Farm management under uncertainty

Material Information

Farm management under uncertainty implications for beef cattle production
Added title page title:
Beef cattle production
Zimet, David J., 1948-
Publication Date:
Physical Description:
x, 137 leaves : ill. ; 28 cm.


Subjects / Keywords:
Agricultural land ( jstor )
Beef ( jstor )
Calves ( jstor )
Crops ( jstor )
Farms ( jstor )
Herds ( jstor )
Pastures ( jstor )
Soybeans ( jstor )
Stocker cattle ( jstor )
Watermelons ( jstor )
Beef cattle -- Economic aspects -- Florida ( lcsh )
Farm management -- Florida ( lcsh )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Thesis (Ph. D.)--University of Florida, 1985.
Includes bibliographical references (leaves 133-136).
General Note:
General Note:
Statement of Responsibility:
by David Zimet.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000555130 ( ALEPH )
ACY0007 ( NOTIS )
13720749 ( OCLC )

Full Text







This dissertation is dedicated

to my children,

Zacharia and Nathanial,

my wife, Ann,

and to the future.


I would like to thank all those who helped me conduct the

research and prepare this document. Prominent among this group are my

committee members, Mr. Jim Pheasant and Mr. Larry Halsey as well as

the rest of the Jefferson County Cooperative Extension Service staff.

I would also like to express my appreciation to Mrs. Pat French who

typed this document and edited it in light of the dictates of the

Graduate School. I am pleased to acknowledge the monetary support

given this research effort by the National Science Foundation (grant

BNF 821-8894) and the State of Florida. Lastly, but most importantly,

I would like to thank the agricultural producers of Jefferson County

who taught me so much and had patience while so doing.



ACKNOWLEDGMENTS.................................................. iii

LIST OF TABLES ................................................... vi

LIST OF FIGURES.................................................. ix

ABSTRACT......................................................... x

CHAPTER I INTRODUCTION........................................ 1

Beef Production in the Southeastern United States... 1
Beef Cattle Production in Jefferson County, Florida. 2
Review of Previous Studies.......................... 5
Accounting and Cost Considerations.................. 7
Decision Making and Methods of Analysis............. 9
Stochastic Dominance................................ 9
Mathematical Programming............................ 11
Quadratic Programming, MOTAD, and Risk........... 12
Target MOTAD..................................... 14
Hierarchical Decision Models........................ 15
Problem Statement................................... 16
Objectives .......................................... 17
Procedure........................................... 18


Previous Studies.................................... 21
An Application of MOTAD to a Beef Production
Problem .......................................... 27

MODELS .............................................. 30

Hierarchical Decision Models........................ 32
The Development of Decision Trees................... 33
Decision Trees for Beef Producers in Jefferson
County ........................................... 34
The Decision to Grow Cash Crops and the Decision
to Have a Beef Cattle Operation............... 39
The Cow-Calf Versus Stocker Decision............. 41


Limitations of Hierarchical Decision Models.........
Hierarchical Decision Models and Mathematical
Programming Models...............................
Mathematical Programming Model Specifications
and Hierarchical Decision Models..............

MODEL SPECIFICATION.................................

Activities and Budgets..................
Commercial Crops and Forages.........
Beef Cattle Enterprises..............
The Constraints .........................
Technical Constraints................
Non-Technical Constraints............





RESULTS AND ANALYSIS ................................

Results and Analysis: Unconstrained Watermelon
Annual Income Levels and Commodities.............
Peanut and Watermelon Acreage....................
Resource Use .....................................
Results and Analysis: Constrained Watermelon
Annual Income and Commodity Production...........
Peanut and Watermelon Acreage....................
Resource Use.....................................
Income Targets and Variation........................
The Unconstrained Model and Target Income
Variation .....................................
The Constrained Model and Target Income
Variation .....................................
Summary of Results ..................................

SUMMARY AND CONCLUSIONS .............................

Summary .............................................
Conclusions ........................................
Limitations of the Present Study and
Recommendations for Future Research..............

DECISION TREES ......................................


LITERATURE CITED .................................................

BIOGRAPHICAL SKETCH..............................................









1.1 Number of steers, steer calves, bulls and bull calves
in the Florida panhandle............................... 3

1.2 A comparison of cow herd and stocker herd sizes from
various studies and sources............................ 6

2.1 Relative feeder-calf prices used in other studies...... 24

4.1 Prices used to calculate returns....................... 51

4.2 Yields used to calculate returns....................... 52

4.3 Deflated gross return, cost, and net return per acre:
Dryland corn........................................... 53

4.4 Deflated gross return, cost, and net return per acre:
Irrigated corn......................................... 54

4.5 Deflated gross return, cost, and net return per acre:
Peanuts ................................................ 55

4.6 Deflated gross return, cost, and net return per acre:
Dryland soybeans....................................... 56

4.7 Deflated gross return, cost, and net return per acre:
Irrigated soybeans ..................................... 57

4.8 Deflated gross return, cost, and net return per acre:
Watermelon............................................. 58

4.9 Deflated gross return, cost, and net return per acre:
Wheat.................................................. 59

4.10 Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 350 pound calf in April/May........ 61

4.11 Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 450 pound calf in May/June......... 62

4.12 Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 450 pound calf in October/November. 63


4.13 Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 350 pound calf in September/October 64

4.14 Initial and final weights, beginning months, number of
months and stocking rates of specified post-weaning
programs ............................................... 67

4.15 Final weights and average (1973-1983) deflated gross
returns, costs and net returns per head of principal
beef enterprises....................................... 68

4.16 Available acreage by land type......................... 72

4.17 Monthly labor availability ............................. 74

4.18 Annual production loan funds available................. 75

5.1 Net return, product mix and level of negative deviation
from income targets for both models.................... 81

5.2 Annual levels of expected net return and levels of
total negative deviations from annual income targets
for both models ........................................ 82

5.3 High and low use of borrowed capital, labor, irrigated
land, and dry crop land by level of deviation of net
return for both models................................. 85

5.4 Opportunity cost/marginal values per acre of the peanut
quota, constrained watermelon acreage, and fenced crop
land by level of deviation of expected net return for
both models ............................................ 87

5.5 Review of recent producer action....................... 93

5.6 Degree negative deviation from target incomes low and
high targets attained with corresponding net returns... 98

5.7 Degree of negative deviation from target incomes,
income-targets, and optimum product mix for the
unconstrained model.................................... 100

5.8 Degree of negative deviation from target incomes,
income-targets, and optimum mix for the constrained
model .................................................. 102


B.1 Costs per acre of producing a rye-ryegrass pasture..... 115

B.2 Costs per acre of producing a bahiagrass-clover pasture 116

B.3 Costs per head of overwintering a 350 pound spring
farm-raised calf to 670 pounds at a 1.5 stocking rate.. 117

B.4 Costs per head of backgrounding a 450 pound fall farm-
raised calf to 796 pounds.............................. 118

B.5 Costs per head of overwintering a 350 pound spring
farm-raised calf to 642 pounds at a 2.0 stocking rate.. 119

B.6 Costs per head of backgrounding a 350 pound farm-
raised fall calf to 746 pounds ......................... 120

B.7 Costs per head of backgrounding a 450 pound farm-
raised fall calf to 856 pounds......................... 121

B.8 Costs per head of conditioning a 350 pound farm-raised
fall calf to 515 pounds................................ 122

B.9 Costs per head of conditioning a 450 pound farm-raised
fall calf to 510 pounds................................ 123

B.10 Costs per head of overwintering a 400 pound purchased
calf to 658 pounds..................................... 124

B.11 Costs per head of producing a 450 pound fall calf...... 125

B.12 Costs per head of producing a 350 pound fall calf...... 127

B.13 Costs per head of producing a 450 pound spring calf.... 129

B.14 Costs per head of producing a 350 pound spring calf.... 131




1.1 Map of north Florida counties........................... 4

3.1 The decision to produce cash row crops.................. 35

3.2 The land use decision for land not in commercial row
crop production......................................... 37

3.3 The decision to operate a stocker or a cow-calf
operation ............................................... 38

5.1 Income target limits obtained for specific levels of x,
unconstrained model..................................... 95

5.2 Income target limits obtained for specific levels of X,
constrained model....................................... 97

A.1 The decision to impose controlled breeding.............. 113

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy




December 1985

Chairman: Thomas H. Spreen
Major Department: Food and Resource Economics

An analysis of a typical crop and livestock farm in North Florida

is presented. The analysis incorporated the potential competition and

complementarity among crop and beef cattle enterprises. A Target

MOTAD model was developed to account for risk in the decision

framework. Hierarchical decision models were used to support and/or

specify the MOTAD model specification.

The results indicated that when income risk was ignored peanuts,

watermelon, and stocker cattle were the only enterprises included in

the optimal solution. When income risk was heavily weighed, the

optimal solution included peanuts, watermelon, stocker cattle, cow-

calf, and irrigated soybeans. The results suggested that the

persistence of cow-calf production may be explained as a stabilizer of



Beef Production in the Southeastern United States

Beef production is economically important to the Southeast region

of the United States and is widespread throughout that region of the

country. According to the 1978 Census of Agriculture, only one county

in the states of Alabama, Florida, Georgia, Mississippi, North

Carolina and South Carolina had no beef cattle. The same information

held true for the 1982 Census of Agriculture. Despite this situation

recent analyses have demonstrated that beef production is unprofitable

(Carpenter et al., 1979; Schupp et al., 1979, Wise and Saunders,

1977). One group of authors (Musser et al., 1975) stated that beef

production in the Georgia Piedmont could only be explained in terms of

utility maximization rather than income maximization or other

financial well-being. A similar situation has also been described in

Arizona (Smith and Martin, 1972). The purpose of this dissertation is

to determine whether the same is true for Florida, and if so, to try

to determine why beef cattle are produced in North Florida.

There are several stages to beef production in the United States.

The first stage is the cow-calf operation. In this phase a brood cow

produces a weaned calf. Weaning occurs at various ages (Three to nine

months) and various weights (350 pounds to 700 pounds) depending upon

cow and calf management practices and geographic location. Sometimes

the weanling calf then goes through a conditioning stage in

preparation for the second major stage, backgrounding. Usually, the

calf directly enters into the backgrounding program. A calf in a

backgrounding program is called a stocker calf. Backgrounding is a

forage-based feeding system. Next the feeder calf is finished,

usually on grain-based rations in a feedlot, and then slaughtered.

There is a degree of geographic specialization in the beef

subsector. Generally, the Southeast produces calves and backgrounding

and finishing occur in the northern and southern Plains states.

Florida is not an exception to this pattern.

Beef Cattle Production in Jefferson County, Florida

On January 1, 1984, Florida had an estimated 1,220,000 beef cows

(Florida Crop and Livestock Reporting Service, 1984), a number

exceeded by only eight states. During 1983, approximately 1,100,000

calves (including dairy) were born in Florida (Florida Crop and

Livestock Reporting Service, 1984). Of these, approximately 231,000

were kept as cow replacements; 465,000 weighed less than 500 pounds

and were still in the state; only 91,000 (about 8%) weighed over 500

pounds and were still in Florida. Thus, as in the rest of the

Southeast, cow-calf operations predominate other beef cattle

enterprises in Florida.

Of the total of 391,066 (Table 1.1) steers, steer calves, bulls

and bull calves that were reported for Florida in the 1978 census of

agriculture (U.S. Department of Commerce, 1980), 71,000 were reported

in the 22 county area stretching from Dixie, Lafayette, Suwannee and

Hamilton Counties in the east to Escambia County in the west (Figure

Table 1.1.

Number of steers, steer calves, bulls and bull calves
in the Florida panhandle

Steers, Steer Calves Percent of
County Rank Bulls and Bull Calves Panhandle


Jackson 1 10,912 15.3
Jefferson 2 10,354 14.6
Suwannee 3 8,017 11.3
Madison 4 5,973 8.4
Walton 5 5,173 7.3
Gadsden 6 4,719 6.6
Holmes 7 4,652 6.5
Leon 8 2,996 4.2
Washington 9 2,971 4.2
Okaloosa 10 2,528 3.6
Santa Rosa 11 2,203 3.1
Escambia 12 2,047 2.9
LaFayette 13 1,962 2.8
Hamilton 14 1,860 2.6
Taylor 15 1,205 1.7
Calhoun 16 1,198 1.7
Dixie 17 877 1.2
Gulf 18 601 0.8
Wakalla 19 386 0.5
Liberty 20 316 0.4
Bay 21 150 0.2

Source: U.S. Department of Commerce, 1978 Census of Agriculture.

Figure 1.1. Map of north Florida counties.

1.1). (Franklin County data are not specified and are therefore

excluded from the total.) Of the animals in the Panhandle, 10,354

(almost 15%) were reported for Jefferson County (the focus of the

present study), ranking it second in the Panhandle to Jackson County.

Another way to rate the importance of backgrounding in Jefferson

County is to compare the "steers, etc." category to the total number

of cattle and calves in the county. A total of 24,760 (including

dairy) head were reported for the county in the 1978 census. That is,

steers, etc. were 41.8% of the total cattle population in 1978. In

dollar terms, sales of $5,892,000, were reported for cattle and

calves, of which 59.2% was for cattle. Logically, the vast majority

of these sales would have had to be from steer sales. (For example,

in the Waukeenah Board Sale of May, 1983, 1,266 steers were sold.)

Total cattle and calves sales were approximately 34.4% of the total

farm sales.

Review of Previous Studies

Because of the economic importance and widespread geographic

distribution of beef production in the South, it has been analyzed in

the context of the general farm as well as in an isolated setting.

Compared to Census of Agriculture data (Table 1.2), studies based upon

optimizing models (Allison and Bell, 1978; Johnson et al., 1979; Wise

and Saunders, 1977) indicate that the various phases of beef

production are more widespread geographically in the Southeast than is

considered to be optimum. This is especially true for the

backgrounding of stocker calves. The stocker calf herds are much


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demonstrate they ought to be.

Accounting and Cost Considerations

Beef production in Florida persists even though it can be

characterized as group of low profit enterprises (Allison, 1981).

Studies conducted in Florida and neighboring states (Georgia

Cooperative Extension Service, 1982; Ross et al., 1983; Simpson et

al., 1982; Kunkle et al., 1984) have demonstrated losses in cow-calf

and stocker operations. In comparison it was found in a recent study

(Zimet et al., 1984) that producers in Jefferson County, Florida,

believe that they generally break even and that they earn a profit

once every three to five years. This finding implies that, at least

from the point of view of the producer, the studies tend to

overestimate costs. Sources of this over-estimation include

1. over allocation of indirect and overhead costs, such as

machinery and land;

2. over-estimation of input levels, such as fertilizer and feed;


3. over-estimation and over-allocation of labor.

The critical aspects of the allocation/estimation of land and labor

are discussed later in this dissertation (Chapter IV). Beef

production can be viewed in many cases as a productive, often risky,

way to utilize residual and/or marginal land and residual labor. More

specifically, when beef production fits into the entire farm operation

so that it does not compete with crops (the primary set of

enterprises) for land and labor, the producer will not necessarily

allocate all the associated costs to the beef enterprise. For the

cow-calf enterprise (which has weaned calves as its primary product),

these costs are a higher proportion than they are for the stocker

operation (Simpson et al., 1982) which starts with weanlings and sells

feeder calves. This logic also helps to explain why, once the

decision to more fully utilize resources via a beef herd is made, some

people have cow herds and in addition have backgrounding programs and

others do not. Thus, for some, the backgrounding operation adds

flexibility to the use of resources. For others, backgrounding

operations compete for those resources. Therefore, cow-calf

operations and stocker operations can be viewed as being either

competitive or complimentary for the use of farm resources.

Land can be viewed as a speculative investment as well as a

productive resource. Land ownership, however, is not cost-free.

Property taxes must be paid, although using the land for agricultural

purposes reduces the property tax burden. In addition, payments made

to purchase productive resources are deductible business expenses for

federal income tax. Thus, for the speculator, a "forgiving"

enterprise such as a beef operation (Hewitt and Holt, 1983) has

certain tax advantages. A cow-calf enterprise also has a tax

advantage over a stocker operation in that the brood cows can be

viewed as long term capital. Thus profits resulting from their sale

are taxed as long term capital gains. These considerations must be

balanced against the actual cost of the purchase as well as the

anticipated rate of land appreciation. Thus, in an area where real

land values increase slowly, speculation would not be too prominent.

Decision Making and Methods of Analysis

Given the wide occurrence of beef production, the studies which

indicate that it is not profitable, and the perception by producers

that it is only marginally profitable (Smith and Martin, 1972; Zimet

et al., 1984), it can be inferred that the decision by the producer to

manage a beef operation is complex. Some of the non-technical

considerations encountered in this decision are relevant to the

specification of models that seek to analyze beef production. There

are various ways to analyze resource allocations in a framework that

includes risk. Prominent among these methods are various types of

mathematical programming and stochastic efficiency or dominance. A

method that has been recently developed by Tauer is Target MOTAD

(Tauer, 1983). Target MOTAD combines the computational ease of linear

programming with the concepts of second degree stochastic dominance.

Stochastic Dominance

A method developed to deal with risk is stochastic dominance

(henceforth referred to as SD). In first degree SD (henceforth

referred to as FSD), the first moment about the origin of net returns

(a random variable) is used to determine whether a discrete set of

inputs and/or outputs is preferred over another discrete set. When

one set has an income equal to that of the other set but with a lower

cumulative density at a minimum of one point it is to be preferred.

Farm plan F dominates plan G in the sense of FSD if FI(Y) < GI(Y) for

all possible income levels, where F,(Y) and G,(Y) are the cumulative

probability distributions of the probability density functions f(y)

and g(y), respectively, and y is income. Second degree stochastic

dominance (henceforth referred to as SSD) is less restrictive than

FSD. It requires that the variance (the moment about the mean or

second moment) be at least as small as the variance from the other

discrete set of inputs and/or outputs. There is the additional

requirement that the variance derived from the first discrete group be

smaller than that derived from the second group in at least one


Under stochastic dominance a functional form of the utility

function is not assumed. In terms of income and utility, FSD is based

upon the assumption that more income is preferred to less. SSD

assumes there is decreasing and positive marginal utility of income.

Thus SSD applies to people who are risk averse.

Similar to FSD, SSD is represented by cumulative probability

distributions. Farm plan F is more efficient in terms of second

degree stochastic efficiency than farm plan G if F2(R) < G2(R) for all

possible income levels and the strict inequality holds at least once.

F2(R) is the integral of the cumulative probability function Fi:

F2(R) = f F1(y) dy

and G2(R) is the cumulative density function of Gl:

G2(R) = f Gl(y) dy.

Anderson et al. describe the difficulty with using SD criteria,

In decision problems involving continuous decision
variables, it would be convenient to conduct
efficiency analysis in a manner broadly analagous
to those of continuous response analysis .
unfortunately this is impossible because the
analysis of stochastic efficiency is intrinsically
a discrete affair involving pairwise comparisons.
(1977, p. 302)

They go on to state that the difficulty can be overcome by the

application of Monte Carlo programming. By using the vegetable

production problem used by Hazell in 1971, Anderson et al. (1977) were

able to compare SD and E-V efficient sets.

In order to obtain a set of 20 SD efficient farm plans they had

to analyze 48 plans which were obtained via Monte Carlo programming.

This particular problem had only four production alternatives.

Problems for the general farms of north Florida would require more

alternatives and thus many more simulations. This makes the SD method

unattractive as a tool to analyze whole-farm plans.

Mathematical Programming

In contrast, mathematical programming models are prescriptive

decision tools that respond to the question, "given the technical

requirements of potential alternative actions, the resource base, and

certain non-technical requirements, what product mix or resource

allocation will most efficiently obtain the specified goal or

objective?" By their nature, these models are more applicable to the

analysis of firm rather than aggregate problems.

Quadratic Programming, MOTAD and Risk

Quadratic programming (henceforth referred to as QP) is a

programming method which seeks to optimize a quadratic objective

function subject to a set of linear constraints. Income variation can

be viewed as a measure of risk of an economic enterprise. Variance,

of total net returns, is a quadratic function. Thus, QP can be used

to minimize risk subject to a set of linear technical and non-

technical constraints. Frequently income requirements are included in

the non-technical constraint subset. When parametric programming is

performed, an expected income-variance (henceforth referred to as E-V)

frontier is constructed. This frontier defines the trade-off between

risk (as defined by variance of income) and income. A standard

mathematical representation of E-V using QP is

n n
Minimize Z = E Ex x s
k=l j=l k kj

subject to

E ak x. b. i = 1, m
j=l 1
E f. x. =
j=l J J

where x. > 0 j = I,..., n

x. is the level of the jth activity;

skj is the covariance of net return between k and j;

a. is the use of resource i by activity j;

b. is the amount available of resource i;

f. is the expected net return from activity j;

X is a parameter to be varied from 0 upward.

The theoretical properties of E-V analysis (which include a quadratic

utility function) are retained only when net returns are normally

distributed or when enough observations are used so that the central

limit theorem can be applied (Anderson et al., 1977, p. 197).

An alternative to EV analysis is MOTAD, the minimization of total

absolute deviations, developed by Hazell (1971). The analysis upon

the MOTAD model is expected income-absolute deviation of income

(henceforth referred to as E-A) analysis. The MOTAD model is fully

linear and thus can use the linear programming alogorithm.

There is one other major difference between E-V and E-A analysis.

In E-V analysis, the semi-variances caused by positive and negative

deviations from the mean are weighted equally. Expected income-

absolute deviation analysis permits differential weighting of positive

and negative deviations. Hazell compares this aspect of the E-V model

and the E-A model as follows:

there may be no a priori reason to assume
that he (the producer) attaches any disutility to
positive income deviations so that using an E-V
criterion may lead to unnecessarily conservative
farm plans. Markowitz suggested that when total
gross margins cannot be expected to be
symmetrically distributed, an expected return-
negative semi-variance criterion might provide a
better approximation of an individual's utility
function. Such a model can be solved only
through Monte Carlo techniques (1971, p. 60)

Hazell gives the following mathematical representation of the

MOTAD model:

Minimize A =h (y +
h=l + +
subject to l (chj fj)x yh + Yh =0

(h = 1, s)

and jI f x.=
Zj a .xj bi (i = 1,. m)

x, yh+ Yh- 0 (for all h, j).
(1971, p. 57)


A = total absolute income deviation;

Yh = the positive deviation from the mean in period h

Yh = absolute value of the negative deviation in period h;
f. = expected return of the j activity, and
x. is the level of the j activity;

chj = the return per unit of the j activity at the hth
observation, and

X = a scalar;

a.. = the per unit resource requirement of resource i by
-1 activity j, and

b. = availability of resource i.
Target MOTAD

Tauer developed a modification of the MOTAD model which is.

"computationally efficient and generates solutions meeting the second-

degree stochastic dominance test" (1983, p. 606). He termed the model

Target MOTAD. The model maximizes expected income subject to

technical and income requirement constraints. (No functional form of

the utility function is assumed.) The negative deviations from the

target level of net return of the firm (Yh) are weighted according to

their probability of occurring (Ph). In most empirical applications,

Ph is set equal to I/s.

Max E (z) = Z f.x.
j=l3 3

E a. .x. b. i = 1,..., m
j=l 1 3

Z c .x. + Y > T h = 1,..., s
1hj 3 h h

E Ph = h

x. ; Y> 0,
3 h

where E(z) is the expected return of the plan; f. is the expected

return of enterprise j and x. is the level of enterprise j; chj is the

unit return of enterprise j in period h; a.. is the technical

requirement of enterprise j for resource j and b. is the available

level of resource j; Th is the target return level for the firm in

period h; A is a constant that is parametized from M to 0 and h is the

number of states of nature or observations. A Target MOTAD model of a

general, crop-beef, farm in Jefferson County, Florida, is developed

and analyzed in this dissertation.

Hierarchical Decision Models

Mathematical programming models yield direct answers to specified

management problems. They are not, however, directly related to the

decision process of the individual farmer. The specification of

objectives, production alternatives, and constraints are usually

exogenous to the programming model. The development and analysis of

hierarchical decision models (henceforth referred to as HDMs) permit

these subjective considerations to be elicited from the decision

makers themselves and analyzed within a formal methodological

framework. Mukhopahyay (1984) made this argument relative to decision

process models and statistical approaches. Her argument is broadened

here to include mathematical programming models as well. She stated

that by focusing

*. on identifying alternative choices, and then
specifying the set of conditions leading to each
alternative outcome, we come to understand the
process which generates observable behavior. In
short, we not only discover the factors which
enter into choices; we can specify the inter-
relationships between factors (1984, p.

The complimentary nature of mathematical programming models and

HDMs is explained in Chapter III. The compatability should prove

useful to analyze the problem understudy in this dissertation. The

apparent inability of standard economic analyses to explain the

persistence and geographical distribution of beef production indicate

the need to account for other, more subjective, information when

specifying programming models.

Problem Statement

In recent years economists have had difficulty in justifying beef

production with the application of the formal tools of economic

analysis. Because rational economic behavior on the part of the

producer is usually assumed, this difficulty leads to an apparent

paradox when compared with the widespread persistence of beef

production, particularly in the Southeast. Florida, especially the

Panhandle, experiences the same situation as the Southeast as a whole.

For the Southeast, the apparent unprofitability of beef

production has been documented (Carpenter et al., 1979; Schupp et al.,

1979; Wise and Saunders, 1977). Musser et al. (1975) have

characterized cow-calf production in the Georgia Piedmont as

"conspicuous production" because it is difficult to explain in purely

financial terms why people continue to produce beef. They argue that

the satisfaction and prestige embodied in a cow-calf operation must be

taken into account when trying to explain the occurrence of beef

production. Others have found this to be true for the West,

particularly the Southwestern United States [see Smith and Martin

(1972) for a bibliography].


The overall objective of this dissertation is to help explain why

north Florida farmers choose to produce beef. In order to achieve

this goal several specific objectives or tasks have been accomplished.

They are

1. review previous beef production and whole-farm planning/

optimization models;

2. describe the use of hierarchical decision models (HDMs) and

explain how they can be used to predict the decision of a

producer to have a beef operation (their use as it relates

to the type of beef operation is also explained);

3. describe several types of beef production operations in north

Florida; and

4. use optimization methods in conjunction with HDMs to

determine optimal size herds, calving and weaning dates,

and product mix for a specific producer.


The first objective entails a literature review of methods of

farm planning/optimizing models. The emphasis is on work that has

been done in the Southeast. However, a study from Washington is also

included. The review is done in order to describe how various types

of models have been used. Ways to incorporate some of the aspects of

either technique or general approach of the previous studies into the

present study were also sought.

Given that neither income nor income tax breaks (Smith and

Martin, 1972; Bostwick, 1969) alone help to clarify the question of

why some people raise beef, other aspects should be investigated and

analyzed. One approach is to gain further insight into the decision

framework of the producer so that the decisions made do not seem

illogical or capricious. The second objective entails the application

of HDMs to the problem of delineating the structure of producer

decision making.

An analysis of the decision framework of the (beef) producer

suggests that a producer confronts a series of decisions regarding his

beef operations. The series:

1. the decision whether or not row crops should be produced;

2. the decision of what to do with the land that is not used

for row crop production (for whatever reason), and if beef

is to be produced on this land;

3. the decision of what type of beef operation (cow-calf as

compared to stocker, for example) to have.

The analysis describes the decision system as perceived by producers

and it is possible to reshape some HDMs (depending on the nature of

the criteria) into specified constraints of mathematical programming

models. An HDM per se, however, yields a qualitative (yes/no)


All of the optimizing models developed include information either

directly from the HDMs or obtained from interviews used to construct

the decision models. This information is used to help define the

economic, decision, and production system as perceived by producers.

The optimizing models are used to help address the following issues

for specific producers:

1. What is the optimum sales weight (range) for calves?

2. Is it better to raise calves born by cows owned by the

producer to feedlot ready weights (about 700 pounds or more)

or is it better to purchase conditioned weanlings (250-400

pounds) and raise them to feedlot ready weights?

These questions are addressed in a mixed (crop and livestock) farm

model. (The beef operations are not analyzed in isolation.)

To accomplish the overall goal and these objectives, beef

production and beef producers of Jefferson County, Florida (Figure 1),

were analyzed. Jefferson County was selected because a variety of


operation types (variations of both cow-calf and stocker operations)

occur there, and because the County Extension Director was supportive

of the effort.


A method that could be used to analyze a given situation at the

farm level is the enterprise budget. Such budgets have been used by

Ross et al. (1983), Simpson et al. (1982), and Wise (1974) to describe

resource requirements for producing specific commodities at specific

locations with specific input levels and technology. These analyses,

however, indicate little regarding optimal resource allocation. A

mathematical programming model of a typical farm is an appropriate

model to solve the resource allocation problem.

Previous Studies

There have been previous attempts--some successful, others not

successful--to include beef production in general farm models.

Several studies that occurred in the South are the focus of the review

presented here. However, a study from the Columbia River Basin,

Washington, is included because of the method of analysis that was

used. In recent times (since about 1975), stocker operations have not

entered into optimal solutions with realistic herd sizes while cow-

calf operations have not been considered because of low or negative

net returns.

A study by Musser et al. (1975) analyzed this phenomenon, calling

it conspicuous production, analogous to the idea of conspicuous

consumption developed by Thorstein Veblen. The authors stated, "past

studies on maximum profit farm organization have indicated that

beef cows are not competitive with other enterprises" (1975, p. 89).

Their analysis of a typical farm (using cost data developed by Wise)

was based upon a utility function subject to an implicit production

function and a profit function. Using this technique they developed a

production frontier for beef cows and profits. The resulting profit

maximizing cow herd size ranged from zero to 20 cows for a general

crop and livestock farm. This number is well below observed herd

sizes (Table 1.2).

Wise and Saunders (1977) performed a linear programming analysis

of large commercial farms in the South. Beef and feed farms as well

as general farms were included in the analysis. The objective was to

maximize net returns to the labor and management of an operator of a

typical farm. Twenty-three subregions were included in the study. In

the optimum solutions for the general farms, 19 of the subregions

included brood cow herds. The average size for the cow herd was 33

head (Table 1.2). The range, however, was from 134 cows to four cows.

About half of the 23 calves from these cows were fed to slaughter

weights, one-quarter were kept for backgrounding and one-quarter were

sold at weaning. Backgrounding purchased weanlings for 150 days

predominated the beef enterprises. The average herd size was 295

head, but only 14 of the subregions had this type of operation.

When compared to the situation presented in the 1974 and the 1978

Census of Agriculture, several things become apparent. First,

backgrounding and cow-calf herds occur in all regions of the South.

Secondly, under favorable beef prices in the pre-1975 period, farms

that had over $2,500 in gross sales and operated on at least 100

acres, had an average cow herd size of about 45 head, almost one-third

greater than optimum. A similar analysis, based upon a similar price

structure, was conducted for small farms by Allison and Bell (1978).

The optima obtained in that study were much closer to the 1974 Census

of Agriculture data for all farms (Table 1.2).

The optima for purchased calves (Table 1.2) are much larger than

the observed number. This could be caused by two factors--the

relatively favorable 1969 beef prices used in both studies (Table 2.1)

and that neither analysis took risk into account. The latter point

could be critical as the estimated variance of net returns per head to

land and management for a north Florida winter backgrounding program

during the 1960/61-1975/76 period (Ross et al., 1983) was $753.24.

Furthermore, of these 16 years, four years had negative returns. Thus,

even in a favorable period, the relatively high profit stocker

operation lost money 25% of the time. (This can be compared to the six

year 1976/77-1981/82 period which had negative net returns for three


Johnson et al. (1979) conducted a study similar to those of Wise

and Saunders (1977) and Allison and Bell (1978). Johnson et al.

(1979), however, concentrated on the Georgia Coastal Plain as compared

to the latter two which considered the entire Southeast. Another

critical difference is that Johnson et al. (1979) used 1976 prices.

These prices were much less favorable for beef than they were in 1969

(Table 2.1). As indicated in Table 2.1, relative beef prices decreased

by about 50% when compared to corn, soybeans, tobacco, peanuts, and

feeder hogs. Unfortunately, Johnson et al. (1979) did not

Table 2.1. Relative feeder-calf prices used in other studies.

Wise and Saunders,
Allison and Bell Johnson et al. Prevatt

Year of Prices 1969 1976 1973-1977

Price of choice, 250-500
pound, feeder steers
($/cwt) 34.00 36.10 32.91

Price ratios:

Steer:Corna 32.4 13.8 12.9

Steers:Soybeana 15.5 6.5 5.5

Steers:Peanutsb 340.0 180.5 172.5

Steers:Tobaccob 68.0 32.8 32.1

Steers:Feeder Hogsc 0.9 0.5 NA

aBased upon per bushel corn or soybean prices.
Based upon per pound peanut or tobacco prices.
cBased upon hog price per hundred weight.
Source: Wise and Saunders (1977), Allison and Bell (1978), Johnson
et al. (1979), Prevatt (1979).

include a cow-calf enterprise among the alternatives of the linear

programming model they developed. They differentiated between small,

medium, large and extra large farms as well as full- and part-time

small farm operators. In the Johnson et al. (1979) analysis, only

medium-sized farms had some optimum solutions with small stocker

operations. Because the price of beef increased dramatically from 1976

to 1978 (from $36.10 to $61.45 per hundred weight for 400 to 500 pound

feeder calves), the analysis was also conducted with 1978 beef prices.

However, "these increased cattle prices had very little effect on farm

organization on all farm sizes. The feeder calf on winter grazing

operation entered the solution on the medium-size farm, but the

organization was not different from the base solution" (Johnson et al.,

1979, p. 26).

It can be argued that for an on-going beef operation one year is

similar to any other year. It also can be argued that a cow-calf

operation and, because of permanent pasture development, to a lesser

extent a stocker operation are multi-period, dynamic enterprises and

should be modeled as such. Prevatt (1979) did so using 1973-1977 as

the years of analysis. This study concentrated on the

technical/nutritional requirements of a beef cow-calf herd. The

objective was to maximize net returns to land, labor, management and

fixed cow herd and several cropping alternatives. This type of

objective exaggerates the concerns related to over estimation of costs

expressed in Chapter I of this dissertation. More specifically,

because a cow herd is a capital investment not all fixed costs should

be excluded from the cost calculations. Furthermore, three of the five

years in which the study takes place have favorable beef prices. [The

net return ratio beef:crops decreased from 0.7 in 1973 to 0.6 in 1977

(Prevatt, 1979, p. 53, 58).] When added to the land constraint which

limits one-half the available land to permanent pasture production, and

stringent culling criteria, beef production is almost inevitable. As a

result, a cow herd of approximately 100 is included in the optimum


These general farm models have not included risk considerations.

As implied above, if variance of net returns is used as the measure of

risk, the consideration of risk can be critical because of observed

large variances of net returns. Thomas et al. (1972) incorporated

constrained risk minimization into a general farm model of a typical

farm in the Columbia Basin of Washington.

The model developed by Thomas et al. (1972) used separable

programming to approximate the variance-covariance of income function

(based upon 1950-1969 data) of five crop and eight livestock

enterprises. The objective was to maximize expected income "subject to

appropriate physical and financial constraints and an upper bound on

income variance" (Thomas et al., 1972, p. 262). By use of appropriate

constraints, acceptable levels of risk were specified as were

acceptable levels of income. An approximation of variance was

developed by dividing variance into positive and negative semi-

variance. The approximation was then simulated by a "piecewise linear

approximation" (Thomas et al., 1972, p. 262).

Cow-calf and cow-yearling enterprises were included among the six

beef enterprises. Other beef enterprises included were spring/summer

backgrounding, fall/winter backgrounding and two finishing operations.

Only the two finishing operations and one of the backgrounding

operations entered the optimal solution. The number of head remained

stable as the acceptable level of variance was changed. It is assumed

that the cattle for these post-weaning programs are available from

another region of the state or country. The specific value of the

study to the panhandle of Florida is limited because of differences in

product mix potentials, harvest period and therefore price of

commodities, and the economic feasibility of finishing cattle.

There is another difficulty with this study. Separable

programming was used to develop an estimate of the variance-covariance

matrix in order to generate efficient or optimum plans that "minimize

variance for a given level of expected returns" (Thomas et al., 1972,

p. 260). The major problem associated with a variance-covariance

based analysis is that both positive and negative deviations are

weighted equally. Obviously, a farmer would welcome positive income

deviations and thus these deviations should receive less weight than

negative deviations.

An Application of MOTAD to a Beef Production Problem

Angirasa et al. (1981) utilized the E-A criterion to study

production of a typical East Texas cow-calf operator. One of their

objectives was "to develop expected profit-risk efficient sets" (1981,

p. 89). They analyzed three types of beef production/sales

alternatives--sales of weanlings, feeder calves, and forage-finished

cattle. A simulation model was used for the feed requirements aspect

of the model and various forage and feed combinations (for example,

coastal bermudagrass overseeded with rye-ryegrass, coastal

bermudagrass alone, and common bermudagrass overseeded with crimson

clover-ryegrass are included as production alternatives). Prices used

to construct the revenue deviation submatrix were from the period


Part of the analysis included certainty of returns (i.e., a

straightforward linear programming problem). Under these conditions

the standard cow-calf operation predominated. When the MOTAD model

was used, however, backgrounding increased when the risk constraint

was made more restrictive. (This is not surprising since

backgrounding calves that were not purchased is a form of hedging as

sale weight and even price, up to a certain point, can be controlled

by the seller or producer.) In terms of the Florida panhandle this

analysis by Angirasa et al. (1981) should be improved upon. First,

only cow-based beef enterprises are considered. This situation is not

common in the panhandle which has many types of general farms, but few

commercial farms which produce only beef. In addition the study

assumed a large farm, with a large resource base and a high level of

management. Thus, little direct light is shed upon the issue of why

people raise beef in the Southeast. As stated by the authors,

a word of caution is also warranted concerning the
empirical findings of this study. These results
are based upon the analysis of a large farm, high
level of management, and Hereford-type cattle at
one location only. Given its limited resources, a
small farm may or may not find these management


practices equally profitable Any
extrapolation from the results of this study
warrants consideration of the model and its
assumptions. (Angirasa et al., 1981, p. 9)


Some social scientists, including agricultural economists, have

determined that simplistic optimizing models do not always explain

and/or predict adequately the behavior of the producers (for example,

Barlett, 1980; Chibnik, 1980; Day and Cigno, 1978; Gladwin, 1975;

Johnson, 1980; Smith and Martin, 1972; Willis and Perlack, 1980).

There are several themes that are found in the literature related to

decision making that suggest explanations as to the inadequacy, with

respect to predicting producer behavior, of the simple optimizing

models. Some scientists claim that decision making is too complex to

be modeled with no subjective criteria and/or constraints. Among

these authors are those who offer ways to improve upon the solution

algorithm by generalizing it while others suggest that other

methodologies would be more appropriate. In the former group are

those who include risk in their production models (Dillon and

Anderson, 1971), multiple objective functions (Candler and Boehlje,

1971), or constrain optimal outcomes to be consistent with previous

behavior or decisions (Day and Cigno, 1978).

Those who call for different methodologies or solution algorithms

of a different type have found the usual algorithm applied by

economists to be empirically inaccurate or unusable. Johnson states,

for example,

I will argue that the formal model is by itself
virtually uninterpretable without reference to an
ethnographic context that can be provided only by
participant observation over a long term field
research. This is no momentary obstacle but
is, rather, an inherent limitation on the extent
to which formal models can account for observed
outcomes of agricultural decisions. (1980, p. 20)

Gladwin argues that the mental processes assumed by optimizing models

are too complicated because they ignore decision rules. She states

Most of the currently popular theories, however,
suffer from the fact that they do not take into
account the simplifying procedures or heuristics
that people use in real life to make their
decision-making process easier. (1980, p. 45)

Chibnik (1980) notes that models based upon the optimization of a

single goal are often inaccurate because of the over-riding importance

of the constraints, and the difficulty of determining constraints and

specifying a single objective.

Johnson (1980) offers no real alternative to the commonly used

optimizing algorithm. Gladwin (1975) and Chibnik (1980) stress the

importance of predicting historical choice outcomes. Chibnik states

that observed, identifiable, quantitative information (size of

household, for example) can be used to predict both qualitative and

quantitative decisions. The approach used by Gladwin, termed

hierarchical decision models (HDMs), normally yields discrete,

qualitative (yes/no; do/do not) results. Before application of HDMs

to a standard optimizing algorithm is discussed, HDMs and their use

are described more fully.

Hierarchical Decision Models

Decision is the critical word for researchers in this method of

analysis. Sen breaks the decision process into four basic steps: "(1)

definition of the objective, (2) identification of possible choices,

(3) collection of relevant information, and (4) drawing of appropriate

inferences" (1977, p. 3). The process by which HDMs are developed and

the models themselves help the researcher focus on those four steps

from the point of view of the decision-maker. Gladwin et al. state,

researchers can build models of the
decision-making process that incorporate farmers'
decision criteria and constraints. The models of
decision-making are hierarchically ordered on the
basis of the characteristic to be maximized,
incorporating alternative branches based on the
constraints and criteria of the farmers. (1984, p.

The importance of incorporating the perspective of the decision-maker

should not be over-looked. As Anderson et al. state,

Some people have been unable to tolerate the
sacrifice of "scientific objectivity" inherent in
the personal approach. But "objectivity" in
science is a myth, in life an impossibility, and
in decision-making an irrelevance. (1977, p. 18)

In other words the perception of the situation by the economic agent

is critical. What the agent believes to be the most important

problems and constraints to overcoming them are important to the

analysis of decision-making and the development of programs to assist

the group of agents in question. Decision trees, a methodology which

lends itself to subjective orientation, were used in the present


The Development of Decision Trees

A decision tree is a graphic representation of an HDM. It is a

flow chart of the decision process. Gladwin (1979) describes the

construction of a decision tree as a five step process to be completed

after open-ended interviews are used to elicit criteria from the

economic agents in their own words. The remaining four steps are

1. Arrange constraints and categories of the agents into a flow

chart using the language of the agents.

2. Trace the paths through the charts of the agents originally

sampled to create a composite chart in order to test its descriptive


3. Develop a more generalized model based upon the original

model; and

4. Test the generalized model.

It is the first step, the elicitation of criteria in the words of the

economic agents which is critical to the specification of the decision

tree model. The other four steps help to assure that the analysis is

orderly and the model accurate.

For the present analysis a draft questionnaire was designed only

after some time was spent with the producers learning their "language"

and gaining an appreciation for their production systems and problems.

After some revision of the questionnaire, a somewhat formal, open-

ended questionnaire which asked questions about management practices

was administered. Thus insight was gained as to how producers make

decisions and what they focus on.

Decision Trees for Beef Producers in Jefferson County

Several decisions must be made before a person becomes a beef

producer. First, the decision to become a farmer must be made.

Second, the use of (potential) crop land must be decided and third a

decision regarding the use of land that is not cropped must be made.

The latter two decisions were analyzed as was the decision of what

type of beef enterprise to operate. Decision trees (Figures 3.1, 3.2,

and 3.3) were made of those decisions in order to clarify the decision

framework of producers. Many of the criteria that were determined to

be important via the decision tree analysis were used to develop the

mathematical programming model used in this research. (For a

discussion of how to read a decision tree see Appendix A.)

The three HDMs were developed in the same way. The initial step

was a set of informal, unstructured interviews with ten Jefferson

County beef producers as well as extension workers and employees of

the Soil Conservation Service. After discussing certain aspects of

those interviews with agronomy, animal science, and extension

specialists at the University of Florida, a questionnaire was

developed and tested on ten producers. It was revised slightly as a

result of the test. Personal interviews were then conducted with 28

current and two former beef producers. The questions were generally

open-ended in order to obtain the opinions of producers about various

management practices and marketing schemes. In addition, specific,

technical questions (about calving rates, fertilizer application

rates, and use of pesticides, for example) were also asked. Each

interview required from one to two hours to conduct. The survey took

Given you're a producer and not just an Investor :

Produce cash row crops; don't produce them

Do you have enough land available for row crop production?

yes I

Do you have the strength and health to grow cash crops?2

for Part-time Farmer:


for Full-time Farmer :


Returns/manhour, risk cash crop

Returns/acre, risk cash crop


Did you have a strategy to
decrease risks of row crops?/




Take the risk, grow c
row crops


Does the potential profit of \
cash row crops outweigh greater
risk of cash row crops?

Did you have to take the risk\9
because the opportunity
risk was greater?

ash Don't take the risk;
|I don't grow cash row crops

Did you have land unsuitable or marginal
for cash crop production left?

yes n

Go to beef cattle decision Slop

Go to beef cattle decision.

Fig. 3.1. The decision to produce cash row crops.


Fie. 3.2.

The land use decision for
land not in commercial
row crop production.

6e- 0llc0,0on Not to Gro- C..h ow Croap on Some Land
8-*t Catlel Oth.,er LvetIo Timber T#,0 Cr0op. flay

KW.l tht land suIatt *or po .ure hNay tre cfopl Oa lmberT

.-. .mtion /
(.~ ~ ~ ~ ~~ ~G b"..i .,cn.. .------

t1D0 ea i, tl o f tI l "hi* land? a*t ime t

I II..B. 00.0 r.. r /................. \

SWele 1ire too many markeltnlg ndor production

Ellml .la he ohlr ..ll. Olc t I Stag
stagS 2

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pl ale.d Staea 17 /

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X htll p... Stage 1

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no At tie t 11 t id you 700 l 0
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place over a four-month period during the late winter and spring of

1983. As part of the analysis of the data obtained, the HDMs

represented by the decision trees displayed in Figures 3.1, 3.2, and

3.3 were developed. The decision trees were tested over a five-month

period in early through mid 1984.

The Decision to Grow Cash Crops and the Decision to Have a Beef Cattle

Farms are endowed with different types of land. In very broad

terms there is land suitable for commercial row crop production and

land that is not. Land might fall into the latter group because of a

variety of reasons such as the soil profile and stability, the

drainage situation, the topography, or accessibility for machinery.

Decisions must be made concerning the use of either type of land

before it is put into production.

The decision to grow cash crops

There are several constraints to being able to produce cash crops

(Figure 3.1). First the land must be suitable in terms of quantity

available and quality for such production (Criterion 1). In addition

the human resources in terms of strength (Criterion 2), knowledge

(Criterion 4), and time (Criterion 5) must also be available. The

availability of capital for equipment as well as for operating

expenses is also to be considered (Criterion 3). The potential risks

and returns for cash crops compared to those of the major alternative,

livestock (Criteria 6A and 6B), need also be taken into account.

Finally, in the event that land is still available the producer should

consider other production alternatives (Figure 3.2). This model was

tested on 25 producers. It was accurate in 23 cases (92.0%).

The decision to have a beef cattle operation

Beef cattle production is a way to utilize land that is not used

for row crops (Figure 3.2). The land, however, must also be suitable

for beef production. If it is suitable for beef it would also be

suitable for other products (Criterion 1). Criterion 2 through

Criterion 4 in Figure 3.2 consider the cash flow horizon of timber and

tree crops. Many producers stated that they were not in a position to

wait the necessary time to obtain a positive cash flow from their

land. Some stated that the time necessary for tree crops to generate

a positive cash flow was not too long, but that tree crops required

too much labor during the warm season to fit into their farm

management scheme (Criterion 5).

Primary among the livestock alternatives to beef are sheep and

goats. In north Florida, they face uncertain markets (Criterion 6).

Hogs are another livestock alternative to beef. Hogs, however,

require a relatively high investment in facilities as well as high

nutritional requirements. The nutritional requirements are usually

met by farm-grown corn. Thus, there are production difficulties

associated with hog production (Criterion 6).

Jefferson County producers stated that they must like any non-row

crop alternative they consider (Criterion 7). If beef cattle are

preferred then the technical considerations regarding production must

be taken into account (Criteria 9 and 12 through 15). Criteria

similar to these are discussed below in the section about the cow-calf

versus stocker decision. Criterion 10 primarily considers crop

failure. Hobbyists, semi-retirees and retirees are included in the

group of potential beef producers via Criterion 11. To test the HDM

represented in Figure 3.2, 24 producers were interviewed. The model

was accurate in 23 cases (95.8%) for the beef production phase and in

15 cases (62.5%) concerning the other products.

The Cow-Calf Versus Stocker Decision

Coincident with the decision to produce beef cattle is the

decision of what type of herd to operate (Figure 3.3). In Florida as

in other Southern states, raising stockers is potentially more

profitable than owning a cow-calf herd (Ross et al., 1983). Yet,

according to the 1978 Census of Agriculture (U.S. Department of

Commerce), more producers have cow-calf herds than stocker herds.

Obviously, from the point of view of many producers, there are

disadvantages and/or constraints to owning a stocker operation. These

are represented by the first criterion and the criteria on the left

hand path of the tree.

The first criterion is scale of operation, a barrier to entry to

backgrounding for producers with limited resources. Scale is

important because of the requirements of the feedlot operators. While

conducting field research in Jefferson County it was discovered that

there were no small stocker herds (under 30 head) and that most were

over 100 head. This led to an attempt to analyze the size

requirements of a stocker herd. Backgrounding feeder cattle is an

intermediate step in the production of high quality beef. It precedes

intensive feeding of the animals in a confined feedlot. Presently,

feedlots require lots of approximately 40 uniformly-sized feeder

cattle. The broker for the feedlot must assemble such lots for their

clients. The brokers seek to do so with minimum effort. A small beef

producer may find it impossible to produce 40 (or even the major

portion thereof) uniformly-sized cattle. Failure to supply a minimum

25 to 30 head usually results in a price discount, thereby reducing

the profitability of the backgrounding operation.

From the point of view of the producer, scale is important

because returns per animal are low and marketing costs per animal,

especially hauling animals to and from the farm vary inversely with

the number of animals. During interviews several farmers claimed that

hauling fees with less than half a truckload of animals (i.e., less

than 25 to 30 animals) are excessive.

Other important aspects of the decision are the short and long

run returns (Criteria 2 and 3 in Figure 3.3) to each type of beef

operation. If the producer believes a stocker operation would be less

profitable than a cow-calf operation, he should not operate a stocker

enterprise. If he believes that it would be more profitable to have a

stocker operation for either time horizon, he should then consider the

flexibility of the operations (Criterion 4). The relative importance

of profit and flexibility (Criterion 5) must also be considered..

The production of high quality winter forage is another critical

aspect of backgrounding (Criterion 8). It is through the consistent

production of such forage that risk can be reduced and profitability

can be increased. The risk of the stocker operation is greater than

that of the cow-calf operation because of price fluctuation as well as

dependence upon weight gain--the critical factor in a successful

backgrounding program.

There are reasons other than scale, risk, and availability of

winter pasture which inhibit or prevent producers from running stocker

operations. A producer must know how to run a successful

backgrounding program (Criterion 7). Most producers, especially those

from a farm background, have a reasonable understanding of animal

health and nutrition needs. Producers who originally lack this

knowledge can obtain it from a number of sources. Marketing know-how

is another matter. There are two marketing aspects related to the

management of a stocker herd. First, the right kind of animal must be

purchased; and second, the animal must be sold. The former is

critical as animals that will gain efficiently are keys to success.

The ability to purchase such animals can be described as a learned art

that is not just "picked up." Being able to produce an adequate

supply of temporary winter pasture (Criterion 8 of Figure 3.3) is also

critical. If a producer has a winter backgrounding program he must be

able to produce such pasture in a timely fashion in order to obtain

good weight gains. Thus the producer must ask himself whether he has

enough time, the proper machinery and equipment, and the know-how to

plant combinations of cool season forage. If he cannot do so, he

should not do winter backgrounding.

As compared to these disadvantages of a stocker operation,

however, are the advantages of greater profitability and greater

flexibility. The stocker operator can change herd size according to

anticipated market conditions and available time and pasture. In

comparison, the cow-calf operator invests a good deal of time and

management in the breeding program, trying to develop a brood cow herd

that does well under the conditions of the specific farm. He would

thus be reluctant to sell-off part of his breeding stock in a bad year

in order to decrease herd size. Similarly, increasing herd size in

the short run is also more difficult for the cow-calf operator.

Finding the "right" brood cows or raising replacement heifers of good

quality is a long-run proposition. If a producer has none of the

above motivations to run a stocker operation or if he cannot meet the

requirements of such an operation, he should not background calves.

In Figure 3.3, such producers would pass to the cow-calf branch (right

hand side) of the decision tree.

Like the stocker operation, a cow-calf operation has certain

advantages and disadvantages. The major disadvantage is that it is

less profitable than a stocker operation of sufficient size. In

addition, cow-calf operators, more so than stocker operators,

justifiably believe that they will lose money for approximately three

years while starting up the operation (Zimet et al., 1984). While

heifers mature, management experience is gained, and a production

system is established, they lose money. In contrast, stocker

operations lose money for perhaps two years while managers gain

experience and establish a production system. Thus Criteria 3 and 9

ask if the producer believes that such losses can be sustained.

Beef producers in Jefferson County, Florida, believe that cow-

calf operations do have some advantages (Zimet et al., 1984). Because

brood cows are long-term investments which generate a product

(calves), they are viewed as a form of savings (Criterion 10). They

can serve as collateral for loans as well as a source of capital

through sales. The flexibility as regards the sale date of calves is

another advantage. Stocker calves should be kept until they reach

profitable weights whereas weanlings can be sold upon weaning or a few

months afterwards depending upon market and forage conditions. Thus,

weanlings can be available for sale for a few months while stocker

calves should be sold during a period that lasts but a few weeks.

Cow-calf operations, however, are not necessarily profitable. In

addition, not all producers find the advantages of a cow-calf

operation to be attractive. The HDM presented in Figure 3.3, with

Criterion 12 eliminated, was tested by interviewing 30 producers. It

was correct for 26 (86.7%) of the producers.

Limitations of Hierarchical Decision Models

Because hierarchical decision models yield qualitative (yes or

no) results, they are of limited use in prescribing solutions to

intercommodity resource allocation problems. For example, without an

exhausting process HDMs could not be used to prescribe how many acres

of corn and soybeans should be planted given the decision to plant

both. Hierarchical decision models can, however, help to clarify

economic issues as perceived by the economic agent in question.

Therefore, they allow for better understanding of the subjective

decision framework. This understanding can lead, in turn, to a better

specification of constraints and objectives for optimizing models.

The limited quantitative information obtained is not the only

shortcoming HDMs suffer. Because they are developed by a method that

is completely dependent upon the population and its circumstances, the

effectiveness of the HDMs is confined almost completely to the

population in question. Thus, hierarchical decision models should not

be used to answer specific "what if" questions. For example, the

effects on production of a marginal price change could not be

projected or estimated via an HDM. In comparison, programming models

permit sensitivity analysis to parameter, including price changes. In

addition, the effects of new types of production techniques could be

projected via the programming models, but HDMs cannot be utilized in

such fashion. These limitations do not prevent HDMs from being

complementary to optimizing programming models.

Hierarchical Decision Models and Mathematical Programming Models

Given the limitations of the HDMs as well as the need to specify

mathematical programming models used for farm planning realistically,

the potential complimentary aspects of the two methodologies should be

realized. The potential complementary relationship between

Hierarchical Decision Models and mathematical programming models is

illustrated by the series of decisions of (1) whether or not to grow

cash crops (Figure 3.1); (2) what to produce on land not used for

commercial crops (Figure 3.2); and (3) the decision to operate a cow-

calf herd or a purchased stocker herd (Figure 3.3).

Mathematical Programming Model Specification and Hierarchical Decision

Some of the important decision criteria in Figures 3.1, 3.2, and

3.3 were used in the specification of a Target MOTAD model of a

medium-sized Jefferson County crop and beef farm. The use of a Target

MOTAD model to analyze product mix and resource allocation reflects

the need, as expressed in each of the three HDMs, to explicitly

consider net return, risk and the potential trade-off between them.

In addition, Criterion 3 of Figure 3.3 considered a multi-year

planning horizon and the need to obtain a positive annual cash flow

consistently. The use of annual income targets in a Target MOTAD

model mirrored these criteria.

In the case of crops, specific requirements, type of land,

capital and labor were included in the HDM. These were translated

into the specification of two land groups for crop production as well

as annual capital and monthly labor requirements for each crop

production alternative.

Similar to crops, the beef production alternatives used two types

of land in addition to annual credit and monthly labor requirements.

The two types of land were permanent pasture, considered to be

unsuitable for crop production, and fenced non-irrigated crop land.

The former were to be used for warm season improved pastures and the

latter for cool season pasture and warm season native grasses. The

first criterion, herd size, of the decision as to what type of beef

enterprise to operate, is an economic, not a technical, requirement of

production. It was mapped onto a herd size requirement in the Target

MOTAD model. Flexibility (Criterion 4 of the decision tree of that

decision) is also a non-technical consideration. By including various

post-weaning marketing options for calves and by allowing stocker herd

size to vary, the flexibility criterion was considered in the Target

MOTAD model.

Knowledge and ability are producer characteristics that were

included explicitly as constraints in the HDMs. When production

alternatives are included in a mathematical programming model,

relevant knowledge and ability are assumed. Such was the situation in

the present analysis. If, however, the producer in question stated

that he lacked such knowledge and ability for specific products they

would have been excluded from Target MOTAD model.

In sum, specification of a mathematical programming model can be

aided by the previous development of a (series of) hierarchical

decision modelss. In the present case the general type of

programming model to be used was determined by the HDMs. (A Target

MOTAD model has the characteristics sought.) Some of the technical

and non-technical constraints were included in the Target MOTAD model

because of the role they played in the decision trees. The decision

criteria that were mapped directly onto the Target MOTAD model are

further specified in Chapter IV.


A Target MOTAD model of a typical, medium resource base general

crop and beef farm in north Florida was developed. The objective of

the model was to maximize the expected net return to management, land

used for winter pasture production, operator labor, and labor used for

beef production for the eleven year period, 1973-1983. The objective

accurately represents the cost allocation used by producers. A

discussion of the various other segments of the model is presented in

the following sections. The costs and returns were first calculated

in current dollars and were then transformed to constant 1977 dollars.

To deflate costs, the index of "prices paid by farmers for commodities

and services, interest, taxes and wage rates" was applied. The index

of "all farm products" (U.S. Department of Agriculture, 1984, p. 7)

was used to deflate returns.

Activities and Budgets

The crops included in the model are those that are commonly grown

in Jefferson County. The warm season crops included corn drylandd and

irrigated), peanuts, soybeans drylandd and irrigated), and watermelon.

Cool season crops were winter wheat for grain and rye-ryegrass

pasture. Bahiagrass-clover pasture and native grasses were the other

forages included in the model. All the forages were considered to be

intermediate products with no commercial value. The deflated net

returns used in the model for each commercial crop are given in Tables

4.3 through 4.9.

Commercial Crops and Forages

Upon review of production and cost records of two producers in

Jefferson County and at the suggestion of the two producers, it was

decided to utilize the commercial crop resource requirements available

from the Georgia Cooperative Extension Service (University of Georgia,

various issues) as the basis for the costs of all commercial crops

except for watermelon. The watermelon costs of production estimates

were based upon the cost estimates prepared by Hewitt (n.d.) and

Westberry (n.d.). In all cases the estimated costs of production were

verified with producers, agricultural scientists and other

publications when applicable. The prices of the resources required

for production of an acre of each crop were applied to obtain the

appropriate annual cost per acre (Tables 4.3 through 4.9). Prices

(Table 4.1) and yields per acre (Table 4.2) were obtained from the

Florida Agricultural Statistics (Florida Crop and Livestock Reporting

Service, various issues), and the U.S. Department of Agriculture

(various issues, b).

The forage budgets were based primarily upon data obtained from

interviews of producers. In addition a few other publications were

utilized to gain insight into some aspects of machinery and equipment

costs. (The forage production budgets used are presented in Appendix

B). The stocking rates used for the various beef production

Table 4.1. Prices used to calculate returns.

Corna Peanutsa Soybeansa Watermelon Wheatd
Year (bushel) (pound) (bushel) (cwt) (bushel)


1973 2.55 0.162 5.65 2.725b 2.60

1974 3.30 0.180 7.30 2.425b 3.80

1975 2.70 0.199 4.40 3.800b 3.10

1976 2.60 0.204 7.00 2.650b 3.00

1977 1.60 0.207 6.00 2.350b 2.20

1978 2.10 0.213 6.80 2.750b 3.00

1979 2.85 0.211 6.60 3.800b 3.75

1980 3.40 0.220 7.90 5.65 b 3.65

1981 2.85 0.273 6.20 5.35 b 3.32

1982 2.45 0.240 5.45 5.05 b 3.05

1983 3.80 0.240 8.15 4.00 c 3.20

aSource: U.S. Department of Agriculture, Agricultural Prices, Annual

bSummary,various issues. Florida prices were used.
Source: Florida Crop and Livestock Reporting Service, Vegetable
Summary, various issues, average June-July price.
dPrice reported by Jefferson County producers.
Source: U.S. Department of Agriculture, Agricultural Prices, Annual
Summary, various issues. Georgia prices used.

Yields used to calculate returns.

Dryland Irrigated Dryland Irrigated
Corn Corn Peanuts Soybeans Soybeans Watermelon Wheat
Year (bushel)a (bushel)b (pound)a (bushel)a (bushel)c (cwt) (bushel)e


1973 55 110 2420 20 34 144 22

1974 52 104 3100 25 42 160 23

1975 45 90 3360 26 44 200 27

1976 66 132 2630 27 46 190 31

1977 37 74 2530 23 39 180 33

1978 40 80 3310 21 36 155 32

1979 60 120 3220 30 51 140 35

1980 60 120 2850 23 39 175 33

1981 60 120 2715 21 36 145 43

1982 70 140 2835 29 49 150 42

1983 66 132 2425 24 41 155 39



Florida Crop and Livestock Repoi
various issues. Jefferson Count
corn yields were assumed to be
soybean yields were assumed to

ting Service, Field Crop
~y data were used.
200% of dryland corn yields.
be 170% of dryland soybean

Florida Crop and Livestock Reporting Service, Vegetable
various issues. North Florida yields were used.
U.S. Department of Agriculture, Field Crop Summary, various
Georgia data were used.

Table 4.2.

Table 4.3. Deflated gross return, cost,
Dryland corn.

and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 143.11 125.70 17.41

1974 163.43 148.15 15.28

1975 120.30 170.79 -50.49

1976 168.23 185.00 -16.77

1977 59.20 181.00 -121.80

1978 73.04 148.47 -75.43

1979 129.55 154.47 -24.92

1980 152.24 157.97 -5.73

1981 123.02 149.33 -26.31

1982 128.95 161.15 32.20

1983 187.16 134.16 53.00

Mean -18.51

bSee Tables 4.1 and 4.2 for details.
Source: University of Georgia (various issues).

Table 4.4. Deflated gross return,
Irrigated corn.

cost, and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 286.22 233.94 52.28

1974 326.86 265.25 61.61

1975 240.59 316.18 -75.59

1976 336.47 272.63 63.84

1977 118.40 286.00 -167.60

1978 146.09 280.56 -134.47

1979 259.09 256.91 2.18

1980 304.48 265.94 38.54

1981 246.04 294.00 -47.96

1982 257.90 312.74 -54.84

1983 374.33 296.27 78.06

Mean -16.72

See Tables 4.1 and 4.2 for details.
Source: University of Georgia (various issues).

Table 4.5. Deflated

gross return, cost, and net return per acre:

Deflated Deflated Deflated
Year Gross Return Cost Net Return


1973 400.04 289.09 110.95

1974 531.43 354.32 177.11

1975 662.02 385.39 276.63

1976 526.00 402.58 123.42

1977 523.71 392.00 131.71

1978 613.07 372.22 240.85

1979 512.27 341.46 170.81

1980 467.91 338.41 129.50

1981 533.23 351.33 181.90

1982 511.58 387.90 123.68

1983 441.57 370.81 70.76

Mean 157.94

bSee Tables 4.1 and 4.2 for details.
Source: University of Georgia (various issues).

Table 4.6. Deflated gross return,
Dryland soybeans.

cost, and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 115.31 104.86 10.45

1974 173.81 100.99 72.82

1975 113.27 129.21 -15.94

1976 185.29 137.90 47.39

1977 138.00 118.10 19.90

1978 124.17 133.33 -9.16

1979 150.00 104.11 45.89

1980 135.60 121.01 14.59

1981 93.67 125.33 -31.66

1982 118.84 129.30 -10.46

1983 145.97 127.33 18.64

Mean 14.77

aSee Tables 4.1 and 4.2 for details.
bSource: University of Georgia (various issues).

Table 4.7. Deflated gross return, cost,
Irrigated soybeans.

and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 196.02 194.58 1.44

1974 292.00 198.21 93.79

1975 191.68 209.21 -17.53

1976 315.69 223.63 92.06

1977 234.00 209.90 24.10

1978 212.87 230.79 -17.92

1979 255.00 212.72 42.28

1980 229.93 210.87 19.06

1981 160.58 214.67 -54.09

1982 200.79 222.29 -21.50

1983 249.37 216.77 32.60

Mean 17.66

aSee Tables 4.1 and 4.2 for details.
Source: University of Georgia (various issues).

Table 4.8. Deflated gross return, cost,

and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 400.41 216.90 183.51

1974 369.52 244.32 125.20

1975 752.48 272.25 480.23

1976 493.63 288.04 205.59

1977 432.00 265.40 157.60

1978 370.65 269.12 101.53

1979 403.03 337.72 65.31

1980 737.87 335.44 402.43

1981 558.09 343.53 214.56

1982 569.55 434.01 135.54

1983 462.69 458.99 3.70

Mean 188.66

aSee Tables 4.1 and 4.2 for details.
Source: 1980-1983 (Hewitt, n.d.); previous to 1980 (Westberry,

Table 4.9. Deflated

gross return, cost, and net return per acre:

Deflated Deflated Deflated
Year Gross Returna Cost Net Return


1973 71.63 91.69 -20.06

1974 83.24 90.74 -7.50

1975 82.87 108.65 -25.78

1976 91.18 100.95 -9.77

1977 72.60 90.90 -18.30

1978 83.48 91.48 -8.00

1979 99.43 84.55 14.88

1980 89.89 93.48 -3.59

1981 102.71 102.00 0.71

1982 96.32 102.55 -6.23

1983 93.13 99.38 -6.25

Mean -8.17

aSee Tables 4.1 and 4.2 for details.
Source: University of Georgia (various issues).

alternatives are shown in Table 4.15. As stated above, forage was

considered to have no commercial value.

Beef Cattle Enterprises

Several classes of beef cattle operations were included in the

model. There were cow-calf enterprises, a summer conditioning program

for calves born the previous fall, and warm and cool season

backgrounding programs. (See Appendix B for the budgets of the key

beef enterprises included in the model.) The purchase of calves for

backgrounding was permitted in the cool season only.

Cow-calf operations

Four basic cow-calf enterprises were considered. Two calving

months, March and November, with two weaning weights, 350 pounds and

450 pounds, were included. The difference in weaning weights was made

possible by a longer period prior to weaning and a lower stocking rate

for the cow-calf combination that produced the 450 pound calf. The

monthly nutritional requirements were based upon those developed by

Melton for a Brahman-cross cow in north Florida (Melton, 1978). The

age of the cow and the pregnancy and lactation status were accounted

for in those estimates. The assumed age distribution and the months

of calving and weaning of the present study were applied to the

estimates developed by Melton (1978) to obtain the nutritional

requirements of the cow herd (Tables 4.10 through 4.13).

Four of the cow-calf enterprise options used bahia-clover pasture

to meet warm season nutritional requirements. Another set of four

Table 4.10.

Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 350 pound calf in April/May.

Month of Calving: November

Available Energy Available Energy Energy from
Metabolizablg from Bahiagrass- from Rya-Ryegrass from Protein
Month Requirement Clover Pasturec Pasture Haye Supplement

M Cal

Nov. 606 -- 115 355 136

Dec. 606 -- 345 244 17

Jan. 606 -- 655

Feb. 662 -- 754

March 664 813

April 664 1524

May 470 1931

June 470 2033

July 488 1728

Aug. 512 1118 -

Sept. 553 406 118 29

Oct. 563 203 244 116

aA composite cow, based upon a 15% culling rate.
Based upon Melton (1978).
cOne acre of Bahiagrass pasture overseeded with clover.
dOne-half acre of rye-ryegrass pasture.
eA total of 0.6 tons of hay fed.
A total of 2.35 hundred weight of 30-35% protein supplement fed.

Table 4.11.

Monthly energy requirements for a North Florida Brahman-
cross cowa weaning a 450 pound calf in May/June.

Month of Calving: November

Monthly Available Energy Available Energy Energy from
Energy from Bahiagrass- from Rya-Ryegrass from Protein
Month Requirementb Clover Pasturec Pasture Haye Supplement

M Cal

Nov. 606 -- 11 355 136

Dec. 606 -- 345 244 17

Jan. 606 -- 655

Feb. 662 -- 754

March 664 975

April 667 1828

May 672 2317

June 600 2439

July 488 2073

Aug. 512 1341 -

Sept. 553 487 71 --

Oct. 563 243 244 58

aA composite cow, based upon a 15% culling rate.
bBased upon Melton (1978).
c One and two-tenths acres of Bahiagrass pasture overseeded with clover.
dOne-half acre of rye-ryegrass pasture.
eA total of 0.6 tons of hay fed.
A total of 1.8 hundred weight of 30-35% protein supplement fed.

Table 4.12.

Monthly energy requirements for a North Florida Brahman-
cross cow weaning a 450 pound calf in October/November.

Month of Calving: March

Monthly Available Energy Available Energy Energy from
Energy b from Bahiagrass- from Ryq-Ryegrass from Protein
Month Requirement Clover Pasturec Pasture Haye Supplement

M Cal

March 606 975

April 606 1828

May 606 2317

June 662 2439

July 664 2073

Aug. 667 1341 --

Sept. 672 487 185 --

Oct. 670 243 -- 324 103

Nov. 488 136g 115 237

Dec. 512 45g 345 122

Jan. 553 -- 655

Feb. 563 -- 754

aA composite cow, based upon a 15% culling rate.
Based upon Melton (1978).
dOne and two-tenths acres of Bahiagrass pasture overseeded with clover.
One-half acre of rye-ryegrass pasture.
eA total of 0.6 tons of hay fed.
A total of 90 pounds of 30-35% protein supplement fed.
Assumed to be available from residual pasture.

Table 4.13.

Monthly energy requirements for a North Florida Brahman-
cross cowa weaning a 350 pound calf in September/October.

Month of Calving: March

Monthly Available Energy Available Energy Energy from
Energy from Bahiagrass- from Ryq-Ryegrass from Protein
Month Requirement Clover Pasturec Pasture Haye Supplement

M Cal

March 606 813

April 606 1524

May 606 1931

June 662 2033

July 664 1728

Aug. 667 1118 --

Sept. 470 406 70 --

Oct. 470 203 -- 244 23

Nov. 488 89g 115 284

Dec. 512 45g 345 122

Jan. 553 -- 655

Feb. 563 -- 754

aA composite cow, based upon a 15% culling rate.
Based upon Melton (1978).
cOne acre of Bahiagrass pasture overseeded with clover.
One-half acre of rye-ryegrass pasture.
eA total of 0.5 tons of hay fed.
A total of 20 pounds of 30-35% protein supplement fed.
Assumed to be available from residual pasture.

options used native grass pastures instead of bahia-clover. The

native grasses were assumed to be Guinea grass and crab grass growing

in fields that produced cool season forage. The grasses thus utilized

residual fertilizer. The assumed stocking rate for the heavier

weaning alternative was one cow per 1.5 acres of native grass as

compared to one cow per 1.2 acres of improved pasture. In addition,

the enterprises that utilized native grass required additional

supplemental feeding to meet nutritional requirements. Upon weaning,

calves were either sold or passed to a feeding program.

In order to determine the weight of calves available for sale,

several assumptions and calculations were made. The majority of the

assumptions were averages derived from a survey of 50 Jefferson County

beef producers. A calving rate of 92% and a 2% calf mortality rate

were assumed. Thus 90 calves would be available from 100 cows.

Assuming that 50% of the calves were bulls and 50% were heifers, 45

calves of each type were available. Of these, 15 heifer calves were

assumed to be required for cow replacement. In sum, 45 steer calves

and 30 heifer calves, a total of 75 from a potential 100 were assumed

to be available for a post-weaning option. On the basis of a cow and

calf pair the assumed situation dictated that sales weight was 75% of

the assumed 350 pound and 450 pound weaning weights.


It was assumed that an individual calf started a post-weaning

production option at one of the two possible weaning weights. Thus,

when the assumptions concerning the calf crop were applied to the

post-weaning production options, it was necessary to assume that 1.33

cows (1.0 cow divided by 0.75 calves per cow = 1.33 cows per calf)

were required to produce one calf. In this dissertation conditioning

was defined as a 90 to 120 day backgrounding program. Conditioning

was considered only when lush warm season grazing was available. At

the end of the conditioning program additional gain would be necessary

to attain finishing weight.1

Final calf weights of the conditioning and backgrounding programs

were estimated by a growth simulation model for stocker cattle (Spreen

et al., 1985). The final weight (Table 4.14) was then reduced by 2%

to account for calf mortality and for calves born at the end of the

calving season. This weight was then multiplied by the appropriate

monthly price to obtain an estimate of total returns. A marketing fee

of one and one-half percent was also deducted from total returns to

arrive at the gross returns used to calculate the net returns (Table

4.15) used in the model.

The weight and receipts estimates were made in a similar fashion

for the purchased-calf backgrounding options. Two of these options

were included to reflect different situations. In the first option,

the purchased stocker option was independent from the cow-calf

options. Both were charged proportional shares for warm season

pasture production. In the other option, the stocker enterprise was

charged with the warm season improved pasture production costs. The

cows, however, were permitted to graze the residual pasture cost-free.

iPre-conditioning is the post-weaning phase which prepares calves for
shipping. Calves are vaccinated and allowed to graze good forage in
order to prepare them for the stress of transport.

Table 4.14.

Initial and final weights, beginning months, number of
months and stocking rates of specified post-weaning

Stocking Rate
Initial Final Beginning Number Bahia- Rye-
Weight Weight Months of Months clover ryegrass

Head per acre
Light calf 350 515 April/May 4 2.0 NAb
Heavy calf 450 592 June 3 1.0 NAb
Heavy calf 450 510 June 3 2.0 NAb

of fall calf:
Light calf 350 767 April/May 12 1.0 1.5
Light calf 350 746 April/May 12 2.0 2.0
Heavy calf 450 856 June 10 1.0 1.0
Heavy calf 450 796 June 10 2.0 1.5

Backgrounding of
spring calf:
Light calf 350 670 October 7 5.0a 1.5
Light calf 350 642 October 7 5.0a 2.0
Heavy calf 450 727 November 6 5.0a 2.0

of purchased
calf: 400 658 December 5 5.0a 2.0

bFor the month of April only.
NA denotes not applicable.

Table 4.15.

Final weights and average (1973-1983) deflated gross
returns, costs and net returns per head of principal
beef enterprises.

Average Average Average
Final deflated deflated deflated
weighta gross returnsc costs net returns

pounds dollars per head

Cow-Calf on bahia-clover

Fall calf weaned
Fall calf weaned
Spring calf
weaned light
Spring calf
weaned heavy

Cow-Calf on
native grass

Fall calf weaned
Fall calf weaned
Spring calf
weaned light
Spring calf
weaned heavy

























- 5.02














of fall calf







Table 4.15--Continued.

Average Average Average
Final deflated deflated deflated
weighta gross returnsc costs net returns

pounds dollars per head

of spring calf

Light calf 670 280.06 286.77 6.71
Light calf 642 267.68 280.21 -12.53
Heavy calf 727 303.89 319.81 -15.92

Backgrounding of
purchased calf 658 274.06 215.18 58.88

Cow-calf linked with
purchased stocker calf

Fall calf weaned heavy 450 195.81 b 159.46c 36.35
Purchased calf 658 274.06 226.33 47.73

bCorresponds to weights in Table 13.
Includes income from cull cows.
Includes cost of cow-calf operation at production of 1.33 cows per
stocker calf.

Given that the stockers were sold in early May, this system permitted

the cows to receive supplemental feeding in April and early May and

graze cost-free through the summer. Both situations had a 2.0

stocking rate for the stocker calves on the rye-ryegrass pasture.

Two variations of a purchased stocker enterprise were included

because other stocking rates proved to be much less attractive. A

lower stocking rate of 1.5 was too costly and had a much lower net

return because of under utilization of resources. A higher stocking

rate (2.5) required that more supplements be purchased or caused a

lower rate of gain to occur, which resulted in a lower net return than

the 2.0 stocking rate option.

The Constraints

All production options, either crop or livestock, require

resources. It is the technical constraints of a programming model

that describe the resource base available to the economic agent.

Other, non-technical constraints describe other types of requirements.

Both types are described in the following subsections.

Technical Constraints

The major technical constraints are the basic agricultural

inputs--land, labor and capital. Land and labor resources available

were considered to be identical every year. The amount of available

labor, however, varied on a monthly basis while the amount of land

available was held constant both on a monthly and annual basis. The

per unit (per head of cattle and per acre of each crop) requirements

for land and labor for each commodity did not vary. The capital

requirements for each commodity did vary annually. The variation was

necessary because, unlike the objective function, the capital

requirements and constraints were valued in current dollars.

Land and labor

Four types of land--irrigated crop land, unfenced non-irrigated

crop land, fenced non-irrigated crop land and permanent pasture--were

included in the model (Table 4.16). No transformation of land from

one type to another was permitted. Prohibiting the transformation of

permanent pasture to crop land is a result found in the HDM analysis

of the decision as to whether to produce commercial row crops. The

separate accounting of fenced, non-irrigated crop land is also

consistent with the HDM analysis. Some producers, including those

explicitly used to develop the target MOTAD model, stated that they

have had, or anticipated, erosion problems due to such a

transformation. It was decided to hold irrigated, dry crop land and

fenced acreage at actual levels of availability on a specific farm

(Table 4.16). This was done so that the results of the model could be

compared to an actual situation. Thus, the constraints for all four

land groups were specified at existing levels.

Similar to other inputs, land costs were charged on an as-used

basis. Thus, costs were net of land purchase costs for unused land.

As stated above, land costs that were charged varied over the eleven-

year period. In addition, the charges for each of the land groups was

distinct. Although peanuts were not produced on irrigated land, the

Table 4.16. Available acreage by land type.

Land Type

Irrigated crop land

Total non-irrigated crop land

Fenced non-irrigated crop land

Permanent pasture






land use charge for their production was at the irrigated land rate.

This was done in accordance with rental practices common to the

Florida Panhandle.

Unlike land, labor was considered to be homogeneous. Labor

availability was based upon the employment of two full-time workers--

an owner/manager and a full-time employee. Monthly labor availability

(Table 4.17), however, varied by month. Consistent with work load

requirements, both the employee and the farm operator were assumed to

be available to work more hours during the warm season than during the

cool season. It was also assumed that the employer would perform

proportionately more work during the cool season. These assumptions

conform with the practice of using the off-season to compensate

employees for overtime worked during the cropping season.

Similar to crop land used for winter forage production, labor

used in beef production was treated as a residual and no charge was

made for it. This conforms with the time flexibility of chores

related to beef and forage production as well as the attempt of

producers to keep employees active all year. In accordance with

normal procedures in Jefferson County, crop labor was charged at the

minimum wage rate for the year in question.


The capital requirements used in the model were based entirely

upon short-term production credit. They were to cover all out-of-

pocket cash expenses for production purposes. Fixed costs, the cost

of capital items such as machinery and land purchase charges were not

Table 4.17. Monthly labor availability.

Month Available Man-Hours

January 360

February 387

March 462

April 462

May 473

June 462

July 473

August 473

September 462

October 344

November 294

December 294

Table 4.18. Annual production loan funds available.

Year Available Loan Funds

1973 200,000

1974 200,000

1975 200,000

1976 200,000

1977 250,000

1978 250,000

1979 250,000

1980 300,000

1981 300,000

1982 300,000

1983 300,000

included in the credit requirements of the various products. Interest

was charged at the annual rate indicated by the Georgia Extension

Service. The amount available annually (Table 4.18) was based upon a

limit of 300,000 dollars for 750 acres of crop land available, an

average of 400 dollars per acre for 1983. This amount was then

adjusted to conform with the index of "farm real estate value"

reported in the table entitled "Economic Trends" (U.S. Department of

Agriculture, 1984b), and was then rounded off to the nearest 50,000


Non-Technical Constraints

In addition to the technical requirements of land, labor and

capital, non-technical requirements and constraints were also

specified. Foremost among these were the minimum income targets.

Income constraints and variation

The income requirements were set on the basis of interviews with

producers. Based upon the interviews it was determined that 15,000

dollars would be considered a good farm income in 1983. To this

figure 9,000 dollars was then added. The addition was made to allow

for capitalization and payment for some of the unused resources. The

sum was deflated by the 1977 consumer price index. The target income

was 14,000 dollars in 1977 constant dollars. The scalar A was the

parameter that controlled the total of the annual negative deviations

from the annual target. When A was unconstrained, the model was

similar to a straightforward linear programming model. As X was made

smaller via parametric programming, smaller total annual negative

deviations from the annual target were permitted. When A became

sufficiently small, changes in the solution basis occurred. The

values of X and the annual income targets are related. Just as the

target was held constant and the amount of permitted deviation varied,

the level of deviation was held constant and the target varied. The

result was a range of targets which can be viewed as the area of

interest for each set value of X. The lowest value of the range for a

given value of X is the target which an be attained each year. The

upper band of the range is the highest income target that can be

attained with a specific level of permitted deviation. The solution

to the latter is the linear programming solution to a net return

maximization problem with a negative income deviation constraint.

Peanut and watermelon acreages

The history of the various methods used to control peanut acreage

and production in the United States is well known. In 1982, the

United States changed from the strict acreage control of the allotment

program to the quota system. The quota system is based upon weight

and guarantees that a specific weight (the quota) can be sold at a

subsidized price. The possibility of having some type of

restriction/subsidy was allowed for with a corresponding constraint.

It was also thought that watermelon might enter a solution at

unrealistically high levels. The capability of restricting watermelon

acreage was built into the model as well. Neither of these

constraints were activated for the initial solution attempt.



The results from two specifications of the model are presented

below. The difference between the specifications is that the level of

watermelon acreage was unconstrained in one and was limited to a

maximum of 40 acres in the other. The former specification is

referred to as the unconstrained model and the latter is referred to

as the constrained model. Both sets of results are based upon the

results of parametric programming. The scalar X which controlled the

total amount of negative deviation from annual income targets was

lowered systematically until its value was zero. As determined by the

solution alogorithm, specific values of X caused the solution basis to

change. At each change of the basis, the value of X and the results

were reported.

Previous to the summary discussion, however, a short review of a

preliminary model is presented. In the preliminary model the value of

X was not varied or constrained. Peanut, watermelon and fenced dry

land crop acreage also were unconstrained. It was anticipated that

the optimal stocker herd size might have been at the lower limit of 25

head, but with a smaller true optimum. This would have caused a

discrete programming problem which allowed the stocker herd size to be

zero. The preliminary solution indicated a large herd size so this

was not an issue. Thus, the preliminary model was the same as the two

ultimately used to complete the present study.

Because of the large positive net returns generated by peanuts

and watermelon as compared to the other commercial crops included in

the study, it was anticipated that peanuts and watermelon would

dominate the solution. This is what occurred. Approximately 90 acres

of watermelon and 120 acres of peanuts were included in the solution.

In addition, a fall stocker herd of 450 head was indicated. Given a

stocking rate of 2.0 per acre this meant 225 acres of nonirrigated

crop land was utilized for forage production in the cool season. To

try to overcome the discrepancy between observed and modeled behavior,

peanuts were limited to 70 acres. This resulted in watermelon

production increasing to approximately 110 acres.

The producer whose resource base was being explicitly included in

the model was contacted and the solution was discussed with him. He

stated that in previous years he used about 235 acres for cool season

production divided among 110 acres for wheat and 125 acres for cool

season pasture. He stated that he has been limited to 125 fenced

acres for the pasture. Thus, the fenced acreage constraint level was

specified. In addition, he stated that he was planning to reduce his

watermelon acreage to 30 to 40 acres because of harvest labor

difficulties. This observation determined the watermelon acreage

constraint. Favorable experience with the peanut quota the previous

year had made him decide to expand from one contract to three.

Because of the ability to sell more than the amount allocated under

the quota at the set price, he stated that he would produce about 90

acres of peanuts.

These considerations were included as constraints in the Target

MOTAD model. The results from the model with no watermelon

constraint, the fenced acreage constraint, and the peanut acreage

constraint of 90 acres are presented and analyzed first. Next, the

results and analysis of the constrained model are given. When

appropriate, a comparison is made between the results of the two model


Results and Analysis: Unconstrained Watermelon Acreage

After the initial solution of unconstrained set of models, only

two changes in basis occurred in order to arrive at the point at which

no variation from the targeted income of 14,000 dollars took place in

any of the 11 years (i.e., when A = 0). The products included in the

solution varied somewhat as the amount of variation changed (Table

5.1). There was a trade-off between variation and income (Table 5.1).

Income and variation were at their greatest values as well as their

lowest levels simultaneously.

Annual Income Levels and Commodities

With the exception of 1974, the target income was attained every

year in all solutions of the unconstrained model (Table 5.2). When

income variation was not controlled the 11 year average income

obtained from the production of nuts, watermelon and a purchased

stocker herd was enough to maximize net return. No particular year

was of concern as regards the attainment of the target income. If

Table 5.1.

Net return, product mix and level of negative deviation
from income targets for both models.

Net Irrigated Purchased Brood Brood
Xc Return Peanut Watermelon Soybeans Stockers Cowsa Cows

---$--- ------- Acres

------------- --------- Head

> 600.75 40,371.30




> 1692.50
























35 0

35 0

32 8

19 40

aThese cows graze residual permanent pasture.
These cows graze native grass pasture during the warm season.
cX is the sum of the products of negative deviations from annual income
targets times the probability of occurrence of such a deviation.

















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0 0

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the negative deviation from the annual target of a particular year was

great relative to the amount of variation permitted, the solution

basis might have to change. Furthermore, under the controlled

situation, if a particular product had a bad year the solution would

be influenced. Such was the case of the present model in 1974.

The net return for the purchased stocker operation was low in

1974 relative to the mean (used as the objective function value).

Irrigated soybeans, which had a good year in 1974, entered the

solution in order to compensate for the deviation caused by the

stocker herd. Soybeans had a good year because the product prices

were favorable, not because of extraordinary yields. Peanuts and

watermelon were the only viable alternatives to the irrigated

soybeans. Peanut acreage was already at its upper limit and could be

expanded no further. Because March labor was already fully utilized,

watermelon acreage could not be increased.

The availability of fenced crop land for cool season pasture

limited stocker production when variation from the target was

unconstrained. This was also true when soybean production was

adequate to off-set the variation. It was only when no variation was

permitted that the stocker herd decreased.

When no negative variation in net return was permitted, the

addition of the irrigated soybean production was not enough to off-set

the variation from the target. Thus, the stocker herd was reduced

from 250 head to 226 head. The reduction freed some labor so that an

additional acre each of irrigated soybeans and watermelon could be


Peanut and Watermelon Acreage

March labor availability was the factor that limited watermelon

production in the unconstrained model. Thus, for the resource base

available watermelon production was at its optimum. In comparison,

peanut production was limited by an exogenous variable, the peanut


In the preliminary specification of this model, peanut acreage

was not controlled. Optimum peanut production was appreciably greater

than the controlled amount finally indicated. Thus, there was a loss

in net return due to the diminished production. This loss was $87.51

per acre when variation in annual income was not constrained and

$71.42 under both levels of control. The amount was less than the

value to the objective function of an acre of peanuts. The reduction

in value occurred because watermelon production would have had to be

reduced in order to permit increased peanut production to occur.

Resource Use

Most of the available resources were not used entirely in order

to arrive at the various optimum solutions. For example, the use of

borrowed capital ranged from 35.7% in 1977 when income was allowed to

vary freely to 65.8% in 1982 and 1979 when a moderate level of

variation was allowed. Irrigated land use ranged from 19.7% to 94.8%

(Table 5.3). The only use for dry crop land was peanut production.

Thus, its use was of low intensity. A maximum of 43% of such land was









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Of the resources available only labor in March and April and

fenced acreage proved to be binding when watermelon was not limited

(Table 5.3). March labor had values of $71.18 per additional man-hour

when annual income was permitted to vary freely and $47.68 in both

instances the variation was controlled. April labor, which was

binding only when the variation from the target income was controlled,

had a value of $46.88 per man-hour in both cases.

April labor availability affected the value of fenced acreage in

the case when negative annual income variation was permitted at a

moderate level. Because of the April labor requirements of the

purchased stocker herd, if more than 125 fenced acres were available

only 125 acres would be used. In comparison, when annual income

variation was not controlled, an additional acre of fenced crop land

would have added $52.55 to the mean net return of the 11 year period

(Table 5.4).

Results and Analysis: Constrained Watermelon Acreage

The results of the constrained model follow the same pattern as

those of the unconstrained model. Because watermelon production could

not be used to meet the target income to the extent as in the

unconstrained model, more changes in basis occurred as less deviation

from the target was permitted. In addition, variation was greater and

income less at all comparable steps in the constrained model as

compared to the unconstrained model (Table 5.2).

Table 5.4. Opportunity cost/marginal values per acre of the peanut
quota, constrained watermelon acreage, and fenced crop
land by level of deviation of expected net return for
both models.

Peanut Watermelon Fenced
Model Quota Acreage Crop Land




































aNO~ applicable.

aNot applicable.
bNot applicable.
Not applicable.

Watermelon acreage was not
Not all fenced acreage was

constrained directly.
used in this

Annual Income and Commodity Production

As in the case of the unconstrained model, 1974 proved to be a

year in which it was difficult for the constrained model to attain the

income target. The reason for this is the same as in the

unconstrained model. The decrease in watermelon acreage in the

constrained model, however, caused 1973 to be a year in which earning

$14,000 was difficult as well. The target was difficult to reach in

1973 because, like 1974, it was a bad year for stocker operations

(Table 5.2).

When variation from targeted income was controlled slightly (X =

1181.5), the purchased stocker herd was reduced from 250 to 214 head

(Table 5.1). The reduction helped to compensate for the variation

from target income caused by the poor years of 1973 and 1974 as well

as the reduced watermelon acreage. In addition, a 35 head cow herd

which grazed residual warm season pasture was included in the

solution. The brood cow enterprise selected was based upon improved

warm season pasture. Calving occurred in November and the weaning

weight was 450 pounds in this enterprise. This addition enabled the

fenced crop land to be fully utilized despite the reduction in the

stocker herd. The 1973 income situation was improved by including the

cow herd. The reduction of the stocker herd improved the 1974


These changes were not enough to compensate for stricter control

of the negative deviation from targeted income (X = 652.7). As in the

unconstrained model, the inclusion of irrigated soybeans decreased the

variation. The addition of 160 acres of soybeans, however, caused all

irrigated acreage to be utilized in May and June (Table 5.3). Thus,

the tighter control of variation (X = 465.9) required other changes in

product mix to be made. Total annual negative deviation from the

income target would increase with the reduction of peanut and

watermelon acreage and would decrease increases of their acreages.

Such an increase was prohibited by direct constraints. Once again a

decrease in the stocker herd size (Table 5.3) helped to decrease the

1974 variation. The decrease in herd size was not large enough to do

away with the 1974 variation entirely. This reduction in income

deviation was partially effected by a decrease in the cow herd that

grazed residual warm season pasture. The herd was reduced from 35 to

32 head. Furthermore, eight cows which grazed native grasses during

the warm season were included in the solution. Calves produced under

this option were born in the fall and weaned at 450 pounds in the


When no negative deviation from annual income targets was

permitted (x = 0), the size of the cow herd which grazed native

pasture in the warm season was increased from eight to 40 head. In

addition, the size of the other cow herd was decreased from 32 to 19

head. These changes permitted a decrease in the soybean acreage to

occur. That decrease was necessary because, although the 1974 income

situation could be improved by soybean production, a concommitant

deterioration occurred in 1973. This occurred because poor yields

prevented irrigated soybeans from covering land use fees in 1973.

Thus, while improving the average situation when some negative annual

income variation was permitted, soybeans made the 1973 situation worse

when no variation was permitted.

Peanut and Watermelon Acreage

The restriction of peanut acreage had additional value to the

objective function in the set of solutions when watermelon acreage was

constrained. This value was lowest when income variation was not

controlled and greatest when variation was tightly controlled. The

values ranged from $126.24 per acre (the explicit value of an acre of

peanuts to the objective function) to $244.30 per acre (Table 5.4).

The value of an additional acre of peanuts increased because, unlike

the unconstrained watermelon situation, peanuts were not in

competition with watermelon for March labor.

It is clear that an increase in watermelon acreage would increase

the value of the objective function in the constrained acreage set of

solutions. The additional amount to be earned ranged from the

explicit value used in the objective function ($156.96 per acre) when

income variation was not controlled to $293.52 per acre when only

slight variation was permitted. The latter value held when no

variation was permitted (Table 5.4). This was an analogous situation

to that of peanuts. The value of an additional acre of watermelon

increased because of the lack of competition for March labor with

other crops.

Resource Use

As could be expected, resource use was generally lower in the

constrained model than in the unconstrained model. This was true

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