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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 situa-
tion. 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 dual
purpose 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 . . . . ... . . iii
LIST OF FIGURES. . . . . ... . .. iv
INTRODUCTION . . . . ... . ... 1
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. . . . . .. .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
ii
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 programming
example. . . . . ... ....... 34
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 sub-
tropical 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.
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 ana-
lytical 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 informa-
tion 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 eco-
nomic and management considerations. This is the "how much to produce"
decision. Finally, the latter information is compared to determine
"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 XI) 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 Y1a, Yib, Y1c in the figure. The lowest output is Yia 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 iso-
cost lines is economically the most efficient (least-cost) combination of
+ \\-- Line of least cost
Isoquant (outputs)
Y1 c
Yib
Yia
SIsocost curve (costs)
Input X2
Figure 1.--Example of the production economic decision
about how to produce
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
pointI are 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 Xi and X2 in the formula
Y1 =f(Xi X2...X ) means that all inputs other than the supplement (X1)
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 (XI) is divided by the price of the output (P ). In
effect, it is x The slope of the line is determined by the relation
y
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
Where X_ PX2
X2 P 1
Optimum
output
/
Maximum (C)
Yi= f (X11X2 ...Xn)
Input (X1)
Figure 2.--Example of the production economic decision
how much to produce
Tangency
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,eventhough the economically opti-
mal production level can be determined, in practice this entrepreneurial
management objective is seldom achieved as there are usually some inter-
personal, 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 pro-
duction, 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 pro-
duction 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.
The third of the three decisions, "what to produce," is decided upon
after sufficient knowledge is obtained about the relevant production func-
tions. Some production functions of interest to cattlemen are relation-
ships 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 enter-
prises. 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 use which, 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,
Isorevenue or
isoprice lines
1 Isoresource or
production pos-
Ri R2 Ci sibility curves
Output (Y2)
Figure 3.--Example of the production economic decision
,hpw -much to produce
/. /
r/'y/
such as milk or fed steers, could be produced. The location of Ci 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 expan-
sion 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 (Cl 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
operations: 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 responses 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 l.--Inventory, animals marketed and production measures for typical 100 animal unit steer, dairy and cow/calf
operations in Colombia, 1981a
Steersb 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
Heifers No. -- -- 25 15 11
3-4 yr. old steers No. -
2 yr. old steers or bulls No. 99 99
Yearling steers or bulls No. -- -- 1 1 1
Bulls No. -- -- 3 3 3
Horses No. 1 1 -- 1
Total animals No. 100 100 101 101 101
Number of animals marketed annually
Cows No. -- -- 24 12 10
Heifer calves No. -- -- 8 20 27
Steer or bull calves No. -- -- 32 32 38
Bulls No. -- -- 1 1 1
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 1 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 16,0254
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
shows it to be uneconomic. The data shown are the inputs for the proposed management plan.
analysis of the 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
Commodity & 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
Dominican 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.
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
1981 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
Beef/supplement -
Milk/supplement --z
= Honduras
= Costa Rica
= Colombia
= Panama
= Ecuador
= Venezuela
= Dominican Republic
I I
CR C
- I I I
I I I I
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 -- 12,220, 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
Insurance -- ---
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, without 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, l98l--continiued
Steersa
No With
Item suDolement suonlement
Dairy
Dual
Purebred nuronose
Gross income
Beef
Milk
Total
Net income above cash expenses
Beef
Milk
Total
-------------------------U.S. dollars--------------------------
36,485b
36,485
9,4541
81,119m
90,573
40,575
2,544
2,544
7,055
62,956
70,011
30,737
14,384
14,384
5,394
5,394
Net income above all expenses
Beef
Milk
Total
Cost, cash only, per head per day (steers) or
per cow per year (others)
No supplemental feed
Beef
Milk
With supplemental feed
Beef
Milk
Cost, all expenses, per head per day (steers) or
per cow per year (others)
No supplemental feed
Beef
Milk
With supplemental feed
Beef
Milk
29,125 19,637
694 473
853n
See page 19 for footnotes. Continued
Beef,
cnw/calf
Table 4.-- Computation of annual costs for 100 animal
unit steer, dairy and cow/calf operations in Colombia, 1981--continued
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
Steers Dairy
No With Dual Beef
Item supplement supplement Purebred purpose cow/calf
Cost, cash on----------------------------------------U.S. dollars----- ---------------
Cost, cash only per kilo U ol
No supplemental feed
Beef 0.79 -- -- 0.56
Milk -- --
With supplemental feed
Beef --- --
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
Cost, cash only, per hectare
No supplemental feed
Beef 24 --- --- 90
Milk -- 275 199 --
With supplemental feed
Beef -- 500 393
M4kI -- -- --
Cost, all expenses, per hectare
No supplemental feed
Beef
Milk
With supplemental feed
Beef
Milk
Income per hectare
Gross
Net
Above cash costs
Above all expenses
See page 19 for footnotes.
50 ---
-- 390 310
-- -- 614 504
364.85 906 700
25 406 307
0 -- 291 196
139
144
54
5
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.
g Cash expenses ($2,955) divided by 98 = $34.15 per steer divided by 210 days = $0.14.
hNo 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.
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 sup-
plemental feeding is profitable, and the optimal amount of feed.
With Supplemental Feeding
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 pro-
duce 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)
Q Q AQ P .MPP PxQx VC+ FC P .Qy TR-.TC ATC ATR
SAQy AQ
---------- Kilos ---------- ------------- -- ---------------U.S. dlars---------------------------------
10.-00 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
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 -1.49
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) = $0.28per kilo .
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 kilo liveweight.
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 supple-
ment 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 supple-
ment), MVP is declining, thus indicating an uneconomic level. The rela-
tionship 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 con-
stant 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 (Q ). 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 sup-
plement is fed, the additional gain does not cover feed costs, and there
is a loss of $0.77 per head per day.
With supplement
Pasture only
/
Supplement (kgs.)
Figure 5.--Beef production per head, with and without supplement,
example problem for steers, Colombia, 1981
1.75 -
1.50-
1.25-
1.00-
0.75
0.50-
0.25-
0-
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 con-
clusion, as with the previous method, is that supplement feeding in un-
economic. 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 should not be
practiced with the input-output relationships given. As such, computa-
tions 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 manage-
ment 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 pro-
ducing 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
in Table 1. The major constraining factor in this alternative, as in all
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 con-
clusion, as with the previous method, is that supplement feeding in un-
economic. 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 should not be
practiced with the input-output relationships given. As such, computa-
tions 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 manage-
ment 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 pro-
ducing 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
in Table 1. The major constraining factor in this alternative, as in all
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 percent death 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. Cal-
culations 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 sup-
plement 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, it is multiplied
by a 305 day lactation to arrive at 1,113 kilos per cow annually. Multi-
plying 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 vealers 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 total Annual Marginal Marginal
head ration Annual prdduc- produc- produc- cost cost cost milk beef revenue net cost revenue
of supplement supplement tion tionc tion d (VC)e (FC) (TC) (Rm) (Rb) (TR) Income (MC) (MR)
Qx QYm Qyb Px.Qx VC+FC Pyb+y Pb+Q b R+Rb TR-TC ATC ATR
AQYm m
---------------------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.
bcows only fed during 305 day lactation.
c305 day lactation.
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
calf production is retained for replacement. Thus, 45 percent (heifer calves)
minus 33 percent=12 percent of potential heifer calves for sale. This, plus
45 percent male calves, gives 57 percent for sale. Then, 35 kg. x 57 percent
= 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.
price of supplement (Px) = F$0.281.
x
fPrice of milk (Pym) 0.37
gPrice of beef (Pyb) = J$0.94 for calves and ($0.75 for cull cows.
Using data from footnote d, 20 kq. calves x $0.94=$18.80 per
cow, plus 150 kg. of cows x $0.75=$112.50, for a total of
$131.30. The weighted average price is about $0.77.
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 ex-
penses.
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 supple-
ment 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 in-
cluded, 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) (R ) (Rb) (TR) income (MC) (MR)
Q, Qym QYb P,.xQ VC+FC Pyb+m Pb+Qb 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.
bCows fed only during 305 day lactation.
c305 day lactation.
Assumed 90 percent calf crop and calves sold as vealers weighing 40 kgs.
Also, cows are assumed to be replaced every 6 years and that 17 percent of
calf production is retained for replacement. Thus, 45 percent (heifer calves)
minus 17 percent=28 percent of potential heifer calves for sale. This, plus
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.
price of supplement (P) = 0.28
fPrice of milk (Pym) = $0.37
gPrice of beef (Pyb) = J$0.94 for calves & j$0.75 for cull cows.
Using data from footnote d, 29 kg. calves x $0.94=$27.26 per
cow, plus 77 kg.of cows x $0.75=$57.75, for a total of $85.01.
The weighted average price is about $0.80
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
male 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 mid-
1981,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 method for determining what type of system would be
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
male 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 mid-
1981,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 method for determining what type of system would be
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 XI) and pasture or
roughage, which is called X2, had been determined, and that the resulting
production function only had one variable input, XI. 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
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 in-
creased enough, would lead output to diminish. The combination called
"X", which is made up of XI 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 programming 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 earlier. It is
assumed that the farmer-cattle raiser has the 100 hectares previously
described, but can only access $10,000 in operating capital for cash expenses,
and 200 hours of labor (the constraints) (Table 8). Also it is assumed that
this person only wants to use the land for cattle, and that the options
being considered are a cow/calf breeding herd, a dual purpose dairy opera-
tion or a combination of enterprises.
The objective is to determine the optimal amount of land for each
operation. In other words, once again, the concept of the "what to produce"
part of production economics has to be dealt with. The input costs, labor
Table 8.--Input and output specifications for linear programming example
Dairy,
Input dual
Input or output availability purpose Cow/calf
Beef production per hectare (kg.) a -- 88 160
Production cost per hectare ($) -- 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.) -- 0 142
Operating capital
Available 10,000 --
Required ($/ha,) -- 70 80
Hectare constraint (ha.) 143 125
a See Table 1.
bSee Table 4.
c See Table 2.
c See Table 2.
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 com-
binations 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 com-
binations 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 in-
dicate 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.
Labor
Land
25 50 75 100 125 150 25 50 75 100 125
Hectares dual purpose Hectares dual purpose
Panel A Panel B
150-
S125-
(
o
u
0 100
Land
S 75
'\ Capital 7
*-. ^< *s
25 50 75 100 125 150
Hectares dual purpose
Panel C
A
6/> Land
-B
I
Labor
C
1 I I I I I I
25 50 75 100 125 150
Hectares dual purpose
Panel D
Figure 6.--Determination of corner solutions, linear programming example
Land
150
150
125
4-
(0
U.
75 100
o
- 75
4-,
U
cI
Labor
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 re-
drawn 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 multi-
plied 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
2This is not exactly correct since there can be a case where the
optimal solution is, in this case, either B or C (indeterminant solution)
when any points on the line between B and C would be optimal. However,
I.P. alaorithms will always find the corner solutions.
Table 9.--Calculation of net returns from various corner solutions, linear programming example
Cow/calf
Operating
cost Price Enterprise
per ha. per kilo total
--------------Dollars--------------
C(
0.90
0.90
Land
--Ha.--
rner A
Dual
Prod. per ha.
Beef Milk
---- Kgs. ----
14,400
13,900
500
Corner B
13,320
12,858
462
Corner C
20.0
20.0
20.0
1,702
1,702
purpose
Operating Price per kilo
Operation Price per kilo Enterprise Total both
per ha. Beef Milk total enterprise
------------------ -Dollars------------------
0.30 0.37 5,251
-- -- 3,780
-- -- 1,471
0.80 0.37 14,003
-- -- 10,080
3,923
1,933
3,923
Prod.
per ha.
--Kgs.--
160
Land
--Ha.--
100.0
100.0
100.0
Income
Cost
Net
Income
Cost
Net
Income
Cost
Net
92.5
92.5
92.5
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 func-
tion 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
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 trans-
portation 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 deter-
mining 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 programming, 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 early 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 opera-
tion 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,
39
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 mis-
leading when attempting to determine "what to produce."
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).
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