.

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 identical with A except that the possibility of livestock feeding is excluded. Model C is characterized by limited enterprise alternatives.
Three adjustments are possible in response to a change in water supply, namely, a change in rate of application, a change in acreages of crops with differing water requirements, and a change in total irrigated crop acreages. To allow for the possibility of varying the rate of application to a given crop three possible rates of water application, and therefore three yield levels, are con-

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) (hu.) Corn (silage) (ton) Beans (cwt.) Sugar heets (ton) Onions (cwt.) PQtatoes (cwt.)

South Platte Valley

12 17 16 262

Delta and Montrose counties

2.56 2.65
42 59 11 16 15 308 192


4.5 4.5 75 95
20 21 22 450 225

Survey yields with
normal water application

Av. Low

3.31 2.69 51 63 13 15
14 298 171

2.7 1.9 38
12 11
222 145

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

The census figures are county averages. Therefore, they include some dryland crops, especially in the South Platte Valley. The average yields, which were taken from a survey of the Uncompahgre Project, closely approximate 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 bogs are shown as enterprise possibilities 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 liog-raising 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 1954-1958.5

The prices of livestock used are a 10-year average of the period 1949-1958.' A 10-year average was used to include one complete cycle of livestock prices.

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

Costs of production used in this study for both crops and livestock are only those variable costs incurred in actual- production. Fixed costs of the farm are not deducted from the net revenue of any enterprise. Variable costs include such items as interest cost of operating capital, seasonal 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 supplementation from other studies.8 All costs were adjusted to 1959 prices

by the use of relative cost indexes as published by the U. S. Department 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 livestock enterprises are calculated by using recommendations from Morrison's Feeds k Feeding. A listing of costs, prices, yields, and corresponding net revenue is presented in tables I and 11 of the Appendix.

the various operations for each crop,.10. Secondary sources are used to compute total monthly labor requirements f or each crop."
Labor requirements for swine are taken from a bulletin by Hardin, Weigle, and Wann .12

Estimated monthly labor requirements for crops are shown in Appendix table 111. Results from a survey of fanns in the Uncompahgre Project area are used to estimate the timing of

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 43102,'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).

Variable Costs of Production

Input Requirements

mentioned (see footnote 10) .
Water requirement estimates described above pertain to the 11 normal" use of crops with corresponding "normal" yields. To allow for varying rates of application of water, requirements f f. I ; III I I

The labor requirements for both sheep and beef feeding are taken from a study by Delwin Stephens." For a detailed breakdown of labor requirements for the'livestock enterprises see Appendix table IV.

Water - -- -1. y V%_ a Vvk::;.Lk:;
Wat . er requirements of each also estimated.16 It is assumed
crop are broken down to month- that certain irrigations during
ly consumptive use requirements the season would not be made
from the first of April through as the rate is varied, and that
September as shown in Appendix water use is in increments of aptable V. The water use of each proximately 20 percent, that is,
crop is distributed over the grow- from 100 to 80 to 60 percent. ing season by taking the total These water-use levels and corconsumptive use estimates responding yields are shown in
sug- Appendix table V.
gested by Blaney et al .14 These have been compared with data Operating capital
from other sources.15 The final consumptive use estimates are Operating capital requirements
distributed over the months on are the variable cost items of inthe basis of practices reported by terest, machinery repair, hired farmers in the survey previously labor, etc., discussed above.
13Delwin M. Stephens, Op. cit.
14H. r. 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.
16Sketchy data from the following published studies are used in making these estimates:
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 Relationships Under Irrigation," Research in the Upper Colorado River Basin, General Series Paper 669, July 1959.
0. W. Howe and H. F. Rhoades, "Interrelation of Moisture, Plant Population and Fertility oil 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. Stanbcrry, "Irrigation Practices for the Production of Alfalfa," The Yearbook of Agriculture, 1955, U. S. Department of Agriculture.
Experiment Station irrigation specialists at Colorado State University were also consulted in making these estimates.

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 capital which will return 9 percent.

Although it is necessary to use absolute figures f or 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 Iand to capital are crucial in determining optimum enterprise combinations, as long as the size of operation is sufficient to justify the investment in equipment. The land limitation

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 imposed for these crops. It was assumed that government planting allotments would limit wheat to 15 acres and su-ar 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

Z 4,

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-yqar of labor, Western Slope of Colorado.

Resource Limitations

used is 160 acres, with other resource 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 twocounty area have approximately one man per 65 acres. The survey 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 limitation in the study. This is equivalent 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 distributed 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 requirements of sugar beets, onions, and potatoes are treated as a variable cost and deducted from net revenue.

Water supply
Optimum enterprise combinations for the three farm models are programmed for three water supply levels. The overall quantity and monthly distribution of the "full supply" level for the study closely approximates the 1958-1959 average deliveries to the Uncompahgre Project. Actual 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 limi tational.

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

April May June July August September Total

Acre-feet-peracre 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

'Assuming 50 percent of the water delivered is used by crops, then the consumptive use for a 160-acre farm would be one-half the acre-feet-per-acre deliveries 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 implied consumptive use on the project, assuming a 50 percent efficiency of use, gives presumptive evidence that efficiency of use may vary over the season. Computed consumptive use requirements for the three models at the three water supply levels are shown in table 3.
Actual acre-feet-per-acre del iveries t o t h e Uncompahgre Project and implied consumptive use, assuming a 50 percent efficiency, 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 except July and possibly April. For instance, the computed requirements 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 acres.
In changing the water supply levels in the programming models, the changes are made by increments in each month. Hoever, only the monthly supplies that become limiting are crucial to the change. Non-limiting monthly quantities are shown in table 3 as consumptive use requirements.

As discussed in the introductory section, the simplex procedure of solving a linear programming. problem results in estimates of the marginal values of limiting resources as a byproduct of getting an optimum solution. These marginal resource v a I u e s 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 result 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 additional 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 use d water in model A at the number one level of water s u p p I y are $14.49, $38.49, and $14.40 respectively for July, August, and September. Notice that the values are different for each model. The reason is that each model has different activities and, therefore, different timing in demand for water. Models A and B are alike in crop enterprises, but different in that model A has a livestock enterprise. The livestock enterprise demands for April labor results in a different optimum crop combination with different monthly requirements and therefore, a different demand price for water.
Table 5 s h o w s timing of water's availability is an important 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 additional water to a farm or farming area, to specify timing of delivery and also cropping system to which the water is applied.
How relative distribution of water by months affects its value is apparent. Look at thexelative change in monthly quantities

Farm Organization and Water Values
Marginal Values of Limiting Resources

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 Modell 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

and Se'ptember water value decreased 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 m a d e by calculating change in revenue between water supply levels for each model.

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 increase of 120 percent in value of July water. Value of August water decreased by 74 percent

Optimal Enterprise Combinations

problem handled by traditional budgeting methods, but it is brought more sharply into focus in the procedure of linear programming.
Requirements for enterprises ,,ary in total use and in timing of use of resource inputs. Therefore, the optimum farming system is not necessarily one that

Change in revenue between water supply levels results from change in the optimum farming system. These crop combinations are prescribed in linear programming 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

acres for the change from level two to three.
In model B most of the change from level one totwo is an increase 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 restricted, so they cannot come in at any higher level than this restriction.
Most adjustments which increase revenue and, therefore, the resulting value of water occur: (1) in substituting corn grain, corn silage, and clover (seed) for the small grain crops, and 2) in increasing total acres irrigated. Watex 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 instance, would be greater than the increase when this increment is applied to the next best alternative, 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 indicate that it is not profitable to grow small grain crops and al-

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

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 increases up to the third level, which is near full supply. Full supply is defined as the point at which water- is no longer limiting. Optimum enterprises for these three w a t e r 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 w a t e r requirements; and a change in rate of application to existing crops.
Total acreage irrigated increases 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


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:
Onions, 8 8 8 8 8 8
Sugar beets, 10 10 10 10 10 10
Potatoes, 10 10 4 10 10 10
Beans, 7 38
Beans, 2 16
Corn grain, 14 32 23 21 44 47
Corn grain, 7 9
Corn silage, 40 22 42 42 32
Corn silage, 1 42 10 20 31 1
Corn silage, 14
Wheat, 15 15 15 15 15
Barley, 41 60
Barley, 7 1 3
Clover, 20 48 51 14 42 60
Alfalfa 3 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 certain specialized areas, but one would not think it to be generally true, since these crops are quite widely grown in the irrigated valleys. One explanation for this result is the advantages of a crop rotation scheme, which are not accounted for in these models.
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 subnormal 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 ears with an insufficient. supply of water to finish the crop.

Change in net revenue The increase in' net revenue which comes from the chances
in enterprises resulting from changes in' water level are presented 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

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

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 enterprise, so the differences in the changes in revenue result from this fact. Model C, with limited enterprise alternatives, has approximately one-half as great an increase in revenue as model A for the change from water supply level one to two.
However, for the change from level two to three, model A shows the least increase. This mav follow from the discreteness of the changes in water supply and the peculiarities of the three models, and may not have any real significance. T h a t t h e overall change for model C is less than for B does suggest that the existence ofmany crop alternatives

increase income possibilities associated with a change in water supply. This is to be expected in light of the fact that, as mentioned earlier, multiple resource restraints result in multiple enterprises 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 availability 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 acreages 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 alternatives could not as effectively


169 149 151

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

I 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, Qiven the assumptions 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 unirrivated land for dryland crops. This possibility 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 result from additional use of the assumed quantities available.
As seasonal capital did not become limiting, its cost was subtracted out of the revenue figures, 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 factor.

Another way to arrive at a value for water would be to subtract the opportunity cost of land and labor from the change in revenue. It beino, 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 optimum combinations of 'enterprises would change. Opportunity 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 estimates presented in table 9. Note that increases in revenue attributed to the change in water supply were reduced by approximately 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

another watershed, a diversion that would increase the supplies in both seasons. Under these conditions, the only changes in supply to which the'chan ges 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 efficiency and three yield levels. Acre-foot values range from approximately $41 for model A, with high yields and a 60 percent efficiency of water use, to approximately 39 cents for model C, with low yields and a 40 percent efficiency of water use. Model A has a higher value for

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 deliveries 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, various types of water supply changes might be considered. For instance, an area with a superfluous amount of early-season water and a shortage of late-season water might receive more water consequent to a diversion from

TABLE 11. Consumptive use requirements for late water and returns per acrefoot 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
Potatoes, 22.75 40.27 1.77
Beans, 8.62 10-26 .91
Alfalfa,, 7.17 2.08 .29
Alfalfa, 5.86 7.79 1.33 22 29.26

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

water b et w e e n water supply levels one and two than model B because of the livestock enterprise. Model A was included in this study for comparison purposes, and presentation of estimates from this model are not intended as an argument for including livestock enterprises in calculating water values. Further discussion of this question is contained in the following section.
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 headgate, assuming 'a 50 percent water-use efficiency. Thus with average yields for the farm represented by model A, the estimated value of water for an increase from 2.18 to 3.02 acre-feet pet acre, or 0.84 acre-feet per acre, is $2C86; 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 acrefoot respectively for models A, B, and C.
Calculations displayed in table 10 are demonstrative evidence of the need for considering marginal 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 exchange. If a "free water market" existed for the farm situations represented in the table, there would probably not be an equal use of water for all farms. Farms with high yields and greater 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 computed 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 enterprise.
In table I I the net revenue for each enterprise has been divided by the total consumptive use requirements for July, August, and September, that is, the lateseason 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 models. 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 lateseason water is approximately the same as the second level in the previous models. Several alternatives exist for using extra water, namely, increasing the rate of application on corn, substituting corn for barley, substituting potatoes for corn, and substituting 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 silage, to corn silage, would require an additional 0.25 acre-foot of water per acre and would increase revenue by $2.26 per acre. This amounts to a value of $9.05 per acre-foot of water actually consumed by the crop. The eturn to water delivered at the farm headgate would depend upon the efficiency of use, being $4.52 at 50 percent efficiency. Substituting corn silage2 for barley would require an additional 0.67 acrefoot 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 headga e, again supposing a 50 percent 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 silage, requires, but a slight amount of extra labor and would be an adjustment easily made without changing the resource availabilities on the farm.

Appendix table III shows that the substitution of potatoes for barley would require an additional 23 hours of labor per acre. The substitution of corn silage, 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-. member while barley requires none. The feasibility of this adjustment would depend upon the

Implications for Economic The linear programming models of this study demonstrate the effect of certain factors upon the marginal value of water and indicate the type of adjustments that would be economic in response to a change in water supply. The kind of adjustments farmers can and do make to a change in water supply determines in part the value of the additional water. Conditions of the market for products and for input factors, native land characteristics, and so on, also help determine value of presently used water and of marginal increments.

flexibility of the labor supply.
It must be concluded that the value of an additional quantity ,of water depends upon the complement of other resources that can be combined with the additional water. In the above example the value of an additional acre-foot of water could be $4.52 or $16.16, depending u p o n whether additional labor. was available.

Evaluation of Water Use
Several of these factors effecting water values have been considered in this study and estimates of their effects presented. It was suggested earlier that an understanding of the quantitative economic relationships within the firm regarding marginal values of water would be useful in considering some of the aggregate 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 use.

of supply, the value of water would be increased by transferring J u I y a n d 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

Marginal value products presented 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 between farms.
In model B at the first level

Timing of Water Deliveries

the model C farm with an increase in value of ($13.44 $7.74) + ($36.09 - $23.85)
Institutional restraints in many areas of the irrigated West discourage the trading and transfer of water between farms. The above figures suggest costs that may result from sucli 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 developed.
It may be inferred that the water transfers mentioned resulted 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 productivity, and differences in management 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 direction.

Both table 5 and table 10 indicate the disparity in marginal values that may occur between farms with different productive capacities. Where marginal adjustments in farm supply are prevented by institutional arrangements we observe situations such as exist on the Uncompahgre Project. On this project, in western Colorado, the acrefeet-per-acre deliveries are fixed for each farm, having been originally allocated on the basis of consumptive u s e requirements for soils classified on tile basis of

structural characteristics rather than productivity."' Reported yields for various soil classes in the project differ considerably. Yields on the poor soils are approximately 50 to 60 percent of those on the best soils.19 This is approximately the same range as used in this study between the high and low productivity situations.
Institutions which prohibit exchange of water between farms make it impossible to achieve an economically efficient u s e of water resources in this area.

17 Raymond L. Anderson, "Operation of the Irrigation Water Rental Market in the South Platte Basin." Paper delivered at American Farm Economics Association meeting at Ames, Iowa, Aug. 1960.
- 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.

Farm Productivity and Marginal Values of Water

This discrepancy from efficiency is sizable even when considering only the differences in yield on the various soil classes. The estimates presented in table 10 indicate that an approximate difference of 50 percent in yields between 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 quantity 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 tile second level of supply, which is 3.02 acre-feet per acre. The marginal value products would be approximately equal, being $14.22 and $13.04 respectively at these levels, as shown in the table.

Two items of interest regarding p r o j e c t evaluation have evolved from thisstudy. 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 attributable 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 selling 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, efficiency 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 production opportunities were assumed. Whether or not the change in the residual properly reflects the returns to water depends upon the assumptions regarding the opportunity costs of the additional capital and labor.

Project Evaluation

When considering the sizable increase in the amount of labor needed iv h e n 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 subtracted from the change in net revenue, the change in revenue was reduced by approximately onethird. This indicates the importance of labor costs in imputing value to increments of water.
We have also shown that some ad justments 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. However, this is not an argument against including additional operator or family labor as a cost in computing the value of additional water. Linear programming procedures particularly emphasize 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 engaged 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 entering only one unspecified opportunity cost activity.
A factual problem exists in deciding 'g upon a figure to use for the net revenue of this activity. Most farm operators would probably 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 1. 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

2.6 .8
2.2 53 11.3 12.6
44 248

1.6 .8
1.5 36
8.2 9.8
34 200

$ 1.88 21.71 21.71 27-00 1.32 7.85 5.92 13.91 3.00 1.65

$36.54 47.78

41.71 46.87
54.03 76.20

$33.90 36.95 39.67

35.79 39.32 49.87 68.84

$32-10 22.60 35.47

23.85 26.98 39.97 55.46

$36.78 23.86

41.45 52.04 33.59

$30.02 19.50 37.10

34.17 49.38
24.72 98.08

62.67 18.71

$22.24 12.14 22.40

23.67 37.39 M 18.05

41.88 11.51 137.15

26.40 23.53 21.13 22.56
385.42 356.72 312.85 285.08

: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.

two net revenue figures must be

TABLE 11. Animal feeding costs

Beef 1 Aitter hogs 2-Litter hogs

Hay $ 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 .17.95 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 I -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
Alnil .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
2 3 Alfalfa 1
2 3 Clover 1
2 3 Barley 1
2 3 Corn grain 1
2 3 Corn silage 1
2 3 Beans 1
2 3 Sugar beets 1
2 3 Onions 1
2 3 Potatoes 1
2 3

2.29 2.60 2.50
4.00 4.00 3.50
4.00 4.00 4.00 3.23 3.25 3.50 2.86 2.83 2.80 2.86 2.83 2.80

2.42 2.36
4.00 4.14 4.00

4.58 3.90 2.50
4.00 4.00 3.50
4.00 4.00 4.00 3.21 3.25 3.50

3.57 3.66 3.60
4.58 4.84 4.72 4.00 4.14 4.00 2.36 2.33 2.57

8.00 4.00 4.00 4.00 4.00
8.00 4.00 4.00 4.00

5.72 5.66 5.60 5.72 5.66 5.60 10.71 10.89 7.20
4.58 4.84 4.72 8.00 .6.21
9.44 6.99 7.71