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Method and theory for determining optimal types of cattle for tropical and subtropical livestock enterprises

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Method and theory for determining optimal types of cattle for tropical and subtropical livestock enterprises
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Simpson, James R.
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University of Florida -- Department of Food and Resource Economics -- Institiute of Food and Agricultural Sciences
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Farming ( LCSH )
Agriculture ( LCSH )
Farm life ( LCSH )
South America ( LCSH )
University of Florida. ( LCSH )
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South America
North America -- United States of America -- Florida

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Full Text
METHOD AND THEORY FOR DETERMINING
OPTIMAL TYPES OF CATTLE FOR TROPICAL AND
SUBTROPICAL LIVESTOCK ENTERPRISES By
James R. Simpson
CTA Report 4 May 1982
THE FOOD AND RESOURCE ECONOMICS DEPARTMENT




ABSTRACT
This report is designed to help in the decision-making process
involving selection of the type cattle enterprise for a particular situation. The data are specific to Colombia, South America in 1981, but the theory and budgeting procedure hold for all tropical and subtropical areas.
A review of production economics theory and the elements of budgeting livestock operations is provided. Examples are provided for a steer operation, purebred and dual purpose dairy enterprise and a cow/calf business. It is shown that simple budgeting is adequate when land is the only constraint.
A review of linear programming is also provided. A graphical analysis is carried out to determine the optimal land use for the cow/calf and dualpurpose alternatives when there are labor and capital constraints in addition to a land constraint. The report is primarily a teaching aid for understanding budgeting and linear programming techniques for determining optimal land use in cattle operations.
Key words: Cattle, beef cattle, cows, steers, budgeting, dairy cattle, tropical, subtropical, linear programming.




TABLE OF CONTENTS
Page
ABSTRACT i
LIST OF TABLES .
LIST OF FIGURES iv
INTRODUCTION I
BASIC ECONOMIC DECISIONS . . . . . . . . . . 2
THE "HOW" AND "HOW MUCH" TO PRODUCE DECISIONS: SOME THEORY . . 3
FINISHING STEERS: AN ALTERNATIVE . . . . . . . . 10
No Supplemental Feeding . . . . . . . . . . 13
With Supplemental Feeding . . . . . . . . . . 20
PUREBRED AND DUAL PURPOSE DAIRY CATTLE:- A SECOND ALTERNATIVE . 24
Purebred Dairy Cattle . . . . . . . I . . . 24
Dual Purpose Dairy Cattle . . . . . . . . . . 27
A BEEF COW-CALF OPERATION AS A LAST EXAMPLE . . . . . . 29
COMPARISON OF THE SYSTEMS . . . . . . . . . . 29
LINEAR PROGRAMMING IN LIVESTOCK PRODUCTION ECONOMICS . . . 30 SUMMARY AND CONCLUSIONS . . . . . . . . . . . 38
REFERENCES 40




LIST OF TABLES
Table Page
1 Inventory, animals marketed and production measures for
typical 100 animal unit steer, dairy and cow/calf
operations in Colombia, 1981. .. .. .. .... ....11
-2 Reported input-output price relationships for seven Latin American countries, 1981 .. .. .... .. ....12
3 Input-output price ratios for seven Latin American countries, 1981 .. ... .... .. .... .....14
4 Computation of annual costs for 100 animal unit steer, dairy and cow/calf operations in Colombia, 1981 .. ....16
5 Example of calculating where the input price = MVP, and where MC=MR in determining how much supplement to feed
steers, Colombia, 1981 .. .. .... ...... ...21
6 Example of calculating where MC=MR in determining how much supplement to feed purebred dairy cows, Colombia, 1981 ..28
7 Example of calculating where MC=MR in determining how much supplement to feed dual purpose cows, Colombia, 1981 . 32
8 Input and output specifications for linear programming
example . . . . . . . . . . . .
9 Calculation of net returns from various corner solutions, linear programming example. .. .. ...... ....36




LIST OF FIGURES
Figure Page
1 Example of the production economic decision about how to
produce. .. .. ... ...... .... .... ..4
2 Example of the production economic decision how much to
produce. .. .. ... ...... .... .... ..6
3 Example of the production economic decision about what to
produce. .. .. ... ...... .... ........9
4 Input-output price ratios for selected countries in Latin
America, 1981. .. .. .... ..... ...... ...15
5 Beef production per head, with and without supplement,
example problem for steers, Colombia, 1981 .. .. .....23
6 Determination of corner solutions, linear programing
example .. .. ... .... .... ...... ...34
iv




METHOD AND THEORY FOR DETERMINING OPTIMAL TYPES OF CATTLE
FOR TROPICAL AND SUBTROPICAL LIVESTOCK ENTERPRISES James R. Simpson
Owners of agricultural and livestock enterprises throughout the
tropics and subtropics, just as enterpreneurs in the temperate regions, are faced with selecting the optimal type of cattle for their operations. If the tropical countries were developed economies with an attendant efficient transportation infrastructure, the more temperate regions likely would tend to specialize in milk production, with the hotter areas devoted to beef cattle. But, the realities are that in every tropical or subtropical country there are extreme climatic variations, a wide range (and shortage) of management skills and enterpreneurial interest in milk production, instability in beef/milk price ratios, an uncertain political situation, and a poor transportation and milk handling system which results in high transport costs. Consequently, except for a few isolated cases,
there is virtually no regional specialization in milk orbeef production.
INTRODUCTION
It is within the severe constraints identified above that cattlemen, researchers and government planners are required to make major long-term financial decisions about the type of livestock operation which best suits specific conditions and, as part of that decision, the optimal type of cattle for them. This report is designed to help in the decision-making process involving selection of the type cattle enterprise for a particular situation. The data are specific to situations in parts of Latin America
JAMES R. SIMPSON is associate professor of food and resource economics.




2
in 1981, but the theory and budgeting procedure hold for all tropical and subtropical areas.
A critical assumption in this study is that the producer has decided
to utilize part of the enterprise for cattle and, consequently, the analytical framework is restricted to determining the optimal type of cattle enterprise rather than cattle versus crop production, or other types of enterprises such as hogs or poultry. The major possibilities evaluated are: steer fattening, dairy only, dual purpose (milk and beef) and a cow/calf beef operation. Other possibilities are any combination of the above four possibilities.
BASIC ECONOMIC DECISIONS
Production economics is the tool for determining the optimal type of cattle operation for a given piece of land. The crux of production economics is that there are three major production decisions which all cattle raisers consciously or subconsciously make, whether they operate under the most primitive nomadic conditions or with extremely sophisticated management. The decisions are: (1) how to produce; (2) how much to produce; (3) what to produce..
The first of the three decisions, "how to produce," provides necessary background information for the determination of what and how much to pro-duce. The decisions are not made just in the formative stages of an operation, but should be periodically reevaluated in light of new information and changing input/output price relationships.
The first step is setting forth a farm plan. Then, budgets are developed to provide the economic relations in the "how to produce" decision. Then, an optimal level of production is estimated given economic and management considerations. This is the "how much to produce"' decision., Finally, the latter information is compared to determine




.3
"what to produce." In the initial part of this report alternative budgets are developed for the four classes of livestock and the results compared. The latter part of the report is devoted to explaining the method for "what" to produce in a linear programming framework. Steers are chosen as the livestock class for most of the explanation about method and theory.
THE "HOW" AND "HOW MUCH" TO PRODUCE
DECISIONS: SOME THEORY
As an example of the decision "how" to produce, assume first that
results from the local experiment station show one of the best production methods for steers to be with improved perennial pastures and supplement feed. There are, of course, various supplements, but the research indicates that 16 percent protein concentrate (called input or factor X1) has given good results. This factor, along with pasture, which is called X2, is the factor-factor relationship shown in Figure 1. The two factors may be substituted in different proportions and amounts to provide various levels of output which, represented by the curved lines called isoquants, are denoted as Yla, Ylb, Y~c in the figure. The lowest output is Yla while the highest level of output is Y1c. The straight lines between the two' axes are called isocost lines or constant cost lines as they represent various combinations of inputs that can be purchased by a given outlay.
As greater amounts of the two factors are utilized, higher levels of output, say kilos of beef per steer or hectare, are obtained. There are, of course, an infinite number of isoquants (because there are an infinite number of output levels) just as there are an infinite number of output combinations (along any one isoquant). For simplicity, only two inputs are shown in the figure. The tangency point between an isoquant and isocost lines is economically the most efficient (least-cost) combination of




4
.- Line of least cost
Isoquant (outputs) Y1 c
Yib
Yia
Isocost curve (costs) Input X2 Figure 1.--Example of the production economic decision about how to .produce




5
inputs for producing that level of output. The tangency points may be connected by a line indicating the least-cost combination of inputs (at the given input prices) for producing any particular level of output. Any combination of inputs (at the given prices) other than the tangency point Iare not optimal solutions. The points may be connected by a line of least-cost which represents the most efficient input combinations for
any given set of outputs.
The second economic question, "how much to produce," is graphically shown in Figure 2. The vertical line between X, and X2 in the formula Y1 =f(11I X2... .Xn) means that all inputs other than the supplement (XI) are being held constant. The production function OA shown in Figure 2 bends because output is now represented on the vertical axis, while inputs are shown on the horizontal axis. Output increases up to a certain point
(C) after which it begins to decline because "too much" of the input is used.
The straight line OB represents a line in which the price of the input being varied (X1) is divided by the price of the output (P y). In effect, it is x The slope of the line is determined by the relation
Py
between this input and output. Optimum output, in this factor-product relationship, is where the marginal physical product (MPP) is equal to the inverse of the price ratios, i.e., price of the supplement divided by price of the output. The equality is determined by the point of tangency. This relationship is also known as producing where marginal revenue just equals marginal cost, where the term "marginal" means the last additional increment. In other words the "economically rational" cowman would continue increasing the quantity of supplement, i.e., the 16 percent protein
1 Where PX2




6
B
Optimum Tangency Maximum (C)
output
Y,= f (X11X2 ...Xn)
A
0
0
Input (X 1)
Figure 2.--Example of the production economic decision how much to produce




7
concentrate until cost of the next input unit just equals the additional income. This assumes that the other input(s) such as pasture (X2) are held constant at some given level. The uses of these measures are described later in an example problem.
It is important to recognize that,even though the economically optimal production level can be determined, in practice this entrepreneurial management objective is seldom achieved as there are usually some interpersonal, culturally oriented constraints which lead to other input use levels. For example, although the economically rational entrepreneur attempts to maximize profits, some people feel compelled to maximize production, thus inevitably employing economically excessive input levels. In many cases, quantity of the input used is lower than the economic optimum due to unavailability of supplies or failure to calculate the optimal production level. In some areas, especially Africa, there are social constraints such as communal grazing systems and status which leads to high cattle inventory levels and low off-take.
A return is now made to an important aspect in the first of the production decisions, "how to produce" (a factor-factor problem). By holding all inputs, except the ones being evaluated, constant it is possible to portray the law of diminishing returns (also called the law of variable proportions) which states that,if an input is applied to a fixed factor, eventually, if enough is applied, total output will begin to increase at a decreasing rate (the inflection point) and may approach a maximum at which time output could begin to decrease (point C in Figure 2). In the example cited, if the supplement is fed at too high levels (relative to their ability to digest it properly), especially in recently weaned calves, many of them probably would become sick, go off feed and some might even die. The result would be a decrease in output.




8
The third of the three decisions, "what to produce," is decided upon after sufficient knowledge is obtained about the relevant production functions. Some production functions of interest to cattlemen are relationships of gain by weight classes, sexes and breeds of cattle on different type forages. Additional useful information would be alternative forage yield responses with different input combinations such as fertilizer, mowing or water. Additionally, data on interrelationships like average daily gain from supplemental feeding and various carrying capacities would be useful. Seasonality effects are also evaluated within this decision framework.
Assuming that the production function information, or at least some estimates, have been obtained, the problem is one of relating input costs with output prices. In this relationship, which is graphically depicted in Figure 3, the curved lines represent two possible output relationships. For example, a rancher has the option of using his or her land for a dairy operation (YI), fattening steers (Y2) or some combination of both enterprises. There are, of course, many possible output combinations. The amount of potential production depends on the production functions which, in turn, depend on the amount of input usewhich, finally, is constrained by resource availability. The curved lines are thus called isoresource or production possibility curves.
The optimal amount of each possible output is determined by the tangency of the isorevenue with the production possibility curve. In other words, the criteria for determining the optimal amount of outputs depends on a combination of the physical, cost and price relationships. If more inputs are used in the production processes, the isocost curve is shifted out, say from C1 to C2, so that more of each potential output,




9
Expansion path
. Isorevenue or
D isoprice lines
C2
Isoresource or production posRi R2 Ci sibility curves
Output (Y2)
Figure 3.--Example of the production economic decision
,how mucb to produce
j;/ ,.




10
such as milk or fed steers, could be produced. The location of C1 and C2 is determined by the input constraints, such as the amount of land available. In the diagram (Figure 3) only one resource constraint can be shown. The tangency of the new isoprice lines with the new isocost curves may or may not lead to the same proportion of outputs. An expansion path can be drawn through the tangency points to show the optimal combinations at different output levels. Given the production possibilities curve associated with the given constraint, the most rational economic decision in maximizing revenue is to produce at the tangency points where the slope of the isoprice lines (C1 and C2) is the inverse of the relative output prices (Footnote 1). Some example problems are now given.
FINISHING STEERS: AN ALTERNATIVE
Information on cattle inventory, number of animals marketed annually and production measures is provided in Table 1 for two types of'steer oper ations: without supplemental feeding and with supplemental feeding. In addition, the table contains information on a purebred dairy operation (Holstein cattle), a dual purpose cattle operation (Zebu cross) and a beef cattle cow/calf enterprise (Zebu cross cattle). These examples will be discussed later. The operations are assumed to be in a tropical or subtropical area of Colombia. Pastures are in improved perennial grasses.
Table 2 contains input-output price relationships for seven tropical or subtropical Latin American countries in early 1981. The data were compiled from 28 usable respb-nses obtained from a survey taken among more than 200 Latin American participants attending the 1981 Latin American Livestock and Poultry Short Course at the University of Florida. The product-product price ratios between beef and milk and the output-input




Table I.--Inventory, animals marketed and production measures for typical 100 animal unit steer, dairy and cow/calf
operations in Colombia, 1981a
Steers Dairy
No With Dual Beef,
Item Units supplement supplement Purebred purpose cow/calf
Inventory
Total animal units A.U. 100 100 100 100 100
Pasture land Ha. 100 100 100 100 100
Crop land Ha.
Livestock
Mature cows No. 72 83 85
Hei fers No. 25 15 11
3-4 yr. old steers No. -- -2 yr. old steers or bulls No. 99 99 -Yearling steers or bulls No. --11
Bulls No. 3 3 3
Horses No. 1 1 1
Total animals No. 100 100 101 101 101
Number of animal s marketed annually
Cows No. 24 12 10
Heifer calves No. a-- 20 27
Steer or bull calves No. 32 32 38
Bulls No. --11
Mature steers No. 98 98 -Total animals No. 98 98 65 65 65
Production measures
Calf crop (weaned) Pct. 90 90 90
Death loss (weaned calves & older) Pct. 1 I 1 1 1
Replacement rate Pct. -- 33 17 12
Milk production per cow Kg. -- 3,045 2,050
Total milk production Kg. ---219,240 170,150
Gain per day Kg. 0.30 0.80c ---Length of feeding Days 210 210 -Purchase weight Kg. 375 280 -Total gain Kg. 63 68 -Sale weight Kg. 438 448 185
Total beef production (sales) Kg. 42,924 --12;240 8,798 16,025-d
Total additional beef/milk production Kg. 6,174 --12,240 8,798 16,025
Production per hectare
Beef Kg. 62 --122 88 160
Milk Kg. ---2,192 1,702
a Data gathered from personal interviews#
b Additional information is provided in the footnotes to Table 4. No total sales are shown as analysis of the plan
shows it to be uneconomic. The data shown are the inputs for the proposed management plan.
C Estimated only for planning purposes in determining cost per head per day with supplement feeding. See Table 4.
d There are 27 heifer calves and 38 bull calves or 65 total calves at. 185 kg. each 12,025 kg. plus 10 cull cows
at 320 kg. each -3,200 kg. plus one bull at 800 kg. -16,025 kg.




(12)
Table 2. Reported input-output price relationships for seven Latin American countries, 1981
Steers Straight Dual Beef,
No With dairy purpose cow
Comodity & country feeding feeding cows cows calf
------------- Dollars per kilo ------------Milk
Colombia 0.37 0.37
Costa Rica 0.25 0.25
Dominican Republic 0.60 0.60
Ecuador 0.63 0.63
Honduras 0.55 0.55
Panama 0.40 0.40
Venezuela 1.36 1.36
Calves
tolombia 0.94 0.94 0.94
Costa Rica 0.55 0.55 0.65
Dominican Republic 1.25 1.25 1.30
Ecuador 0.81 0.81 0.81
Honduras 0.33 0.33 0.33
Panama 0.38 0.38 0.38
Venezuela 1.03 1.03 1.28
Steers, slaughter
Colombia 0.85 0.85
Costa Rica 0.68 0.68
Dominican Republic 1.25 1.25
Ecuador 0.81 0.81
Honduras 0.42 0.42
Panama 0.41 0.41
Venezuela 1.55 '1.55
Supplement (16%)
Colombia 0.28 0.28 0.28 0.28
Costa Rica 0.19 0.19 0.19 0.19
Domilnican Republic 0.18 0.18 0.18 0.18
Ecuador 0.20 0.20 0.20 0.20
Honduras 0.09 0.09 0.09 0.09
Panama 0.20 0.20 0.20 0.20
Venezuela 0.25 0.25 0.25 0.25
Cull cows
Colombia 0.75 0.75 0.75
Costa Rica 0.52 0.52 0.52
Dominican Republic 0.90 0.90 0.90
Ecuador 0.81 0.81 0.81
Honduras 0.32 0.32 0.32
Panama 0.30 0.30 0.30
Venezuela 1.60 1.60 1.60
Source: Survey of participants at the 1981 Latin American Livestock
and Poultry Short Course, University of Florida.




13
price ratios between milk and supplement, and beef and supplement are given in Table 3. The ratios for the purebred dairy operation are graphed in Figure 4.
No Supplemental Feeding
As indicated, the decision criteria determining the optimal output
and use of inputs in the question; "how much to produce" is where marginal revenue equals marginal cost (MR=MC) or, alternatively, where the marginal value product (MVP) equals the input cost. In this section an example is provided which explains both the method for arriving at the optimal level as well as the concept of marginal revenue and marginal cost. It relates return to a cattleman who is interested in fattening steers on pasture. The focus is determining whether supplementing them with concentrate (in the amounts determined to be a least-cost combination) will yield a profit, and the amount of feed to use per head.
The analysis begins-by budgeting a steer operation in Colombia in for which there is no supplemental feeding. The 100 hectares of
improved pasture land have a carrying capacity of 100 animal units or 99 head of two year old steers, plus one horse (Table 1). The 99 steers, with an initial weight of 375 kilos, are purchased at $0.85 per kilo (all monetary figures are in United States dollars). There is an investment of $52,100 (Table 4). Annual expenses, without the purchased steers, is $2,385, while the cost is $33,941 with the steers included. The largest non-cash cost is $2,036 for interest on cash costs or, alternatively if the steers previously belonged to the operator, opportunity cost on the money tied up in the steers as well as other cash expenses. Total expenses, without purchased animals, are $4,976, while they are $36,532 with the
cattle included.




14
Table 3.--Input-output price ratios for seven Latin American countries, 1981
Steers Dairy
With Dual Beef,
Item feeding Purebred purpose cow/calf
Beef/milk
Colombia -- 2.54:1 2.54:1
Costa Rica -- 2.20:1 2.20:1 -Dominican Republic -- 2.08:1 2.08:1 -Ecuador -- 1.29:1 1.29:1 -Honduras -- 0.60:1 0.60:1 -Panama -- 0.95:1 0.95:1 -Venezuela -- 0.76:1 0.76:1 -Milk/supplement
Colombia -- 1.32:1 1.32:1
Costa Rica -- 1.32:1 1.32:1 ""
Dominican Republic -- 3.33:1 3.33:1
Ecuador -- 3.15:1 3.15:1 -"
Honduras -- 6.11:1 6.11:1 -Panama -- 2.00:1 2.00:1 ""
Venezuela -- 5.44:1 5.44:1 -Beef/supplement
Colombia 3.04:1 3.36:1 3.35:1 3.36:1
Costa Rica 3.58:1 2.89:1 2.89:1 3.42:1
Dominican Republic 6.94:1 6.94:1 6.94:1 7.22:1
Ecuador 4.05:1 4.05:1 4.05:1 4.05:1
Honduras 4.67:1 3.67:1 3.67:1 3.67:1
Panama 2.05:1 1.90:1 1.90:1 1.90:1
Venezuela 6.20:1 4.12:1 4.12:1 5.12:1
Source: Table.2,




15
8
7
I
Beef/supplement /
I
6
I
I
I
5- Milk/supplement H Honduras
I
H =Honduras
CR = Costa Rica 4-I
C = Colombia % ,O1 P = Panama
i/
3- / E = Ecuador
2-\ Beef/milk-../ DR = Dominican Republic
.* ** 0 /
0
I I I I I I I
H CR C P E V DR
Country
Figure 4.--Input/output price ratios for selected countries in Latin
America, 1981




Table 4.--Computation of annual costs for 100 animal unit steer, dairy and cow/calf operations in Colombia, 1981
Steers Dairy
No With Dual Beef,
Item supplement supplement Purebred purpose cow/calf
------------------------ U.S. dollars -------------------------Investment
Owned land 50,000 50,000 50,000 50,000 50,000
Buildings and improvements 2,000 2,000 15,000 12,000 2,000
Machinery and equipment 100 3,000 7,000 5,000 3,000
Livestock ...- 56,400 45,100 35,500
Total 52,100 55,000 128,400 112,100 90,500
Cash expenses
Purchased steers 31,556 23,562-- -- -Hired labor -- 400 10,440 10,080 700
Supplemental feed
Maintenance .-- 12,220k 6,610 5,790
Increased production .... 22,438 19,359 -Salt and minerals 30 30 175 175 175
Repairs and maintenance
Buildings and improvements 50 50 275 100 50
Machinery and equipment 50 65 350 50 50
Veterinary services and supplies 350 400 700 400 400
Taxes 100 100 400 "375 300
Seed and fertilizer 1,500 1,500 1,500 1,500 -Machinery
Operating 255 350 400 50 350
Hired -- 300 250 -Transportation 50 50 100 75 75
I n s u r a n c e .-.- - .
Utilities .-- 400 50 -Miscellaneous -- 10 300 200 100
Total, without purchased animals or supp. 2,385 2,955 27,560 19,915 8,990
Total, withcut supplement 33,941 26,517 27,560 19,915 8,990
Total, with supplement -- -- 49,998 39,274 -Noncash costs
Depreciation
Buildings and improvements (5% annually) 50 -- 750 600 100
Machinery and equipment (10% annually) 5 -- 700 500 300
Int. or opp. cost on cash expenses (12% annually) 2,036 ..--h -- 539p
Management ($10,000/yr. full time) 500 -- 10,000 10,000 4,000
Total 2,591 -- 11,450 11,100 4,939
Total, all expenses, w/o purchased animals
or supp. 4,976 -- 39,010 31,015 13,929
Total, all expenses, w/o supp. 36,532 -- 39,010 31,015 13,929
Total, all expenses, with supp. -- -- 61,448 50,374 -See page 19 for footnotes. Continued




Table 4.-- Computation of annual costs for 100 animal unit steer, dairy and cow/calf operations in Colombia, 1981--continued
Steersa Dairy
No With Dual Beef,
Item supplement supplement Purebred purpose cow/calf
----------------------- U.S. dollars -------------------Gross income b 1
Beef 36,485 -- 9,4541 7,055 14,384
Milk -- 81,119m 62,956 -Total 36,485 -- 90,573 70,011 14,384
Net income above cash expenses
Beef 2,544 .-- -- 5,394
Milk -- --.-...
Total 2,544 -- 40,575 30,737 5,394
Net income above all expenses
Beef 47 ...--. 455
Milk ....
Total 47 -- 29,125 19,637 455
Cost, cash only, per head per day (steers) or
per cow per year (others)
No supplemental feed
Beef 0.12c 0.141 I06
Milk _3681 24
With supplemental feed
B e e f --..- -. .. .
Milk .... 694 473 --Cost, all expenses, per head per day (steers) or
per cow per year (others)
No supplemental feed d
Beef 0.24 --- --- 164
M i l k --.- -. .. .
With supplemental feed
B e e f --.. .- -.. .
Milk 853n 607
See page 19 for footnotes. Continued




Table 4.-- Computation of annual costs far 100 animal unit steer, dairy and cow/calf operations in Colombia, 1981--continued
Steers Dairy
No With Dual Beef
I temn supplement supplement Purebred purpose _cow/calf
Cost, cash only Per kilo US olr---------No supplemental feeder
Beef 0.79e --- 0.56
Milk - ----With supplemental feed
Beef --- 0 0--Milk -- 0.23 0.23 -Cost, all expenses, per kilo
No supplemental feed
Beef 0.85 ---- -- 0.87
Milk ---- -With supplemental feed
Beef ------ ----Milk -- 0.28 0.30 00
Cost, cash only, per hectare
No supplemental feed
Beef 24 ----- --- 90
Milk -- --275 199 -With supplemental feed5039
Beef -5033Milk --- ---
Cost, all expenses, per hectare
No supplemental feed
Beef 50 ----- --Milk -- --390 310
With supplemental feed---13
Beef--13
Milk -- --614 504-Income per hectare
Gross 364.85 --906 700 144
Net
Above cash costs 25 --406 307 54
Above all expenses 0 --291 196 5
See page 19 for footnotes. Continued




Table 4.--Computation of annual costs for 100 animal unit steer, dairy and cow/calf operations in Colombia, 1981--continued
a 99 steers at 375 kg. ea. = 37,125 kg. times $0.85 = $31,556. b 98 steers at 438 kg. ea. = 42,924 kg. times $0.85 = $36,485. c Cash expenses ($2,385) divided by 98 = $24.34 per steer divided by 210 days = $0.12. d All expenses ($4,976) divided by 98 = $50.78 per steer divided by 210 days = $0.24. e Cash expenses ($33,941) divided by 42,924 kgs. = $0.79. f 99 steers at 280 kg. ea. = 27,720 kg. times $0.85/kg. = $23,562. q Cash expenses ($2,955) divided by 98 = $34.15 per steer divided by 210 days = $0.14. h No charge as there is frequent income from sale of milk. i Cash expenses ($27,560) divided by mature cows (72) = $368. J Cash expenses ($19,915) divided by mature cows (83) = $240. k Supplement feed per cow (1,113 kgs.) from Table 5, times $0.28 per kilo = $311.64
per cow times 72 cows = $22,438.
1 $131.30 per cow (Table 5) times 72 cows = $9,454. m 3,045 kg. per cow (Table 5) times 72 cows = 219,240 kg. times $0.37 per kg. = 81,119. n $61,448 divided by 72 cows = $853. O $61,448 divided by 219,240 kg. = $0.23. P Interest on cash expenses for one half the year. c 27 heifer calves plus 38 bull calves = 65 total calves times 185 kg. = 12,025 kg.
times $0.94 = $11,304 plus 10 cull cows at 320 kg. ea. = 3,200 kg. times $0.75 = $2,400 plus one 800 kg. bull times $0.85 = $680 for a total of $14,384. The
weighted average price is $0.90.




20
There is a gross income of $36,485 from sale of 98 steers (assumes one died) weighing 438 kg. each, and a net income above cash costs of $2,544. When non-cash costs are included there is a gain of $47 for the entire operation. Net income above cash is $25.44 per hectare, while it is $0.47 per hectare when all expenses are included. The cost per head per day, only taking into account cash costs, is $0.12. This number is used in the next section, which is an example of determining whether supplemental feeding is profitable, and the optimal amount of feed.
With Supplemental Feedingi
It can be assumed that the operator contemplating feeding steers would plan on purchasing 280 kilo animals, feed them for 210 days and, with a projected gain of 0.80 kilos per day, sell them at 448 kilos each (Table 1). If this strategy were followed, there would be additional
expenses associated with the activity such that total cash expenses would increase from $2,385 to $2,955. The cost per head per day would thus be $0.14 (Table 4).
Two closely related means for determining the optimal production
level are given in Table 5. The first one is producing where the input
price just equals the value of the last unit of product, i.e., the marginal value-product (MVP). The MVP is calculated by multiplying price times
the MPP, where MPP is the change in the quantity of beef production divided by the change in the quantity of input. For example, the change from 3.80 kilos of supplement to 4.00 kilos is 0.20 kilos. This quantity, divided into 0.10 kilos of beef (0.60-0.50) gives a marginal physical product (MPP) of 0.50. That physical measure multiplied by the price of beef ($0.85 per kilo liveweight) gives the MVP. The decision rule is to produce where the value of the last additional unit of product (MVP) just




Table 5.--Example of calculating where the input price = MVP, and where MC=MR in determining how much supplement to feed steers, Colombia,
1981a
Decision rule: produce where input price=MVP Decision rule: produce where MC=MR, i.e. where MC=Price.of beef
Marginal Marginal Supplement
Daily per Additional physical value variable Fixed Total Total Marginal Marginal
head ration beef product product cost cost cost revenue Net cost revenue
of supplement production (MPP) (MVP) (VC)b (FC)c (TC) (TR)d income (MC) (MR)
Qx Qy y Py.MPP Px.Qx VC+ FC Py .Qy TR-TC ACTOR
AQx AQy AQy
---------Kilos ---------- .----------------------- ------ U.S. dollars -------------------------------------0.0-0 .30 0.00 0.12 0.17 0.26 0.14
0.05 0.04 5.40 0.85
3.80 0.50 ------------------------1.06 0.14 1-20 0.43 -0.77 ------------------------0.50 0.43 0.60 0.85
4.00 0.60 1.12 0.14 1.26 0.51 -0.75
0.40 0.34 0.70 0.85
4.25 0.70 1.19 0.14 1.33 0.60 -0.73
0.40 0.34 0.70 0.85
4.50 0.80 1.26 0.14 1.40 0.68 -0.72
0.20 0.17 1.40 0.85
5.00 0.90 1.40 0.14 1.54 0.77 -0.77 2
0.11 0.01 2.50 0.85
5.90 1.00 1.65 0.14 1.79 0.85 -0.94
0.04 0.03 6.20 0.85
7.00 1.05 1.96 0.14 .2.10 0.89 -1.21
0.00 0.00 5.60 0.85
8.00 1.05 2.24 0.14 2.38 0.89 -L49
aAll costs are on a per kilo basis in the input price=MVP analysis, and on a per head per day basis for MC=MR.
price of supplement (Px) =1$0.28per kiloI.
cThe fixed cost, i.e., the one that does not vary is from Table 4. The cost Is $0.12 (first column) without supplement feeding. It increases to $0.14 (second column of Table 3) to account for additional costs incurred in feeding the supplemental feed.
price of beef (Py)" = $0.85 per kill. liveweight.




22
equals the product price. From Table 2 it is determined that the price of supplement feed in Colombia is $0.28 per kilo. From this it can be determined that the only place where MVP = input price is for no supplement feed. All supplement levels beyond that point either have an MVP above input cost, or where MVP is equal to it (about 4.50 kg. of supplement), MVP is declining, thus indicating an uneconomic level. The relationship between beef production and supplement is shown in Figure 5.
The second method to determine the optimal feeding level is equating marginal cost with marginal revenue. This decision rule first requires calculation of the daily supplement feed cost. In this decision rule, for convenience, all costs are on a per head per day basis. Multiplying the supplement unit cost ($0.28 per kilo) times the daily quantity yields the variable cost, so termed since it is the one which is being varied. Then, the fixed costs (fixed in the sense that they are being held constant while the quantity of supplemental feed is being varied) are added. The-cost per head per day of $0.12 calculated in Table 4 is entered in the-first row, the one with no supplemental feeding. The calculations in Table 4 show that the fixed cost would be $0.14 per head per day if there were supplemental feeding. This figure is thus entered in each of the other rows in the fixed cost column. Total cost, shown in the next column, is the sum of fixed and variable costs.
Total revenue is calculated by multiplying beef price ($0.85 per kilo) times quantity of beef produced (Qy). Net income per head per day, the difference between the total revenue and total cost columns, is $0.14 with no supplemental feeding. If the lowest feeding level, 3.80 kilos of supplement is fed, the additional gain does not cover feed costs, and there is a loss of $0.77 per head per day.




23
1.75
1.50 1.25
C
S1.00
0
0.75 With supplement
0.75
0.50 Pasture only
0.25
0 a a a a a I
1 2 3 4 5 6 7 8 9 10
Supplement (kgs.)
Figure 5.--Beef production per head, with and without supplement, example problem for steers, Colombia, 1981




24
Marginal cost is calculated by dividing the change in total cost
by the change in beef output. For example, the MC of $5.40 is the result of dividing $1.08 ($1.20-$0.12) by 0.20 (0.50-0.30). The marginal revenue of $0.85 for that same feeding level is the product of dividing the change in total revenue which is $0.17 ($0.43-$0.26) by change in quantity, i.e., 0.20 (0.50-0.30). Marginal revenue, it should be noted, is equivalent to product price. The decision rule is to produce where MC=MR so the conclusion, as with the previous method, is that supplement feeding in uneconomic. Every level of supplement provides a negative net income. MC is equal to MR at about 4.25 kg. per head per day, but this level is simply the point where losses are minimized if cattle were to be fed supplement.
The conclusion reached is that supplemental feeding sho uld not be practiced with the input-output relationships given. As such, computations of depreciation, gross income, net income and so forth are not made.
PUREBRED AND DUAL PURPOSE DAIRY CATTLE: A SECOND ALTERNATIVE
The previous situation contains an implicit assumption that management would utilize the inputs in the manner specified in the budgets. The examples in this section are for the same management level. Two breeds are compared, a straight dairy breed, Holstein-Friesian, and dual purpose cattle such as a Shorthorn-Zebu cross. The manager is interested in Producing an optimal level of milk in each case. However, it is specifically recognized that the dual purpose breed will require much less supervision and input cost.
Purebred Dairy Cattle
The assumptions about inventory and production measures are given
inTable 1. The major constraining factor in this alternative, as in all




25
the others, is that only 100 hectares of land are available, however, a small part of.it is seeded and fertilized to provide more and better quality forage for milking cows. Fewer Holstein cows (72) can be carried than the dual purpose breed (83) because more replacements are carried since cows are culled every three years-for the Holstein operation versus every six years for the dual purpose breed. A 90 percent calf crop and
1 percentdeath loss are assumed.
Total cash expenses without additional supplement feed are $27,560 or $368 per cow (Table 4). This "fixed" cost is then used in Table 6 to determine the in-barn feeding level where marginal cost equals marginal revenue (the method for determining the optimum by equating MVP and the input price is not shown). The optimal feeding level is calculated at
3.65 kilos per day or 1,113 kilos per head for a 305 day lactation. Calculations where the optimal supplement use are determined can be considered the "how much to produce" part of the decision-making process. There are other questions which affect the "how much to produce" question, but supplement feed is, by far, the most important one in both steer fattening and milk production, and thus it is the only one considered.
After the optimal level of 3.65 kilos is calculated, i t is multiplied by a 305 day lactation to arrive at 1,113 kilos per cow annually. Multiplying this times 72 cows, and then by $0.28 cost per kilo of supplement, gives a cost of $22,438 annually. This is added to the other costs in Table 4 to arrive at the total cost expenses for the operation of $49,998. Total expenses, including non-cash costs, are $61,448. The gross return, including sale of dealers and cull animals, is $90,573. This income is based on $0.37 per kilo of milk, and about $0.77 weighted average price of live cattle. The cost per kg. of milk produced is $0.23 when only cash




Table 6.--Example of calculating where MC=MR in determining how much supplement to feed purebred dairy cows, Colombia, 1981a
Annual Daily Annual Supplement Annual Annual Annual Annual Annual
Daily per milk milk beef variable fixed total revenue revenue tptal Annual Marginal Marginal
head ration Annual prdduc- produc- produc- cost cost cost milk beef revenue net cost revenue
of supplement supplements tion tionc tion d (VC)e (FC) (TC) (Rm) (Rb) (TR) income (MC) (MR)
Qx QYm QYb PxQx VC+FC Pyb+QYm Pyb+QYb Rm+Rb TR-TC ATC ATR
AQYm Am
---------------------Kilos------------------------------ ----------------------------------U.S. dollars---------------------------------------------0.00 0 1,180 3.87 170 0 368 368 437 131 568 200
.12 .37
0.45 137 1,500 4.92 170 38 368 406 555 131 686 280
.14 .37
0.90 275 1,775 5.82 170 77 368 445 657 131 788 343
.17 .37
1.35 412 2,000 6.56 170 115 368 483 740 131 871 388
.17 .37
1.80 549 2,225 7.30 170 154 368 522 823 131 954 432
.17 .37
2.25 686 2,455 8.05 170 192 368 560 908 131 1,039 479
.18 .37
2.73 833 2,680 8.79 170 233 368 601 992 131 1,123 522
.22 .37
3.20 976 2,865 9.39 170 273 368 641 1,060 131 1,191 550
.22 .37
3.65 1,113 3,045 9.98 170 312 368 680 1,127 131 1,258 578
... .. ... .. .. .. .. ... .. ... .. .. .. ... ... .. .... ...57 .37
4.10 1,251 3,111 10.20 170 350 368 718 1,151 131 1,282 564
.42 .37
4.55 1,388 3,203 10.50 170 389 368 757 1,185 131 1,316 559
aCosts are on a cost per head per year basis. e I
bcows only fed during 305 day lactation. Price of supplement (Px) = .
c305 day lactation. fPrice of milk (Pym) = .
dAssumes 90 percent calf crop and calves sold as vealers weighing 35 kgs.
Also, cows are assumed to be replaced every 3 years and that 33 percent of 9Price of beef (Pyb) = $0.94 for calves and ($0.75 for cull cows
calf production is retained for replacement. Thus, 45 percent (heifer calves) Using data from footnote d 20 k?. calves x $0.94=$18.80 per
minus 33 percent=12 percent of potential heifer calves for sale. This, plus cow, plus 150 kg. of cows x $0.75=$112.50, for a total of
45 percent male calves, gives 57 percent for sale. Then, 35 kg. x 57 percent $131.30. The weighted average price is about $0.77.
= 20 kgs. of calf equivalents for sale per cow. For cull cow sales, assuming
cows weigh 455 kgs., then 33 percent of that is 150 kgs. for sale annually.
Total kgs. for sale is thus 170.




27
expenses are included, and $0.28 per kg. for all expenses. The net income per hectare above cash expenses is $406, while it is $291 above all expenses.
Dual Purpose Dairy Cattle
The method for evaluating the dual purpose operation is the same as for the purebred alternative. But, although more cows (83) are carried, total expenses (without in-barn supplemental feed) are lower on the dual purpose operation than the Holstein operation. This is largely because less supplemental feed is provided in the pasture. The "fixed" cost of $240 per cow is used in Table 7 to calculate the optimal level of supplement feed, which is 2.73 kilos per head per day for cows in lactation. Total cash cost for the whole operation with supplement feed is $39,274
which, subtracted from $70,011 gross income,.yields a net income above cash costs of $30,737. Net cash income above all expenses is $19,637. Cost per kg. of milk for cash costs only is, coincidentally, the same as for the Holstein operation, $0.23. Cost per kg. including all expenses is $0.30. Net income per hectare is $307 when only cash costs are included, and $196 when all costs are. covered.
An interesting phenomenon is revealed by the data with respect to
beef production. The examples show that less beef is produced per hectare than for the Holstein operation (88 kilos versus 122 kilos). This is because there are fewer cows sold, since the replacement rate is much lower. If, however, the offspring were fattened rather than being sold as vealers, then beef offtake would be higher than that shown but, of course, milk production would be much lower. The operation would then be a mixed milk-beef fattening situation as well, rather than just a dual purpose cattle dairy operation. In other words, care must be taken to




Table 7.--Example of calculating where MC=MR in determining how much supplement to feed dual purpose cows, Colombia, 1981a
Annual Daily Annual Supplement Annual Annual Annual Annual
Daily per milk milk beef variable fixed total revenue revenue Total Marginal Marginal
head ration Annual b produc- produc- produc- cost cost cost milk beef revenue Net cost revenue
of supplement supplement tion tionc tiond (VC)e (FC) (TC) (Rm) (Rb) (TR) income (MC) (MR)
Qx QYm QYb PxQx VC+FC Pyb+QYm yb+QYb Rm+Rb TR-TC ATC ATR
AQym AQym
--------------------------Kilos-------------------------- ---------------------------------------U.S. dollars---------------------------------------0.00 0 900 2.95 106 0 240 240 333 85 418 166
0.15 0.37
0.45 137 1,150 3.77 106 38 240 278 426 85 511 221
0.20 0.37
0.90 275 1,350 4.43 106 77 240 317 500 85 585 256
0.21 0.37
1.35 412 1,535 5.03 106 115 240 355 568 85 653 286
0.21 0.37
1.80 549 1,725 5.66 106 154 240 394 638 85 723 317
0.22 0.37
2.25 686 1,900 6.23 106 192 240 432 703 85 788 344
0.27 0.37
2.73 833 2,050 6.72 106 233 240 463 759 85 844 359
-.. ... ... .. ..- ... .. ... ..- ... .. ... ... .. ... ... .. ... ... ... .. ... ... .. .-- --- --- -- --- --- -- --- --- -- 0 .53 0 .37
3.20 976 2,125 6.97 106 273 240 513 786 85 871 346
0.60 0.37
3.65 1,113 2,190 7.18 106 312 240 552 810 85 895 331
0.80 0.37
4.10 1,251 2,240 7.34 106 350 240 592 829 85 914 308
3.70 0.37
4.55 1,388 2,250 7.38 106 389 240 629 833 85 918 277
aCosts are on a cost per head year basis. eprice of supplement (Px) = .
bCows fed only during 305 day lactation. fPrice of milk (Pym) = .
c305 day lactation.
dgPrice of beef (Pyb) = $50.94 for calves) & j$0.75 for cull cows dAssumed 90 percent calf crop and calves sold as vealers weighing 40 kgs. Using data from footnote d= $0.94 fork. calves x $0.94=$27.26 prcull cows
Also, cows are assumed to be replaced every 6 years and that 17 percent of Using data from footnote 29 g. a tlo=$27.26 per
calf production is retained for replacement. Thus, 45 percent (heifer calves) cow, plus 77 kg.of cows x $0.75=$57.75, for a total of $85.01.
minus 17 percent=28 percent of potential heifer calves for sale. This, plus The weighted average price s about $0.80
45 percent male calves, gives 73 percent for sale. Then, 40 kg.x 73 percent =29 kgs. of calf equivalents for sale per cow. For cull cow sales, assuming cows weigh 455 kgs.,then 17 percent of that is 77 kgs. for sale annually. Total kgs. for sale is thus 106.




29
carefully specify the assumptions about management and input/output relationships..
A BEEF COW-CALF OPERATION AS A LAST EXAMPLE
This example begins with the same 100 hectares as in the previous example. The stocking rate is one animal unit per hectare which means that the land has a capacity for 85 mature cows with a 90 percent calf crop and a 12 percent replacement rate. Thus, 27 heifer calves and 38 ma le calves can be sold annually (Table 1). With calves sold at 185 kilos, there is a production of 160 kg. per hectare (including cull animals).
Cash expenses amount to $8,990 while non-cash expenses add another $4,939 for a total of $13,929 (Table 4). The cash only cost per kg. of beef produced is $0.56, while it is $0.87 including all costs. Gross income is $14,384. Net income above cash costs is $5,394 while it is $455 above all expenses. There is a net return of $54 per hectare above cash costs and $5 above all expenses.
COMPARISON OF THE SYSTEMS
The highest total net income in the five alternatives is the purebred dairy operation where the entire operation nets $29,125 above all expenses. The lowest, under the assumptions specified and data for Colombia in mid1981,is the steer operation where $47 is netted above all expenses. It must be emphasized again that, while the input-output relationships were derived from survey data, the production and most costs are synthesized from a variety of sources. Furthermore, the operations in Colombia will vary considerably. Thus, no attempt is made to recommend any one operation, but rather to show the rithod for determining what type of system would be




30
best under given conditions. Simple budgeting is adequate here as an analytical tool since there are no constraints, such as labor or capital, placed on the operation which would make a combination of enterprises most profitable. In the next section this problem is dealt with.
LINEAR PROGRAMMING IN LIVESTOCK PRODUCTION ECONOMICS
In the previous example it was assumed that the optimal combination of the two inputs, i.e., supplemental feed (called X1) and pasture or roughage, which is called X2,, had been determined, and that the resulting production function only had one variable input, X1. But, there are many other combinations of inputs which likely could have been used. As might
well be imagined,.the arithmetic can quickly become tedious when an attempt is made to find an optimal solution to a problem involving two or more inputs in conjunction with two or more products. As a consequence, a quantitative method called linear programming was designed to handle this task. It was greatly popularized by Earl 0. Heady and Wilfred Candler in their 1958 book entitled Linear Programming Methods and has become one of the most utilized tools in agricultural economics as well as many other disciplines. It can be used with the budgets shown in Table 4, but is
not a substitute for budgeting.
An important aspect of linear programming, and the reason for its
name, is that the production functions (Figure 2) are assumed to be linear. In other words, in linear programming each of the inputs is utilized in fixed proportions, which means that output is determined by the limiting input. This is because, in linear programming (LP), one input cannot substitute for another one. For example,-in an LP problem, within one
activity, machinery cannot be used in place of labor but rather the two




31
are used in a fixed ratio to each other. The two could be interchanged between activities, such as hay or pasture.
Care must be taken to avoid confusing the production functions just described, which result from the expansion path of two or more inputs (Figure 1) and the production function described in Figure 2. In the latter function, all inputs are held constant except one which, if increased enough, would lead output to diminish. The combination called 'T', which is made up of X, and X2, constitutes the one input, for in linear programming all inputs increase at a fixed rate. Output would, of course, continue to expand to unreasonable extremes as a result of fixed input-output relationships, except for the restrictions on the amount of inputs available. These limitations are called constraints. The three parts of a linear programing problem are:
1) Define the constraints;
2) Develop the objective function, which is either maximization
or minimization of something; and
3) Set forth the alternative ways to achieve the objectives.
LP concepts may be considered by working through a simple maximization problem which is an expansion of the example presented ea rlier. It is assumed that the farmer-cattle raiser has the 100 hectares previously described, but can only access $10,000 in operating capital for cash expenses, and 200 hours of labor (the constraints) (Table 8). Also it is assumed that this person only wants to use the land for cattle, and that the options being considered are a cow/calf breeding herd, a dual purpose dairy operation or a combination of enterprises.
The objective is to determine the optimal amount of land for each
operation. In other words, once again, the concept of.the "what to produce" part of production economics has to be dealt with. The input costs, labor




32
Table 8.--Input and output specifications for linear programing example
Dairy,
Input dual
Input or output availability purpose Cow/calf
Beef production per hectare (kg.) a 88 160
Production cost per hectare ($) b 504 139
Milk production per hectare (kg.)a 1,702 --Price per kilo
Beef ($)c 0.80 0.90
Milk ($)c -- 0.37 -Labor
Available (hr.) 200 -- --Required (hr,/ha.) -- 10.0 1.4
Hectare constraint (ha.) 142
Operating capital
Available 10,000 -- -Required ($/ha,) -- 70 80
Hectare constraint (ha.) 143 125
a See Table 1.
b See Table 4.
c See Table 2.




33
and operating capital requirements for the enterprises are given in Table 8 along with the outputs and expected prices from the steer fattening and the cow-calf operations. It should be noted that, all of the specifications are the same as those presented in the earlier tables.
The problem can be solved geometrically by labeling hectares devoted to the dual purpose operation on the horizontal axis, and hectares in the cow/calf enterprise on the vertical axis (Panel A, Figure 6). The second step is plotting the three constraints. In Panel A, a point is marked at 100 hectares of land on both the vertical and horizontal axis, and a straight line drawn between them. This line reveals all possible combinations in land use between each enterprise. The cattleman could use less than 100 hectares since land is not the only restriction, but the maximum is 100 hectares.
The next step is adding the labor constraint to Panel B, which already has the land constraint drawn in. A maximum of 200 hours of labor is available which means only 20 hectares could be devoted to the dual purpose operation. Since only 1.4 hours per hectare are needed for the cow/calf enterprise, 142 hectares could potentially be handled. As with the 1
constraint, the two points are plotted on the vertical and horizontal axis, and a straight line drawn between them. This line shows all possible combinations of dual purpose and cow/calf operation that can be produced with only 200 hours of labor.
After labor, the capital constraint is added in. Calculations indicate that the $10,000 of available operating capital would permit use of 125 hectares ($10,000 L $80/ha.) in a cow/calf operation. Utilizing all the capital for a dual purpose operation would permit 143 hectares ($10,000 1 $70/ha.) to be utilized if that much land were available.




34
150- 150125- 12500 Labor
100- 1000
S 75- Land E 7544)) Land
J 50 5025- 25-I
I
0- 025 50 75 100 125 150 25 50 75 100 125 150
Hectares dual purpose Hectares dual purpose
Panel A Panel B
150- 150I
125-%" 125- Labor A
Land
100- n 100Land
75- / 75" 1
4-) Capital u. --Labor
50- 50
11
25N 25
C
0- 0, ~I I I I
25 50 75 100 125 150 25 50 75 100 125 150
Hectares dual purpose Hectares dual purpose
Panel C Panel D
Figure 6.--Determination of corner solutions, linear programming example




35
Each of these points are plotted on the appropriate axis in Panel C to which the land and labor constraints have previously been drawn in. The line is outside the land and capital lines which means that capital is not a constraint in either one of the operations.
Now that all of the constraints have been properly plotted, the profit maximization combination can be identified. The optimal level will always be located at a "corner" where the inside constraint lines intersect, or where the inside constraint lines cross the axis. These points are given the labels 0, A, B and C in Panel D which has been redrawn from Panel C. Land and labor are the two effective constraints. The optimal production combination will never fall on the straight line segment of the restriction lines. 2
One way to determine the most profitable "corner" is to calculate the income and cost at each corner. This has been done in Table 9. In corner 0, which is the intersection of the breeding and dual purpose axes, there is no production and consequently no net income. Corner "A", which is constrained by land at 100 ha., has all resources used in the cow/calf operation. The 100 hectares given in this activity solution are multiplied by the originally specified 160 kilos of live beef production per ha. which, at $0.80 per kilo, provides a gross income of $14,400. The operating cost of $139 per ha. results in $13,900 for the 100 hectares, or a total net income of $500 for the entire operation. The net income of $5 per hectare ($500 divided by 100 hectares) is the same as shown in Table 4 in the simple budgeting example. The gross income and total costs are slightly different than the ones in the table due to rounding errors
2 This is not exactly correct since there can be a case where the
optimal solution is, in this case, either B or C indeterminatet solution) when any points on the line between B and C would be optimal. However, L.P. alaorithms will always find the corner solutions.




Table 9.--Calculatlon of net returns from various corner solutions, linear programming example
Cow/calf Dual purpose
Operating Prod. per ha. Operating Price per kilo
Prod. cost Price Enterprise cost Enterprise Total both
Item Land per ha. per ha. per kilo total Land Beef Milk per ha. Beef Milk total enterprise
--Ha.-- --Kgs.-- -------------Dollars -------------- --Ha.------- Kgs. ---- -------------------- Dollars ---------------------Corner A
Income 100.0 160 --- 0.90 14,400 0 0 0 0 0 0 0 --Cost 100.0 --- 139 -- 13,900 0 0 0 0 0 0 0 --Net 100.0 --- --- 500 0 0 0 0 0 0 0 500 C
Corner B
Income 92.5 160 --- 0.90 13,320 7.5 88 1,702 --- 0.30 0.37 5,251 -Cost 92.5 --- 139 -- 12,858 7.5 -- -- 504 -- -- 3,780 -Net 92.5 --- --- 462 7.5 .. ......... 1,471 1,933
Corner C
Income 0 0 0 0 0 20.0 88 1,702 --- 0.80 0.37 14,003 -Cost 0 0 0 0 0 20.0 -- -- 504 -- -- 10,080 -Net 0 0 0 0 20.0 .. ......... 3,923 3,923




37
in the input and output specifications.
Corner "B" is the intersection of the land and labor constraints.
The optimum for the breeding herd is 92.5 hectares with 7.5 for the dual purpose enterprise. A net income of $462 and $1,471 are derived from the two operations respectively, for a total net income of $1,933. Corner "C", in which the only enterprise is dual purpose cattle, provides a net income of $3,923 even though only 20 hectares can be utilized given the constraints. The net return per hectare in Table 4 is $196 per hectare.
Multiplying this times 20 hectares is $3,920, i.e., the same as the L.P. example with allowance for rounding errors. The conclusion is that the operator would be best off with only 20 hectares of dual purpose cattle, leaving the rest of the land idle. The constraints are quite realistic in that part of the labor constraints could be considered the operator himself.
The optimal solution provides the answers to the three production questions "what," "how" and "how much" to produce. The "what" analysis indicates that strictly a dual purpose operation, even though all land is not used, would maximize income. "How" refers to the inputs, 20 ha.
of land, 200 hours of labor and the optimal amount of supplement calculated in Table 7. The analysis shows that some land and capital would be left over so that, if the operator had correctly specified the production function relationships, then 80 hectares and $8,600 in operating capital could be invested in other activities. In other words, the analysis not only provides an answer to the three questions, but also provides information which can be used for planning related operations.
The linear programming example just provided demonstrates the use for a production level decision problem. Naturally, most L.P. problems




38
have many more activities and are thus solved with computers rather than by hand. In addition to the maximization type problem, a common use of L.P. is in least cost cattle ration formulation and minimization of transportation cost in transportation problems. Also, L.P. has been extended to regional and national problems for whole sectors.
SUMMARY AND CONCLUSIONS
The purpose of this report has been to explain the method for determining the optimal cattle enterprise on a given amount of land. It was shown that three questions must be answered: how to produce, how much to produce and what to produce. Information on the first two are a requisite for answering the third question.
Simple budgeting was used to arrive at the highest profit operation when there was one constraint, land. This technique is a component part of linear programing, but is-not a substitute for it. A graphical analysis using linear programming was shown as a means to arrive at the optimal combination of resources.when there are:two or more constraints, but it is apparent that a computer is needed with more than just a few entries as the calculations soon become tedious.
Most of the data in this report were gathered from a survey conducted in ear ly 1981. The examples, for Colombia, show that a purebred Holstein
operation would be the highest profit enterprise under current conditions but, of course, a relatively high management level is required. A dual purpose dairy operation with no fattening of calves was indicated as the second best alternative. The analysis also showed that a cow/calf operation was only marginally profitable and that steer finishing is not practical either with or without supplement feed when interest on purchased cattle, or opportunity cost on owned cattle is taken into account. Naturally,




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there will be wide variations in net returns depending on the location in the country, and regional differences in input costs and output prices. This analysis is for a semi-tropical area.
Perhaps the most important point in this report is an explanation of the need to evaluate the component parts of "net return," and the importance of carefully specifying management level, input use and outputs. As a result, it becomes clear that cost per kilo produced, cost per hectare, output per cow and so forth are important concepts, but can be very misleading when attempting to determine "what to produce."




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REFERENCES
Calo, L.L., et al. 1973. "Simultaneous Selection for Milk and Beef
Production Among Holstein-Friesians," Journal of Dairy Science 56:8,
pp. 1080-1084.
de Alba, Jorge. 1978. "Progress in the Selection of the Latin American
Dairy Criollo," World Animal Review 28, pp. 26-30.
Doll, John P. and Frank Orazem. 1978. Production Economics: Theory with
Applications. Columbus, Ohio: Grid, Inc.
Frisch, J.E. and J.E. Vercoe. 1978. "Utilizing Breed Differences in
Growth of Cattle in the Tropics," World Animal Review 25, pp. 8-12.
Heady, Earl 0. and Wilfred Candler. 1958. Linear Programming Methods.
Ames: Iowa State University Press.
Martin, Lee R. (Ed.). 1977. A Survey of Agricultural Economics Literature,
Vol. 2, Quantitative [sic] Methods in Agricultural Economics 1940s
to 1970s. St. Paul: University of Minnesota Press.
Simpson, James R. 1979. "Determining Optimal Types of Cattle for Tropical
and Subtropical Dairy Operations," Proceedings, Fourteenth Annual Meeting on Livestock and Poultry in Latin America, University of
Florida (May).