• TABLE OF CONTENTS
HIDE
 Title Page
 Abstract
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Basic economic decisions
 The "how' and "how much" to produce...
 Finishing steers: An alternati...
 Purebred and dual purpose dairy...
 A beef cow-calf operation as a...
 Comparison of the systems
 Linear programming in livestock...
 Summary and conclusions
 Reference






Title: Method and theory for determining optimal types of cattle for tropical and subtropical livestock enterprises
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Permanent Link: http://ufdc.ufl.edu/UF00054788/00001
 Material Information
Title: Method and theory for determining optimal types of cattle for tropical and subtropical livestock enterprises
Physical Description: Book
Language: English
Creator: Simpson, James R.
Affiliation: University of Florida -- Department of Food and Resource Economics -- Institiute of Food and Agricultural Sciences
Publisher: Department of Food and Resource Economics, Institute of Food and Agricultural Sciences, University of Florida
Publication Date: 1982
 Subjects
Subject: Farming   ( lcsh )
Agriculture   ( lcsh )
Farm life   ( lcsh )
South America   ( lcsh )
University of Florida.   ( lcsh )
Spatial Coverage: South America
North America -- United States of America -- Florida
 Notes
Funding: Electronic resources created as part of a prototype UF Institutional Repository and Faculty Papers project by the University of Florida.
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Bibliographic ID: UF00054788
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 15030465

Table of Contents
    Title Page
        Title Page
    Abstract
        Page i
    Table of Contents
        Page ii
    List of Tables
        Page iii
    List of Figures
        Page iv
    Introduction
        Page 1
    Basic economic decisions
        Page 2
    The "how' and "how much" to produce decisions: Some theory
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
    Finishing steers: An alternative
        Page 10
        Page 11
        Page 12
        No supplement feeding
            Page 13
            Page 14
            Page 15
            Page 16
            Page 17
            Page 18
            Page 19
        With supplemental feeding
            Page 20
            Page 21
            Page 22
            Page 23
    Purebred and dual purpose dairy cattle: A second alternative
        Page 24
        Purebred dairy cattle
            Page 24
            Page 25
            Page 26
        Dual purpose dairy cattle
            Page 27
            Page 28
    A beef cow-calf operation as a last example
        Page 29
    Comparison of the systems
        Page 29
    Linear programming in livestock production economics
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
    Summary and conclusions
        Page 38
        Page 39
    Reference
        Page 40
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 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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