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A mathematical programming model of the U.S. beef sector

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Title:
A mathematical programming model of the U.S. beef sector
Creator:
Peters, Mark A., 1956-
Publication Date:
Language:
English
Physical Description:
vi, 251 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Beef ( jstor )
Calves ( jstor )
Capital costs ( jstor )
Cattle ( jstor )
Hamburgers ( jstor )
Meats ( jstor )
Poultry ( jstor )
Slaughter ( jstor )
Steak ( jstor )
Supply ( jstor )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1990.
Bibliography:
Includes bibliographical references (leaves 246-250).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Mark A. Peters.

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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.
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001667719 ( ALEPH )
24655764 ( OCLC )
AHX9530 ( NOTIS )

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A MATHEMATICAL PROGRAMMING MODEL
OF THE U.S. BEEF SECTOR


















By

MARK A. PETERS


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1990














ACKNOWLEDGMENTS


It has been a very rewarding learning experience to

work with Dr. Thomas H. Spreen, chairman of my dissertation

committee. Dr. Spreen provided many helpful insights. I

appreciate his efforts in making the completion of this

dissertation possible and in finding me employment.

I would also like to thank Dr. John S. Shonkwiler, Dr.

William G. Boggess, Dr. Timothy G. Taylor, and Dr. Douglas

G. Waldo for serving on my dissertation committee. My

appreciation is also extended to Dr. Rodney R. Martin at

Auburn University and Dr. Kenneth E. Nelson at the Economic

Research Service for providing me with much needed

information.

Financially speaking, I am grateful to the Food and

Resource Economics Department of the University of Florida

for funding much of my stay here as well as to the USDA

which provided me with a fellowship for three years.

Emotionally speaking, I am indebted to the friends I

have made in Gainesville and to my family who have supported

me during this endeavor. I am especially indebted to May

Mercado who gave me her unconditional love.















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS . ii

ABSTRACT . .

CHAPTERS

1. CHANGES OCCURRING IN THE STRUCTURE OF THE
U.S. BEEF INDUSTRY .. .. 1

Objectives 11
Overview of Study .. 12

2. MATHEMATICAL PROGRAMMING AND SECTOR LEVEL
ANALYSIS .......... .. .. 13

Incorporating Demand Systems into
Mathematical Programming Models 15
The Integrability Problem 18

3. A MODEL OF THE U.S. BEEF SECTOR 27

Organization of Beef Sector 27
Supply Response .. 46
The Model ... 47

4. SPECIFICATION OF AN INVERSE DEMAND SYSTEM
FOR FRESH MEATS .. 76

Criteria for Selecting a Demand System
to be Used in the Programming
Model 76
The Two-Stage Budgeting Process and the
Representation of Consumer
Preferences ... .80
The Derivation of the Inverse Almost
Ideal Demand System 88
The Data .90
Estimation Procedures .. 97
The Results .. 98


iii










Adjustments Made to Demand Equations

5. DESCRIPTION OF ACTIVITY ANALYSIS MODEL OF
BEEF PRODUCTION SYSTEM .

6. BASE RESULTS AND SIMULATIONS .

The Base Run ... .
Scenarios .. .. .

7. SUMMARY AND CONCLUSIONS .


APPENDICES


A. TRANSFORMATIONS OF EXPENDITURE AND PRICE
DATA ................

B. TRANSFORMATIONS TO COST OF PRODUCTION
DATA .

C. GAMS PROGRAM ..............

D. THE EMPIRICAL COMPENSATED DEMAND SYSTEM


REFERENCES .. .

BIOGRAPHICAL SKETCH .


S 210


S 213

S 223

S 244

S 246

S 251


117


123

148

148
157

198














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


A MATHEMATICAL PROGRAMMING MODEL OF THE U.S.
BEEF SECTOR

By

Mark A. Peters

December, 1990

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


The main purpose of this study was to build an econom-

ic model of the U.S. beef sector for use in policy analysis.

The model developed is a price endogenous spatial equilib-

rium model. It integrates a system of demand equations for

beef with an activity analysis model of the U.S. beef pro-

duction system. The representation of the beef production

system partitions the U.S. into five supply regions and four

production stages. The representation of demand for beef

partitions the U.S. into four demand regions.

The use of this methodology has been limited by

restrictions placed on model formulation by integrability

conditions. A new approach was used to solve the integra-

bility problem. In this approach a compensated demand








system is used in place of the more generally used uncom-

pensated demand system.

An inverse Almost Ideal Demand System (AIDS) contain-

ing eight meat commodities was derived and estimated for

each of the four demand regions. The demand systems were

estimated by pooling the data on household expenditures on

meat obtained from the Consumer Expenditure Survey, 1982-

1986.

The model was used to analyze the impact of an in-

crease in poultry consumption, an increase in beef imports

and an increase on beef imports on participants in the beef

sector. Increased levels of poultry consumption and

increased levels of beef exports caused a decline in the

quantity of beef produced and a decline in the size of fin-

ished cattle. Increased exports of beef caused both the

quantity of beef produced and the size of finished cattle to

increase.

The impact of these adjustments on participants in the

sector depended on the location of the supply region and the

stage of production. The quantity of beef produced declined

significantly in the Southeast due to an increase in poultry

consumption or beef imports. The decline in the size of

finished cattle caused the quantity of cattle finished to

decline in the Southwest and to increase in the Plains. The

increase in cattle size due to an increase in exports of

beef caused the quantity of cattle finished in the Southwest

to increase and to decline in the Plains.















CHAPTER 1
CHANGES OCCURRING IN THE STRUCTURE OF THE U.S.
BEEF INDUSTRY


The beef industry is one of the most important com-

ponents of the U.S. agricultural sector. In 1985 consumer

expenditures on beef totaled $45.6 billion (USDA, 1988)

while on farm cash receipts for beef totaled $29.1 billion.

This amount represented 20% of total on-farm cash receipts

in the entire agricultural sector for that year (USDA,

1988). In addition, the industry is the major consumer of

grains, and as a consequence, changes in the beef industry

which affect the supply and demand for beef reverberate

throughout the agricultural sector.

The beef industry is in a state of flux with major

changes occurring in its structure in both supply and

demand. On the supply side the geographic location of

production operations is moving westward and sizes of

operations are increasing. Specialization in production is

intensifying as large commercial feedlots and single species

meatpacking plants increase in numbers. Vertical integra-

tion is also increasing as meatpacking firms continue to

integrate the functions carried out by independent whole-

salers into their operations. On the demand side, there has

been a dramatic shift in the pattern of meat consumption.

1










Poultry's share of household expenditures on meat has

increased, while beef's share of meat expenditures has

declined. The effect of this shift in the pattern of meat

consumption is reflected in the decline in the level of per

capital consumption of beef throughout the eighties.

The changes presently occurring in the structure of

the supply side of the beef industry are largely attributed.

to two events: the advent of irrigation in the high plains

states and the introduction of boxed beef in the meatpacking

industry in the mid-sixties. The introduction of irrigation

in the high plains has been responsible for the geographic

shift in the location of feeding and slaughtering operations

while boxed beef is responsible for the increasing size of

meatpacking plants and increased vertical integration in the

processing and distribution of fresh beef.

Historically, cattle feeding has been located in areas

of highly concentrated feed grain production known as the

cornbelt, but starting in 1960 a gradual shift occurred in

its location as cattle feeding moved away from the cornbelt

to the western cornbelt and high plains states of Texas,

Nebraska, Kansas, Iowa and Colorado. This shift is primar-

ily a result of the greater availability of feed grain

supplies in the plains states and economies of scale result-

ing from large commercial feedlots (McCoy and Sarhan, 1988)

made possible by the introduction of irrigation and the low

opportunity cost for land compared to crop production on











nonirrigated lands in this region. Both the greater avail-

ability of feed grains and economies of scale led to lower

average costs of production, giving these states a compara-

tive advantage in cattle feeding over the central cornbelt

states.

The movement of the meatpacking industry has followed

that observed for feedlots. Most cattle are slaughtered

within 100 miles of where they are finished. This is not

surprising given the nature of meatpacking which is essen-

tially a process of reducing the size of the primary input.

Thus, the closer the meatpacking facility is located to

where the live animal is produced, the less weight that

needs to be shipped long distances. When live animals were

produced by small atomized producers widely dispersed geo-

graphically, the high cost of assembly and transporting the

animals to slaughter made it economically infeasible to

locate meatpacking facilities at any other location than at

the terminal points of transportation routes. However, with

the development of large scale feedlots assembly costs were

greatly reduced. Thus, the meatpacking facilities were

located closer to the areas where the large feedlots were

located.

The introduction of boxed beef in 1969 is the most

significant technological innovation to occur in the meat-

packing industry during the past thirty years. Both the

increase in size of meatpacking plants and the increase in









4
level of concentration in the meatpacking industry have been

attributed to the introduction of boxed beef and the econ-

omies of scale associated with this technology. It has also

transformed the distribution sector since it eliminated the

need for specialty wholesalers to service large retail out-

lets such as grocery chains (Duewer, 1984).

Boxed beef is the end product of a process by which

the carcass of the slaughtered cow is fabricated (cut) into

primals, subprimals or both, vacuum wrapped and shipped to

wholesalers or retailers. Primal cuts consist of the major

divisions of the carcass such as rounds, loins, and chucks,

while subprimals cuts include the smaller cuts obtained from

these divisions, such as chuck steak, and chuck roasts.

Since its introduction the amount of beef marketed as

boxed beef has increased steadily and by 1983 accounted for

nearly 90% of fresh beef marketing (Duewer, 1984). There

are large economies of scale associated with boxed beef.

Before the introduction of boxed beef the efficient size

packing plant had a capacity of 250,000 head while after its

introduction the efficient size plant had a capacity of

1,000,000 head (Marion). In addition to economies of size,

boxed beef was widely adopted by the meatpacking industry

because it permitted less fat and bone to be shipped,

allowed the buyer to order specific cuts, reduced shrinkage

during shipping, increased the shelf life of the product,

and required less space in shipping (Nelson, 1987a).










As important as the changes occurring in the

production of beef are, the most important change is

occurring on the demand side where a dramatic shift has

occurred in the pattern of meat consumption highlighted by

poultry's supplanting of beef as the major meat product

consumed (Table 1.1). For thirty years prior to 1977, per

capital levels of beef consumption had increased steadily at

approximately the same rate as the rate of growth in

personal income, reaching a high of 94.0 lbs. in 1976. In

1977, the level of beef consumption dropped to 91.0 Ibs.

marking the beginning of a period of sharp decline in per

capital levels of beef consumption. The decline continued

until 1980 when beef consumption dropped to a level of

76.4 lbs. per person. From 1980-1986 per capital beef

consumption leveled off, but began to decline again in 1987

when it dropped to 73.4 Ibs. During the 1977-1987 time

period the level of beef consumption declined by 18.0 lbs.

per person. In contrast, the per capital level of

consumption of chicken increased steadily during this same

time period and in 1987 surpassed that of beef. In 1975 the

level of poultry consumption stood at 48 lbs. per person and

climbed to a level of 77 lbs. per person in 1987 (Table

1.1). This represents an increase in the level of poultry

consumption of 29 lbs. per person.

In addition to the change which has occurred in the

consumption pattern among the major meat species, a change












TABLE 1.1


COMPARISON OF PER CAPITAL CONSUMPTION OF BEEF AND
POULTRY TO THE RELATIVE PRICE OF POULTRY TO
BEEF. 1975-87.


Relative Price
Consumption Consumption of Poultry in
Year of Beef of Poultry Terms of Beef


lbs. $

1975 88.0 48.3 .955
1976 94.2 51.6 .947
1977 91.4 52.9 .958
1978 87.2 55.5 .860
1979 78.0 60.1 .708
1980 76.4 60.3 .706
1981 77.1 62.0 .729
1982 76.8 63.4 .706
1983 78.2 64.7 .725
1984 78.1 66.5 .793
1985 78.8 69.7 .791
1986 78.4 72.0
1987 73.4 77.8


Source: USDA, 1987.









7
has also occurred in the pattern of consumption found within

the beef category itself. In 1965, steak ranked as the

number one beef cut in terms of quantity consumed with

roasts ranked second and ground beef third. However, by

1984 the picture had changed dramatically as hamburger was

now ranked number one, steak had dropped to number two and

roasts came in third.

Among agricultural economists there has been con-

siderable debate over the major factors contributing to the

changes occurring in the pattern of meat consumption and to

the decline in levels of per capital beef consumption. Some

have attributed these changes to a fundamental shift in the

structure of the demand for meats, due either to increased

health concerns on the part of consumers (Chavas, 1983;

Braschler, 1983; and Buse, 1986) or an increased desire for

convenience in food preparation (Carnes, 1984; Eales and

Unnevehr, 1988; and Duewer, 1984). Others assert that the

changes which have occurred in the pattern of meat consump-

tion are easily explained by changes which have taken place

in such traditional economic variables as the relative price

of beef to poultry, income, and the demographic composition

of the U.S. population (Haidecker et al., 1982; Chalfant and

Alston, 1988; Hager, 1985; Dahlgran, 1987; Heien and Pom-

pelli, 1988).

With regard to the argument that there has been a

shift in consumer preferences due to increased health











concerns and need for greater convenience in food

preparation, two explanations are usually given to explain

how these concerns cause consumers to eat less beef. The

first explanation is that the U.S. population has become

increasingly concerned about the fat content of their diets

due to reports that over consumption of fat leads to heart

disease and other health problems. This has led them to try

to reduce the amount of fat consumed, especially animal

fats. Beef products contain more fat than poultry products.

Consequently consumers desire to consume more poultry and

less beef in order to reduce the amount of fat in their

diet. The second explanation is that the number of two-

income households has increased rapidly during the 1975-1987

time period. As a consequence Americans have less time to

spend on meal preparation and desire greater convenience or

ease of use in food products. The traditional beef

products, roasts in particular, require considerably more

preparation time and come in larger portions than poultry

products. Thus consumers desire more poultry and less beef.

With regard to the argument that it is changes in

economic variables such as prices and income which have

caused the decline in beef consumption and not a shift in

preferences, its supporters point out that the relative

price of beef compared to poultry increased significantly

during the period in which the changes in the consumption

pattern occurred. During the 1975-1985 time period the











price of poultry relative to the price of beef declined by

17% (see Table 1.1). The primary cause of the decline in

the relative price of poultry to beef being increased effi-

ciency in the production of poultry which has not been

matched by beef producers. Thus as beef becomes more expen-

sive relative to poultry consumers demand more poultry and

less beef.

The debate over the cause of declining beef consump-

tion is not just of esoteric interest to econometricians,

but has important implications for the beef industry as

well. Already, the beef industry is putting its energy into

efforts to increase the demand for beef. These efforts

include the generic promotion of beef, development of a new

grading system by the USDA, private labeling, and the devel-

opment of new products such as lean beef. However, if the

major cause of the decline in beef consumption is due to the

increase in the relative price of beef to poultry then the

current efforts by the industry to increase demand will be

futile. In this case beef producers should have greater

success in regaining market share if they concentrate on

reducing the cost of producing beef.

All other things being equal, one of the major impacts

of the decline in beef consumption will be a reduction in

the overall size of the nation's beef herd. It is also

likely that the decline in beef consumption and the con-

sequent reduction in the beef herd will accelerate the










current trends in the beef sector with regard to the shift

in location of the beef herd, the increase in the scale of

operations and the increase in the level of concentration in

meatpacking as higher cost participants are squeezed out.

Thus one question which needs to be answered is to

what extent these trends will continue. If so, who will be

the winners and the losers?

Other areas of concern raised by the current trends

focus on their impact on the efficiency of beef production.

For example, will increased concentration in meatpacking

allow meatpackers to exercise a degree of monopsony power

and reduce returns to cattle producers?

Also, the industry's efforts to increase the demand

for beef through the introduction of new products such as

lean beef and restructured beef cuts has raised many ques-

tions concerning the impact of these new products on the

sector. How successful will a new product need to be in

order to prevent further reductions in the herd size? How

will the type of production systems used to produce the new

beef products affect the structure of the sector? Will the

new production systems change the location of beef produc-

tion in the U.S.? If meatpacking firms integrate backwards

into the production of beef cattle in order to ensure proper

quality of their product, how will this affect cow-calf

producers?









11
Policy makers have expressed a need for an integrated

model of the U.S. livestock sector which would enable them

to assess the impact of the changes in the structure of the

U.S. livestock sector on the different sets of producers in

the sector (Nelson et al., 1988). The changes that are

occurring in the consumption of beef only serve to highlight

the need for the development of a model of the beef sector-

for policy analysis. The purpose of this dissertation is to

develop a model for analyzing the impact of changes in the

pattern of consumption of meat on the beef industry.


Objectives
The main objective of this research is to develop an

integrated model of the U.S livestock sector to be used for

policy analysis. The primary use of the model in this study

will be to determine the long run impact of the decline in

the consumption of beef on the size and location of the beef

herd. To this end the following subobjectives are outlined:

1. Determine the technological coefficients on pro-

duction activities occurring in the beef industry.

2. Estimate a system of regional inverse demand

equations for meats to determine the interdepend-

encies among the various meat products.

3. Develop a price endogenous spatial equilibrium

programming model of the livestock sector which

incorporates a detailed representation of produc-

tion activities occurring on the supply side and a









12

set of inverse demand equations for meats to rep-

resent the demand side.

4. Use GAMS (General Algebraic Modeling System) as a

matrix generator and report writer in order to

facilitate the flexibility of the model and to

promote its continued usage in the future.


Overview of Study

In the second chapter a discussion of the issues

surrounding the use of mathematical programming to conduct

economic analysis at the sectoral level is presented. A

detailed discussion of the problems associated with incor-

porating a system of demand equations into a mathematical

programming model and the representation of supply curves

with an activity analysis model is provided. In Chapter 3

the mathematical formulation of the mathematical programming

model of the U.S. beef sector is developed. Chapter 4 con-

tains the specification and estimation of a system of demand

equations for fresh meats. Chapter 5 contains the empirical

model used for the analysis, and in Chapter 6 the model is

used to analyze the impact of the decline in beef consump-

tion on the beef sector.














CHAPTER 2
MATHEMATICAL PROGRAMMING AND
SECTOR LEVEL ANALYSIS

Mathematical programming models have been used exten-

sively by agricultural economists to model the livestock

industry (Nelson, 1987b). Samuelson (1952) was the first to

demonstrate that the spatial equilibrium problem could be

cast as a constrained maximization problem. Since then many

extensions of the model have been formulated. Takayama and

Judge (1971) demonstrated how a spatial equilibrium problem,

which incorporates linear supply and demand equations, could

be solved as a quadratic programming problem. The applica-

tion of this formulation, however, has been limited by com-

putational difficulties caused when nonlinear demand and

supply equations are introduced. Separable programming

techniques developed by Duloy and Norton (1975) broadened

the scope of problems which could be solved using this type

of analysis by approximating the nonlinear model in such a

way as to allow the simplex algorithm to be used to generate

solutions. They accomplished this by approximating the non-

linear demand and supply equations with linear line seg-

ments. Hazell and Scandizzo (1977) further extended the

applicability of the spatial equilibrium analysis by incorp-

orating risk behavior into the formulation. McCarl and

13









14
Spreen (1980) discussed price equilibrium models which could

be formulated with implicit supply relationships. They have

shown that a sectoral level analysis of the type being con-

sidered here may be effectively conducted using a price

endogenous mathematical programming model. McCarl and

Spreen also provide a good summary of the use of these types

of models by agricultural economists.

The multicommodity price endogenous programming prob-

lem seeks to determine the vectors of prices and quantities

which establish a price equilibrium in the markets of sever-

al related markets. It takes as data the technological

coefficients on production activities, levels of fixed

resources, demand relationships of final products, and sup-

ply relationships for purchased inputs and generates a solu-

tion which gives the equilibrium prices and quantities of

final goods, the usage pattern for the factors of produc-

tion, prices of purchased factors, and imputed prices for

owned resources and production activities. The equilibrium

is partial because such factors as consumer income and the

prices of commodities not endogenous to the system are

treated as exogenous variables.

There are several advantages to using a programming

model over other techniques given the goals of the study.

First, the model's explicit representation of producer

behavior allows each production unit to adjust endogenously

its supply of products and its use of production inputs.










Thus, the model is able to simulate the response of pro-

ducers to changes in the economic environment, making it

possible to identify not only increases or decreases in

supply caused by changes in exogenous variables, but to also

identify the pattern of production activities used. Second,

the model allows for the introduction of new production

activities. Thus, it is possible to simulate the impact of

these activities on the profitability of the activity and

the effects they will have on the rest of the sector.

Third, it does not require knowledge of derived demand and

supply curves at each production level of the sector, but

only input supply and final product demand curves.

In addition, a price endogenous mathematical program-

ming model theoretically allows the introduction of changes

in the demand structure for goods, whether they are due to a

shift in consumer preferences or the introduction of new

products. Thus, it is possible to determine the impact of

the introduction of new technologies, new products, and

changes in the demand structure on the industry.


Incorporating Demand Systems
into Mathematical Programming Models

The Spatial Equilibrium Model

In order to mathematically formulate the price

endogenous programming problem, let













Pi = di(Q1,Q21* IQj I)


denote the inverse demand equation for commodity i, Pi is

the demand price of commodity i, Q1, i=l,---,n is the

quantity demanded of commodity i, and I is consumer income.

Let


pJ = sJ (Q1,Q2,...,QIlZ)



be the inverse supply equation for commodity j, PJ is the

supply price of commodity j, QJ, j = 1,---,n is the quantity

supplied of commodity j and Z is a vector of supply

shifters. The constrained optimization problem can be

written as

n
Max NSB = f f f***' di(QI,Q21,--,Q) dQ1dQ2".'dQ.
i=l
(2.1)

n
-_ f 'f... f-s(Q1,Q2,...,Q") dQ'dQ2-- dQn
j=1


s.t. Qi < Qi i=l,--* ,n (2.2)



Qi, Qi 2 0 (2.3)










The objective function (2.1) maximizes the sum of

areas under each demand function less the sum of the areas

under each supply function. The inequality (2.2) insures

that the quantity demanded is less than or equal to quantity

supplied (no excess demand). Expression (2.3) imposes the

nonnegativity conditions.

Expression (2.1) is a simplification of the integra-

tion that must be performed to properly describe consumer's

plus producer's surplus in a multicommodity framework. Fol-

lowing Hazell and Norton (1986, p. 168), a series of line

integrals are performed in which the first term is




Qi
f Di(Q1, Q2, ,Qn) dtl
0



but all succeeding terms are



Qi
f Di(Q1,Q2,7 I,Qn I Q1=0,Q2=2,*.,Qi-1=0)di
0



and similar expressions are formed when integrating the

supply functions. For further explanation see Hazell and

Norton.

If the demand and supply relationships are linear,


e.g.









18


n
Pi = g, E hi, Qk i=l,--,n
k=l
and
n
p = el + E fik Qk j=l,-",n
k=1



then (2.1) (2.2) can be written as a quadratic programming

problem

n n n
Max E giQi 1/2 : E QiQkhik (2.4)
i=l i=l k=l


n n n
M eJQj 1/2 E : QjQkfjk
j=1 j=1 k=1


s.t. Qi s Qi, i=l,---n (2.5)


Qi,Q' e 0. (2.6)



The Integrability Problem

Two important assumptions are made to ensure that the

solution of (2.1) (2.3) is unique. The first assumption

is that the income generated from the commodities under

study does not affect consumer demand. If the sector under

study is small relative to entire economy, this assumption

should not prove to be restrictive. Otherwise a general

equilibrium framework must be employed. The second

assumption is that the demand and supply functions are

integrable.











Integrability requires that the Jacobian matrix of

both the demand system and the supply system be symmetric.

It also requires that the Jacobian matrix of the demand

system be negative definite and the Jacobian matrix of the

supply system to be positive definite. Symmetry requires

that



adi ad

aQk 8Qi
and
asj 8sk

aQk aQo



This ensures that the optimal solution to the constrained

maximization problem does not depend on the order of

integration. If this requirement is not satisfied there

will be as many optimal solutions as there are possible

orderings for integration.

Of the two integrability conditions the symmetry

requirement for demand systems is believed to be the most

difficult to fulfill. The negativity requirement is

generally believed to be satisfied if the demand equations

are downward sloping and the supply equations are upward

sloping.

In the case of supply functions, symmetry is not a

stringent requirement following Zusman (1989), ". in the










case of supply functions the classical assumptions of the

theory of production, in fact, yield the symmetry con-

ditions" (p. 55). However, in the case of consumer demand

functions, symmetry is a very stringent requirement. The

demand relationship consists of a symmetric substitution

effect plus an income effect. The income effect is not gen-

erally symmetric. Thus, the assumptions of demand theory do

not yield the symmetry conditions.


Approaches to Handling the Integrability Problem

Several approaches have been used to deal with the

integrability problem posed by demand systems with non-

symmetric cross-price effects. An ad hoc approach is to

simplify the demand system so that each demand function

includes only own price and own quantity (Hazell and Norton,

1986, p. 168). In this case, all cross-price effects are

zero and hence the integrability condition is satisfied.

Another approach is to reformulate the problem by

incorporating both price and quantity variables into the

primal form of the model (Plessner and Heady). Thus both

price and quantity equilibrium conditions are imposed in the

primal as opposed to (2.1) (2.3) in which quantity equil-

ibrium conditions are imposed in the primal and price equil-

ibrium conditions are imposed implicitly through the dual.

In the case of linear supply and demand equations, the

primal-dual formulation is












n n n n
Max Z (gi hikQk)Q (ej + E fkQk)QJ
i=1 k=l j=1 k=1


s.t. Qi Q1i 0

Pi(Qi Q') = 0

n
(g, E hikQk) Pi 0
k=1


n
Qi(gi E hkQ, pi) = 0
k=l


n
(e + E fikQk) + Pi 0
k=l


n
Qi(e+ + 2
k=l


i=1,-**,n
i=l,-*-n


i=l,--*n




i=l,*--n


fikQk + Pi) = 0


QQiQpi s 0



The objective function no longer represents the area between

the demand and supply functions but represents net social

monetary gain (Takayama and Judge, 1971).

This problem can be solved using linear complemen-

tarity programming (LCP) (Takayama and Judge, 1971;

Stoecker, 1974). The computer code LINDO (Schrage, 1984)

has an option which uses LCP. To be solved by LINDO, the

demand system must be linear. For many problems, this










approach is theoretically sound and computationally

tractable. For large problems, however, it may pose a

problem of size. For example, a problem with 10 commod-

ities, 1000 other primal variables, 10 market clearing

inequalities and 500 resource constraints would result in an

LCP with 1520 variables and 3,040 constraints.

A third approach to the integrability problem is to

transform the demand system so that the Jacobian matrix is

symmetric. This is accomplished by averaging the cross-

price effects and entering them in the off diagonal posi-

tions. The problem with this solution is that the first

order conditions are altered so that price no longer needs

to equal marginal cost. Consequently, the new optimal

solution no longer satisfies the conditions for a competi-

tive equilibrium.

A fourth approach is to use the compensated (Hicksian)

demand system rather than the uncompensated (Marshallian)

demand system. The Marshallian demand systems do not, in

general, satisfy the integrability conditions because the

assumptions of demand theory do not imply that the system's

Jacobian matrix will be either negative definite or sym-

metric. However, economic theory does imply that the

Jacobian matrix of the compensated demand system will be

negative semi-definite and symmetric. Thus it is

unnecessary to reformulate the problem.










Following Silberberg (1978, pp. 232-40), let Q, =

di"(p,, 21, ,p,m) i=1,-**,n represent the uncompensated

demand system and Qi = dh(pi,p,21..,pi,uo) i=l,--*,n

represent the corresponding compensated system of demand

equations. The Slutsky decomposition of the uncompensated

system can be written


adi"(p,m) adh(p,uo) adi"
S-- Ql" (2.7)
a pj a pj Cm


It shows that the change in the quantity of commodity i

demanded due to a change in the price of commodity j can be

split into two parts: a substitution effect and an income

effect. The substitution matrix is negative definite and

symmetric. In equation (2.7) it is represented by the

cross-price effect of the Hicksian demand system. Thus, the

Jacobian matrix of the compensated demand system is both

negative definite and symmetric,



aQi(p,u) aQj(p,uO)

8pj api


thereby satisfying the integrability conditions of the price

endogenous mathematical programming model.

Is the use of compensated demand functions in price

endogenous mathematical programming models appropriate? The

answer depends on the difference in the equilibrium position









24
arrived at when a system of compensated demand equations is

used instead of the corresponding system of ordinary demand

equations.

As shown in Figure 2.1, equilibrium price and quantity

(point E) generated by the simultaneous solution of the

uncompensated demand equation (DO) and the supply equation

is identical to the price-quantity pair resulting from the

simultaneous solution of the compensated equation (Db) and

the supply equation. But if supply shifts from S to S1, the

equilibrium established by the uncompensated demand equation

is at point A, while the equilibrium suggested by the

compensated demand equation is point B. The difference in

quantity demanded is qh-ql" and the difference in price is

plh -pl"

The difference between quantity demanded and the

difference in price will be determined by three factors:

(1) the magnitude of the movement away from the original

equilibrium, (2) the magnitude of the income elasticity of

the commodity for which the price changed, and (3) the share

of consumer's income spent on the commodity. Peters and

Spreen (1989) examined at the difference in the solutions

found by using the compensated and uncompensated demand

systems. They used the demand system for meat estimated by

Eales and Unnevehr (1988) to simulate the equilibrium estab-

lished by the uncompensated and compensated demand system.

They found that for many agricultural products, such as



















p


q q




Figure 2.1. Change in equilibrium along
compensated and uncompensated demand curves due to
an exogenous shift in supply.










beef, there will be little difference between the two

solutions.

This fourth approach is the one that will be used to

formulate the programming model of the U.S. beef sector. It

has been selected because it permits the integrability con-

ditions to be satisfied without reformulating the problem

as required in complementary programming. This preserves

the economic meaning of the objective function, reduces the

size of problem to be solved, and permits nonlinear demand

systems to be used with little cost with respect to the

accuracy of the solution.















CHAPTER 3
A MODEL OF THE U.S. BEEF SECTOR


The purpose of this chapter is to develop a price

endogenous sectoral level programming model of the U.S. beef

sector. It is important that the model accurately portray

the activities occurring in the sector. In the first

section the production activities which are found in the

sector are described. This has the additional benefit of

providing a foundation for validating the base model. The

material contained in this section has been drawn from four

major sources: Marion (1986), McCoy and Sarhan (1988),

Simpson and Farris (1982), and Nelson (1987a). In the

second section the cattle cycle, sector supply response and

the usefulness of static versus dynamic models of the sector

are discussed. In the final section the mathematical formu-

lation of the model is laid out and described.


Organization of the Beef Sector

The organization of the beef sector is complex and the

task of coordinating production activities in the industry

is difficult. The time frame for producing beef is long.

It takes about 2 1/2 years from the time of breeding to the

slaughter of a mature animal. Also, a relatively large

proportion of cattle and calves change ownership as they

27










move through the stages of production, except at the

distribution stage where processors and retailers have taken

over wholesale activities. Coordination is made even more

complex by the distance between the major areas of beef

production and the main demand centers.

Given the complexity of its organization it is con-

venient to arrange production activities occurring in the

sector into a vertical system (Figure 3.1). There are five

major stages of production in the vertical system: cow-

calf, growing, finishing, slaughtering and processing, and

distribution. The initial products (beef calves) enter the

system at the cow-calf stage and are passed sequentially

through the next four stages of production until they reach

their final form (fresh beef products). At this point they

are sold to consumers and exit the system.


The Cow-Calf Stage

The primary activities occurring at the cow-calf stage

are the maintenance and breeding of the cow herd and the

production of stocker or feeder calves. This includes

feeding, breeding and culling of the cow herd and the

production of calves. The primary inputs required at this

stage of production are land for grazing, breeding stock,

and harvested roughage. The level of investment for

operators is high. Consequently, operations are affected by

changes in land values and interest rates.






















COOROINATIONN
EXCHANGE


Intemal or Market *



Internal or market ..



Market ............




L
Market or Formula -
Price Agreement -


Contracts *


FUNCTIONAL STAGES


TYPICAL
C0ua 6


cull
cows






I]


and


I HRI


Market


I Consumer i


Source: Marion, 1986.


Figure 3.1. Organization of the beef sector.









30
Calves are weaned at the age of six months. They are

then either retained for replacement of culled breeding

stock or to expand the cow-herd, sent to the growing stage,

or sent directly to the finishing stage. The decision to

carry the weaned calf into the growing stage is determined

by the availability of forage. In some operations calves

are placed on feed for a short time after they are weaned

and then sold as vealers.

The decision to retain the weaned calf for the cow

herd is based on the size of herd the cow-calf operator

wants to maintain. If the cow-calf operator feels the cow

herd needs to be increased then more calves need to be

retained than the number required for replacement of culled

breeding stock. Likewise, if the operator wants to decrease

the size of the cow herd, then less calves will be retained

than the amount needed to replace culled breeding stock.


The Growing Stage

In the growing stage weaned calves are placed on

forage and roughage for a period of 6 to 12 months for the

purpose of increasing the development of the body frame.

This stage in the production process is often referred to as

the stocker or backgrounding stage. From the growing stage

stockered cattle are either sent directly to the slaughter

plant for processing as nonfed beef or sent to the finishing

stage to be fattened for slaughter. The most common route

used is from backgrounding to the finishing stage then to










the processing stage to be slaughtered. While the market-

ings of nonfed beef are significant the far greater amount

of cattle are marketed as fed beef. For example, in 1988,

fed beef comprised 78% of the total of beef cattle

slaughtered (USDA, 1989). In addition, most of the nonfed

beef slaughter comes from beef and dairy culls.


The Finishing Stage

At the finishing stage the cattle are confined in a

feedlot and placed on a high concentrate ration. The major

production inputs used at this stage are feeder cattle,

feed, feeding facilities, feed storage facilities, and feed

processing and delivery equipment. Feeder cattle enter the

feedlot from either the cow-calf or stocker stages. The

animals are kept on the feedlot for varying lengths of time

depending on their placement weight and the slaughter cattle

to corn price ratio. The lower the ratio the shorter the

period of time the cattle are retained on the feed lot.

Cattle placed in feedlots immediately after weaning are

fattened to a light slaughter weight (900-1100 lbs.).

Yearlings are either short-fed to a light weight or long-fed

to a heavy slaughter weight (1200-1300 lbs.). Older place-

ment cattle are finished heavy. The usual time period for

finishing is six months. From the finishing stage the

cattle are sent to the meatpacking plant for slaughter.

The three production stages described above are not

totally separate or distinct from each other. A large









32
portion of enterprises found at these levels of the vertical

system have integrated more than one of the production

stages into their operations. However, it is uncommon for

all three stages to be completely integrated under the

umbrella of a single enterprise. The stocker stage is the

least distinct of the production stages as it is often

integrated into either the cow-calf or finishing stages.


The Slaughtering and Processing Stage

The slaughtering and processing stage encompasses all

activities involved in the slaughter of beef cattle and the

cutting of carcasses into smaller units for sale to inde-

pendent wholesalers or retail outlets. Primary inputs used

at this stage are slaughter cattle, facilities, labor, and

containers. Live animals can enter the meat-packing plant

from the cow-calf stage, the stocker stage, the finishing

stages or the dairy herd. They are killed, halved, dressed

and their carcasses chilled. The chilled carcasses are then

either sold or cut up further into boxed beef. The calves

coming from the cow-calf stage or the dairy herd are pro-

cessed as vealers, while cattle coming from the stocker

stage or the culled dairy and beef herd are slaughtered as

nonfed beef.


The Distribution Stage

The distribution system for fresh beef is complex and

contains many components (Figure 3.2). The wholesaler























a;

*4



4
a









*4



04


4.



0
Go
c


















(0

El
r O U

0



0
C4



0 U U



0 *5
CU C


















U H










classification includes both the activities of processors

and retail enterprises which perform the wholesale function

as well as independent wholesale organizations. At present

the marketing of beef products is dominated by processors

that sell directly to retail outlets. It is estimated that

over 80% of total beef production is marketed as boxed beef

(Duewer, 1984).

In the distributing stage fresh beef is moved from the

processing stage to the retail outlets. Retail outlets can

be broken into two groups: retail supermarkets and the

hotel, restaurant, and institutional (HRI) trade. Retail

supermarkets are the most significant outlet for fresh beef

although the importance of the HRI trade is growing. Large

retail supermarkets maintain central warehouse facilities

for handling boxed beef purchased from the meat packing

plant. Some of the supermarket chains also maintain a

central cutting facility where carcasses are fabricated into

boxed beef.

Many of the smaller food stores and HRI outlets

require the services of independent wholesalers. Brokers do

not take ownership of the beef products but execute sales on

a commission basis. Jobbers buy and sell to retail custom-

ers. Purveyors also sell on their own account, but

specialize in providing beef to a special set of clientele,

such as expensive hotels.










Regional Structure of the Industry

Cattle raising' is widely dispersed throughout the

U.S. Some 31 states individually account for at least 1% of

total beef cattle production (Table 3.1). However, cattle

raising is not evenly distributed geographically. Of the 19

states producing less than 1% of the total amount of beef

cattle, 15 are located in the heavily populated Northeast.

On the other hand the top 6 producing states account for 41%

of production. All are located west of the Mississippi

River and east of the Rocky Mountains. In all, 57% of beef

cattle production is located between the Mississippi River

and the Rocky Mountains.

Most beef cattle operations are small, with an average

herd size of 34 head. Seventy percent of calves produced

come from cow herds with less than 200 head (Nelson, 1987a).

Boykin et al. (1980) has identified four production

systems which characterize the type of enterprises involved

in cattle raising: cow-calf-feeder, cow-calf-slaughter,

stocker purchase-slaughter sales, and stocker purchase-

feeder sales. The cow-calf-feeder system includes both the

cow-calf and cow-calf-yearling operations. In the cow-calf

operation calves are sold after weaning, whereas in the

cow-calf-yearling operation, calves are carried over into

the growing stage and then sold to a feedlot for finishing.



'Cattle raising includes both the cow-calf and stocker
stages of production.












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In the cow-calf-slaughter system weaned calves are carried

over into the stocker stage and sold as slaughter calves or

kept in the stocker stage longer and sold as nonfed beef.

In some instances operators using this system will place

stocker cattle into feedlots and then sell them as fed

cattle. In the stocker purchase-slaughter sales system

weaned calves are purchased and placed on small grasses,

field stocks, and other feed sources through the growing

stage, then placed in a feedlot for finishing and then sold

for slaughter. Finally, in the stocker-purchase-feeder

sales system, operators purchase weaned calves and place

them on range or pasture during the growing stage. Feeder

cattle are then sold to feedlots for finishing.

The type of beef production system found in a region

is determined by availability of forage, feed, and alter-

natives to cattle production. Of the four systems described

the most prevalent is the cow-calf-feeder system. The cow-

calf system predominates in the southeast while cow-calf-

stocker operations are common in the great plains states.

In the midwest the stocker purchase-slaughter sale system

predominates.

Given the current conversion rate of feed into gain

for beef cattle the finishing of beef cattle occurs pri-

marily in the regions where feed grains are produced (see

Table 3.2). Finishing operations are more highly concen-

trated geographically than cattle production. In 1988, the














TABLE 3.2.


NUMBER OF CATTLE FEEDLOTS AND FED CATTLE MARKETED BY
SIZE OF FEEDLOT CAPACITY, 13 STATES, 1987.


Cattle Feedlot Capacity (head)

< 1.000 1.000-2,000 2,000-3.999 4,000-7,999
Marketed Marketed Marketed Marketed
State Lots (000 hd) Lots (000 hd) Lots (000 hd) Lots (000 hd)


ARIZ 9 17 0 0 -
CALIF 10 3 5 7 7 15 10 51
COLO 140 45 50 90 55 200 30 265
IDAHO 35 10 15 10 15 30 6 50
ILL 8,750 725 40 60 10 40 0 0
IOWA 9,655 1,215 250 321 95 214 -
KANS 1,627 70 92 71 57 190 34 267
MINN 5,931 432 53 65 16 43 0 0
NEBR 8,950 1,340 175 340 135 570 77 690
OKLA 206 30 4 17 3 8
S DAK 4,146 269 24 67 17 77 13 237
TEX 849 90 9 20 12 35 21 170
WASH 62 6 7 35 -

TOTAL 40,353 4,226 723 1,061 409 1,320 211 1,690


Source: USDA, 1989.
















TABLE 3.2--Extended


Cattle Feedlot Capacity (head) Total
of all
8,000-15.999 16.000-31.999 > 32.000 Feedlots
Marketed Marketed Marketed Marketed
Lots (000 hd) Lots (000 hd) Lots (000 hd) Lots (000 hd)


6 177 5 266 20 4
11 98 11 266 6 365 60 7
16 310 11 425 8 895 310 22
6 100 4 260 81 4
0 0 0 0 8,800 8
0 0 0 0 10,000 17
49 1,014 26 1,065 15 1,353 1,900 40
0 0 0 0 0 0 6,000 5
45 920 13 540 5 500 9,400 49
8 83 4 142 5 410 230 6
0 0 4,200 6
36 625 40 1,385 33 2,930 1,000 52
5 33 6 342 80 4

185 3,285 119 4,347 81 7,042 42,081 229










top 13 states with respect to number of cattle on feed

account for 85% of fed beef marketed and the top 6 states

account for 67% of fed beef marketed (see Table 3.3).

Finishing operations can be grouped into farmer and

commercial classifications. The typical farmer operated

feedlot maintains a one time carrying capacity of less than

1,000 head. The feedlot is often just one of several

enterprises operated on the farm, and cattle are on feed

only part of the year. In contrast, the commercial feedlot

has a one-time carrying capacity greater than 1,000 head are

operated as single enterprises and feed cattle the year

round. Regionally, the majority of the farmer feedlots are

found in the midwestern states of Iowa, Illinois, and

Nebraska, while the commercial feedlots are found in the

southwest and great plains states. While a majority of

feedlots are farmer feedlots the majority of fed slaughter

cattle come from the commercial feedlots. Feedlots with a

capacity of less than 1,000 head accounted for 18% of cattle

marketed in 1987, whereas feedlots with capacity of greater

than 8,000 head accounted for 64% of cattle marketed in that

year (see Table 3.3).

The location of slaughter and processing plants mir-

rors the location of feedlots (see Table 3.4). Most cattle

are slaughtered less than 100 miles from where they were

fed.














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Due to the substantial economies of scale associated

with boxed beef two types of enterprises have evolved. The

efficient size of slaughter-processing plant which produces

boxed beef as an output is believed to be between 500,000 to

1 million head annual capacity (Marion, 1986). One type is

the large slaughter-processor with plant capacity often

exceeding 500,000 head who specialize in fed beef and sell

their output as boxed beef. The other type of enterprise

operates a smaller capacity plant and caters to smaller,

specialized customers. The number of firms at this stage is

small. Concentration measures indicate that the top four

firms involved in slaughter and processing of beef account

for 82% of fed beef slaughtered (Marion, 1986).


Dairy Herd

The culls from the dairy herd are a significant source

of beef, typically accounting for 20% of total cattle

slaughter. As a consequence, the amount of dairy culls

slaughtered do have an important effect on price received by

producers in the beef sector. However, the quantity of

culls coming from the dairy sector is not determined by con-

ditions found in the beef system, but by conditions prevail-

ing in the dairy sector. Thus the supply of dairy culls is

exogenous to the beef system. The slaughter of cull cows is

more dispersed than the slaughter of fed beef reflecting the

distribution of cow-calf operations and the dairy herd.










Foreign Trade

Like the dairy herd, foreign trade is significant but

does not play a major role in the decisions made by beef

producers. Thus, level of imports and exports can be treat-

ed as exogenous to the sector. It must noted here, the role

of foreign trade is increasing and that domestic beef

producers hope that increase in beef exports to foreign mar-

kets will offset the decline in beef consumption in the U.S.


Supply Response
Given the long lag in time from when the decision to

produce a calf is made to the time that the live animal is

slaughtered, the decisions made at the cow-calf stage ultim-

ately determine the supply of beef at any point in time.

Thus, the sectors supply response of the sector is deter-

mined by the ability of cow-calf operators to increase or

decrease the number of feeder calves produced.

Cow-calf operators cannot increase production rapidly

in response to favorable market conditions due to two

related factors. First is the length of time it takes to

produce new breeding stock. It takes two years to produce a

heifer for breeding purposes. Second, there are no alter-

native uses for breeding stock other than for the production

of calves. As a consequence, breeding stock in excess of

the amount needed to meet calf production needs are not kept

but sold for slaughter.









47
The slowness of the supply response is believed to be

the principal cause of the cattle cycle. The cattle cycle

has been observed to last 10 years starting with a 3 to 4

year period of contraction in the number of beef cattle

produced followed by a 6 to 7 year period of expansion.

The discussion on the sector's supply response raises

the issue of time and the appropriateness of casting the

model of the beef sector in a static or dynamic framework.

A resolution to the time problem depends on the type of

information one is interested in gaining. If one is inter-

ested in forecasting the prices received by producers or

cattle numbers at any particular point in time then a

dynamic framework is appropriate. However, if one is inter-

ested in long-run trends then the dynamic framework is a

hindrance. The seasonal fluctuations and production cycles

which are incorporated in a dynamic model only serve to hide

the trend. In this case a static framework is appropriate.


The Model
The description of the organization of the beef sector

serves as a conceptual framework with which to mathematic-

ally formulate the programming model. The system for beef

production is represented by a linear activity analysis

model. Regional differences in the production of beef are

accounted for by building an activity analysis model for

each supply region. The demand for beef is represented by a

system of demand equations for meat at the retail level.









48
Transportation activities permit the transportation of live

animals between supply regions and boxed beef from supply

regions to demand regions. The size of the breeding herd,

the level of beef imports and the level of dairy culls

slaughtered are exogenously determined.

Conceptually the model is not complicated. It is a

spatial equilibrium model where the supply functions are

being implicitly represented have been replaced by a linear

activity analysis model of beef production. The mathe-

matical representation of the model is complicated by the

number of dimensions to each variable. However, the

production activities in one region are simply replicated

for the other supply regions. The supply models differ by

the values of their parameters. Variables and their

dimensions are defined in Tables 3.5 and 3.6.

The beef production system as represented by the

following model draws heavily from earlier versions of the

model developed by Nelson et al. (1982), Kennedy (1982), and

Disney (1989). The structure of the model and variable

definitions are as defined in Nelson et al. and Kennedy.

The parameter values were updated by Disney.












TABLE 3.5. VARIABLE DIMENSION DEFINITIONS


Description


Regions
Supply regions are identified by:
(i,i')=1,2,3,4,5






Demand regions are identified by:
j=1,2,3,4


Production Stages
Production stages are identified
by:
s=1,2,3,4,5


The Cow-calf Stage
Production processes used are
identified by:
kl=1,2


i=1 Southeast
i=2 Midwest
i=3 Southwest
i=4 Plains
i=5 West



j=l= Northeast
j=2= South
j=3= Midwest
j=4= West


s=l = cow-calf stage
s=2 = stocker or growing
stage
s=3 = finishing stage
s=4 = slaughtering stage
s=5 = hamburger processing
stage


kl=1 = producing a weaned
calf
kl=2 = culling breeding stock


Subject











TABLE 3.5.--Continued


Description


Types of cattle produced are
identified by:
ul=1,2



The Stocker Stage
Type of animal used in production
activities are identified by:
v2=l

Production processes used are
identified by:
k2=1,2




Types of cattle produced are
identified by:
u2=1,2



The Finishing Stage
Type of animal used in production
activities are identified by:
v3=1,2,3




Production processes used are
identified by:
k3=1,2,3,4,5,6


ul=l = weaned calf
ul=2 = cull





v2 = weaned calf




k2=1 = producing a yearling
k2=2 = producing a 1 1/2 year
old




u2=1 = yearling
u2=2 = 1 1/2 year old





v3=1 = weaned calf
v3=2 = yearling
v3=3 = 1 1/2 year old




k3=l = producing 900 lb.
animal from a weaned
calf


Subject











TABLE 3.5.--Continued


Description


k3=2 = producing 1100 lb.
animal from a weaned
calf
k3=3 = producing 1200 lb.
animal from yearling
k3=4 = producing 1300 lb.
animal from 1 1/2 year
old
k3=5 = producing 900 lb.
animal from yearling
k3=6 = producing 1100 lb.
from 1 1/2 year old


Types of cattle produced are
identified by:
u3=1,2,3,4


u3=1
u3=2
u3=3
u3=4


The Slaughtering Stage
Types of meatpacking plants used
are identified by:
1=1,2,3,4,5






Type of animal used in production
activities are identified by:
v4=1,2,3,4,5,6,7


= 900 lb. animal
= 1100 lb. animal
= 1200 lb. animal
= 1300 lb. animal


1=1 = plant
1=2 = plant
1=3 = plant
1=4 = plant
1=5 = plant


v4=1 = 900 lb. fed animal
v4=2 = 1100 lb. fed animal


Subject











TABLE 3.5.--Continued


Description


v4=3
v4=4
v4=5
v4=6
v4=7


= 1200 lb. fed animal
= 1300 lb. fed animal
= yearling
= 1 1/2 year old
= cull


Production activities used
are identified by:
k4=1,2,3,4,5,6,7
















Product forms produced are
identified by:
u4=1,2,3,4,5


k4=1 = fabricate 900
animal
k4=2 = fabricate 1100
animal
k4=3 = fabricate 1200
animal
k4=4 = fabricate 1300
animal
k4=5 = fabricate year
k4=6 = fabricate 1 1/
old
k4=7 = fabricate cull


u4=1
u4=2
u4=3
u4=4
u4=5


lb. fed


lb.

lb.


lb. fed


ling
2 year


= roast
= steak
= lean trim
= medium trim
= fat and bone


v5=l = roast
v5=2 = steak


Subject


fed

fed


The Hamburger Processing Stage
Product forms used are identified
by:
v5=1,2,3,4











TABLE 3.5.--Continued


Description


Production activities used are
identified by:
k5=1,2,3,4,5,6,7


























Product forms sold are
identified by:
u=1,2,3


v5=3 = lean trim
v5=4 = medium trim


k5=1 = make hamburger from
primal cuts obtained
from 900 lb. fed
animal
k5=2 = make hamburger from
primal cuts obtained
from 1100 lb. fed
animal
k5=3 = make hamburger from
primal cuts obtained
from 1200 lb. fed
animal
k5=4 = make hamburger from
primal cuts obtained
from 1300 lb. fed
animal
k5=5 = make hamburger from
primal cuts obtained
from yearling
k5=6 = make hamburger from
primal cuts obtained
from 1 1/2 year old
k5=7 = make hamburger from
primal cuts obtained
from culls


u=l = hamburger
u=2 = roast
u=3 = steak


Subject












TABLE 3.6 VARIABLE DEFINITIONS

Variables Description


fj(Y) represents the market level inverse demand
system for beef in the jth demand region.

PjU represents the price received for beef
product u consumed away from the home (the
hotel, restaurant, and institutional trade)
in demand region j.

AYj,, the quantity (cwt/year) of beef product u
consumed away from the home in demand region
j.
P. represents the price received for beef
product u exported to other countries.
EYU represents the quantity (cwt) of beef
product u exported on an annual basis.
rdi the price of dairy culls in the ith supply
region.
ZDi the quantity (head) of dairy culls in the
ith supply region utilized in the beef
production system.

rlia1 the price of weaned beef calves (ul=l) or
beef culls (ul=2) in supply region i.

ql,i,kl the level (head) of breeding herd activity
kl utilized in region i.

Z1,i,um quantity (head) of weaned beef calves and
beef culls in region i utilized in the beef
production system.

r2,i,k2 the cost ($/hd) of stockering activity k2 in
supply region i.
q2,i,k2 the level (head of cattle) of stockering
activity k2 utilized in region i.

r3,i,k3 the cost ($/head) of feeding activity k3 in
region i.











q3,1,k3


r4,i,



q4,i,l,k4






qs,ilk5


1,1'



X3,i'''U1-1


X3,i,i',u2


X4,1i,*,1,u2,v4


T,.i',uD


X4,i,i',1,ul-2,v4-7


the level (head of cattle) of feeding
activity k3 utilized in region i.

the cost ($/head) of slaughtering and
producing boxed beef in plant 1 in supply
region i.

the level (head of cattle) of slaughtering
activity k4 utilized in plant 1 in supply
region i.

the cost ($/cwt.) of manufacturing hamburger
in plant 1 in region i.

the level (cwt.) of the k5 hamburger pro-
duction activity utilized in plant 1 in
supply region i.

cost of transporting weaned calves(ul=1) or
beef culls (ul=2) from supply region i to
supply region i'.

number of weaned calves (ul=1) in supply
region i transported to region i' to be
utilized in stockering activities.

number of weaned calves (ul=1) transported
from region i to region i' to be utilized in
feeding activities.

cost of transporting stockered cattle
(u2=yearling or 1-1/2 year old) from supply
region i to supply region i'.

number of stockered cattle,(u2=yearling or
1-1/2 year old) transported from region i to
region i' to be utilized in feeding
activities.

head of stockered cattle (u2=yearling or 1-
1/2 year old) transported from region i to
be slaughtered in plant 1 in region i'.

cost of transporting culls (uD=dairy) from
supply region i to supply region i'.

number of beef culls (ul=2) transported from
region i to be slaughtered in plant 1 in
region i'.










X4,i,iI,,,.-,iv4-7 number of dairy culls (uD=l) shipped for
slaughter from region i to plant 1 in region
i'.

Ti,r,u3 cost of transporting fed beef (u3=900 lbs.,
1100 lbs., 1200 Ibs., or 1300 Ibs.) from
supply region i to supply region i'.

X4,ii',1,,u3,v4 head fed beef (u3=900 lbs., 1100 lbs., 1200
lbs., or 1300 lbs.) transported from region
i to plant 1 in region i'.

TIj,u.- cost of transporting imported beef
(u=hamburger) to demand region j.

XIj,u.I quantity of hamburger (u=l) imported to
demand region j.

TEj,u cost of transporting exported beef (u=roast
or steak) from supply region i to export
markets.

XEn,u quantity of beef products (u=steak or roast)
exported from supply region i.

Tij,u cost of transporting beef products
(u=hamburger, roast or steak) from supply
region i to demand region j.

Xiju quantity of beef products (u=hamburger,
roast or steak) shipped from supply region i
to demand region j.

Mj,u marketing margin ($/cwt.) for beef product
u=hamburger, roast or steak) in demand
region j.

Yj,u quantity (lbs./month) of beef product u
consumed at home in demand region j.

Ij quantity (cwt.) of hamburger available for
importation.
RICJ,n quantity of beef product u consumed away
from home in demand region j.

Zi,, quantity (cwt.) of beef product u sold in
supply region i.
Z4,i,1,u4,14 quantity (cwt.) of primal cut u4 produced in
plant 1 in supply region i from production
activity k4.











Z4,,1,,u4


5s,1,U1,,v5


quantity (cwt.) of primal cuts (u4=roast or
steak) in region i allocated to sales
activity.

quantity (cwt.) of primal cuts (u4=roast,
steak, lean trim or medium trim) in region i
allocated to hamburger activity.

the percentage of fat found in primal cut v5
used in the hamburger activity in supply
region i.

quantity (cwt.) of primal cut v5 used by one
unit of hamburger production activity k5 in
plant 1.

the maximum percentage of fat permitted in
hamburger in supply region i.

head of cattle slaughtered in plant 1 in
supply region i.

capacity (head of cattle) of slaughter plant
1 in supply region i.

quantity (cwt.) of primal cut u4 produced by
one unit of the k4th slaughter activity of
plant 1 in supply region i.

quantity (head) of cattle used by one unit
of production activity k4 in plant 1 in
supply region i.

adjustment to live animal numbers due to
shrinkage during transit from supply region
i to supply region i'.

adjustment to final beef product weights due
to shrinkage during transit from supply
region i to demand region j.

quantity (head) of live animal v4
slaughtered in plant 1 in region i.

head of fed cattle u3 produced in supply
region i.

head of live animal v3 placed on feedlots in
supply region i.


Cs,,1,vS,k5


FATi


TCAPI,i


S,j


Z4,1,l,v4


23,i,u3


Z3,l,v3


c4,i,l,v4,k4










d3,1,3, k3 quantity (head) of fed cattle produced by
one unit of feeding activity k3 in supply
region i.

c3,,v3,k3 quantity (head) of live animals v3 used by
one unit of feeding activity k3 in supply
region i.

Zz,i,u2 head of stockered cattle u2 produced in
supply region i.
Z2,i,v2 head of live animal v2 used in stockering
activities in supply region i.

d21,i,2.k2 quantity (head) of stockered cattle produced
by one unit of stockering activity k2 in
supply region i.

c2,iv2,2 quantity (head) of live animals v2 used by
one unit of stockering activity k2 in supply
region i.

Z1,iu1 head of weaned calves or culls (ul=1 or 2)
produced by breeding and maintenance
activities in supply region i.

Zo,i,vl head of breeding stock used in breeding and
maintenance activities in supply region i.

dl,i,ul,kl quantity (head) of weaned calves (ul=l) or
culls (ul=2) produced by one unit of
breeding (kl=1) and maintenance (kl=2)
activities in supply region i.

c1,i,vl,kl quantity (head) of breeding stock vl used by
one unit of breeding (kl=l) or maintenance
(kl=2) activity in supply region i.
ZDi quantity of dairy culls from supply region i
utilized.


dairy cull supply in region i.


DAIRYi










The Oblective Function


4 4 3
max NSB = M J f(Y)dy, dy3 + 2 2 Pj.Ayj,
j=i L j=l u=l



3 5
+ E P, EY, E rdi ZDi
u=2 i=1



5 2
E. rl,iUl Z,i,l
i=l ul=l



5 2
r2, i,k2 q2,i,k2
i=l k2=1



5 6
~- r3,i,ik3 q3,i,k3
i=l k3=1



5 5 7
r4,i,l q4,i,l,k4
i=l k3=1 k4=1



5 5 4
E rs5,,1 q5,i,1,k5
i=l 1=1 k5=1



5 5
T=1i,i ,,l-1 X ,ii',ul1-
i=1 i'=1













Ti,i',ul-1 X3,ii,u11-


2

u2=1


5 5
- i'=
i=l i'=l


5
- 2
i=1


5

i'=1


5 5
- i'
i=l i'=l


5
- 2
i=l



4
J-
j=l


5

i'=l


5

1=1



5
2
1=1



5

1=1 i


5

1=1


(TIJu-l+ Mj,u.1) XIJ,u-1


5 3
-= u3=2
i=l u3=2


5
- 2
i=l 1


4

j=1


TEi,u XEi,u





T,,u X.j.u


5

i=l


5
-1
i=l


5
E
i'=l


5

i'=l


2

u2=1



4

13=1


6

v4=5



4
v4=
v4=1


Ti,i',u2 X3,i,1',u2


Ti',1,,,u12 X4,ii',1,ul-2,v4-7


Tii',u2 X4,i,i',l,u2,v4





i,i',u3 X4,i,i', ,u3,v4


Ti,i',uD X4,i,i',l,uD,v4-7











The objective function is maximizing the area under-

neath the demand curves in all the demand regions minus the

total cost of activities at each stage of production and

total transportation costs. It also takes account of expen-

ditures on away from home consumption and the cost of

importing beef.

Constraints

The maximization of the objective function is subject

to a number of constraints. The constraints embody the

production activities, transportation activities and the

equilibrium conditions for a competitive market. They are

expressed as follows:

1. Dairy cull supply constraint.



ZDi DAIRYi : 0; i=1,*--,5;



This constraint ensures that the number of dairy culls

utilized in region i is no greater than the number of

dairy culls available in region i.

2. Dairy cull transfer constraint.



5 5
-ZDi + 2 2 X4,,i,,l, s 0; i=l,-' ,5;
i'=l 1=1 uD=l;


This constraint guarantees that the number of dairy

culls transferred from region i (X4,i,,, ,1,) is less than











or equal to the number of dairy culls utilized in

region i (-ZD,).

3. Maintenance of breeding herd constraint.



2
-Zo,i,vi + Z Cl,,vlkl ql,i,kl 0;
kl=l
i=l,**,5;
vl=l;
kl=1,2;


This constraint ensures that the number of cows

utilized in the replacement and breeding activities

(cl,ivlkl ql1,i,kl) in region i is less than or equal to

the number of cows available in region i (Zo,i,vj).

4. Weaned calf and cull production constraint.



2
Zi,,u dli,ul,kl ql,i,k < 0; i=l, ,5;
kl=l ul=1,2;



This constraint ensures that the number of weaned

calves or culls produced in region i (dl,i,ul,k ql,i,ki)

is greater than or equal to the available supply of

weaned calves or culls in region i (Z1i,,,a).











5. Beef cull transfer constraint.



5 5
-Zi,1,ui-2 + E 2 X4,i,,,i,2.2 0; i=1,*'',5;
i'=1 1=1



In this constraint the cattle culled from the breeding

herd are transferred to the slaughter-processing stage.

It ensures that the number of beef culls transferred

from region i to the slaughtering stage (X4,,1,i.1*2) is

less than or equal to the available supply of beef

culls in region i (Z1,,i1.2).

6. Weaned calf transfer constraint.



5 5
-Z1,1,.1-1 + X2,i,i',aul- + X3,ii,ul. < 0;
i'=1 i'=l
i=1,** ,5;



In this constraint weaned calves in region i are

transferred to either the stocker or finishing stages.

It guarantees that the number of weaned calves

transported from region i to the stocker (X2,i,i'.1) and

finishing stages (X3,i,i',u-1i) is less than or equal to

the supply of weaned calves in region i (Z1,1,ul.1).









64

7. The receipt of weaned calves into the stockering stage

constraint.



5
Si,i, X2,iiui'l + Z2,i,v2 -' 0; i=1,'* ,5;
i'=l v2=1;



This constraint assembles weaned calves for use in

stockering activities in region i. It ensures that the

number of weaned calves assembled for use in stockering

activities (Z2,1,12) is no greater than the number of

weaned calves shipped to the stockering stage in region

i times a shrinkage parameter which adjusts the number

of weaned calves shipped for injury and death in

transit (si,, X2,ii,ul=1 ).

8. The utilization of calves in the stockering stage

constraint.



2
-Z2,i,v2 + 2 C2,i,v2.k2 q2,i,k2 < 0;
k2=1
i=1,- ,5;
v2=1;
k2=1,2;


This constraint ensures that the number of weaned

calves utilized in the stockering activity in region i

(c2,i,v2,k2 q2,i,k2) is no greater than the supply of
stocker calves in region i.











9. The stocker output constraint.



2
Z2,1,-2 2 d2,i.u2,k2 q2,ik2 < 0;
k2=1
i=1, 5;
u2=1,2;



This constraint ensures that the number of stockered

cattle produced in region i (d2,i,. k2 q2,i,k2) is greater

than or equal to the available supply of stockered

cattle in region i (Z2,i.u2).

10. The transfer of stockered cattle constraint.



5 5 5
Z2,i.u + E X3,ii',u2 + X4,i,i'lu2 < 0;
i'=1 i'=1 1=1
i=1," ,5;
u2=1,2;
k2=1,2;


This constraint transfers stockered cattle in region i

to either the finishing or slaughter stages. It

guarantees that the number of stockered cattle trans-

ported from region i to the finishing (X3,i,,.,,3) and

slaughter stages (X4,i,1.,,3) is less than or equal to the

available supply of stockered cattle in region i

(Z2,1,u2)











11. The receipt of weaned calves into the finishing stage

constraint.



5
tS i, X ,i,i',ui.i + Z3,i,v3.1 : 0;
i'=1
i=l,---,5;



This constraint collects weaned calves for use in the

finishing stage in region i. It ensures that the

number of weaned calves collected for use in feeding

activities (Z3,1,,.1) is no greater than the number of

weaned calves shipped to the finishing stage in region

i times a shrinkage parameter which adjusts the number

of weaned calves shipped for injury and death in

transit (sl,i, X3,iiU-.1).

12. The receipt of stockered cattle into the finishing

stage constraint.



5
2 X3,i,i',u2 + Z3,i,3 0; i=l,' ,5
i'=l u2=l, v3=2;
u2=2, v3=3;



This constraint collects stockered cattle for use in

the finishing stage in region i. It ensures that the

number of stockered cattle collected for use in feeding

activities (Z3,1,3) is no greater than the number of

stockered cattle shipped to the finishing stage in









67
region i times a shrinkage parameter which adjusts the

number of stockered cattle shipped to region i for

injury and death in transit (s,i, X3,1,1,,,3).

13. The utilization of cattle in the finishing stage

constraint.



4
Z3,,v3 + E C3,1, q3,, s 0; i=1, --,5;
k3=1 v3=1,---,3;


This constraint ensures that the head of cattle

utilized in feeding activities in region i (c3,,v3,3 *

q3,i,3) is no greater than the supply of cattle for

finishing in region i (Z3,1,,3).

14. The finishing stage output constraint.



4
Z3,i,u3 ~ d3,,u3,k3 q3,i,k3 0; i=1, ,5;
k3=1 u3=1,---,4;


This constraint ensures that the number of finished

cattle produced in region i (d3,i,.3,k3 q,,,,,3) is greater

than or equal to the available supply of finished cat-

tle in region i (Z3,,,,3).

15. The transfer of finished or fed cattle constraint.



5 5
Z3u,u3 + 0 2 X4,i,i,,l,u3 0; i=1, 0;,5;
i'=l 1=1 u3=1,-' ,4;











This constraint transfers finished cattle in region i

to the slaughter stage. It guarantees that the number

of fed cattle transported from region i to the

slaughter stage (X4,i,i,1,u3) is less than or equal to the

supply of finished cattle in region i (Z3,,3).

16. The receipt of culls into the slaughter stage con-

straint.



5
Z4,i,l,v4-7 3 Si,i, X4,i,i',l,ul-2
i=l



si,, X4, i,i,,1,U 0; i=1, '1,5;
1=1,-**,5;



This constraint assembles culls for slaughter in region

i. It ensures that the number of culls assembled for

use in slaughtering activities (Z4,1,,,,4.7) is no greater

than the number of beef culls shipped to the slaughter-

ing stage in region i times a shrinkage parameter which

adjusts the number of weaned calves shipped for injury

and death while in transit (si, X4,i,i,,,-,,2) and

the number of dairy culls shipped to the slaughtering

stage in region i times a shrinkage parameter

(Sii, X4,i,i',I,ul-2) *











17. The receipt of stockered cattle into the slaughter

stage constraint.



5
Z4,iv4 si, X4,1, ,u2 0; i=1,- ,5;
i'=l 1=1,***,5;
v4=5,6;
u2=1,2;


This constraint assembles stockered cattle for

slaughter in region i. It ensures that the number of

stockered cattle assembled for use in slaughter

activities (Z4,1,1,,4) is no greater than the number of

stockered cattle shipped to the slaughter stage in

region i times a shrinkage parameter which adjusts the

number of stockered cattle shipped to region i for

injury and death in transit (si,i, X4,i,i',1,u2).

18. The receipt of finished cattle into the slaughter stage

constraint.



5
Z4,i,l,v4 si,i, X4, i,,,1,u3 0; i=1,-- ,5;
i'=1 1=1,-- ,5;
v4=1,-* ,4;
u3=1,-**,4;


This constraint assembles finished cattle for slaughter

in region i. It ensures that the number of fed cattle

assembled for use in slaughter activities (Z4,i,.,v4) is

no greater than the number of fed cattle shipped to the









70
slaughter stage in region i times a shrinkage parameter

which adjusts the number of fed cattle shipped to

region i for injury and death in transit (s,, *



19. The utilization of cattle in the slaughter stage

constraint.



7
Z4,1,1,v4 E2 C4,i,i,,v4,k4 q4,,l,lk4 0;
k4=1 i=1,-",5;
1=1,-- ,5;
v4=1,"--,7;


This constraint ensures that the quantity of cattle

slaughtered in plant 1 (c4,i,l,v4,k4 q4,i.ik4) is no

greater than plant i's supply of slaughter cattle



20. The slaughter activity output constraint.



7
Z 4,1,.1 4, 2: d4,i,l,u4,k4 q4,i,l,k4 < 0; i=1 5 ;
k4=1 1=1,---,5;
u4=1,"**,5;


This constraint guarantees that the number of primal

cuts produced by plant 1 (d4,,1,4 q4,,1.,k4) is greater

than or equal to the available supply of primal cuts in

plant 1 (Z4,i,1,u4).











21. The slaughter of cattle in meatpacking plant

constraint.



7
2 q4,1,i,kM QA,i.I = 0; i=1,* 0,5;
k4=1 1=1,**-,5;



This constraint accounts for the head of cattle

slaughtered in plant 1 in region i.

22. The slaughter capacity constraint.



QAi,i TCAPi, 0; i=1,'*',5;
1=1,-** ,5;


This constraint requires that the quantity of cattle

slaughtered does not exceed plant capacity.

23. The transfer of primal cuts to sale and hamburger

processing activities constraint.



Z4,ilu4 + 6Z4,1,l,.4 + 8'Z5,i,1,.15 0;

i=4,...,5; 1=1,***,5;
u4=1,'--,4; v5=1,-'',4;
a = 1 if u4=1,2
0 if u4=3,4,5
a' = 1 if v5=1,-**,4;
0 if v5=5;


This constraint allocates the quantity of primal cuts

produced in plant 1 to sales or hamburger processing

activities. It ensures that the quantity of primal











cuts allocated to sales and hamburger processing

(Z4,1,1,v4 + Zs,i,1,vs) is less than or equal to the quantity

of primal cuts available in plant 1 (Z4,i,1,u4,k4).

24. Regional supply of steaks and roasts constraint.



5
S Z4,1,,4 + Z,u 0; i=1,--,5;
1=1 u4=1, u=2;
u4=2,u=3;


This constraint assembles all the steaks and roasts al-

located to the sales activity in the meatpacking plants

in region i (Z4,,,1,,4) at a single distribution center.

It guarantees that the quantity of steaks and roasts

available for distribution in region i (Zi,,) is no

greater than the quantity of steaks and roasts al-

located to sale by the meatpacking plants in region i.

25. Utilization of primal cuts in the production of

hamburger constraint.



4
Z5,i,1,vs + Z C5,i.l,v5,k5 qs,i,l,k5 0;
k5=1
i=1,-**,5;
l=1l,--*5;
v5=1,-**,4;


This constraint ensures that the quantity of primal

cuts used to produce hamburger in plant 1 (cs5,i,,v5,ks

qs,i.l,ks) is less than or equal to the quantity of primal









73
cuts allocated to the hamburger processing activity in

plant 1 (Zsi,ls ).

26. The hamburger processing constraint.


4 5
2 Z
k5=1 1=1


qs,1,1,ks + Zi,-,,, 0;


This constraint ensures that the quantity of hamburger

in region i (Z,,,,) is no greater than the quantity of

hamburger produced in the meatpacking plants in region

2 (ksHam qf,i,1,k5) t

27. Hamburger fat content constraint.


4 5
k2 E
k5=1 1=1


a5,i,k5 q5,i,1,k5 FATi Zi,u.1 s 0;


This constraint ensures that percentage of fat by

weight contained in hamburger produced in region i does

not exceed 27%.

28. The transfer of boxed beef constraint.


4

j=1


Xi,j,u + XEi,u Z,., 0;


This constraint transfers box beef cuts from supply

region i to domestic and foreign markets. It ensures


i=1,... 5;
u=1,---,3;










that the quantity of boxed beef cuts transported from

supply region i (X,,j,. + XEi,u) is less than or equal to

the supply of boxed beef cuts in region i (Zi,u).

29. Hamburger import constraint.




j Xj,u.i I < 0; u=l;



This constraint ensures that the quantity of hamburger

imported is less than or equal to an exogenously

determined supply of imported hamburger.

30. Beef consumption constraint.



8XIju-1 Ei sij Xi,j,u

+ (.12) Yj,u + AYJ,U < 0; u=1,2,3;
j=1,- -,4;
8= 1 if u=l
0 if u=2,3;


This constraint ensures that the quantity of fresh beef

consumed at and away from the home (Yj,u + AYJ,U) in

demand region j is less than or equal to the quantity

of foreign and domestically produced transported to

region j (X,,j, + XFj,u,-).

31. Away from home consumption constraint.



AYJ,u + HRIj,u = 0; j=l,'" ,4;
u=l,** ,3;








75

This constraint requires that away from home

consumption of beef in region j equal the away from

home demand for beef.















CHAPTER 4
SPECIFICATION OF AN INVERSE DEMAND
SYSTEM FOR FRESH MEATS


The purpose of this chapter is to specify a system of

demand equations for fresh meats to be used in the pro-

gramming model. The demand system needs to satisfy the

restrictions placed on it by both economic theory and the

programming model.

The first section of the chapter lays out the con-

ditions the demand system needs to satisfy in order for it

to be incorporated into the programming model (Table 4.1).

In the second section of the chapter a demand system for

fresh meats which is consistent with the conditions

established is derived. Characteristics of the data, the

estimation procedure used and the estimated system are

discussed in the third section. In the final section the

demand system to be used in the programming model and a

description of the steps taken to incorporate the estimated

demand system into the programming model are discussed.


Criteria for Selectinq a Demand System to be
Used in the Programming Model

The first condition which the demand system must meet

in order to be used in the programming model is that it be

specified in price-dependent or inverse form. This

76









77

TABLE 4.1. THE CRITERIA USED FOR SELECTING AN APPROPRIATE
SYSTEM OF DEMAND EQUATIONS.

1. They must be specified in price-dependent form.

2. They must satisfy the integrability conditions of the
price endogenous mathematical programming model.

a. Negative definite Jacobian matrix
b. Symmetric cross-quantity effects

3. They must satisfy nonseparability of preferences among
the various meat products.










condition is imposed by the formulation of the programming

model being used. By specifying the demand system in price-

dependent form it is much easier to formulate the program-

ming model and to make economic interpretations.

In demand theory, the demand system is usually derived

by assuming that prices and income are given and that it is

the quantity consumed which is adjusted by consumers in

order to maximize their utility. As a result the consumer's

demand system is specified in quantity-dependent form.

Fortunately, one of the basic results obtained through the

use of duality theory is that the consumer's preferences can

be represented by either the quantity-dependent demand

system or the associated inverse demand system. Anderson

(1980) has further shown that the inverse demand systems

have properties analogous to the properties of the quantity-

dependent demand systems.

In many cases the use of an inverse demand system is

just a matter of expedience with regards to the modeling

effort. There being no reason to represent the demand

relationship in inverse form other than to make the for-

mulation of the programming model simpler and easier to

interpret in an economic sense (see Takayama and Judge,

1971). However, for a product such as beef, the production

decisions are made long before the final product is avail-

able to consumers. This implies that at any given point in

time the supply of beef is fixed, and it is the price of










beef which must adjust in order to achieve market equilib-

rium. Given this it can then be argued that the demand for

beef should be specified in its inverse form, not only

because it is more convenient for modeling purposes, but

because it properly represents the manner in which

equilibrium in the market for beef is determined.

The second condition which the demand system must

fulfill is that it satisfy the integrability conditions of

the programming model. The integrability conditions require

that the Jacobian matrix of the demand equations be negative

definite and have symmetric cross-quantity effects. As dis-

cussed in Chapter 2 the integrability conditions ensure that

a unique solution exists.

A third condition which must be satisfied by the de-

mand system is that it reflect the nonseparability of pref-

erences for meat products by species. The reason for this

assumption about the separability of consumers' preferences

for fresh meat is discussed in greater detail in the next

section.

In addition to the conditions just discussed it is

important that the demand system reflect regional differ-

ences in consumer preferences for meat. This is based on

the assumption that differences in the levels of fresh meat

consumed between regions is determined not only by differ-

ences in population and level of income between regions, but

also by differences in their customs and traditions.









80
Finally, given the controversy over whether a shift in

consumer preferences for meat has occurred the data used to

estimate the demand system should come from the period after

the change in the structure in the demand for meat is

believed to have occurred. This will ensure that the estim-

ated parameters will reflect the current demand structure

for fresh meat.


The Two-Stage Budgeting Process and the
Representation of Consumer Preferences

According to demand theory the fundamental decision

facing consumers is how to allocate their income among the

available goods so as to maximize their utility. This

decision is determined by the consumer's preferences, the

prevailing commodity prices and the consumer's income.

While the consumer's preferences are unobservable they can

be represented by a system of demand equations which relates

the utility maximizing level of consumption to prices and

income.

Demand theory assumes that consumers know and take

into consideration all commodities available when making

their consumption decisions. This implies that the system

of demand equations should contain all commodities. How-

ever, empirical demand equations only contain the commod-

ities of interest and a small subset of related commodities.

One reason for this is that it is impractical to estimate a

demand system which contains all commodities. A second










reason for this is the realization that consumers do not

take into consideration all goods when they make their

expenditure decisions, but only a subset of related goods.

Thus, a demand system, if appropriately defined, only needs

to contain the commodities of interest in order to appropri-

ately represent the consumer's behavior.

The two-stage budgeting process is often used to

represent the consumer's decision-making process and to

define the set of commodities to be included in the demand

system. In the two-stage budgeting process the consumer

first decides how to allocate his or her income over a broad

category of goods, then in the second stage how to allocate

each category's expenditures over the goods contained in

them.

The two-stage budgeting process is used to construct a

utility tree which shows which goods consumers take into

consideration when making their expenditure decisions. The

utility tree depicted in Figure 4.1 demonstrates how the

two-stage budgeting process is used to select the commod-

ities to be included in a demand system. The branches of

the tree represent the budget or expenditure categories and

nodes or leaves on the branches represent the commodities

contained in each of the budget categories. By following

along the branches of this tree one can follow the process

used by the consumer when making a decision to purchase a

particular good. The first leaf on the tree represents all

































































*4

:>4

f-I

4a
41









r1

*^









83
available goods. At this stage the consumer decides how to

allocate expenditures among housing, transportation, food,

and entertainment located at the nodes at the end of each

branch. Then in the next stage the consumer then decides

how to allocate food expenditures among the items in the

food category, such as meats, dairy products, grains, and

fruit.

In order for a particular decision tree to be an

appropriate representation of the consumer's budgeting pro-

cess, the consumer's preferences must be weakly separable

according to the branches of the decision tree. Weak sepa-

rability implies that each branch of the decision tree can

be defined by a separate sub-utility function. Thus, the

two-stage budgeting process provides a theoretical founda-

tion for demand systems which only contain a portion of the

goods available by allowing a demand system to be derived

from the sub-utility function containing the goods of

interest.

There are any number of decision trees which could be

used to represent consumers' decisions to purchase fresh

meats. Two likely candidates are represented in the two

panels found in Figures 4.2 and 4.3.

The utility tree in Figure 4.2 represents a two-stage

budgeting process for fresh meat based on the animal species

from which the meat comes. At the first level of
























































Figure 4.2. Utility tree A.



























































Figure 4.3. Utility tree B.










decision-making the consumer has a given level of expendi-

tures to allocate to food. The consumer then decides how to

allocate the given level of expenditure between meat and

nonmeat categories. At the second level the consumer then

decides the amount of expenditures for meat to allocate to

the purchase of beef, pork, and poultry. At the final level

of the decision tree the consumer then decides the amount of

beef expenditures to spend on hamburger, steak, and roasts.

The utility tree in Figure 4.2 represents the two-

stage budgeting process underlying most empirical studies of

the structure of the consumer's demand for meat. To a large

extent this has been simply a matter of expedience. For the

most part the data on consumption of meat has been based on

disappearance and not on knowledge of the amount actually

purchased by consumers at the retail level. The information

available is published by species. It is also argued that

the assumption that consumers determine how much to spend on

beef, pork and poultry before selecting the particular beef

pork or poultry product they purchase reflects the way con-

sumers budget their meat expenditures. One only need to

look at the meat case at the supermarket where meat is sepa-

rated by species to find corroboration of this observation.

The decision tree in Figure 4.3 represents an

alternative view of the consumer's budgeting process for

meats. In this case, once the consumer determines the

allocation for meat expenditures then the consumer does not










make a further distinction between the different meat

products based on origin of species alone. The consumer

decides how much of food expenditures to allocate towards

the purchase of meat, then at the next level determines the

amount to spend on the various meat products represented in

the diagram. This utility tree implies that consumers'

preferences for meat are weakly separable while their

preferences for hamburger, steaks, roasts, pork, whole

chickens, and chicken parts are not.

Recent empirical evidence indicates that consumers do

not make a distinction between meat products based on

species of origin alone. It indicates that consumers

determine how much of their food expenditures to spend on

meat and then decide how much of their meat expenditures to

spend on steaks, roasts, hamburger, pork, whole chickens,

chicken parts and other meat products (Eales and Unnevehr,

1988) as represented by the utility tree in Figure 4.3.

Thus, in order for a system of demand equations to be

consistent with the decision making process of the consumer

it must be specified at a level which encompasses all meat

cuts, not just those of a particular species. It is a

maintained assumption of this study that consumers'

preferences for fresh meat are weakly separable from all

other goods but not separable among the various meat

products.










The Derivation of the Inverse
Almost Ideal Demand System

Consider the Almost Ideal Demand System (AIDS) pro-

posed by Deaton and Muellbauer (1980). The AIDS model was

developed to test the restrictions on consumer demand

derived from demand theory. As a result it is possible to

impose symmetry of the substitution matrix during estim-

ation. Furthermore, the AIDS model is specified in level

form. This gives it an advantage over the Rotterdam model

which is specified in first difference form because this

permits it to be readily incorporated into a static pro-

gramming model. The AIDS model also has the advantage that,

as long as consumer's preferences are of the price independ-

ent generalized logarithmic (PIGLOG) form, it permits per-

fect aggregation over consumers without assuming that pref-

erences are additive. Thus, with this particular demand

system there is a theoretical justification for imposing

demand restrictions based on individual behavior at the

market level.

Deaton and Muellbauer (1980) derive the AIDS model by

applying Shepherd's Lemma to an expenditure function. An

inverse demand system analogous to the AIDS model can be

derived by specifying a distance function which is dual to

the expenditure function used by Deaton and Muellbauer

(1980) and applying the Shepherd-Hancock Lemma. By using

the distance function similar in form to the AIDS










expenditure function the properties possessed by the AIDS

model are carried over into the inverse demand system.

The distance function is

In D(U,q)= a(q) +U*b(q) (4.1)
where
a(q)= a. + E ai*lnqi + 1/2 EE Yij Inqglnqj (4.2)
i ij
and

b(q)=p)lqPi (4.3)

U represents the level of utility and q is the vector of

commodities consumed. D(U,q) is homogenous in q if Ea=I,,


EiYij = jYij = pi = 0, and yj = Yji.

The compensated share equations in quantity dependent

form are derived by taking the partial derivatives of the

distance function with respect to In q,. Resulting in


wi = ai + E Yij In qj + UpiP.Iqg, (4.4)


The equations are functions of quantity and utility and

represent the compensated inverse demand system in share

equation form. If it is assumed that preferences are homo-

thetic then it is possible to substitute real expenditures

(X/P) for utility. An estimable system which does not rely

on the assumption that preferences are homothetic is found

by deriving an expression for utility from the distance









90
function, 4.1-4.3, and then substituting this expression for

U in 4.4.

Utility maximization implies that D(U,q)=1 and along

with 4.1-4.3 that


U = -(a, + E ai*lnqi + 1/2 EE Yij Inqilnqj)/PJIq (4.5)
i ij

Substituting the result from 4.5 into 4.4 and simplifying

results in



Wi = ai + E Ylnqj Piln(Q) (4.6)


where

ln(Q) = a(q), E ai = 1, yij = yl, Ej yij = 0 E yij = 0

and

E, Pi = 0.
The system of share equations represented by 4.6 are

functions of q alone and represent the uncompensated inverse

demand system. It is linear in parameters if ln(Q) is

approximated by Ekwklnqk.


The Data
Data on the level of household expenditures on fresh

meat products were obtained from the Bureau of Labor Sta-

tistics (BLS) Consumer Expenditure Survey (CES), 1982-1986.

The survey is a representative sample of the U.S. popula-

tion. It records the weekly expenditures of a household











over a two week period. The U.S. is divided into four

regions: Northeast, South, Midwest and West (Figure 4.4).

As with all household surveys a zero level of expenditures

was reported for any particular commodity for many of the

households. Consequently, the data were aggregated from the

household level to the regional level in order to eliminate

the possibility of having zero as an observation.

Expenditure levels for 22 meat products are reported

in the survey which were in turn aggregated into eight

categories for estimation purposes (see Table 4.2). This

aggregation process used the formulas provided in the CES

documentation (see Appendix A for the formulas). The new

data set contains the level of average monthly household

expenditure on the eight aggregate meat commodities by

region.

Data on monthly prices of meat products in the four

demand regions were also obtained from the BLS. The data

contain the U.S. average price as well as separate regional

prices for 24 meat products. The prices reported were

roughly consistent with the commodity categories obtained

from the expenditure survey (see Table 4.2). In the several

instances where multiple prices were reported for a single

expenditure category in the CES data the prices were

averaged together. There were three exceptions to this

procedure. In the steak category the price for porterhouse

steak was not used in calculating the average price for















TABLE 4.2


EXPENDITURES AND PRICES REPORTED FOR MEAT COM-
MODITIES BY THE BUREAU OF LABOR STATISTICS (BLS)
AND THE COMMODITY CATEGORY USED IN THE DEMAND
SYSTEM.


Prices Expenditures Aggregate
Reported Reported Commodities


Turkey


Chicken Legs
Chicken Breast

Whole Chicken

Beef Liver
Bologna
Franks

Ham, canned
Sausage
Other Ham
Pork Chop
Bacon
Pork Shoulder
Pork Roast

Porterhouse Steak
T-Bone Steak
Chuck Steak
Sirloin Steak
Round Steak

Rib Roast
Round Roast
Chuck Roast


Ground Chuck
Ground Beef


Other Poultry

Chicken Parts


Whole Chickens

Other Meat
Other Meat
Other Meat


Canned Ham
Pork Sausage
Ham (excluding canned)
Pork Chops
Bacon
Other Pork
Other Pork

Other Steak
Other Steak
Other Steak
Sirloin Steak
Round Steak

Other Roast
Round Roast
Chuck Roast


Ground Beef
Ground Beef


Other Poultry

Chicken Parts


Whole Chickens


Other Meat


Pork








Steak





Roast


Ground Beef










other steak. This was done because its price was reported

for only two of the demand regions. In the ground beef

category only the price for ground chuck was used because

the ground beef price was not reported prior to 1984. In

the pork category only the prices for sausage, canned ham,

pork chop, and bacon were used. Pork shoulder, pork roast

and other ham were not used because their prices were not

consistently reported in any of the demand regions.

The eight price indexes were calculated by using a

weighted average of the prices of the individual elements of

a meat category. The weights used were the individual

commodities' share of consumer's expenditures on the

aggregate commodity categories.

As alluded to above there was a problem with missing

observations in the price series provided by the BLS. In

some cases the entire price series for a commodity was not

reported in one of the demand regions. This was particu-

larly true for steak prices in the West region (see Table

4.3).

In the instances where this occurred three different

approaches were used to impute the missing prices. The

first approach was to use a price of a substitute commodity

to represent the missing price series. This was done in the

case of pork where the canned ham price was used as a proxy

for the fresh ham prices. It was also done in the case of

other steak where the porterhouse price was used as a proxy




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FILES


A MATHEMATICAL PROGRAMMING MODEL
OF THE U.S. BEEF SECTOR
By
MARK A. PETERS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1990

ACKNOWLEDGMENTS
It has been a very rewarding learning experience to
work with Dr. Thomas H. Spreen, chairman of my dissertation
committee. Dr. Spreen provided many helpful insights. I
appreciate his efforts in making the completion of this
dissertation possible and in finding me employment.
I would also like to thank Dr. John S. Shonkwiler, Dr.
William G. Boggess, Dr. Timothy G. Taylor, and Dr. Douglas
G. Waldo for serving on my dissertation committee. My
appreciation is also extended to Dr. Rodney R. Martin at
Auburn University and Dr. Kenneth E. Nelson at the Economic
Research Service for providing me with much needed
information.
Financially speaking, I am grateful to the Food and
Resource Economics Department of the University of Florida
for funding much of my stay here as well as to the USDA
which provided me with a fellowship for three years.
Emotionally speaking, I am indebted to the friends I
have made in Gainesville and to my family who have supported
me during this endeavor. I am especially indebted to May
Mercado who gave me her unconditional love.
ii

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
ABSTRACT V
CHAPTERS
1. CHANGES OCCURRING IN THE STRUCTURE OF THE
U.S. BEEF INDUSTRY 1
Objectives 11
Overview of Study 12
2. MATHEMATICAL PROGRAMMING AND SECTOR LEVEL
ANALYSIS 13
Incorporating Demand Systems into
Mathematical Programming Models . . 15
The Integrability Problem 18
3. A MODEL OF THE U.S. BEEF SECTOR 27
Organization of Beef Sector 27
Supply Response 46
The Model 47
4. SPECIFICATION OF AN INVERSE DEMAND SYSTEM
FOR FRESH MEATS 76
Criteria for Selecting a Demand System
to be Used in the Programming
Model 76
The Two-Stage Budgeting Process and the
Representation of Consumer
Preferences 80
The Derivation of the Inverse Almost
Ideal Demand System 88
The Data 90
Estimation Procedures 97
The Results 98
iii

Adjustments Made to Demand Equations . 117
5. DESCRIPTION OF ACTIVITY ANALYSIS MODEL OF
BEEF PRODUCTION SYSTEM 123
6. BASE RESULTS AND SIMULATIONS 148
The Base Run 148
Scenarios .. . 157
7. SUMMARY AND CONCLUSIONS 198
APPENDICES
A. TRANSFORMATIONS OF EXPENDITURE AND PRICE
DATA 210
B. TRANSFORMATIONS TO COST OF PRODUCTION
DATA 213
C. GAMS PROGRAM 223
D. THE EMPIRICAL COMPENSATED DEMAND SYSTEM . 244
REFERENCES 246
BIOGRAPHICAL SKETCH 251
iv

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
A MATHEMATICAL PROGRAMMING MODEL OF THE U.S.
BEEF SECTOR
By
Mark A. Peters
December, 1990
Chairman: Thomas H. Spreen
Major Department: Food and Resource Economics
The main purpose of this study was to build an econom¬
ic model of the U.S. beef sector for use in policy analysis.
The model developed is a price endogenous spatial equilib¬
rium model. It integrates a system of demand equations for
beef with an activity analysis model of the U.S. beef pro¬
duction system. The representation of the beef production
system partitions the U.S. into five supply regions and four
production stages. The representation of demand for beef
partitions the U.S. into four demand regions.
The use of this methodology has been limited by
restrictions placed on model formulation by integrability
conditions. A new approach was used to solve the integra¬
bility problem. In this approach a compensated demand
v

system is used in place of the more generally used uncom¬
pensated demand system.
An inverse Almost Ideal Demand System (AIDS) contain¬
ing eight meat commodities was derived and estimated for
each of the four demand regions. The demand systems were
estimated by pooling the data on household expenditures on
meat obtained from the Consumer Expenditure Survey, 1982-
1986.
The model was used to analyze the impact of an in¬
crease in poultry consumption, an increase in beef imports
and an increase on beef imports on participants in the beef
sector. Increased levels of poultry consumption and
increased levels of beef exports caused a decline in the
quantity of beef produced and a decline in the size of fin¬
ished cattle. Increased exports of beef caused both the
quantity of beef produced and the size of finished cattle to
increase.
The impact of these adjustments on participants in the
sector depended on the location of the supply region and the
stage of production. The quantity of beef produced declined
significantly in the Southeast due to an increase in poultry
consumption or beef imports. The decline in the size of
finished cattle caused the quantity of cattle finished to
decline in the Southwest and to increase in the Plains. The
increase in cattle size due to an increase in exports of
beef caused the quantity of cattle finished in the Southwest
to increase and to decline in the Plains.
vi

CHAPTER 1
CHANGES OCCURRING IN THE STRUCTURE OF THE U.S.
BEEF INDUSTRY
The beef industry is one of the most important com¬
ponents of the U.S. agricultural sector. In 1985 consumer
expenditures on beef totaled $45.6 billion (USDA, 1988)
while on farm cash receipts for beef totaled $29.1 billion.
This amount represented 20% of total on-farm cash receipts
in the entire agricultural sector for that year (USDA,
1988). In addition, the industry is the major consumer of
grains, and as a consequence, changes in the beef industry
which affect the supply and demand for beef reverberate
throughout the agricultural sector.
The beef industry is in a state of flux with major
changes occurring in its structure in both supply and
demand. On the supply side the geographic location of
production operations is moving westward and sizes of
operations are increasing. Specialization in production is
intensifying as large commercial feedlots and single species
meatpacking plants increase in numbers. Vertical integra¬
tion is also increasing as meatpacking firms continue to
integrate the functions carried out by independent whole¬
salers into their operations. On the demand side, there has
been a dramatic shift in the pattern of meat consumption.
1

2
Poultry's share of household expenditures on meat has
increased, while beef's share of meat expenditures has
declined. The effect of this shift in the pattern of meat
consumption is reflected in the decline in the level of per
capita consumption of beef throughout rhe eighties.
The changes presently occurring in the structure of
the supply side of the beef industry are largely attributed
to two events: the advent of irrigation in the high plains
states and the introduction of boxed beef in the meatpacking
industry in the mid-sixties. The introduction of irrigation
in the high plains has been responsible for the geographic
shift in the location of feeding and slaughtering operations
while boxed beef is responsible for the increasing size of
meatpacking plants and increased vertical integration in the
processing and distribution of fresh beef.
Historically, cattle feeding has been located in areas
of highly concentrated feed grain production known as the
cornbelt, but starting in 1960 a gradual shift occurred in
its location as cattle feeding moved away from the cornbelt
to the western cornbelt and high plains states of Texas,
Nebraska, Kansas, Iowa and Colorado. This shift is primar¬
ily a result of the greater availability of feed grain
supplies in the plains states and economies of scale result¬
ing from large commercial feedlots (McCoy and Sarhan, 1988)
made possible by the introduction of irrigation and the low
opportunity cost for land compared to crop production on

3
nonirrigated lands in this region. Both the greater avail¬
ability of feed grains and economies of scale led to lower
average costs of production, giving these states a compara¬
tive advantage in cattle feeding over the central combelt
states.
The movement of the meatpacking industry has followed
that observed for feedlots. Most cattle are slaughtered
within 100 miles of where they are finished. This is not
surprising given the nature of meatpacking which is essen¬
tially a process of reducing the size of the primary input.
Thus, the closer the meatpacking facility is located to
where the live animal is produced, the less weight that
needs to be shipped long distances. When live animals were
produced by small atomized producers widely dispersed geo¬
graphically, the high cost of assembly and transporting the
animals to slaughter made it economically infeasible to
locate meatpacking facilities at any other location than at
the terminal points of transportation routes. However, with
the development of large scale feedlots assembly costs were
greatly reduced. Thus, the meatpacking facilities were
located closer to the areas where the large feedlots were
located.
The introduction of boxed beef in 1969 is the most
significant technological innovation to occur in the meat¬
packing industry during the past thirty years. Both the
increase in size of meatpacking plants and the increase in

4
level of concentration in the meatpacking industry have been
attributed to the introduction of boxed beef and the econ¬
omies of scale associated with this technology. It has also
transformed the distribution sector since it eliminated the
need for specialty wholesalers to service large retail out¬
lets such as grocery chains (Duewer, 1984).
Boxed beef is the end product of a process by which
the carcass of the slaughtered cow is fabricated (cut) into
primáis, subprimals or both, vacuum wrapped and shipped to
wholesalers or retailers. Primal cuts consist of the major
divisions of the carcass such as rounds, loins, and chucks,
while subprimals cuts include the smaller cuts obtained from
these divisions, such as chuck steak, and chuck roasts.
Since its introduction the amount of beef marketed as
boxed beef has increased steadily and by 1983 accounted for
nearly 90% of fresh beef marketings (Duewer, 1984). There
are large economies of scale associated with boxed beef.
Before the introduction of boxed beef the efficient size
packing plant had a capacity of 250,000 head while after its
introduction the efficient size plant had a capacity of
1,000,000 head (Marion). In addition to economies of size,
boxed beef was widely adopted by the meatpacking industry
because it permitted less fat and bone to be shipped,
allowed the buyer to order specific cuts, reduced shrinkage
during shipping, increased the shelf life of the product,
and required less space in shipping (Nelson, 1987a).

5
As important as the changes occurring in the
production of beef are, the most important change is
occurring on the demand side where a dramatic shift has
occurred in the pattern of meat consumption highlighted by
poultry's supplanting of beef as the major meat product
consumed (Table 1.1). For thirty years prior to 1977, per
capita levels of beef consumption had increased steadily at
approximately the same rate as the rate of growth in
personal income, reaching a high of 94.0 lbs. in 1976. In
1977, the level of beef consumption dropped to 91.0 lbs.
marking the beginning of a period of sharp decline in per
capita levels of beef consumption. The decline continued
until 1980 when beef consumption dropped to a level of
76.4 lbs. per person. From 1980-1986 per capita beef
consumption leveled off, but began to decline again in 1987
when it dropped to 73.4 lbs. During the 1977-1987 time
period the level of beef consumption declined by 18.0 lbs.
per person. In contrast, the per capita level of
consumption of chicken increased steadily during this same
time period and in 1987 surpassed that of beef. In 1975 the
level of poultry consumption stood at 48 lbs. per person and
climbed to a level of 77 lbs. per person in 1987 (Table
1.1). This represents an increase in the level of poultry
consumption of 29 lbs. per person.
In addition to the change which has occurred in the
consumption pattern among the major meat species, a change

6
TABLE 1.1 COMPARISON OF PER CAPITA CONSUMPTION OF BEEF AND
POULTRY TO THE RELATIVE PRICE OF POULTRY TO
BEEF. 1975-87.
Year
Consumption
of Beef
Consumption
of Poultry
Relative Price
of Poultry in
Terms of Beef
] hs
c
1975
88.0
48.3
.955
1976
94.2
51.6
.947
1977
91.4
52.9
.958
1978
87.2
55.5
.860
1979
78.0
60.1
.708
1980
76.4
60.3
.706
1981
77.1
62.0
.729
1982
76.8
63.4
.706
1983
78.2
64.7
.725
1984
78.1
66.5
.793
1985
78.8
69.7
.791
1986
78.4
72.0
-
1987
73.4
77.8
-
Source: USDA, 1987.

7
has also occurred in the pattern of consumption found within
the beef category itself. In 1965, steak ranked as the
number one beef cut in terms of quantity consumed with
roasts ranked second and ground beef third. However, by
1984 the picture had changed dramatically as hamburger was
now ranked number one, steak had dropped to number two and
roasts came in third.
Among agricultural economists there has been con¬
siderable debate over the major factors contributing to the
changes occurring in the pattern of meat consumption and to
the decline in levels of per capita beef consumption. Some
have attributed these changes to a fundamental shift in the
structure of the demand for meats, due either to increased
health concerns on the part of consumers (Chavas, 1983;
Braschler, 1983; and Buse, 1986) or an increased desire for
convenience in food preparation (Carnes, 1984; Eales and
Unnevehr, 1988; and Duewer, 1984). Others assert that the
changes which have occurred in the pattern of meat consump¬
tion are easily explained by changes which have taken place
in such traditional economic variables as the relative price
of beef to poultry, income, and the demographic composition
of the U.S. population (Haidecker et al., 1982; Chalfant and
Alston, 1988; Hager, 1985; Dahlgran, 1987; Heien and Pom-
pelli, 1988).
With regard to the argument that there has been a
shift in consumer preferences due to increased health

8
concerns and need for greater convenience in food
preparation, two explanations are usually given to explain
how these concerns cause consumers to eat less beef. The
first explanation is that the U.S. population has become
increasingly concerned about the fat content of their diets
due to reports that over consumption of fat leads to heart
disease and other health problems. This has led them to try
to reduce the amount of fat consumed, especially animal
fats. Beef products contain more fat than poultry products.
Consequently consumers desire to consume more poultry and
less beef in order to reduce the amount of fat in their
diet. The second explanation is that the number of two-
income households has increased rapidly during the 1975-1987
time period. As a consequence Americans have less time to
spend on meal preparation and desire greater convenience or
ease of use in food products. The traditional beef
products, roasts in particular, require considerably more
preparation time and come in larger portions than poultry
products. Thus consumers desire more poultry and less beef.
With regard to the argument that it is changes in
economic variables such as prices and income which have
caused the decline in beef consumption and not a shift in
preferences, its supporters point out that the relative
price of beef compared to poultry increased significantly
during the period in which the changes in the consumption
pattern occurred. During the 1975-1985 time period the

9
price of poultry relative to the price of beef declined by
17% (see Table 1.1). The primary cause of the decline in
the relative price of poultry to beef being increased effi¬
ciency in the production of poultry which has not been
matched by beef producers. Thus as beef becomes more expen¬
sive relative to poultry consumers demand more poultry and
less beef.
The debate over the cause of declining beef consump¬
tion is not just of esoteric interest to econometricians,
but has important implications for the beef industry as
well. Already, the beef industry is putting its energy into
efforts to increase the demand for beef. These efforts
include the generic promotion of beef, development of a new
grading system by the USDA, private labeling, and the devel¬
opment of new products such as lean beef. However, if the
major cause of the decline in beef consumption is due to the
increase in the relative price of beef to poultry then the
current efforts by the industry to increase demand will be
futile. In this case beef producers should have greater
success in regaining market share if they concentrate on
reducing the cost of producing beef.
All other things being equal, one of the major impacts
of the decline in beef consumption will be a reduction in
the overall size of the nation's beef herd. It is also
likely that the decline in beef consumption and the con¬
sequent reduction in the beef herd will accelerate the

10
current trends in the beef sector with regard to the shift
in location of the beef herd, the increase in the scale of
operations and the increase in the level of concentration in
meatpacking as higher cost participants are squeezed out.
Thus one question which needs to be answered is to
what extent these trends will continue. If so, who will be
the winners and the losers?
Other areas of concern raised by the current trends
focus on their impact on the efficiency of beef production.
For example, will increased concentration in meatpacking
allow meatpackers to exercise a degree of monopsony power
and reduce returns to cattle producers?
Also, the industry's efforts to increase the demand
for beef through the introduction of new products such as
lean beef and restructured beef cuts has raised many ques¬
tions concerning the impact of these new products on the
sector. How successful will a new product need to be in
order to prevent further reductions in the herd size? How
will the type of production systems used to produce the new
beef products affect the structure of the sector? Will the
new production systems change the location of beef produc¬
tion in the U.S.? If meatpacking firms integrate backwards
into the production of beef cattle in order to ensure proper
quality of their product, how will this affect cow-calf
producers?

11
Policy makers have expressed a need for an integrated
model of the U.S. livestock sector which would enable them
to assess the impact of the changes in the structure of the
U.S. livestock sector on the different sets of producers in
the sector (Nelson et al., 1988). The changes that are
occurring in the consumption of beef only serve to highlight
the need for the development of a model of the beef sector
for policy analysis. The purpose of this dissertation is to
develop a model for analyzing the impact of changes in the
pattern of consumption of meat on the beef industry.
Objectives
The main objective of this research is to develop an
integrated model of the U.S livestock sector to be used for
policy analysis. The primary use of the model in this study
will be to determine the long run impact of the decline in
the consumption of beef on the size and location of the beef
herd. To this end the following subobjectives are outlined:
1. Determine the technological coefficients on pro¬
duction activities occurring in the beef industry.
2. Estimate a system of regional inverse demand
equations for meats to determine the interdepend¬
encies among the various meat products.
Develop a price endogenous spatial equilibrium
programming model of the livestock sector which
incorporates a detailed representation of produc¬
tion activities occurring on the supply side and a
3.

12
set of inverse demand equations for meats to rep¬
resent the demand side.
4. Use GAMS (General Algebraic Modeling System) as a
matrix generator and report writer in order to
facilitate the flexibility of the model and to
promote its continued usage in the future.
Overview of Study
In the second chapter a discussion of the issues
surrounding the use of mathematical programming to conduct
economic analysis at the sectoral level is presented. A
detailed discussion of the problems associated with incor¬
porating a system of demand equations into a mathematical
programming model and the representation of supply curves
with an activity analysis model is provided. In Chapter 3
the mathematical formulation of the mathematical programming
model of the U.S. beef sector is developed. Chapter 4 con¬
tains the specification and estimation of a system of demand
equations for fresh meats. Chapter 5 contains the empirical
model used for the analysis, and in Chapter 6 the model is
used to analyze the impact of the decline in beef consump¬
tion on the beef sector.

CHAPTER 2
MATHEMATICAL PROGRAMMING AND
SECTOR LEVEL ANALYSIS
Mathematical programming models have been used exten¬
sively by agricultural economists to model the livestock
industry (Nelson, 1987b). Samuelson (1952) was the first to
demonstrate that the spatial equilibrium problem could be
cast as a constrained maximization problem. Since then many
extensions of the model have been formulated. Takayama and
Judge (1971) demonstrated how a spatial equilibrium problem,
which incorporates linear supply and demand equations, could
be solved as a quadratic programming problem. The applica¬
tion of this formulation, however, has been limited by com¬
putational difficulties caused when nonlinear demand and
supply equations are introduced. Separable programming
techniques developed by Duloy and Norton (1975) broadened
the scope of problems which could be solved using this type
of analysis by approximating the nonlinear model in such a
way as to allow the simplex algorithm to be used to generate
solutions. They accomplished this by approximating the non¬
linear demand and supply equations with linear line seg¬
ments. Hazell and Scandizzo (1977) further extended the
applicability of the spatial equilibrium analysis by incorp¬
orating risk behavior into the formulation. McCarl and
13

14
Spreen (1980) discussed price equilibrium models which could
be formulated with implicit supply relationships. They have
shown that a sectoral level analysis of the type being con¬
sidered here may be effectively conducted using a price
endogenous mathematical programming model. McCarl and
Spreen also provide a good summary of the use of these types
of models by agricultural economists.
The multicommodity price endogenous programming prob¬
lem seeks to determine the vectors of prices and quantities
which establish a price equilibrium in the markets of sever¬
al related markets. It takes as data the technological
coefficients on production activities, levels of fixed
resources, demand relationships of final products, and sup¬
ply relationships for purchased inputs and generates a solu¬
tion which gives the equilibrium prices and quantities of
final goods, the usage pattern for the factors of produc¬
tion, prices of purchased factors, and imputed prices for
owned resources and production activities. The equilibrium
is partial because such factors as consumer income and the
prices of commodities not endogenous to the system are
treated as exogenous variables.
There are several advantages to using a programming
model over other techniques given the goals of the study.
First, the model's explicit representation of producer
behavior allows each production unit to adjust endogenously
its supply of products and its use of production inputs.

15
Thus, the model is able to simulate the response of pro¬
ducers to changes in the economic environment, making it
possible to identify not only increases or decreases in
supply caused by changes in exogenous variables, but to also
identify the pattern of production activities used. Second,
the model allows for the introduction of new production
activities. Thus, it is possible to simulate the impact of
these activities on the profitability of the activity and
the effects they will have on the rest of the sector.
Third, it does not require knowledge of derived demand and
supply curves at each production level of the sector, but
only input supply and final product demand curves.
In addition, a price endogenous mathematical program¬
ming model theoretically allows the introduction of changes
in the demand structure for goods, whether they are due to a
shift in consumer preferences or the introduction of new
products. Thus, it is possible to determine the impact of
the introduction of new technologies, new products, and
changes in the demand structure on the industry.
Incorporating Demand Systems
into Mathematical Programming Models
The Spatial Eguilibrium Model
In order to mathematically formulate the price
endogenous programming problem, let

16
^i (Qi , Q2 / * * * , Qj 1)
denote the inverse demand equation for commodity i, Pi is
the demand price of commodity i, Qi, i=l,---,n is the
quantity demanded of commodity i, and I is consumer income.
Let
PJ = si (Q^Q2, ♦ * * ,Qnl Z)
be the inverse supply equation for commodity j, Pj is the
supply price of commodity j, QJ, j = l,*‘*,n is the quantity
supplied of commodity j and Z is a vector of supply
shifters. The constrained optimization problem can be
written as
n
Max NSB = S / /**•/ di(Qi,Q2, • • • ,Qn) dQ^'-dQ,,
i=l
(2.1)
n
-S J /•••/ s^Q^Q2, • • • ,Qn) dQ1dQ2***dQn
j = l
s . t. Qi ^ Q1
i = l/* *• ,n
(2.2)
Qt, Q1 * 0
(2.3)

17
The objective function (2.1) maximizes the sum of
areas under each demand function less the sum of the areas
under each supply function. The inequality (2.2) insures
that the quantity demanded is less than or equal to quantity
supplied (no excess demand). Expression (2.3) imposes the
nonnegativity conditions.
Expression (2.1) is a simplification of the integra¬
tion that must be performed to properly describe consumer's
plus producer's surplus in a multicommodity framework. Fol¬
lowing Hazell and Norton (1986, p. 168), a series of line
integrals are performed in which the first term is
Qi
J Di (, Q2, • • • , Qn) drii
but all succeeding terms are
Qi
/ (Qi / Q2 / * * * f Qn I Qi=0 / Q2=2 / * * * /Qi-i-°)
and similar expressions are formed when integrating the
supply functions. For further explanation see Hazell and
Norton.
If the demand and supply relationships are linear,
e. g.

18
and
n
pi = 9i - 2 h1)t Q* i=l, ♦ * * , n
k=l
n
p3 = e3 + E fjlt Q* j = l f • • • , n
k=l
then (2.1) - (2.2) can be written as a quadratic programming
problem
n
Max E
i=l
giQi - 1/2
n
E
i=l
n
E
k=l
QíQk^íIc
(2.4)
n
- E
j = l
e3Q3 - 1/2
n
E
j = l
n
E
k=l
QjQ^fJk
s. t.
Qi s Q1, i=l,
• • • n
(2.5)
Qi/Q1 * 0.
(2.6)
The Intearabilitv
Problem
important
assumptions
are
made
to ensure
that the
solution of (2.1) - (2.3) is unique. The first assumption
is that the income generated from the commodities under
study does not affect consumer demand. If the sector under
study is small relative to entire economy, this assumption
should not prove to be restrictive. Otherwise a general
equilibrium framework must be employed. The second
assumption is that the demand and supply functions are
integrable.

19
Integrability requires that the Jacobian matrix of
both the demand system and the supply system be symmetric.
It also requires that the Jacobian matrix of the demand
system be negative definite and the Jacobian matrix of the
supply system to be positive definite. Symmetry requires
that
and
3d, . 3d*
dQ* 3Qt
dSj 3s*
3Q* 3Qj
This ensures that the optimal solution to the constrained
maximization problem does not depend on the order of
integrations. If this requirement is not satisfied there
will be as many optimal solutions as there are possible
orderings for integration.
Of the two integrability conditions the symmetry
requirement for demand systems is believed to be the most
difficult to fulfill. The negativity requirement is
generally believed to be satisfied if the demand equations
are downward sloping and the supply equations are upward
sloping.
In the case of supply functions, symmetry is not a
stringent requirement following Zusman (1989), ". . .in the

20
case of supply functions the classical assumptions of the
theory of production, in fact, yield the symmetry con¬
ditions" (p. 55). However, in the case of consumer demand
functions, symmetry is a very stringent requirement. The
demand relationship consists of a symmetric substitution
effect plus an income effect. The income effect is not gen¬
erally symmetric. Thus, the assumptions of demand theory do
not yield the symmetry conditions.
Approaches to Handling the Inteqrabilitv Problem
Several approaches have been used to deal with the
integrability problem posed by demand systems with non-
symmetric cross-price effects. An ad hoc approach is to
simplify the demand system so that each demand function
includes only own price and own quantity (Hazell and Norton,
1986, p. 168). In this case, all cross-price effects are
zero and hence the integrability condition is satisfied.
Another approach is to reformulate the problem by
incorporating both price and quantity variables into the
primal form of the model (Plessner and Heady). Thus both
price and quantity equilibrium conditions are imposed in the
primal as opposed to (2.1) - (2.3) in which quantity equil¬
ibrium conditions are imposed in the primal and price equil¬
ibrium conditions are imposed implicitly through the dual.
In the case of linear supply and demand equations, the
primal-dual formulation is

21
n n n n
Max 2 (g± - 2 h^QJQi - 2 (ej + 2 fjkQk)Qj
i=l k=l j = l k=l
s • t. — Q1, s O i—1 , * / n
Pi(Qi - Q1) =0 i=lf * * *n
n
(g± - 2 hlkQk) - pi s 0 i=l/***n
k=l
n
Qi(gi “ 2 hlkQk - pi) = 0 i=l/***n
k=l
n
- (e1 + 2 fikQk) + pi í 0 i=l r * * * /n
k=l
n
Q1(e1 + 2 fikQk + Pi) = 0 i=l, ♦ * • n
k=l
Qi/QSpi ^ 0
The objective function no longer represents the area between
the demand and supply functions but represents net social
monetary gain (Takayama and Judge, 1971).
This problem can be solved using linear complemen¬
tarity programming (LCP) (Takayama and Judge, 1971;
Stoecker, 1974). The computer code LINDO (Schrage, 1984)
has an option which uses LCP. To be solved by LINDO, the
demand system must be linear. For many problems, this

22
approach is theoretically sound and computationally
tractable. For large problems, however, it may pose a
problem of size. For example, a problem with 10 commod¬
ities, 1000 other primal variables, 10 market clearing
inequalities and 500 resource constraints would result in an
LCP with 1520 variables and 3,040 constraints.
A third approach to the integrability problem is to
transform the demand system so that the Jacobian matrix is
symmetric. This is accomplished by averaging the cross¬
price effects and entering them in the off diagonal posi¬
tions . The problem with this solution is that the first
order conditions are altered so that price no longer needs
to equal marginal cost. Consequently, the new optimal
solution no longer satisfies the conditions for a competi¬
tive equilibrium.
A fourth approach is to use the compensated (Hicksian)
demand system rather than the uncompensated (Marshallian)
demand system. The Marshallian demand systems do not, in
general, satisfy the integrability conditions because the
assumptions of demand theory do not imply that the system's
Jacobian matrix will be either negative definite or sym¬
metric. However, economic theory does imply that the
Jacobian matrix of the compensated demand system will be
negative semi-definite and symmetric. Thus it is
unnecessary to reformulate the problem.

23
Following Silberberg (1978, pp. 232-40), let Qt =
di“(pi, p2l, ♦ * * ,pn,m) i=l,***,n represent the uncompensated
demand system and Q1 = dih(p1,p2, • • • ,Pi,u°) i=l,-**,n
represent the corresponding compensated system of demand
equations. The Slutsky decomposition of the uncompensated
system can be written
Sd^fp^) 3dh(p,u°) 3d1m
* - Qj“ (2.7)
3 Pj 3 Pj 3m
It shows that the change in the quantity of commodity i
demanded due to a change in the price of commodity j can be
split into two parts: a substitution effect and an income
effect. The substitution matrix is negative definite and
symmetric. In equation (2.7) it is represented by the
cross-price effect of the Hicksian demand system. Thus, the
Jacobian matrix of the compensated demand system is both
negative definite and symmetric,
SQ^p,^) = 3Qj(p,u°)
3Pj 3pi
thereby satisfying the integrability conditions of the price
endogenous mathematical programming model.
Is the use of compensated demand functions in price
endogenous mathematical programming models appropriate? The
answer depends on the difference in the equilibrium position

24
arrived at when a system of compensated demand equations is
used instead of the corresponding system of ordinary demand
equations.
As shown in Figure 2.1, equilibrium price and quantity
(point E) generated by the simultaneous solution of the
uncompensated demand equation (D“) and the supply equation
is identical to the price-quantity pair resulting from the
simultaneous solution of the compensated equation (Dh) and
the supply equation. But if supply shifts from S to Slf the
equilibrium established by the uncompensated demand equation
is at point A, while the equilibrium suggested by the
compensated demand equation is point B. The difference in
quantity demanded is q^-q^ and the difference in price is
Pih-Pi“-
The difference between quantity demanded and the
difference in price will be determined by three factors:
(1) the magnitude of the movement away from the original
equilibrium, (2) the magnitude of the income elasticity of
the commodity for which the price changed, and (3) the share
of consumer's income spent on the commodity. Peters and
Spreen (1989) examined at the difference in the solutions
found by using the compensated and uncompensated demand
systems. They used the demand system for meat estimated by
Eales and Unnevehr (1988) to simulate the equilibrium estab¬
lished by the uncompensated and compensated demand system.
They found that for many agricultural products, such as

Figure 2.1. Change in equilibrium along
compensated and uncompensated demand curves due to
an exogenous shift in supply.

26
beef, there will be little difference between the two
solutions.
This fourth approach is the one that will be used to
formulate the programming model of the U.S. beef sector. It
has been selected because it permits the integrability con¬
ditions to be satisfied without reformulating the problem
as required in complementary programming. This preserves
the economic meaning of the objective function, reduces the
size of problem to be solved, and permits nonlinear demand
systems to be used with little cost with respect to the
accuracy of the solution.

CHAPTER 3
A MODEL OF THE U.S. BEEF SECTOR
The purpose of this chapter is to develop a price
endogenous sectoral level programming model of the U.S. beef
sector. It is important that the model accurately portray
the activities occurring in the sector. In the first
section the production activities which are found in the
sector are described. This has the additional benefit of
providing a foundation for validating the base model. The
material contained in this section has been drawn from four
major sources: Marion (1986), McCoy and Sarhan (1988),
Simpson and Farris (1982), and Nelson (1987a). In the
second section the cattle cycle, sector supply response and
the usefulness of static versus dynamic models of the sector
are discussed. In the final section the mathematical formu¬
lation of the model is laid out and described.
Organization of the Beef Sector
The organization of the beef sector is complex and the
task of coordinating production activities in the industry
is difficult. The time frame for producing beef is long.
It takes about 2 1/2 years from the time of breeding to the
slaughter of a mature animal. Also, a relatively large
proportion of cattle and calves change ownership as they
27

28
move through the stages of production, except at the
distribution stage where processors and retailers have taken
over wholesale activities. Coordination is made even more
complex by the distance between the major areas of beef
production and the main demand centers.
Given the complexity of its organization it is con¬
venient to arrange production activities occurring in the
sector into a vertical system (Figure 3.1). There are five
major stages of production in the vertical system: cow-
calf, growing, finishing, slaughtering and processing, and
distribution. The initial products (beef calves) enter the
system at the cow-calf stage and are passed sequentially
through the next four stages of production until they reach
their final form (fresh beef products). At this point they
are sold to consumers and exit the system.
The Cow-Calf Stage
The primary activities occurring at the cow-calf stage
are the maintenance and breeding of the cow herd and the
production of stocker or feeder calves. This includes
feeding, breeding and culling of the cow herd and the
production of calves. The primary inputs required at this
stage of production are land for grazing, breeding stock,
and harvested roughage. The level of investment for
operators is high. Consequently, operations are affected by
changes in land values and interest rates.

COORDINATION/
EXCHANGE
FUNCTIONAL STAGES
TYWCAL
COMBINATIONS
Calf production j cull —
COWS
f :
! Growing j —
M'
Internal or market • ■ order buyers
^aijction
Market
I Feeding |
\
auctions & ^ Cull Dairy Cows
terminals and Bulls
i /
Source: Marion, 1986.
Figure 3.1. Organization of the beef sector

30
Calves are weaned at the age of six months. They are
then either retained for replacement of culled breeding
stock or to expand the cow-herd, sent to the growing stage,
or sent directly to the finishing stage. The decision to
carry the weaned calf into the growing stage is determined
by the availability of forage. In some operations calves
are placed on feed for a short time after they are weaned
and then sold as vealers.
The decision to retain the weaned calf for the cow
herd is based on the size of herd the cow-calf operator
wants to maintain. If the cow-calf operator feels the cow
herd needs to be increased then more calves need to be
retained than the number required for replacement of culled
breeding stock. Likewise, if the operator wants to decrease
the size of the cow herd, then less calves will be retained
than the amount needed to replace culled breeding stock.
The Growing Stage
In the growing stage weaned calves are placed on
forage and roughage for a period of 6 to 12 months for the
purpose of increasing the development of the body frame.
This stage in the production process is often referred to as
the stocker or backgrounding stage. From the growing stage
stockered cattle are either sent directly to the slaughter
plant for processing as nonfed beef or sent to the finishing
stage to be fattened for slaughter. The most common route
used is from backgrounding to the finishing stage then to

31
the processing stage to be slaughtered. While the market¬
ings of nonfed beef are significant the far greater amount
of cattle are marketed as fed beef. For example, in 1988,
fed beef comprised 78% of the total of beef cattle
slaughtered (USDA, 1989). In addition, most of the nonfed
beef slaughter comes from beef and dairy culls.
The Finishing Stage
At the finishing stage the cattle are confined in a
feedlot and placed on a high concentrate ration. The major
production inputs used at this stage are feeder cattle,
feed, feeding facilities, feed storage facilities, and feed
processing and delivery equipment. Feeder cattle enter the
feedlot from either the cow-calf or stocker stages. The
animals are kept on the feedlot for varying lengths of time
depending on their placement weight and the slaughter cattle
to corn price ratio. The lower the ratio the shorter the
period of time the cattle are retained on the feed lot.
Cattle placed in feedlots immediately after weaning are
fattened to a light slaughter weight (900-1100 lbs.).
Yearlings are either short-fed to a light weight or long-fed
to a heavy slaughter weight (1200-1300 lbs.). Older place¬
ment cattle are finished heavy. The usual time period for
finishing is six months. From the finishing stage the
cattle are sent to the meatpacking plant for slaughter.
The three production stages described above are not
totally separate or distinct from each other. A large

32
portion of enterprises found at these levels of the vertical
system have integrated more than one of the production
stages into their operations. However, it is uncommon for
all three stages to be completely integrated under the
umbrella of a single enterprise. The stocker stage is the
least distinct of the production stages as it is often
integrated into either the cow-calf or finishing stages.
The Slaughtering and Processing Stage
The slaughtering and processing stage encompasses all
activities involved in the slaughter of beef cattle and the
cutting of carcasses into smaller units for sale to inde¬
pendent wholesalers or retail outlets. Primary inputs used
at this stage are slaughter cattle, facilities, labor, and
containers. Live animals can enter the meat-packing plant
from the cow-calf stage, the stocker stage, the finishing
stages or the dairy herd. They are killed, halved, dressed
and their carcasses chilled. The chilled carcasses are then
either sold or cut up further into boxed beef. The calves
coming from the cow-calf stage or the dairy herd are pro¬
cessed as vealers, while cattle coming from the stocker
stage or the culled dairy and beef herd are slaughtered as
nonfed beef.
The Distribution Stage
The distribution system for fresh beef is complex and
contains many components (Figure 3.2). The wholesaler

Source: McCoy and Sarhan, 1988.
Figure 3.2. Major components of meat processing and distributing.

34
classification includes both the activities of processors
and retail enterprises which perform the wholesale function
as well as independent wholesale organizations. At present
the marketing of beef products is dominated by processors
that sell directly to retail outlets. It is estimated that
over 80% of total beef production is marketed as boxed beef
(Duewer, 1984).
In the distributing stage fresh beef is moved from the
processing stage to the retail outlets. Retail outlets can
be broken into two groups: retail supermarkets and the
hotel, restaurant, and institutional (HRI) trade. Retail
supermarkets are the most significant outlet for fresh beef
although the importance of the HRI trade is growing. Large
retail supermarkets maintain central warehouse facilities
for handling boxed beef purchased from the meat packing
plant. Some of the supermarket chains also maintain a
central cutting facility where carcasses are fabricated into
boxed beef.
Many of the smaller food stores and HRI outlets
require the services of independent wholesalers. Brokers do
not take ownership of the beef products but execute sales on
a commission basis. Jobbers buy and sell to retail custom¬
ers. Purveyors also sell on their own account, but
specialize in providing beef to a special set of clientele,
such as expensive hotels.

35
Regional Structure of the Industry
Cattle raising1 is widely dispersed throughout the
U.S. Some 31 states individually account for at least 1% of
total beef cattle production (Table 3.1). However, cattle
raising is not evenly distributed geographically. Of the 19
states producing less than 1% of the total amount of beef
cattle, 15 are located in the heavily populated Northeast.
On the other hand the top 6 producing states account for 41%
of production. All are located west of the Mississippi
River and east of the Rocky Mountains. In all, 57% of beef
cattle production is located between the Mississippi River
and the Rocky Mountains.
Most beef cattle operations are small, with an average
herd size of 34 head. Seventy percent of calves produced
come from cow herds with less than 200 head (Nelson, 1987a).
Boykin et al. (1980) has identified four production
systems which characterize the type of enterprises involved
in cattle raising: cow-calf-feeder, cow-calf-slaughter,
stocker purchase-slaughter sales, and Stocker purchase-
feeder sales. The cow-calf-feeder system includes both the
cow-calf and cow-calf-yearling operations. In the cow-calf
operation calves are sold after weaning, whereas in the
cow-calf-yearling operation, calves are carried over into
the growing stage and then sold to a feedlot for finishing.
battle raising includes both the cow-calf and stocker
stages of production.

TABLE 3.1.
NUMBER OF
CATTLE
BY STATE AND
STATE'S
SHARE OF
U.S. TOTAL, 1988.
Region
State
Beef
Cows
Milk
Cows
Total
Beef
of
State's Share
's Share of U.S. of Region
Total Total Total
ooo % %
Northwest
CONN
5.0
37.0
42.0
11.9
©
•
o
1.4
DEL
2.0
9.0
11.0
18.2
0.0
0.5
MAINE
9.0
47.0
55.0
14.5
0.0
2.2
MASS
10.0
33.0
43.0
23.3
0.0
2.7
NH
5.0
23.0
28.0
17.9
0.0
1.4
NJ
11.0
31.0
42.0
26.2
0.0
3.0
NY
112.0
844.0
956.0
11.7
0.3
30.4
PA
206.0
724.0
930.0
22.2
0.6
55.9
RI
0.8
2.9
3.7
21.6
0.0
0.2
VT
9.0
170.0
179.0
5.0
0.0
2.4
TOTAL
369.0
1,921.0
2,290.0
16.1
1.1
100.0
Southeast
ALA
875.0
40.0
915.0
95.6
2.7
12.6
FLA
1,086.0
179.0
1,265.0
85.8
3.3
15.6
GA
703.0
102.0
805.0
87.3
2.1
10.1
KY
1,017.0
218.0
1,235.0
82.3
3.1
14.6
MD
53.0
113.0
166.0
31.9
0.2
0.8
MISS
706.0
68.0
774.0
91.2
2.1
10.1
NC
320.0
105.0
425.0
75.3
1.0
4.6
SC
284.0
43.0
1,190.0
82.9
3.0
14.2
VA
690.0
145.0
835.0
82.6
2.1
9.9
W VA
248.0
31.0
279.0
88.9
0.8
3.6
TOTAL
6,968.0
1,248.0
8,216.0
84.8
21.1
100.0
oo
en

Southwest
Midwest
Plains
ARK
945.0
72.0
1,017.0
92.9
2.9
10.9
LA
615.0
87.0
702.0
87.6
1.9
7.1
OKLA
1,842.0
108.0
1,950.0
94.5
5.6
21.3
TEX
5,260.0
340.0
5,600.0
93.9
16.0
60.7
TOTAL
8,662.0
607.0
9,269.0
93.5
26.3
100.0
ILL
525.0
210.0
735.0
71.4
1.6
5.0
IND
370.0
190.0
560.0
66.1
1.1
3.5
IOWA
1,210.0
299.0
1,509.0
80.2
3.7
11.5
KANS
1,466.0
104.0
1,570.0
93.4
4.4
13.9
MICH
130.0
358.0
488.0
26.6
0.4
1.2
MINN
370.0
810.0
1,180.0
31.4
1.1
3.5
MO
1,866.0
224.0
2,090.0
89.3
5.7
17.7
N DAK
871.0
99.0
970.0
89.8
2.6
8.3
NEBR
1,680.0
100.0
1,780.0
94.4
5.1
15.9
OHIO
412.0
368.0
780.0
52.8
1.3
3.9
S DAK
1,448.0
147.0
1,595.0
90.8
4.4
13.7
WIS
200.0
1,790.0
1,990.0
10.1
10.6
1.9
TOTAL
10,458.0
4,699.0
15,247.0
69.2
32.0
100.0
ARIZ
260.0
90.0
350.0
74.3
0.8
5.7
COLO
778.0
72.0
850.0
91.5
2.4
17.1
IDAHO
510.0
160.0
670.0
76.1
1.5
11.2
MONT
1,275.0
25.0
1,300.0
98.1
3.9
28.1
N MEX
527.0
59.0
586.0
89.9
1.6
11.6
NEV
246.0
19.0
265.0
92.8
0.7
5.4
UTAH
318.0
78.0
391.0
81.3
1.0
7.0
WYO
630.0
10.0
640.0
98.4
1.9
13.9
TOTAL
4,544.0
508.0
5,052.0
89.9
13.8
100.0
u>
-4

TABLE 3.1.—continued
State
Percent
Beef
Milk
Percent Beef
of U.S.
of Region
Region
State
Cows
Cows
Total
of Total
Total
Total
000 % %
West
ALAS
2.5
2.3
•
00
52.1
10.0
0.1
CALIF
895.5
1,004.7
1,900.2
47.1
2.7
47.7
HAW
73.0
12.0
85.0
85.9
0.2
3.9
OREG
547.0
94.0
641.0
85.3
1.7
29.2
WASH
359.0
211.0
570.0
63.0
1.1
19.1
TOTAL
1,877.0
1,324.0
3,201.0
58.6
5.7
100.0
U.S.
TOTAL
32,958.0
10,307.0
43,265.0
76.2
100.0
-
Source; USDA, 1989.
CO
CO

39
In the cow-calf-slaughter system weaned calves are carried
over into the stocker stage and sold as slaughter calves or
kept in the stocker stage longer and sold as nonfed beef.
In some instances operators using this system will place
stocker cattle into feedlots and then sell them as fed
cattle. In the stocker purchase-slaughter sales system
weaned calves are purchased and placed on small grasses,
field stocks, and other feed sources through the growing
stage, then placed in a feedlot for finishing and then sold
for slaughter. Finally, in the stocker-purchase-feeder
sales system, operators purchase weaned calves and place
them on range or pasture during the growing stage. Feeder
cattle are then sold to feedlots for finishing.
The type of beef production system found in a region
is determined by availability of forage, feed, and alter¬
natives to cattle production. Of the four systems described
the most prevalent is the cow-calf-feeder system. The cow-
calf system predominates in the southeast while cow-calf-
stocker operations are common in the great plains states.
In the midwest the stocker purchase-slaughter sale system
predominates.
Given the current conversion rate of feed into gain
for beef cattle the finishing of beef cattle occurs pri¬
marily in the regions where feed grains are produced (see
Table 3.2). Finishing operations are more highly concen¬
trated geographically than cattle production. In 1988, the

40
TABLE 3.2. NUMBER OF CATTLE FEEDLOTS AND FED CATTLE MARKETED BY
SIZE OF FEEDLOT CAPACITY, 13 STATES, 1987.
State
Cattle
Feedlot Capacity
(head)
<
1.000
1.
000-2.000
2.
000-3.999
4,
000-7,999
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
ARIZ
9
17
0
0
.
,
_
_
CALIF
10
3
5
7
7
15
10
51
COLO
140
45
50
90
55
200
30
265
IDAHO
35
10
15
10
15
30
6
50
ILL
8,750
725
40
60
10
40
0
0
IOWA
9,655
1,215
250
321
95
214
-
-
KANS
1,627
70
92
71
57
190
34
267
MINN
5,931
432
53
65
16
43
0
0
NEBR
8,950
1,340
175
340
135
570
77
690
OKLA
206
30
-
-
4
17
3
8
S DAK
4,146
269
24
67
17
77
13
237
TEX
849
90
9
20
12
35
21
170
WASH
62
6
-
-
7
35
-
TOTAL
40,353
4,226
723
1,061
409
1,320
211
1,690
Source: USDA, 1989

41
TABLE 3.2—Extended
Cattle Feedlot Capacity (head)
Total
of all
Feedlots
8.000-15.999
16.000-31.999
>
â–  32.000
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
Lots
Marketed
(000 hd)
__
_
6
177
5
266
20
4
11
98
11
266
6
365
60
7
16
310
11
425
8
895
310
22
6
100
4
260
-
-
81
4
-
-
0
0
0
0
8,800
a
-
-
0
0
0
0
10,000
17
49
1,014
26
1,065
15
1,353
1,900
40
0
0
0
0
0
0
6,000
5
45
920
13
540
5
500
9,400
49
8
83
4
142
5
410
230
6
-
-
-
-
0
0
4,200
6
36
625
40
1,385
33
2,930
1,000
52
5
33
6
342
-
-
80
4
185
3,285
119
4,347
81
7,042
42,081
229

42
top 13 states with respect to number of cattle on feed
account for 85% of fed beef marketed and the top 6 states
account for 67% of fed beef marketed (see Table 3.3).
Finishing operations can be grouped into farmer and
commercial classifications. The typical farmer operated
feedlot maintains a one time carrying capacity of less than
1,000 head. The feedlot is often just one of several
enterprises operated on the farm, and cattle are on feed
only part of the year. In contrast, the commercial feedlot
has a one-time carrying capacity greater than 1,000 head are
operated as single enterprises and feed cattle the year
round. Regionally, the majority of the farmer feedlots are
found in the midwestern states of Iowa, Illinois, and
Nebraska, while the commercial feedlots are found in the
southwest and great plains states. While a majority of
feedlots are farmer feedlots the majority of fed slaughter
cattle come from the commercial feedlots. Feedlots with a
capacity of less than 1,000 head accounted for 18% of cattle
marketed in 1987, whereas feedlots with capacity of greater
than 8,000 head accounted for 64% of cattle marketed in that
year (see Table 3.3).
The location of slaughter and processing plants mir¬
rors the location of feedlots (see Table 3.4). Most cattle
are slaughtered less than 100 miles from where they were
fed.

TABLE 3.3
STATE PERCENTAGE OF
1987.
TOTAL U.S.
FED CATTLE
MARKETED
BY FEEDLOT
SIZE, 13 STATES,
Feedlot
capacity
State
1,000-
1,000 1,999
2,000-
3,999
4,000-
7,999
8,GOO-
15,999
16,000-
31,000
>32,000 Total
%
ARIZ
0.4
o
o
o
o
O
o
0.0
4.1
3.8
K)
O
CALIF
0.1
0.7
1.1
3.0
3.0
5.2
5.2
3.3
COLO
1.1
8.5
15.2
15.7
9.4
9; .18
12.7
9.7
IDAHO
0.2
0.9
2.3
3.0
3.0
6.0
0.0
2.0
ILL
17.2
5.7
3.0
0.0
0.0
0.0
0.0
3.6
IOWA
28.8
30.3
16.2
0.0
0.0
0.0
0.0
7.6
KANS
1.7
6.7
14.4
15.8
30.9
24.5
19.2
17.5
MINN
10.2
6.1
3.3
0.0
0.0
0.0
0.0
2.4
NEBR
31.7
32.0
43.2
40.8
28.0
12.4
7.1
21.3
OKLA
0.7
0.0
1.3
0.5
2.5
3.3
S. 8
3.0
S DAK
6.4
6.3
5.8
14.0
0.0
0.0
0.0
2.8
TEX
2.1
1.9
2.7
10.1
19.0
31.9
41.6
22.9
WASH
0.1
0.0
2.7
0.0
1.0
7.9
0.0
1.8
13 STATES
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Source: USDA, 1989.
OJ

TABLE 3.4. U.S. FEDERALLY INSPECTED CATTLE SLAUGHTER BY REGION, 1988
Types of cattle Total
Dairy Other Bulls &
Region Steers Heifers cows cows Stags Number Percent
000
Northeast
508.6
119.1
599.6
115.0
53.0
1,395.3
4.1
Southeast
134.9
210.2
201.4
540.6
85.9
1,173.0
3.4
Midwest
9,572.5
6,189.8
1,347.0
1,184.3
236.8
18,530.4
54.4
Southwest
3,261.9
1,798.7
132.5
811.2
121.4
6,125.7
18.0
Plains
1,490.5
1,513.5
122.7
238.1
55.2
3,420.0
10.0
West
1,865.0
607.4
475.6
383.2
72.6
3,403.8
10.0
Source; USDA, 1989

45
Due to the substantial economies of scale associated
with boxed beef two types of enterprises have evolved. The
efficient size of slaughter-processing plant which produces
boxed beef as an output is believed to be between 500,000 to
1 million head annual capacity (Marion, 1986). One type is
the large slaughter-processor with plant capacity often
exceeding 500,000 head who specialize in fed beef and sell
their output as boxed beef. The other type of enterprise
operates a smaller capacity plant and caters to smaller,
specialized customers. The number of firms at this stage is
small. Concentration measures indicate that the top four
firms involved in slaughter and processing of beef account
for 82% of fed beef slaughtered (Marion, 1986).
Dairy Herd
The culls from the dairy herd are a significant source
of beef, typically accounting for 20% of total cattle
slaughter. As a consequence, the amount of dairy culls
slaughtered do have an important effect on price received by
producers in the beef sector. However, the quantity of
culls coming from the dairy sector is not determined by con¬
ditions found in the beef system, but by conditions prevail¬
ing in the dairy sector. Thus the supply of dairy culls is
exogenous to the beef system. The slaughter of cull cows is
more dispersed than the slaughter of fed beef reflecting the
distribution of cow-calf operations and the dairy herd.

46
Foreign Trade
Like the dairy herd, foreign trade is significant but
does not play a major role in the decisions made by beef
producers. Thus, level of imports and exports can be treat¬
ed as exogenous to the sector. It must noted here, the role
of foreign trade is increasing and that domestic beef
producers hope that increase in beef exports to foreign mar-r
kets will offset the decline in beef consumption in the U.S.
Supply Response
Given the long lag in time from when the decision to
produce a calf is made to the time that the live animal is
slaughtered, the decisions made at the cow-calf stage ultim¬
ately determine the supply of beef at any point in time.
Thus, the sectors supply response of the sector is deter¬
mined by the ability of cow-calf operators to increase or
decrease the number of feeder calves produced.
Cow-calf operators cannot increase production rapidly
in response to favorable market conditions due to two
related factors. First is the length of time it takes to
produce new breeding stock. It takes two years to produce a
heifer for breeding purposes. Second, there are no alter¬
native uses for breeding stock other than for the production
of calves. As a consequence, breeding stock in excess of
the amount needed to meet calf production needs are not kept
but sold for slaughter.

47
The slowness of the supply response is believed to be
the principal cause of the cattle cycle. The cattle cycle
has been observed to last 10 years starting with a 3 to 4
year period of contraction in the number of beef cattle
produced followed by a 6 to 7 year period of expansion.
The discussion on the sector's supply response raises
the issue of time and the appropriateness of casting the
model of the beef sector in a static or dynamic framework.
A resolution to the time problem depends on the type of
information one is interested in gaining. If one is inter¬
ested in forecasting the prices received by producers or
cattle numbers at any particular point in time then a
dynamic framework is appropriate. However, if one is inter¬
ested in long-run trends then the dynamic framework is a
hindrance. The seasonal fluctuations and production cycles
which are incorporated in a dynamic model only serve to hide
the trend. In this case a static framework is appropriate.
The Model
The description of the organization of the beef sector
serves as a conceptual framework with which to mathematic¬
ally formulate the programming model. The system for beef
production is represented by a linear activity analysis
model. Regional differences in the production of beef are
accounted for by building an activity analysis model for
each supply region. The demand for beef is represented by a
system of demand equations for meat at the retail level.

48
Transportation activities permit the transportation of live
animals between supply regions and boxed beef from supply
regions to demand regions. The size of the breeding herd,
the level of beef imports and the level of dairy culls
slaughtered are exogenously determined.
Conceptually the model is not complicated. It is a
spatial equilibrium model where the supply functions are
being implicitly represented have been replaced by a linear
activity analysis model of beef production. The mathe¬
matical representation of the model is complicated by the
number of dimensions to each variable. However, the
production activities in one region are simply replicated
for the other supply regions. The supply models differ by
the values of their parameters. Variables and their
dimensions are defined in Tables 3.5 and 3.6.
The beef production system as represented by the
following model draws heavily from earlier versions of the
model developed by Nelson et al. (1982), Kennedy (1982), and
Disney (1989). The structure of the model and variable
definitions are as defined in Nelson et al. and Kennedy.
The parameter values were updated by Disney.

49
TABLE 3.5. VARIABLE DIMENSION DEFINITIONS
Subject
Description
Regions
Supply regions are identified by:
(i,i')=l,2,3,4,5
Demand regions are identified by:
j=l,2,3,4
Production Stages
Production stages are identified
by:
s-l,2,3,4r5
The Cow-calf Stage
Production processes used are
identified by:
kl=l,2
i=l Southeast
i=2 Midwest
i=3 Southwest
i=4 Plains
i=5 West
j=l= Northeast
j=2= South
j=3= Midwest
j =4= West
s=l = cow-calf stage
s=2 = stocker or growing
stage
s=3 = finishing stage
s=4 = slaughtering stage
s=5 = hamburger processing
stage
kl=l = producing a weaned
calf
kl=2 = culling breeding stock

50
TABLE 3.5.—Continued
Subject
Description
Types of cattle produced are
identified by:
ul=l,2
The Stocker Stage
Type of animal used in production
activities are identified by:
v2 = 1
Production processes used are
identified by:
k2=l,2
Types of cattle produced are
identified by:
u2=l,2
The Finishing Stage
Type of animal used in production
activities are identified by:
v3=l,2,3
Production processes used are
identified by:
k3=l,2,3,4,5,6
ul=l = weaned calf
ul=2 = cull
v2 = weaned calf
k2=l = producing a yearling
k2=2 = producing a 1 1/2 year
old
u2=l = yearling
u2=2 =11/2 year old
v3=l = weaned calf
v3=2 = yearling
v3=3 = 1 1/2 year old
= producing 900 lb.
animal from a weaned
calf
k3=l

51
TABLE 3.5.—Continued
Subject
Description
k3=2 = producing 1100 lb.
animal from a weaned
calf
k3=3 = producing 1200 lb.
animal from yearling
k3=4 = producing 1300 lb.
animal from 1 1/2 year
old
k3=5 = producing 900 lb.
animal from yearling
k3=6 = producing 1100 lb.
from 1 1/2 year old
Types of cattle produced are
identified by:
u3=l,2,3,4 u3=l = 900 lb. animal
u3=2 = 1100 lb. animal
u3=3 = 1200 lb. animal
u3=4 = 1300 lb. animal
The Slaughtering Stage
Types of meatpacking plants used
are identified by:
1=1,2, 3,4,5 1=1 = plant 1
1=2 = plant 2
1=3 = plant 3
1=4 = plant 4
1=5 = plant 5
Type of animal used in production
activities are identified by:
v4=l,2,3,4,5,6,7 v4=l = 900 lb. fed animal
v4=2 = 1100 lb. fed animal

52
TABLE 3.5.—Continued
Subject
Description
v4=3
v4=4
v4=5
v4=6
v4 = 7
Production activities used
are identified by:
k4=l,2,3,4,5,6,7 k4=l
k4 = 2
k4 = 3
k4=4
k4 = 5
k4=6
k4=7
Product forms produced are
identified by:
u4=l,2,3,4,5 u4=l
u4=2
u4 = 3
u4=4
u4 = 5
The Hamburger Processing Stage
Product forms used are identified
by:
1200 lb. fed animal
1300 lb. fed animal
yearling
1 1/2 year old
cull
fabricate
animal
900 lb.
fed
fabricate
animal
1100 lb.
fed
fabricate
animal
1200 lb.
fed
fabricate
animal
1300 lb.
fed
fabricate
yearling
fabricate
old
1 1/2 year
fabricate
cull
roast
steak
lean trim
medium trim
fat and bone
v5=l,2,3,4
v5 = l
v5=2
roast
steak

53
TABLE 3.5.—Continued
Subject
Description
Production activities used are
identified by:
k5 = l,2,3,4,5,6,7
Product forms sold are
identified by:
u=l,2,3
v5=3 = lean trim
v5=4 = medium trim
k5=l = make hamburger from
primal cuts obtained
from 900 lb. fed
animal
k5=2 = make hamburger from
primal cuts obtained
from 1100 lb. fed
animal
k5=3 = make hamburger from
primal cuts obtained
from 1200 lb. fed
animal
k5=4 = make hamburger from
primal cuts obtained
from 1300 lb. fed
animal
k5=5 = make hamburger from
primal cuts obtained
from yearling
k5=6 = make hamburger from
primal cuts obtained
from 1 1/2 year old
k5=7 = make hamburger from
primal cuts obtained
from culls
u=l = hamburger
u=2 = roast
u=3 = steak

54
TABLE 3.6
VARIABLE DEFINITIONS
Variables
Description
fj(Y)
represents the market level inverse demand
system for beef in the jth demand region.
P1.U
represents the price received for beef
product u consumed away from the home (the
hotel, restaurant, and institutional trade)
in demand region j.
AYj>u
the quantity (cwt/year) of beef product u
consumed away from the home in demand region
j •
Pu
represents the price received for beef
product u exported to other countries.
EYU
represents the quantity (cwt) of beef
product u exported on an annual basis.
rdt
the price of dairy culls in the ith supply
region.
ZD1
the quantity (head) of dairy culls in the
ith supply region utilized in the beef
production system.
ri,i,ul
the price of weaned beef calves (ul=l) or
beef culls (ul=2) in supply region i.
qi.i.ki
the level (head) of breeding herd activity
kl utilized in region i.
Zl.i.ul
quantity (head) of weaned beef calves and
beef culls in region i utilized in the beef
production system.
r2,i,lc2
the cost ($/hd) of stockering activity k2 in
supply region i.
q2,i,k2
the level (head of cattle) of stockering
activity k2 utilized in region i.
r3,i,H3
the cost ($/head) of feeding activity k3 in
region i.

55
*33,i,*3
the level (head of cattle) of feeding
activity k3 utilized in region i.
r4,i,l
the cost ($/head) of slaughtering and
producing boxed beef in plant 1 in supply
region i.
*34,1,1,1(4
the level (head of cattle) of slaughtering
activity k4 utilized in plant 1 in supply
region i.
r5,i,l
the cost ($/cwt.) of manufacturing hamburger
in plant 1 in region i.
*35,1,1,1(5
the level (cwt.) of the k5 hamburger pro¬
duction activity utilized in plant 1 in
supply region i.
Tl,i',ul
cost of transporting weaned calves(ul=l) or
beef culls (ul=2) from supply region i to
supply region i'.
X2,l,i',ul-1
number of weaned calves (ul=l) in supply
region i transported to region i' to be
utilized in stockering activities.
X3,i,i',ul=l
number of weaned calves (ul=l) transported
from region i to region i' to be utilized in
feeding activities.
^1,1', u2
cost of transporting stockered cattle
(u2=yearling or 1-1/2 year old) from supply
region i to supply region i'.
X3,l,i',u2
number of stockered cattle,(u2=yearling or
1-1/2 year old) transported from region i to
region i' to be utilized in feeding
activities.
X4,l,l',l,u2,v4
head of stockered cattle (u2=yearling or 1-
1/2 year old) transported from region i to
be slaughtered in plant 1 in region i'.
^1,1' ,uD
cost of transporting culls (uD=dairy) from
supply region i to supply region i'.
X4,i,i',l,ul-2,v4-7
number of beef culls (ul=2) transported from
region i to be slaughtered in plant 1 in
region i'.

56
X4,i,i',l,uD-l,v4-7
number of dairy culls (uD=l) shipped for
slaughter from region i to plant 1 in region
i' .
Ti,i',u3
cost of transporting fed beef (u3=900 lbs.,
1100 lbs., 1200 lbs., or 1300 lbs.) from
supply region i to supply region i'.
^4,i,l',l,u3,v4
head fed beef (u3=900 lbs., 1100 lbs., 1200
lbs., or 1300 lbs.) transported from region
i to plant 1 in region i'.
TI^u-i
cost of transporting imported beef
(u=hamburger) to demand region j.
XIj(u-l
quantity of hamburger (u=l) imported to
demand region j.
TE1>U
cost of transporting exported beef (u=roast
or steak) from supply region i to export
markets.
XE±.U
quantity of beef products (u=steak or roast)
exported from supply region i.
cost of transporting beef products
(u=hamburger, roast or steak) from supply
region i to demand region j.
X1(j,u
quantity of beef products (u=hamburger,
roast or steak) shipped from supply region i
to demand region j.
Mj.u
marketing margin ($/cwt.) for beef product
u=hamburger, roast or steak) in demand
region j.
Yj.u
quantity (lbs./month) of beef product u
consumed at home in demand region j.
h
quantity (cwt.) of hamburger available for
importation.
RIC3>u
quantity of beef product u consumed away
from home in demand region j.
Zi.u
quantity (cwt.) of beef product u sold in
supply region i.
Z 4, i, 1, u4,k4
quantity (cwt.) of primal cut u4 produced in
plant 1 in supply region i from production
activity k4.

57
Z4,i,l,u4
quantity (cwt.) of primal cuts (u4=roast or
steak) in region i allocated to sales
activity.
Z5,i,l,u4,v5
quantity (cwt.) of primal cuts (u4=roastr
steak, lean trim or medium trim) in region i
allocated to hamburger activity.
a5,i,v5
the percentage of fat found in primal cut v5
used in the hamburger activity in supply
region i.
C5,i,l,v5,k5
quantity (cwt.) of primal cut v5 used by one
unit of hamburger production activity k5 in
plant 1.
FATi
the maximum percentage of fat permitted in
hamburger in supply region i.
head of cattle slaughtered in plant 1 in
supply region i.
TCAP 1>A
capacity (head of cattle) of slaughter plant
1 in supply region i.
^4,i,l,u4,k4
quantity (cwt.) of primal cut u4 produced by
one unit of the k4th slaughter activity of
plant 1 in supply region i.
C4,i,l,v4,k4
quantity (head) of cattle used by one unit
of production activity k4 in plant 1 in
supply region i.
Sl,i'
adjustment to live animal numbers due to
shrinkage during transit from supply region
i to supply region i'.
Si» j
adjustment to final beef product weights due
to shrinkage during transit from supply
region i to demand region j.
Z4,i,l,v4
quantity (head) of live animal v4
slaughtered in plant 1 in region i.
Z3,i,u3
head of fed cattle u3 produced in supply
region i.
Z3,1,V3
head of live animal v3 placed on feedlots in
supply region i.

58
d3
,i,u3,k3
C3,l,v3,lc3
Z2,i,u2
Z2,i,v2
<^2,i,u2,k2
C2,l,v2,k2
Zl,i,ul
Z0,l,vl
^l,i,ul,kl
Cl,i,vl,kl
ZDa
quantity (head) of fed cattle produced by
one unit of feeding activity k3 in supply
region i.
quantity (head) of live animals v3 used by
one unit of feeding activity k3 in supply
region i.
head of stockered cattle u2 produced in
supply region i.
head of live animal v2 used in stockering
activities in supply region i.
quantity (head) of stockered cattle produced
by one unit of stockering activity k2 in
supply region i.
quantity (head) of live animals v2 used by
one unit of stockering activity k2 in supply
region i.
head of weaned calves or culls (ul=l or 2)
produced by breeding and maintenance
activities in supply region i.
head of breeding stock used in breeding and
maintenance activities in supply region i.
quantity (head) of weaned calves (ul=l) or
culls (ul=2) produced by one unit of
breeding (kl=l) and maintenance (kl=2)
activities in supply region i.
quantity (head) of breeding stock vl used by
one unit of breeding (kl=l) or maintenance
(kl=2) activity in supply region i.
quantity of dairy culls from supply region i
utilized.
DAIRYi
dairy cull supply in region i.

59
The Objective Function
4 4 3
max NSB = 2 J f (Y)dyy • • dy3 + 2 2 PjuAyjU
j = l L j = l u=l
3 5
+ 2 Pu EYU - 2 rd± ZDi
u=2 i=l
5 2
^ ^ ri,i,m 21(1#ul
i=l ul—1
5 2
^ 2 ^2,i,k2 <32,1^2
i=l k2=l
5 6
2 2 r3/1/lc3 q3>1,k3
i=l k3=l
5 5 7
2 2 2 r4jl/1 q4,i,i,ic4
i=l k3=l k4=l
5 5 4
2 2 2 r5,i,l Qs.i.l.hiS
i=l 1=1 k5=l
5 5
2 2 X2(i(i-(Ui=i
i=1 i'=l

T=f T=T
n'c'TX n'c'TjJ S S
t s
2=en t=t
n'Tax n'Ta¿ s s -
e s
T-n'CIX (T-n,fW +
T«n
T = P
3 -
T=T T=/T
s s
T=T
3 -
5
T=^a T=e^ T=T 1=,T
fA'en'x' ,T 'T'* tn' * fr s s
T=T
3 -
5
S=^a T=en i=t
»A'jn'x',T'T'»jj zn'.T'Tj^ HSU
9 2 5
T=/T T=T
3 3
5 5
I=T 1= < T T=T
¿.»A'z=xn'T'.T'T'»jj Z-in'T'.T'Tj^ S 3 3
5 5 5
T=jn t=/T
Zn'.T'T'E^ Zn'.T'Tj, rj rj
Z 5
T=T
3 -
5
T=,T T=T
X-Tn',T'T'Ejj X-in'.T'Tj^ r£ ‘ rj
5 5
09

61
The objective function is maximizing the area under¬
neath the demand curves in all the demand regions minus the
total cost of activities at each stage of production and
total transportation costs. It also takes account of expen¬
ditures on away from home consumption and the cost of
importing beef.
Constraints
The maximization of the objective function is subject
to a number of constraints. The constraints embody the
production activities, transportation activities and the
equilibrium conditions for a competitive market. They are
expressed as follows:
1. Dairy cull supply constraint.
i=l,•••,5;
ZDi - DAIRYi * 0
This constraint ensures that the number of dairy culls
utilized in region i is no greater than the number of
dairy culls available in region i.
2. Dairy cull transfer constraint.
5 5
-ZDi + 2 2 X
i'=l 1=1
This constraint guarantees that the number of dairy
culls transferred from region i (X4>i(i, l llD) is less than

or equal to the number of dairy culls utilized in
region i (-ZDi).
Maintenance of breeding herd constraint.
2
”Z0>1>vl + 2 cl,i,vl,ltl ‘ Ql, i,kl ^ Of
kl=l
1=1 ••• R •
X ±t
vl=l;
kl=l,2;
This constraint ensures that the number of cows
utilized in the replacement and breeding activities
(ci,i,vi,ki ’ <3i,i,)ti) in region i is less than or equal to
the number of cows available in region i (Z0/1>vl).
Weaned calf and cull production constraint.
2
kl=l
This constraint ensures that the number of weaned
calves or culls produced in region i (d1#1>ul>kl • q1>1>kl)
is greater than or equal to the available supply of
weaned calves or culls in region i (Z1/1>ul).

63
5. Beef cull transfer constraint
5 5
+ 2* ^ X4(1>1,>1#u2.2 £ 0
i'=l 1=1
i= 1
In this constraint the cattle culled from the breeding
herd are transferred to the slaughter-processing stage.
It ensures that the number of beef culls transferred
from region i to the slaughtering stage (X4>i#1>ul_2) is
less than or equal to the available supply of beef
culls in region i (Z1(i/Ul,2).
6. Weaned calf transfer constraint.
5
5
+ 2 X
i'=l
i=l,•• • ,5
In this constraint weaned calves in region i are
transferred to either the stocker or finishing stages.
It guarantees that the number of weaned calves
transported from region i to the stocker (X2(lfl/=1) and
finishing stages (X34il,iUl,1) is less than or equal to
the supply of weaned calves in region i (Zi^m.j).

The receipt of weaned calves into the stockering stage
constraint.
5
This constraint assembles weaned calves for use in
stockering activities in region i. It ensures that the
number of weaned calves assembled for use in stockering
activities (Z2>1>v2) is no greater than the number of
weaned calves shipped to the stockering stage in region
i times a shrinkage parameter which adjusts the number
of weaned calves shipped for injury and death in
transit â–  X2tUX.tUlml)
The utilization of calves in the stockering stage
constraint.
2
~^2,i,v2 + ^ C2,i,v2.lc2 ‘ ^2,l,lt2 ^ 0
k2 = l
i=l,•••,5;
v2=l;
k2=l,2;
This constraint ensures that the number of weaned
calves utilized in the stockering activity in region i
(c2,i,v2,*2 * q2,i,ic2) is no greater than the supply of
stocker calves in region i.

65
9. The stocker output constraint.
2
^2,i,u2 “ ^ d2,i,u2,k2 * <12,1,112 ^ 0/
k2=l
i=lr* * • /5?
u2=l,2;
This constraint ensures that the number of stockered
cattle produced in region i (d2;1(U2(k2 • q2fl/lc2) is greater
than or equal to the available supply of stockered
cattle in region i (Z21(U2).
10. The transfer of stockered cattle constraint.
5 5 5
~ Z2,i,u2 + S X31 (i'(U2 +2 2 X4(lfi»(1(U2 £ 0;
i'=l i'=l 1=1
i=l,••*,5;
u2=l,2;
k2=l,2;
This constraint transfers stockered cattle in region i
to either the finishing or slaughter stages. It
guarantees that the number of stockered cattle trans¬
ported from region i to the finishing (X3(lii,u3) and
slaughter stages (X41(i, u3) is less than or equal to the
available supply of stockered cattle in region i
( ^2,i,u2 ) *

66
11. The receipt of weaned calves into the finishing stage
constraint.
5
2 slfl. • X3flfl. i=1/ * *,5;
This constraint collects weaned calves for use in the
finishing stage in region i. It ensures that the
number of weaned calves collected for use in feeding
activities (Z3/i#v3.1) is no greater than the number of
weaned calves shipped to the finishing stage in region
i times a shrinkage parameter which adjusts the number
of weaned calves shipped for injury and death in
transit (s1(1, • .
12. The receipt of stockered cattle into the finishing
stage constraint.
5
2 s1>u, • X3 1(1. u2 + Z31(V3 ^ 0; i=l,* • • /5;
i'=l u2=l, v3=2;
u2=2, v3=3;
This constraint collects stockered cattle for use in
the finishing stage in region i. It ensures that the
number of stockered cattle collected for use in feeding
activities (Z31 v3) is no greater than the number of
stockered cattle shipped to the finishing stage in

67
region i times a shrinkage parameter which adjusts the
number of stockered cattle shipped to region i for
injury and death in transit (s*^. • X31,,v3) .
13.The utilization of cattle in the finishing stage
constraint.
4
^3,ifv3 + 2 c3(1>v3>k3 * q3fl/)c3 £ 0
k3=l
i—11 • ••f51
v3=l,•••,3;
This constraint ensures that the head of cattle
utilized in feeding activities in region i (c3(1#v3(k3 •
q3,1/k3) is no greater than the supply of cattle for
finishing in region i (Z3>i/V3).
14.The finishing stage output constraint.
4
Z3,i,u3 ~ 2 d3>l u3^3 • q3,i()c3 ^ 0
k3=l
i=lf*"*f5
u3=l,•••,
This constraint ensures that the number of finished
cattle produced in region i (d3(1/U3 k3 • q3,1/k3) is greater
than or equal to the available supply of finished cat¬
tle in region i (Z3fl>u3).
15.The transfer of finished or fed cattle constraint.
5 5
i=lf• • ' / 5;
u3=l,••’,4;
i'=l 1=1
iffc M

68
This constraint transfers finished cattle in region i
to the slaughter stage. It guarantees that the number
of fed cattle transported from region i to the
slaughter stage (X4>1 >±,#1 #u3) is less than or equal to the
supply of finished cattle in region i (Z3,i>u3).
16. The receipt of culls into the slaughter stage con¬
straint .
5
~ 2 S1>1( • X4
i=l
- s
l.i'
*4.
* 0;
i=1r"'*/5;
1=1/'* */5?
This constraint assembles culls for slaughter in region
i. It ensures that the number of culls assembled for
use in slaughtering activities (Z4 i/1/V4.7) is no greater
than the number of beef culls shipped to the slaughter¬
ing stage in region i times a shrinkage parameter which
adjusts the number of weaned calves shipped for injury
and death while in transit (s1#1, • X4>1>1.>1>ul_2) and
the number of dairy culls shipped to the slaughtering
stage in region i times a shrinkage parameter
* X4(ifi,1>ul,2) .

69
17. The receipt of stockered cattle into the slaughter
stage constraint.
5
Z4,i,l,v4 “ 2 Siri,
i'=l
X
4,l,i',l,u2
s 0?
i=l,•* • ,5;
1=1,•* *,5;
v4=5,6;
u2=l,2;
This constraint assembles stockered cattle for
slaughter in region i. It ensures that the number of
stockered cattle assembled for use in slaughter
activities (Z4,1(1#v4) is no greater than the number of
stockered cattle shipped to the slaughter stage in
region i times a shrinkage parameter which adjusts the
number of stockered cattle shipped to region i for
injury and death in transit (s1#1. • X4(i/1.(1>u2) .
18. The receipt of finished cattle into the slaughter stage
constraint.
Z
4, i,1,v4
5
2 si,i< X4(i>1,>1>u3 ^ 0;
i' = l
i=l,•*•,5;
1=1,’*•,5;
v4=l,•*•,4;
u3=l,••*,4;
This constraint assembles finished cattle for slaughter
in region i. It ensures that the number of fed cattle
assembled for use in slaughter activities (Z4/i(1>v4) is
no greater than the number of fed cattle shipped to the

70
slaughter stage in region i times a shrinkage parameter
which adjusts the number of fed cattle shipped to
region i for injury and death in transit •
19. The utilization of cattle in the slaughter stage
constraint.
Z
4,i,l,v4
7
^ *~4,l,i',l,v4,k4 ' <34,l,l,k4 ^ 0?
k4=l i=l,•••, 5;
1=1,-••,5;
v4=l,• • • ,7;
This constraint ensures that the quantity of cattle
slaughtered in plant 1 (c4,lfl#v4fM • q4,lfi.M) is no
greater than plant i's supply of slaughter cattle
( ^4,l,l,v4 ) •
20. The slaughter activity output constraint.
7
Z4,i,i,u4, “ 2 d4/1>1>u4fk4 • q4,i#1,k4 £ 0; i=lf • ’ *
k4=l 1=1,•••,5?
u4=l,•••,5;
This constraint guarantees that the number of primal
cuts produced by plant 1 (d4flil#u4flt4 • q4,1#lfIt4) is greater
than or equal to the available supply of primal cuts in
plant 1 (Z4.lflfU4).

71
21.The slaughter of cattle in meatpacking plant
constraint.
7
2
k4=l
Q*,!, 1,H4 “ Qa,1,1
0;
i=l,••♦,5;
1=1/•* */5;
This constraint accounts for the head of cattle
slaughtered in plant 1 in region i.
22.The slaughter capacity constraint.
QAifl — TCAPj^ ú 0;
i=1/"*'/5;
1=1/•* */5;
This constraint requires that the quantity of cattle
slaughtered does not exceed plant capacity.
23.The transfer of primal cuts to sale and hamburger
processing activities constraint.
0;
i=4, •• * ,5; 1=1,•*•/5;
u4=i/.-.,4; v5=l,***/4;
5 = 1 if u4=l,2
0 if u4=3,4,5
5 ' = 1 if v5 = l,••• ,4;
0 if v5=5;
This constraint allocates the quantity of primal cuts
produced in plant 1 to sales or hamburger processing
activities. It ensures that the quantity of primal

72
cuts allocated to sales and hamburger processing
(Z4,i,i,v4 + Z5,i,i,V5) is less than or equal to the quantity
of primal cuts available in plant 1 (Z4fl>lfU4rJc4) .
24. Regional supply of steaks and roasts constraint.
5
2
1=1
i=lf* * */5;
u4=l, u=2;
u4=2,u=3;
This constraint assembles all the steaks and roasts al¬
located to the sales activity in the meatpacking plants
in region i (Z4/1>lu4) at a single distribution center.
It guarantees that the quantity of steaks and roasts
available for distribution in region i (Z1;U) is no
greater than the quantity of steaks and roasts al¬
located to sale by the meatpacking plants in region i.
25. Utilization of primal cuts in the production of
hamburger constraint.
i=l,•••,5;
1=1,•••,5;
v5=l,•••,4;
This constraint ensures that the quantity of primal
cuts used to produce hamburger in plant 1 (c5>1(1(V5(X5
5,i,l,v5,k5
is less than or equal to the quantity of primal

73
cuts allocated to the hamburger processing activity in
plant 1 (Z5,1>1>v5).
26. The hamburger processing constraint.
4 5
^ 2 <35,1,1,*5 + 21(U,! £ 0;
k5=l 1=1
i=l,•• • ,5;
27.
This constraint ensures that the quantity of hamburger
in region i is no greater than the quantity of
hamburger produced in the meatpacking plants in region
i (Ek52i <15,1,1,115) •
Hamburger fat content constraint.
4 5
^ ^ a5,i,k5 ‘ <35,1,1,*5
k5=l 1=1
FAT, • Z1/U=1 s 0;
i=l,
,5?
This constraint ensures that percentage of fat by
weight contained in hamburger produced in region i does
not exceed 27%.
28. The transfer of boxed beef constraint.
2 ^i,j,u ■*" XEi i=lf *•'/5;
u=l,•••,3;
This constraint transfers box beef cuts from supply
region i to domestic and foreign markets. It ensures

74
that the quantity of boxed beef cuts transported from
supply region i (Xi>j>u + XEi/U) is less than or equal to
the supply of boxed beef cuts in region i (Z1/U).
29.Hamburger import constraint.
S3 XjUml - I s 0; u=l?
This constraint ensures that the quantity of hamburger
imported is less than or equal to an exogenously
determined supply of imported hamburger.
30.Beef consumption constraint.
— — Si
+ (.12) YJ/U + AYj(U <; 0; u=l,2,3;
j=l,•••,4;
6= 1 if u=l
0 if u=2,3;
This constraint ensures that the quantity of fresh beef
consumed at and away from the home (Yj(U + AYj,u) i-n
demand region j is less than or equal to the quantity
of foreign and domestically produced transported to
region j (X1/j(U + XF^.J .
31.Away from home consumption constraint.
- AY
j/U
+ HRI
j.u
= 0;
j=lf•• ‘ /4;
u=l,•* • ,3?

75
This constraint requires that away from home
consumption of beef in region j equal the away from
home demand for beef.

CHAPTER 4
SPECIFICATION OF AN INVERSE DEMAND
SYSTEM FOR FRESH MEATS
The purpose of this chapter is to specify a system of
demand equations for fresh meats to be used in the pro¬
gramming model. The demand system needs to satisfy the
restrictions placed on it by both economic theory and the
programming model.
The first section of the chapter lays out the con¬
ditions the demand system needs to satisfy in order for it
to be incorporated into the programming model (Table 4.1).
In the second section of the chapter a demand system for
fresh meats which is consistent with the conditions
established is derived. Characteristics of the data, the
estimation procedure used and the estimated system are
discussed in the third section. In the final section the
demand system to be used in the programming model and a
description of the steps taken to incorporate the estimated
demand system into the programming model are discussed.
Criteria for Selecting a Demand System to be
Used in the Programming Model
The first condition which the demand system must meet
in order to be used in the programming model is that it be
specified in price-dependent or inverse form. This
76

77
TABLE 4.1. THE CRITERIA USED FOR SELECTING AN APPROPRIATE
SYSTEM OF DEMAND EQUATIONS.
1. They must be specified in price-dependent form.
2. They must satisfy the integrability conditions of the
price endogenous mathematical programming model.
a. Negative definite Jacobian matrix
b. Symmetric cross-quantity effects
3. They must satisfy nonseparability of preferences among
the various meat products.

78
condition is imposed by the formulation of the programming
model being used. By specifying the demand system in price-
dependent form it is much easier to formulate the program¬
ming model and to make economic interpretations.
In demand theory, the demand system is usually derived
by assuming that prices and income are given and that it is
the quantity consumed which is adjusted by consumers in
order to maximize their utility. As a result the consumer's
demand system is specified in quantity-dependent form.
Fortunately, one of the basic results obtained through the
use of duality theory is that the consumer's preferences can
be represented by either the quantity-dependent demand
system or the associated inverse demand system. Anderson
(1980) has further shown that the inverse demand systems
have properties analogous to the properties of the quantity-
dependent demand systems.
In many cases the use of an inverse demand system is
just a matter of expedience with regards to the modeling
effort. There being no reason to represent the demand
relationship in inverse form other than to make the for¬
mulation of the programming model simpler and easier to
interpret in an economic sense (see Takayama and Judge,
1971). However, for a product such as beef, the production
decisions are made long before the final product is avail¬
able to consumers. This implies that at any given point in
time the supply of beef is fixed, and it is the price of

79
beef which must adjust in order to achieve market equilib¬
rium. Given this it can then be argued that the demand for
beef should be specified in its inverse form, not only
because it is more convenient for modeling purposes, but
because it properly represents the manner in which
equilibrium in the market for beef is determined.
The second condition which the demand system must
fulfill is that it satisfy the integrability conditions of
the programming model. The integrability conditions require
that the Jacobian matrix of the demand equations be negative
definite and have symmetric cross-quantity effects. As dis¬
cussed in Chapter 2 the integrability conditions ensure that
a unique solution exists.
A third condition which must be satisfied by the de¬
mand system is that it reflect the nonseparability of pref¬
erences for meat products by species. The reason for this
assumption about the separability of consumers' preferences
for fresh meat is discussed in greater detail in the next
section.
In addition to the conditions just discussed it is
important that the demand system reflect regional differ¬
ences in consumer preferences for meat. This is based on
the assumption that differences in the levels of fresh meat
consumed between regions is determined not only by differ¬
ences in population and level of income between regions, but
also by differences in their customs and traditions.

80
Finally, given the controversy over whether a shift in
consumer preferences for meat has occurred the data used to
estimate the demand system should come from the period after
the change in the structure in the demand for meat is
believed to have occurred. This will ensure that the estim¬
ated parameters will reflect the current demand structure
for fresh meat.
The Two-Stage Budgeting Process and the
Representation of Consumer Preferences
According to demand theory the fundamental decision
facing consumers is how to allocate their income among the
available goods so as to maximize their utility. This
decision is determined by the consumer's preferences, the
prevailing commodity prices and the consumer's income.
While the consumer's preferences are unobservable they can
be represented by a system of demand equations which relates
the utility maximizing level of consumption to prices and
income.
Demand theory assumes that consumers know and take
into consideration all commodities available when making
their consumption decisions. This implies that the system
of demand equations should contain all commodities. How¬
ever, empirical demand equations only contain the commod¬
ities of interest and a small subset of related commodities.
One reason for this is that it is impractical to estimate a
demand system which contains all commodities. A second

81
reason for this is the realization that consumers do not
take into consideration all goods when they make their
expenditure decisions, but only a subset of related goods.
Thus, a demand system, if appropriately defined, only needs
to contain the commodities of interest in order to appropri¬
ately represent the consumer's behavior.
The two-stage budgeting process is often used to
represent the consumer's decision-making process and to
define the set of commodities to be included in the demand
system. In the two-stage budgeting process the consumer
first decides how to allocate his or her income over a broad
category of goods, then in the second stage how to allocate
each category's expenditures over the goods contained in
them.
The two-stage budgeting process is used to construct a
utility tree which shows which goods consumers take into
consideration when making their expenditure decisions. The
utility tree depicted in Figure 4.1 demonstrates how the
two-stage budgeting process is used to select the commod¬
ities to be included in a demand system. The branches of
the tree represent the budget or expenditure categories and
nodes or leaves on the branches represent the commodities
contained in each of the budget categories. By following
along the branches of this tree one can follow the process
used by the consumer when making a decision to purchase a
particular good. The first leaf on the tree represents all

Figure 4.1.
Utility tree.
oo
to

83
available goods. At this stage the consumer decides how to
allocate expenditures among housing, transportation, food,
and entertainment located at the nodes at the end of each
branch. Then in the next stage the consumer then decides
how to allocate food expenditures among the items in the
food category, such as meats, dairy products, grains, and
fruit.
In order for a particular decision tree to be an
appropriate representation of the consumer's budgeting pro¬
cess, the consumer's preferences must be weakly separable
according to the branches of the decision tree. Weak sepa¬
rability implies that each branch of the decision tree can
be defined by a separate sub-utility function. Thus, the
two-stage budgeting process provides a theoretical founda¬
tion for demand systems which only contain a portion of the
goods available by allowing a demand system to be derived
from the sub-utility function containing the goods of
interest.
There are any number of decision trees which could be
used to represent consumers' decisions to purchase fresh
meats. Two likely candidates are represented in the two
panels found in Figures 4.2 and 4.3.
The utility tree in Figure 4.2 represents a two-stage
budgeting process for fresh meat based on the animal species
from which the meat comes. At the first level of

Figure 4.2. Utility tree A.

85
Figure 4.3. Utility tree B.

86
decision-making the consumer has a given level of expendi¬
tures to allocate to food. The consumer then decides how to
allocate the given level of expenditure between meat and
nonmeat categories. At the second level the consumer then
decides the amount of expenditures for meat to allocate to
the purchase of beef, pork, and poultry. At the final level
of the decision tree the consumer then decides the amount of
beef expenditures to spend on hamburger, steak, and roasts.
The utility tree in Figure 4.2 represents the two-
stage budgeting process underlying most empirical studies of
the structure of the consumer's demand for meat. To a large
extent this has been simply a matter of expedience. For the
most part the data on consumption of meat has been based on
disappearance and not on knowledge of the amount actually
purchased by consumers at the retail level. The information
available is published by species. It is also argued that
the assumption that consumers determine how much to spend on
beef, pork and poultry before selecting the particular beef
pork or poultry product they purchase reflects the way con¬
sumers budget their meat expenditures. One only need to
look at the meat case at the supermarket where meat is sepa¬
rated by species to find corroboration of this observation.
The decision tree in Figure 4.3 represents an
alternative view of the consumer's budgeting process for
meats. In this case, once the consumer determines the
allocation for meat expenditures then the consumer does not

87
make a further distinction between the different meat
products based on origin of species alone. The consumer
decides how much of food expenditures to allocate towards
the purchase of meat, then at the next level determines the
amount to spend on the various meat products represented in
the diagram. This utility tree implies that consumers'
preferences for meat are weakly separable while their
preferences for hamburger, steaks, roasts, pork, whole
chickens, and chicken parts are not.
Recent empirical evidence indicates that consumers do
not make a distinction between meat products based on
species of origin alone. It indicates that consumers
determine how much of their food expenditures to spend on
meat and then decide how much of their meat expenditures to
spend on steaks, roasts, hamburger, pork, whole chickens,
chicken parts and other meat products (Eales and Unnevehr,
1988) as represented by the utility tree in Figure 4.3.
Thus, in order for a system of demand equations to be
consistent with the decision making process of the consumer
it must be specified at a level which encompasses all meat
cuts, not just those of a particular species. It is a
maintained assumption of this study that consumers'
preferences for fresh meat are weakly separable from all
other goods but not separable among the various meat
products.

88
The Derivation of the Inverse
Almost Ideal Demand System
Consider the Almost Ideal Demand System (AIDS) pro¬
posed by Deaton and Muellbauer (1980). The AIDS model was
developed to test the restrictions on consumer demand
derived from demand theory. As a result it is possible to
impose symmetry of the substitution matrix during estim¬
ation. Furthermore, the AIDS model is specified in level
form. This gives it an advantage over the Rotterdam model
which is specified in first difference form because this
permits it to be readily incorporated into a static pro¬
gramming model. The AIDS model also has the advantage that,
as long as consumer's preferences are of the price independ¬
ent generalized logarithmic (PIGLOG) form, it permits per¬
fect aggregation over consumers without assuming that pref¬
erences are additive. Thus, with this particular demand
system there is a theoretical justification for imposing
demand restrictions based on individual behavior at the
market level.
Deaton and Muellbauer (1980) derive the AIDS model by
applying Shepherd's Lemma to an expenditure function. An
inverse demand system analogous to the AIDS model can be
derived by specifying a distance function which is dual to
the expenditure function used by Deaton and Muellbauer
(1980) and applying the Shepherd-Hancock Lemma. By using
the distance function similar in form to the AIDS

89
expenditure function the properties possessed by the AIDS
model are carried over into the inverse demand system.
The distance function is
In D(U,q)= a(q) +U*b(q) (4.1)
where
a(q) = aQ + I a^lnqi + 1/2 EE Yij lnqilnq.) (4.2)
i ij
and
b(q)=PoIIqiPi (4.3)
U represents the level of utility and q is the vector of
commodities consumed. D(U,q) is homogenous in q if Ea^l,
EiYij = ^jYij = EPi = 0, and Y13 = Yji-
The compensated share equations in quantity dependent
form are derived by taking the partial derivatives of the
distance function with respect to In q^ Resulting in
wi = <*! + E Ylj In qj + UpiPJIq^1 (4.4)
j
The equations are functions of quantity and utility and
represent the compensated inverse demand system in share
equation form. If it is assumed that preferences are homo-
thetic then it is possible to substitute real expenditures
(X/P) for utility. An estimable system which does not rely
on the assumption that preferences are homothetic is found
by deriving an expression for utility from the distance

90
function, 4.1-4.3, and then substituting this expression for
U in 4.4.
Utility maximization implies that D(U,q)=l and along
with 4.1-4.3 that
O
U = -(aD + E a^lnqi + 1/2 EE yi:) lnq^nq.,)/PJIq! 1 (4.5)
i ij
Substituting the result from 4.5 into 4.4 and simplifying
results in
Wi = Oi + E3 Yijlnq3 - Piln(Q) (4.6)
where
ln(Q) = a(q) , E± at = 1, Yij = Yji/ Ej Yu = 0 E4 Yij = 0
and
Si Pi = 0.
The system of share equations represented by 4.6 are
functions of q alone and represent the uncompensated inverse
demand system. It is linear in parameters if ln(Q) is
approximated by E^lnq*.
The Data
Data on the level of household expenditures on fresh
meat products were obtained from the Bureau of Labor Sta¬
tistics (BLS) Consumer Expenditure Survey (CES), 1982-1986.
The survey is a representative sample of the U.S. popula¬
tion. It records the weekly expenditures of a household

91
over a two week period. The U.S. is divided into four
regions: Northeast, South, Midwest and West (Figure 4.4).
As with all household surveys a zero level of expenditures
was reported for any particular commodity for many of the
households. Consequently, the data were aggregated from the
household level to the regional level in order to eliminate
the possibility of having zero as an observation.
Expenditure levels for 22 meat products are reported
in the survey which were in turn aggregated into eight
categories for estimation purposes (see Table 4.2). This
aggregation process used the formulas provided in the CES
documentation (see Appendix A for the formulas). The new
data set contains the level of average monthly household
expenditure on the eight aggregate meat commodities by
region.
Data on monthly prices of meat products in the four
demand regions were also obtained from the BLS. The data
contain the U.S. average price as well as separate regional
prices for 24 meat products. The prices reported were
roughly consistent with the commodity categories obtained
from the expenditure survey (see Table 4.2). In the several
instances where multiple prices were reported for a single
expenditure category in the CES data the prices were
averaged together. There were three exceptions to this
procedure. In the steak category the price for porterhouse
steak was not used in calculating the average price for

MIDWEST
Figure 4.4.
survey.
Demand regions as defined in the consumer expenditure

93
TABLE 4.2 EXPENDITURES AND PRICES REPORTED FOR MEAT COM-
MODITIES
AND THE
SYSTEM.
BY THE BUREAU OF LABOR
COMMODITY CATEGORY USED
STATISTICS (BLS)
IN THE DEMAND
Prices
Reported
Expenditures
Reported
Aggregate
Commodities
Turkey
Other Poultry
Other Poultry
Chicken Legs
Chicken Breast
Chicken Parts
Chicken Parts
Whole Chicken
Whole Chickens
Whole Chickens
Beef Liver
Bologna
Franks
Other Meat
Other Meat
Other Meat
Other Meat
Ham, canned
Sausage
Other Ham
Pork Chop
Bacon
Pork Shoulder
Pork Roast
Canned Ham
Pork Sausage
Ham (excluding canned)
Pork Chops
Bacon
Other Pork
Other Pork
Pork
Porterhouse Steak
T-Bone Steak
Chuck Steak
Sirloin Steak
Round Steak
Other Steak
Other Steak
Other Steak
Sirloin Steak
Round Steak
Steak
Rib Roast
Round Roast
Chuck Roast
Other Roast
Round Roast
Chuck Roast
Roast
Ground Chuck
Ground Beef
Ground Beef
Ground Beef
Ground Beef

94
other steak. This was done because its price was reported
for only two of the demand regions. In the ground beef
category only the price for ground chuck was used because
the ground beef price was not reported prior to 1984. In
the pork category only the prices for sausage, canned ham,
pork chop, and bacon were used. Pork shoulder, pork roast
and other ham were not used because their prices were not
consistently reported in any of the demand regions.
The eight price indexes were calculated by using a
weighted average of the prices of the individual elements of
a meat category. The weights used were the individual
commodities' share of consumer's expenditures on the
aggregate commodity categories.
As alluded to above there was a problem with missing
observations in the price series provided by the BLS. In
some cases the entire price series for a commodity was not
reported in one of the demand regions. This was particu¬
larly true for steak prices in the West region (see Table
4.3) .
In the instances where this occurred three different
approaches were used to impute the missing prices. The
first approach was to use a price of a substitute commodity
to represent the missing price series. This was done in the
case of pork where the canned ham price was used as a proxy
for the fresh ham prices. It was also done in the case of
other steak where the porterhouse price was used as a proxy

95
TABLE 4.3 MISSING OBSERVATIONS FOR MEAT PRICES REPORTED BY
THE BUREAU OF LABOR STATISTICS (BLS).
Item
Northeast
South
Midwest
West
Turkey
Chicken Legs
1986
-
1982-85
1980-86
Chicken Breast
-
-
-
-
Whole Chicken
-
-
-
-
Beef Liver
_
1983-85
Bologna
-
-
-
-
Franks
-
-
-
-
Ham, canned
Sausage
1982-86
-
-
-
Other Ham
-
-
1982-86
1982-84
Pork Chop
-
-
-
-
Bacon
-
—
-
-
Pork Shoulder
1982-86
—
1982-85
1982-86
Pork Roast
-
1980-86
1982-86
1982-85
Porterhouse Steak
-
1982,
1985
-
1982-86
T-Bone Steak
1982-86
-
—
1985,
1986
Chuck Steak
-
1986
—
1982-86
Sirloin Steak
-
—
—
1982-86
Round Steak
-
-
-
-
Rib Roast
_
_
Round Roast
—
—
—
—
Chuck Roast
—
_
—
1982-86
Ground Chuck
—
—
—
Ground Beef
1982,
1982,
1982,
1982,
1983
1983
1983
1983

96
for T-bone price in the Northeast Region. In cases where it
was not possible to use a substitute price the missing price
was imputed by regressing the U.S. average price on the
regional prices of a commodity in the same category in order
to determine the relationship between the U.S. average price
and the regional prices. This relationship was then used to
calculate the missing price series. This technique was
applied to beef liver in the Midwest, sausage in the
Northeast, and sirloin and chuck steak in the West.
Finally, in the case of chicken legs where the prices were
missing in both the Midwest and West the missing prices were
imputed by regressing the U.S average price for whole
chickens on the U.S. average price for chicken breasts and
chicken legs in order to determine the relationship between
the price for whole chickens, the price for chicken breasts,
and the price for chicken legs. (The formulas used to
impute prices are found in Appendix A Table A.l.)
There were also a few cases where a small number of
observations were missing within a price series (see Table
4.3). In these cases the missing prices were imputed by
using a forecast based on a simple time series regression on
the price series.
By using the imputed prices the statistical properties
of the estimated parameters are affected and that the
resulting parameter estimates are biased. However, if the
price series with missing observations are dropped then the

97
parameter estimates will be biased as well. This is because
if the missing prices were not imputed the price index for
the aggregate commodity would not account for changes in the
price of a commodity which in many cases accounted for a
major share of consumer's expenditures in that aggregate
meat category. A more representative price index is
obtained by using the information at hand to impute the mis¬
sing prices than by ignoring them. Thus, a more realistic
parameter estimate is obtained by using the imputed prices
rather than dropping the price for which observations are
missing.
Estimation Procedures
The demand model derived earlier was extended by add¬
ing dummy variables in order to account for seasonality in
the monthly data. The extended demand system was estimated
using a full information maximum likelihood dummy variable
(FIMLDV) estimator. An iterative maximum likelihood proced¬
ure is used to allow for contemporaneous correlation in the
error terms of the demand system due to the imposition of
the symmetry conditions. Asymptotically no improvement
results from iterating more than once, however, for finite
samples iterating until convergence is achieved does lead to
improvements in the estimator (Judge et al., 1985).
The FIMLDV was applied to the data in each region
separately. Thus, both intercept and slope parameters are
permitted to vary between regions. In terms of the

98
taxonomy of pooled cross-sectional estimators provided in
Judge et al. (1985), the estimator used can be classified as
a seemingly unrelated regression (SUR). Kmenta (1971) has
indicated that in this case the regional models can be
estimated separately.
The Results
The results from the estimation procedure are shown in
Tables 4.4-4.7. The standard error, the t-statistic and a
Durbin-Watson statistic are reported. The significance lev¬
els of the parameter estimates are mixed. The estimates of
the parameters on the quantity variables with a few excep¬
tions are significant while the effects of the seasonal var¬
iables and the quantity index are generally insignificant.
The Durbin-Watson statistic indicates that there may
be a problem with autocorrelated error terms or misspecif-
ication in some of the demand equations. If there is auto¬
correlation then the t-statistic has no meaning. However,
as pointed out in Judge et al. (1985, p. 493), the Durbin-
Watson statistic is not a system wide test of autocorrela¬
tion, but only a single equation test. Although the use of
the Durbin-Watson test to check for autocorrelation in sys¬
tems of equations is a common practice, little is known
concerning the robustness of the Durbin-Watson test when
applied to a system of equations. Thus, it is possible that
the Durbin-Watson indicates autocorrelation exists when in
reality it does not.

99
TABLE 4.4 NORTHEAST DEMAND REGION RESULTS
Quantity
Equa¬
tion
Inter¬
cept
Ham¬
burger
1
Roasts
2
Steak
3
Pork
4
Other
Poultry
5
Eq. 1
0.10712
0.13696
-0.01366
-0.01645
-0.04072
-0.00633
0.01037a
0.00385
0.00268
0.00275
0.00350
0.00186
10.33b
35.57
-5.09
-5.98
-11.62
-3.40
D.W.
0.4375
Eq • 2
0.14033
0.08175
-0.02393
-0.02033
-0.00373
0.00852
0.00332
0.00263
0.00329
0.00159
16.46
24.63
-9.11
-6.18
-2.34
D.W. 1.4977
Eq. 3 0.21690
0.00902
24.06
D.W. 1.3976
Eq. 4 0.13136
0.01234
10.65
D.W. 1.0133
Eq. 5 0.07975
0.00873
9.14
D.W. 2.4970
0.12588
-0.03357
-0.00798
0.00396
0.00373
0.00172
31.77
-9.00
-4.63
0.16364
-0.00579
0.00666
0.00252
24.57
-2.30
0.03713
0.00215
17.30
Eq. 6
D.W.
0.06435
0.00805
8.00
1.0270
Eq. 7
D.W.
0.09861
0.01274
7.14
0.6340
Eq. 8 0.16158
0.00751
21.52
Standard error
bt statistic.

100
TABLE 4.4—Extended
Quantity
Season Dummy
Whole Parts Other
Chicken Chicken Meat
6 7 8
Quantity
SI
S3
S4
-0.00934
0.00211
-4.44
-0.02118
0.00323
-6.56
-0.02928
0.00250
-11.69
-0.01019
0.00734
-1.39
0.00471
0.00333
1.41
-0.00732
0.00325
-2.25
-0.00375
0.00352
-1.07
-0.00471
0.00182
-2.59
-0.00251
0.00237
-1.06
-0.01288
0.00240
-5.36
0.00039
0.00561
0.07
0.00188
0.00263
0.72
-0.00148
0.00249
-0.60
0.00113
0.00277
0.41
-0.00866
0.00201
-4.32
-0.01462
0.00258
-5.66
-0.02066
0.00271
-7.64
0.00043
0.00580
0.04
0.00095
0.00263
0.36
-0.00285
0.00256
-1.11
0.00089
0.00286
0.31
-0.00926
0.00289
-3.20
-0.01028
0.00341
-3.01
-0.04368
0.00327
-13.35
-0.00901
0.00830
-1.09
-0.00126
0.00377
-0.33
0.00697
0.00370
1.88
-0.00007
0.00415
-0.02
-0.00237
0.00158
-1.50
-0.00483
0.00216
-2.24
-0.00609
0.00149
-4.09
0.01185
0.00642
1.85
-0.00352
0.00283
-1.25
-0.00210
0.00283
-0.74
0.00361
0.00323
1.12
0.04725
0.00241
19.57
-0.00347
0.00234
-1.48
-0.00944
0.00180
-5.25
0.00327
0.00580
0.56
-0.00468
0.00257
-1.83
-0.00093
0.00260
-0.36
-0.00412
0.00278
-1.48
0.07191
0.00433
16.60
-0.01502
0.00208
-7.24
0.00648
0.00948
0.68
0.00273
0.00415
0.66
0.00666
0.00419
1.59
0.00216
0.00437
0.49
0.13164
-0.00321
0.00484
-0.66
-0.00081
0.00224
-0.36
0.00104
0.00213
0.49
0.00016
0.00245
0.06

101
TABLE 4.5 SOUTH DEMAND REGION RESULTS
Quantity
Equa¬
tion
Inter¬
cept
Ham¬
burger
1
Roasts
2
Steak
3
Pork
4
Other
Poultry
5
Eq. 1
0.12131
0.13358
-0.01556
-0.02965
-0.04121
-0.00505
0.00729a
0.00342
0.00280
0.00298
0.00367
0.00132
16.65b
39.03
-5.56
09.96
-11.22
-3.82
D.W.
1.1798
Eq. 2
0.15366
0.07986
-0.01110
-0.02122
-0.00365
0.00934
0.00460
0.00355
0.00469
0.00161
16.45
17.37
-3.13
-4.52
-2.26
D.W.
1.6329
Eq. 3
0.17795
0.12163
-0.03297
-0.00182
0.01230
0.00565
0.00545
0.00205
14.47
21.52
-6.05
-0.89
D.W.
.9388
Eq. 4
0.11621
0.15826
-0.01247
0.01611
0.00953
0.00268
7.22
16.61
-4.76
D.W. .6432
Eq. 5 0.07056
0.00654
10.78
D.W. 2.3908
0.03445
0.00146
23.61
Eq. 6
D.W.
0.06339
0.00660
9.60
1.2515
Eq. 7 0.13688
0.01141
11.99
D.W. 1.2504
Eq. 8 0.16005
0.00479
33.39
aStandard error
bt statistic.

102
TABLE 4.5—Extended
Ouantitv
Quantity
Season Dummy
Whole
Chicken
6
Parts
Chicken
7
Other
Meat
8
SI
S3
S4
-0.00667
-0.00562
-0.02983
-0.02012
0.003000
-0.00127
-0.00495
0.00193
0.00214
0.00204
0.00535
0.00213
0.00228
0.00232
-3.46
-2.62
-14.64
-3.76
1.41
-0.56
-2.13
-0.00990
-0.00312
-0.01529
-0.00645
0.00038
-0.00171
-0.00176
0.00222
0.00249
0.00217
0.00638
0.00252
0.00278
0.00277
-4.47
-1.25
-7.05
-1.03
0.15
-0.61
-0.64
-0.00310
-0.01681
-0.02618
-0.01463
-0.00245
-0.01034
-0.00804
0.00250
0.00351
0.00209
0.00937
0.00379
0.00392
0.00408
-1.24
-4.79
-12.53
-1.56
-0.65
-2.64
-1.97
-0.01267
-0.00220
-0.03526
-0.00504
0.00734
0.00874
0.00930
0.00344
0.00417
0.00279
0.01188
0.04791
0.00505
0.00507
-3.69
-0.53
-12.64
-0.42
1.53
1.73
1.84
-0.00423
0.00120
-3.52
-0.00268
0.00167
-1.61
-0.00428
0.00091
-4.67
0.00108
0.00496
0.22
-0.00097
0.00202
-0.48
-0.00074
0.00208
-0.35
0.01053
0.00220
4.78
0.05148
0.00218
23.58
-0.00786
0.00189
-4.16
-0.00705
0.00139
-5.08
0.00910
0.00497
1.83
-0.00070
0.00197
-0.35
0.00034
0.00208
0.16
0.00221
0.00212
1.04
0.05205
0.00383
13.59
-0.01375
0.00140
-9.85
0.03938
0.00908
4.34
-0.00374
0.00362
-1.03
0.00548
0.00371
1.48
-0.00572
0.00372
-1.54
0.13705
-0.00332
0.00338
-0.98
-0.00287
0.00134
-2.15
-0.00050
0.00149
-0.34
-0.00157
0.00149
-1.05

103
TABLE 4.6 MIDWEST DEMAND REGION RESULTS
Quantity
Equa¬
tion
Inter¬
cept
Ham¬
burger
1
Roasts
2
Steak
3
Pork
4
Other
Poultry
5
Eq. 1
0.10896
0.15321
-0.01717
-0.02902
-0.05532
-0.00429
0.00812a
0.00354
0.00249
0.00256
0.00426
0.00147
13.41b
43.32
-6.89
-11.35
-12.98
-2.91
D.W.
1.0367
Eq. 2
0.14678
0.07764
-0.01700
-0.02047
-0.00150
0.00795
0.00352
0.00226
0.00424
0.00148
18.47
22.09
-7.51
-4.83
-1.01
D.W.
2.0510
Eq. 3
0.19817
0.12197
-0.03283
-0.00354
0.00754
0.00292
0.00393
0.00136
26.27
41.82
-8.36
-2.59
D.W.
1.1309
Eq. 4
0.16072
0.17207
-0.00887
0.01401
0.00961
0.00252
11.47
17.90
-3.52
D.W. 1.0804
Eq. 5
D.W.
0.06466
0.01043
6.20
2.3538
0.03014
0.00205
14.73
Eq. 6
D.W.
0.04274
0.00668
6.40
0.8279
Eq. 7
D.W.
0.08883
0.00427
20.81
1.1056
Eq. 8 0.18914
0.01097
17.24
Standard error
bt statistic.

104
TABLE 4.6—Extended
Ouantitv
Season Dummy
Whole
Chicken
6
Parts
Chicken
7
Other
Meat
8
Quantity
SI
S3
S4
-0.00840
0.00194
-4.33
-0.01176
0.00170
-6.90
-0.02727
0.00365
-7.47
-0.01050
0.00622
-1.69
0.00288
0.00253
-1.14
-0.00403
0.00259
-1.56
-0.00748
0.00279
-2.68
-0.00655
0.00197
-3.32
-0.00598
0.00156
-3.83
-0.00897
0.00366
-2.45
-0.00537
0.00596
-0.90
-0.00215
0.00246
-0.88
-0.00939
0.00250
-3.75
-0.00827
0.00269
03.07
-0.00564
0.00176
-3.20
-0.01066
0.00147
-7.27
-0.02328
0.00338
-6.89
-0.00457
0.00574
-0.80
-0.00207
0.00235
-0.88
-0.00250
0.00239
-1.04
-0.00698
0.00260
-2.69
-0.00841
0.00330
-2.55
-0.00963
0.00246
-3.91
-0.03653
0.00653
-5.60
-0.00050
0.01037
-0.05
0.00232
0.00425
0.55
0.00489
0.00443
1.10
0.00953
0.00468
2.03
-0.00355
0.00122
-2.90
-0.00242
0.00079
-3.08
-0.00597
0.00209
-2.86
0.00142
0.00827
0.17
0.00089
0.00342
0.26
0.00157
0.00342
0.46
0.01101
0.00373
2.95
0.04568
0.00223
20.46
-0.00196
0.00128
-1.53
-0.01117
0.00294
-3.80
-0.00930
0.00511
-1.82
-0.00030
0.00210
-0.14
0.00500
0.00214
2.34
0.00358
0.00233
1.54
0.05444
0.00155
35.16
-0.01204
0.00229
-5.27
-0.00194
0.00223
-0.58
0.00078
0.00130
0.60
0.00283
0.00135
2.09
0.00184
0.00144
1.27
0.12523
0.03075
0.00835
-0.00235
0.00341
0.00164
0.00359
-0.00323
0.00385
3.68 -0.69 0.46 -0.84

105
TABLE
4.7 WEST
DEMAND
REGION RESULTS
Egua-
tion
Inter¬
cept
Ouantitv
Ham¬
burger
1
Roasts
2
Steak
3
Pork
4
Other
Poultry
5
Eg. 1
0.13559
0.13511
-0.00189
-0.03136
-0.04208
-0.00648
0.00917a
0.00441
0.00267
0.00297
0.00379
0.00181
14.79b
30.62
-0.71
-10.55
-11.10
-3.57
D.W.
1.1546
Eg. 2
0.14481
0.04475
-0.00681
-0.01752
-0.00312
0.01426
0.00498
0.00339
0.00433
0.00263
10.15
9.00
-2.01
-4.05
-1.19
D.W.
1.3972
Eg. 3
0.23876
0.13590
-0.04588
-0.01012
0.01216
0.00485
0.00446
0.00244
19.64
28.01
-10.30
-4.15
D.W.
1.1333
Eg. 4
0.12427
0.16471
-0.00935
0.01460
0.00787
0.00299
8.51
20.93
-3.13
D.W.
1.2924
Eg. 5
D.W.
0.02821
0.01125
2.51
2.2659
0.03948
0.00272
14.51
Eg. 6
D.W.
0.07232
0.00568
12.73
1.111
Eg. 7
D.W.
0.11137
0.00904
12.31
0.8655
Eg. 8 0.14468
0.01149
12.60
aStandard error.
bt statistic.

106
TABLE 4.7—Extended
Quantity
Season Dummy
Whole
Chicken
6
Parts
Chicken
7
Other
Meat
8
Quantity
SI
S3
S4
-0.00755
0.00181
-4.16
-0.01238
0.00220
-5.63
-0.03337
0.00341
-9.80
-0.00377
0.00697
-0.54
-0.00068
0.00297
-0.23
-0.00398
0.00286
-1.39
-0.00572
0.00289
-1.98
-0.00102
0.00172
-0.59
-0.00486
0.00267
-1.82
-0.00953
0.00342
-2.79
0.01690
0.01130
1.50
0.00401
0.00490
0.82
-0.00118
0.00456
-0.26
0.00059
0.00475
0.12
-0.00683
0.00194
-3.53
-0.01309
0.00286
-4.57
-0.02181
0.00367
-5.94
0.00360
0.00962
0.37
-0.00791
0.00413
-1.92
-0.00850
0.00388
-2.19
-0.00695
0.00402
-1.73
-0.00950
0.00237
-4.01
-0.01404
0.00326
-4.31
-0.02633
0.00486
-5.42
-0.00321
0.01137
-0.28
0.00249
0.00488
0.51
0.00752
0.00466
1.61
0.01015
0.00477
2.13
0.00006
0.00116
0.05
-0.00153
0.00179
-0.85
-0.00894
0.00248
-3.60
-0.03443
0.00920
-3.74
0.00866
0.00397
2.18
0.00300
0.00373
0.81
0.00891
0.00390
2.28
0.04324
0.00150
28.74
-0.00840
0.00145
-5.79
-0.01001
0.00213
-4.70
0.01003
0.00448
2.24
-0.00037
0.00190
-0.19
0.00031
0.00179
0.18
-0.00107
0.00184
-0.58
0.05794
0.00268
21.61
-0.00365
0.00272
-1.34
0.01271
0.00719
1.77
-0.00134
0.00308
09.44
0.00405
0.00290
1.40
0.00034
0.00301
0.11
0.11364
-0.00183
0.00896
-0.20
-0.00486
0.00385
-1.26
-0.00123
0.00368
-0.33
-0.00625
0.00379
-1.65

107
The appropriate test for autocorrelation would be one
which included the error terms from all the equations. In a
system of equations with first order autoregressive disturb¬
ances , the disturbances in all equations in time period t
are related to the previous period's disturbances by
et = Re,..! + vt
where et is a (M x 1) vector of disturbances in period tf
et_! is a (M x 1) vector of disturbances lagged on time per¬
iod, R is a (M x M) matrix of p^'s and vt is a (M x 1)
vector of random disturbances with E[vlt]=0 and E[vltv;)B]=olj
for t=s, but zero otherwise. R is estimated by regressing
eit On ( ® lt-1 / ®2t-l/ * • • / ®Mt-l) •
Judge et al. (1985, p. 494) propose a likelihood ratio
test for first order autocorrelation in systems of equa¬
tions. Let E represent the ((T-l) x M) matrix obtained from
dropping the first row from the residual matrix of the
estimated system, E_x be the ((T-l) x M) obtained from
deleting the last row from the residual matrix,
2 = ( T-l) _1( E - E.XR)' (E - E.jR)
and 20 = (T-1)_1E'E. Then under the null hypothesis R=0

108
u = (T-l)(In|S01 -In|E|)
converges in distribution to a %(m2) random variable.
The likelihood ratio test was applied to the Midwest
region. The value of the test statistic was 1.932. Con¬
sequently, the null hypothesis that there is no autocor¬
relation could not be rejected. Given the results obtained
for the Midwest the test was not applied to any of the other
demand regions.
The AIDS model has as one of its characteristics that
the parameter on the own-quantity variable is positive.
Thus, it is not possible to determine whether the demand
curves are downward sloping simply by looking at these
parameters. In order to determine this it is necessary to
evaluate the partial derivative of the demand equations with
respect to their own quantity. Given this it is easier to
determine whether the demand curves are downward sloping by
looking at the demand flexibilities.
Flexibilities are calculated at the means of the data
for each of the four demand regions and reported in Tables
4.8-4.11. The formula used to calculate the flexibilities,
eij = + Yij/Wi - Pi/w^Wi + S^lnq^e*., + 6kj)
where is the Kronecker delta (61;) = 1 for i = j; 6Aj = 0
otherwise, was adapted from Green and Alston (1990, p. 443).

TABLE 4.8 FLEXIBILITIES FOR MEATS IN THE NORTHEAST REGION
Description
GB
Roasts
Steak
Pork
Other
Poultry
Chicken
Whole
Chicken
Parts
Other
Meat
Ground Beef
-0.151
-0.089
-0.110
-0.275
-0.040
-0.062
-0.140
-0.201
Roasts
-0.148
-0.109
-0.260
-0.220
-0.041
-0.051
-0.027
-0.139
Steaks
-0.104
-0.152
-0.202
-0.212
-0.051
-0.055
-0.092
-0.130
Pork
-0.193
-0.094
-0.156
-0.270
-0.027
-0.044
-0.051
-0.209
Other Poultry
-0.109
-0.088
-0.186
-0.064
0.018
-0.050
-0.099
-0.080
Chicken, Whole
-0.165
-0.087
-0.158
-0.157
-0.044
-0.102
-0.059
-0.162
Chicken, Parts
-0.203
-0.023
-0.142
-0.157
-0.049
-0.032
-0.261
-0.135
Other Meat
-0.137
-0.060
-0.096
-0.205
-0.028
-0.044
-0.070
-0.250
109

TABLE 4.9 FLEXIBILITIES FOR MEATS IN THE SOUTH REGION.
Description
GB
Roasts
Steak
Pork
Other
Meat
Chicken
Whole
Chicken
Parts
Other
Poultry
Ground Beef
-0.218
-0.085
-0.155
-0.191
-0.149
-0.031
-0.024
-0.029
Roasts
-0.151
-0.150
-0.110
-0.200
-0.150
-0.101
-0.028
-0.039
Steaks
-0.173
-0.069
-0.198
-0.179
-0.153
-0.014
-0.103
-0.012
Pork
-0.161
-0.085
-0.130
-0.356
-0.138
-0.050
-0.007
-0.051
Other Meat
-0.145
-0.101
-0.053
-0.362
-0.123
-0.118
-0.076
-0.053
Chicken, Whole
-0.148
-0.174
-0.072
-0.276
-0.149
-0.126
-0.146
-0.073
Chicken, Parts
-0.177
-0.054
-0.273
-0.215
-0.265
-0.132
-0.373
-0.035
Other Poultry
-0.189
-0.099
-0.168
-0.221
-0.062
-0.044
-0.088
-0.028
o

TABLE 4.10 FLEXIBILITIES FOR MEATS IN THE MIDWEST REGION
Description
GB
Roasts
Steak
Pork
Other
Poultry
Chicken
Whole
Chicken
Parts
Other
Meat
Ground Beef
-0.211
-0.092
-0.156
-0.309
-0.022
-0.047
-0.063
-0.160
Roasts
-0.209
-0.127
-0.196
-0.252
-0.017
-0.177
-0.069
-0.120
Steaks
-0.218
-0.123
-0.123
-0.248
-0.025
-0.042
-0.078
-0.0178
Pork
-0.218
-0.080
-0.129
-0.325
-0.035
-0.033
-0.038
-0.144
Other Poultry
-0.122
-0.045
-0.107
-0.261
-0.060
-0.109
-0.074
-0.172
Chicken, Whole
-0.216
-0.136
-0.127
-0.232
-0.070
-0.099
-0.044
-0.280
Chicken, Parts
-0.204
-0.100
-0.180
-0.171
-0.040
-0.034
-0.097
-0.210
Other Meat
-0.083
-0.035
-0.091
-0.112
-0.026
-0.043
-0.049
-0.264

TABLE 4.11 FLEXIBILITIES FOR MEATS IN THE WEST REGION.
Description
GB
Roasts
Steak
Pork
Other
Poultry
Chicken
Whole
Chicken
Parts
Other
Meat
Ground Beef
-0.261
-0.011
-0.175
-0.239
-0.036
-0.042
-0.069
-0.188
Roasts
0.023
-0.467
-0.060
-0.138
-0.034
-0.044
-0.045
-0.074
Steaks
-0.185
-0.040
-0.173
-0.271
-0.061
-0.041
-0.078
-0.128
Pork
-0.181
-0.075
-0.196
-0.308
-0.040
-0.041
-0.060
-0.114
Other Poultry
-0.347
-0.112
-0.331
-0.513
-0.049
-0.032
-0.087
-0.375
Chicken, Whole
-0.104
-0.011
-0.115
-0.212
0.004
-0.136
-0.155
-0.161
Chicken, Parts
-0.121
-0.055
-0.150
-0.123
-0.018
-0.100
-0.255
-0.016
Other Meat
-0.204
-0.058
-0.133
-0.162
-0.054
-0.061
-0.023
-0.294
112

113
All the own-quantity flexibilities are negative which
is consistent with theoretical expectations. The exception
is the own-flexibility for other poultry in the northeast
region. The positive sign for the own-flexibility of other
poultry while disturbing is not totally inexplicable con¬
sidering the large amount of seasonal variation in the level
of other poultry consumption. There is also a large amount
of seasonal variation in the price of other poultry which
coincides with the variation in consumption levels.
Increased consumption of other poultry and the increased
price of poultry during the fourth quarter is probably due
to the holidays. This is a period when the demand for
turkey increases because it is traditional for Americans to
serve roast turkey for dinner on Thanksgiving and Christmas.
This, combined with the decline in prices and the low level
of consumption of turkey during the other three quarters due
to the demand for turkey shifting inward, provides a plaus¬
ible explanation for the positive sign on the own flexibil¬
ity for other poultry in the Northeast.
A comparison of the own-quantity flexibilities to the
cross-flexibilities indicates that an increase in the quan¬
tity of each meat has a strong negative effect on the prices
of the other meat products. This supports the need to
incorporate interrelated demand systems into the programming
model.

114
Elasticities and flexibilities from other demand
studies are reported in Table 4.12. Of the four studies
only Dahlgran (1987) estimated flexibilities. Unfortun¬
ately, Dalhgran's model only includes a single aggregate
beef variable. Thus, it is not readily possible to make a
comparison between the results from his study to the results
obtained here. Dahlgran's results indicate that the price
for beef is flexible which is opposite of the results
reported in this study. It is possible given the strong
cross effects between the meat products that the dis¬
aggregate products could be inflexible and still have an
aggregate flexibility that is flexible.
The other three studies report only price elastic¬
ities. There is little consistency between the studies in
reported elasticities for ground beef, roast and steak.
While Eales and Unnevehr (1988), and Capps and Havlicek
(1984) report that the demand for ground beef is elastic,
Heien and Pompelli (1988) report that demand for ground beef
is inelastic. Similarly, Eales and Unnevehr (1988) and
Heien and Pompelli (1988) report strong cross effects while
Capps and Havlicek (1984) report relatively weak cross
effects.
It is difficult to evaluate the results obtained here
based on the results obtained in the other four demand
studies. This is because all of the studies differ as to
the type of data used (cross-section, annual time series or

115
TABLE 4.12. ELASTICITIES AND FLEXIBILITIES FOR BEEF REPORTED IN
OTHER DEMAND STUDIES.
Researcher
Model
Equations
Elasticities
Eales and
AIDS
Table
Unnevehr
Gb
Cuts
Gb
-2.593
1.593
Table cuts
0.384
-.684
Capps and
Si-
Gb
Roast
Steak
Havlicek
Branch
Gb
-1.52
.06
.07
System
Roast
0.04
-1.83
.09
Steak
0.04
.07
-1.75
Heien and
AIDS
Gb
Roast
Steak
Pompelli
Gb
-.85
.05
.21
Roast
.13
-1.11
-.39
Steak
-.24
-.17
-.73
Dahlgran
Inverse
Beef*
Pork
Chicken
Rotterdam
Beef
-1.75
-4.39
-.160
Pork
-.81
-1.96
-.267
Chicken
-.63
-.58
-1.72
flexibilities

116
pooled monthly cross-section and time series), the time
period spanned, the method used to obtain data (survey or
disappearances), preference structure assumed and functional
form used. In the demand systems estimated in this
dissertation the data set used pooled cross-section survey
data on monthly household expenditures on meat from 1982-
1986. Eales and Unnevehr (1988) used annual disappearance
data from 1965-1985 in their study, Dahlgran (1987) used
annual disappearance data from 1950-1985, while Capps and
Havlicek (1985) and Heien and Pompelli (1988) used cross-
sectional household expenditure survey data from 1977. All
the studies except this one and Eales and Unnevehr assumed
that preferences were separable by species.
All of these factors will cause the estimated
parameters obtained from the studies to vary. In
particular, one would expect the parameters estimated from
data obtained after the change in the structure of demand
for meat occurred. Monthly data contains more variation
than annual data. Thus, the use of monthly data may cause
there to be an appearance of greater substitution among the
individual meat commodities than actually occurs. Which of
the two, monthly or annual, is more representative of
consumer response to changes in prices is open to debate.
Finally, if preferences for meat are not separable by
species than studies which assume that preferences are

117
separable by species will have different parameter estimates
than those which do not make this assumption.
Adjustments Made to Demand Equations
Before the estimated inverse demand systems, can be
used in the programming model several steps need to be
taken. The first step is to aggregate the household demand
system up to the market level. The second step is to eval¬
uate each demand system's Jacobian matrix to determine the
range of quantities over which it satisfies the negative
definiteness, restriction.
Given that the estimated demand system permits perfect
aggregation the household level demand system can be trans¬
formed into a market level demand system by substituting
q=Y/P and x=M/P (where q represents household consumption, Y
is equal to market level consumption, P represents the total
number of households in the market, x is equal to household
level of expenditures, and M is equal to the level of total
expenditures in the market) into the household level demand
system and simplifying.
It is necessary to evaluate the Jacobian matrix of the
market level demand system for two reasons. The first
reason is that while the symmetry requirement has been
imposed in estimation the negative definiteness of the
system's Jacobian has not been imposed. Secondly, flexible
demand systems such as the AIDS model only satisfy the
demand theory properties locally and not globally. At first

118
this was believed to imply that the demand system would
satisfy the conditions at each of the points in the data
set. However, Caves and Christensen (1980) have pointed out
that in actual practice this has never been true. Evalu¬
ations of the global properties of such flexible functional
forms such as the Leontief and Translog models have indi¬
cated that there is a very small range of values over which .
flexible systems satisfy the properties derived from eco¬
nomic theory.
It is preferable that the demand systems satisfy the
integrability conditions globally. Given the properties of
flexible forms, however, it is unreasonable to expect them
to meet this condition. It does seem reasonable to expect
that they satisfy the integrability conditions over minimum
and maximum quantities of hamburger, steak and roasts
observed in the data set.
Before evaluating the Jacobian matrixes of the market
level demand systems it was necessary to set the levels of
the exogenous variables (pork, other meat, poultry, expend¬
iture and the quantity index) at their means.1 When eval¬
uated at the means of the data only three of the four
Jacobians were negative definite. When the Jacobians were
evaluated at each of the observations in the data set the
xBy holding the quantity index ln(Q) constant the
demand equations only approximate the compensated demand
system. For information on how to obtain the empirical
compensated system see Appendix D.

119
results were mixed. For the Midwest and the Northeast
negative definiteness was rejected at a majority of the data
points. For the West and South the results were better with
negative definiteness holding at 67-83% of the data points.
These results indicate that it is necessary to determine a
range of quantities for which the negative definiteness
property holds in order to use the demand systems for
simulation purposes.
It was decided to adjust the own-quantity parameters
by adding k to them in order to ensure that they satisfy the
negative definiteness criteria. This is common practice in
the engineering literature to adjust the diagonal elements
of a system of equations in order to ensure that their
Jacobians are negative definite. It was also decided that
it would be best to set the exogenous variables at their
minimum values when using them in the programming model.
This was done to ensure the demand systems would be negative
definite over the greatest range possible. This is an
unorthodox procedure in that typically variables are set at
their means of the data. The value used for k was 0.005 in
all regions except for the West where k=.0025 was used.
These two adjustments enabled the demand systems in each
region to be negative definite over the range of values
shown in Table 4.13.
Finally, the demand equations were adjusted by multi¬
plying the original intercept term by the values shown in

120
TABLE 4.13
LOWER AND
HOUSEHOLD
UPPER BOUNDS ON
LEVEL.
BEEF
VARIABLES
r
Area
Bounds
Hamburger
Roast
Steak
{ _LUO / 1UVJ11 Lll )
Northeast
Upper
7.2
3.3
4.0
Lower
2.1
1.0
0.8
South
Upper
8.1
4.0
7.0
Lower
2.4
0.4
1.4
Midwest
Upper
7.7
2.75
3.5
Lower
2.8
1.2
1.475
West
Upper
7.0
2.75
4.0
Lower
2.3
0.4
1.3
TABLE 4.14
ADJUSTMENT
MADE TO INTERCEPT OF
DEMAND
EQUATIONS.
Region
North
Mid-
Equation
east
South
west
West
Hamburger
95
87
90
92
Roast
94
78
80
77
Steak
102
87
85
88

121
Table 4.14. This was done to reorient the demand system in
commodity space so that it forecast prices in the same range
as found in the data used to estimate the demand system. It
was necessary to do this because all the variables in the
demand equations except the beef variables were held con¬
stant at their minimum observed value. Consequently, the
forecasted prices generated using the demand system without
the adjustments made to the intercepts were higher than the
observed prices.
After all the adjustments were made the parameters on
the demand system to be used in the programming model are
shown in Table 4.15. The intercepts have negative signs.
This is because of the negative impact the other meat
products have on the price of the beef products.

122
TABLE 4.15 PARAMETER VALUES FOR MARKET LEVEL DEMAND
EQUATIONS USED
IN THE
PROGRAMMING MODEL
•
Variables
Equation
Inter¬
cept
Ham¬
burger
Roast
Steak
Northeast
Hamburger
Roast
Steak
-1.767
-0.641
-1.265
0.1395
-0.0137
0.0843
-0.0164
-0.0239
0.1284
South
Hamburger
Roast
Steak
-1.463
-0.825
-1.272
0.1361
-0.0156
0.0824
-0.0297
-0.0111
0.1241
Midwest
Hamburger
Roast
Steak
-1.806
-0.653
-1.175
0.1557
-0.0172
0.0801
-0.0290
-0.0170
0.1245
West
Hamburger
Roast
Steak
-1.642
-0.501
-0.147
0.1352
-0.0019
0.0449
-0.0314
-0.0068
0.136

CHAPTER 5
DESCRIPTION OF ACTIVITY ANALYSIS
MODEL OF BEEF PRODUCTION SYSTEM
The purpose of this chapter is to describe the activ¬
ity analysis model used to represent the beef production
system. In the model the U.S. is divided into five supply
regions: the Southeast, the Midwest, the Southwest, the
Plains and the West. The supply regions as shown in Figure
5.1 are consistent with the supply regions reported in the
Census of Agriculture. All five stages of production: cow-
calf, growing, finishing, slaughtering and processing, and
distributing are represented in the model. The flow of
products through the beef production system as represented
in the model is shown in Figure 5.2. Production activities
at each stage of production and the interregional flow of
products from one stage of production to another are
depicted by sets of activity constraints or equations.
The two production activities represented at the cow-
calf stage are the production of weaned calves and the pro¬
duction of culls. After weaning the calves are transferred
to either the stocker (growing) stage or to the finishing
stage, while the culled breeding stock is transferred
directly to the slaughtering stage.
123

Figure 5.1.
Supply regions as defined in model.

125
OUTPUTS
CALVES
CULLS
YEARLINGS
1 1/2 YEAR-OLDS
900 LBS
1100 LBS
1200 LBS
1300 LBS
HAMBURGER
ROASTS
STEAKS
Figure 5.2.
production system.
Activity analysis model of beef

126
Both the supply of calves and the supply of culls are
determined by multiplying the number of cows in the breeding
herd by the calving and culling rates shown in Table 5.1.
The calving rate represents the average rate at which one
cow produces a Stocker or feeder calf over all the herds in
a supply region. The culling rate used is actually the
replacement rate reported in the cow-calf production bud¬
gets. Thus it is being assumed that the cow herd was
neither contracting or expanding in size during the time
period over which the replacement rate was calculated. For
if the breeding herd was decreasing in size during this time
period then by using the replacement rate as a proxy for the
culling rate the model would be underestimating the number
of culls produced while if the size of the breeding herd was
expanding then using the replacement rate as a proxy for the
culling rate would cause the supply of beef culls to be
overestimated.
Reliable production budgets at the cow-calf stage were
not available. As a consequence the size of the breeding
herd is fixed at a predetermined level rather than letting
it be determined by the model. The size of the breeding
herd in each region is fixed at a level which represents the
average size of the breeding herd in each supply region over
the five year period 1982-1986 (see Table 5.1 and Appendix B
Tables B.l and B.2).

127
TABLE 5.1 SIZE OF BREEDING HERD AND CALVING AND CULLING
RATES
Region
Head
Breeding
Stock
Calving
Rate
Culling
Rate
-millions-
Southeast
7.0852
0.59
0.10
Midwest
11.1732
0.61
0.14
Southwest
9.0888
0.63
0.12
West
2.0547
0.57
0.17
Plains
4.9464
0.62
0.16
Sources USDA.
1989.
TABLE 5.2
COST OF PRODUCTION OF COW-CALF STAGE.
Region
Culls
Calves
Southeast
346.937
256.856
Midwest
417.683
303.598
Southwest
384.120
247.026
West
414.094
243.356
Plains
409.851
281.134

128
In the absence of production budgets for cow-calf
activities the market prices for calves and beef culls are
used to represent the costs of production activities at the
cow-calf stage (see Table 5.2). Thus, it is assumed that
the price received is equal to the average cost of produc¬
tion of weaned calves and culls. The prices were obtained
by multiplying the price per lb. for calves and culls ass
reported by USDA times their average weight of calves or
culls.
In the stocker stage weaned calves coming from the
cow-calf stage are used to produce yearlings and 1 1/2 year
olds. The yearlings are produced by placing incoming calves
on pasture for a period of six months while the 1 1/2 year
olds are produced by keeping the incoming calves on pasture
for a period of one year. The yearlings and 1 1/2 year olds
produced are transferred either to the finishing stage or to
the slaughtering-processing stage.
The costs of production at the stocker stage are shown
in Table 5.3. They are derived from production budgets for
stocker operations in each of the supply regions (see
Appendix B Table B.3). The differences in the costs of
production for yearlings and 1 1/2 year olds reflect the
differences in the length of time they are stockered. The
costs shown represent all costs incurred in stockering
activities, such as land and labor, except the cost of the
weaned calf on a per head basis.

129
TABLE 5.3 COST OF PRODUCTION ACTIVITIES AT THE STOCKER
STAGE
Region
Yearling
1 1/2
Years Old
Southeast
91.129
211.953
Midwest
93.701
223.279
Southwest
90.814
215.691
West
110.172
274.496
Plains
104.953
249.682

130
At the finishing stage weaned calves coming from the
cow-calf stage and yearlings and 1 1/2 year olds coming from
the stockering stage are placed on the feedlot where they
are transformed into fed cattle. The fed cattle are then
transferred from the feedlot to the slaughtering-processing
stage. There are six production activities and four alter¬
native finishing weights represented in the model. Each of
the three types of feeder cattle can be raised to two dif¬
ferent weights representing a long and short feeding pro¬
gram. Weaned calves coming from the cow-calf stage are
finished at either 900 or 1,100 lbs., while yearlings coming
from the stockering stage are finished at 900 or 1,200 lbs.,
and 1 1/2 year olds coming from the stockering stage are
finished at 1,100 or 1,300 lbs.
The average costs of each of the six production activ¬
ities are shown in Table 5.4. The costs of production are
calculated from production budgets for each of the feeding
activities (see Appendix B Table B.4). The costs include
all costs incurred at the finishing stage except the cost of
the feeder cattle. The cost of corn along with fixed and
variable costs is explicitly represented in the production
budgets. Thus, it is possible to analyze the impact of
changes in the cost of feed on the cost of the production
activities.
At the slaughter-processing stage live cattle are
rendered into hamburger, roasts, and steaks. The type of

TABLE 5.4 COST OF FINISHING UP TO FINAL WEIGHT
Calf
Region 900 lbs 1,100 lbs
Yearling
1,200 lbs 900 lbs
1 1/2 Years
1,300 lbs 1,100 lbs
$/head
Southeast
276.352
420.049
438.282
199.011
448.765
251.067
Midwest
258.430
392.815
412.881
187.534
422.675
237.169
Southwest
251.582
384.331
401.117
182.138
411.082
238.073
West
290.800
443.034
451.106
205.754
479.130
267.710
Plains
213.875
377.039
396.720
180.332
417.784
233.126
131

132
cattle coining into the slaughter-processing stage are year¬
lings and 1 1/2 year olds from the stockering stage, 900
lb., 1,100 lb., 1,200 lb., 1,300 lb. fed cattle from the
finishing stage, and culls from cow-calf stage and the dairy
herd. The supply of dairy culls is fixed exogenously. Both
the number of dairy culls available in each region and their
cost to the slaughtering plant are shown in Table 5.5. The
live cattle coming into this stage are slaughtered and fab¬
ricated into primal cuts (roasts, steaks, lean trim, medium
trim, and fat and bone). The different cuts and their
weights by live cattle type are shown in Table 5.6. Primal
cuts are transferred either to a sales activity or to a
hamburger processing activity. Only roasts and steaks are
permitted to be transferred directly to the sales activity.
All of the primal cuts except fat and bone may be used in
hamburger production. The production of hamburger produc¬
tion is also constrained by the requirement that hamburger
can consist of no more than 27% fat. Steaks and roasts
contain 20% fat, lean trim contains 15% fat, medium trim
contains 50% trim, and fat and bone is 100%. (See Appendix
B Tables B.5 and B.6 for the derivation of the weight of
each cut.)
The costs of production at the slaughtering and
fabricating step are shown in Table 5.7. These costs
represent the average cost per head in a meatpacking plant
being utilized at full capacity. The differences in the

133
TABLE 5.5 SUPPLY OF DAIRY CULLS AND THEIR COST BY REGION
Region
Number
Cost
-$/head-
Southeast
331,200
346.937
Midwest
2,332,600
417.683
Southwest
200,300
384.120
West
608,400
405.194
Plains
122,900
418.854

TABLE 5.6. WEIGHT OF FABRICATED CUTS BY REGION.
Year-
1 1/2
Region
Cut
900
1,100
1,200
1,300
lings
Years
Culls
cwt
Southeast
Roast
1.203
1.520
1.686
1.856
0.704
0.968
0.398
Steak
1.452
1.835
2.035
2.241
0.846
1.163
0.477
Lean trim
0.535
0.676
0.750
0.826
0.741
1.019
2.319
Medium trim
0.588
0.743
0.824
0.908
0.404
0.556
0.131
Fat and bone
1.521
1.922
2.132
2.347
0.674
0.927
1.050
Midwest
Roast
1.246
1.565
1.731
1.902
0.739
1.004
0.429
Steak
1.503
1.889
2.090
2.296
0.888
1.206
0.513
Lean trim
0.554
0.696
0.770
0.846
0.778
1.057
2.496
Medium trim
0.609
0.765
0.846
0.930
0.424
0.577
0.141
Fat and bone
1.575
1.978
2.189
2.405
0.707
0.961
1.130
Southwest
Roast
1.145
1.461
1.619
1.795
0.658
0.920
0.409
Steak
1.382
1.763
1.954
2.166
0.790
1.105
0.490
Lean trim
0.509
0.650
0.720
0.799
0.692
0.968
2.385
Medium trim
0.560
0.714
0.791
0.878
0.378
0.528
0.135
Fat and bone
1.448
1.847
2.046
2.269
0.629
0.880
1.080
West
Roast
1.179
1.495
1.633
1.831
0.685
0.948
0.435
Steak
1.423
1.805
1.971
2.210
0.822
1.139
0.522
Lean trim
0.524
0.665
0.726
0.814
0.721
0.998
2.536
Medium trim
0.576
0.731
0.798
0.895
0.393
0.544
0.144
Fat and bone
1.490
1.891
2.064
2.314
0.655
0.907
1.148
Plains
Roast
1.199
1.516
1.682
1.852
0.701
0.965
0.440
Steak
1.447
1.830
2.030
2.235
0.842
1.159
0.528
Lean trim
0.533
0.675
0.748
0.824
0.738
1.016
2.565
Medium trim
0.586
0.741
0.822
0.906
0.402
0.554
0.145
Fat and bone
1.516
1.917
2.126
2.341
0.671
01.923
1.162
134

135
TABLE 5.7
AVERAGE COST OF SLAUGHTERING AND
BY REGION.
PROCESSING
HAMBURGER
Region
Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
Live Animal
y y / ilUQLl J '
Southeast
88.585
-
-
-
-
Midwest
77.399
68.938
65.001
62.593
60.650
Southwest
77.399
68.938
65.001
62.593
60.650
West
88.585
-
-
-
-
Plains
77.399
68.938
62.539
-
-
Hamburaer
^ y/ LWL j
Southeast
3.629
-
-
-
-
Midwest
3.060
2.725
2.569
2.474
2.398
Southwest
3.288
2.928
2.761
2.659
2.576
West
3.661
-
-
-
-
Plains
3.143
2.799
2.542
-
-
Source: Nelson, 1989.

136
average cost of slaughtering between the meatpacking plants
are due to the different capacities of the meatpacking
plants used. The cost of slaughtering decreases as the
capacity of the meatpacking plant increases. This reflects
the fact that the meatpacking industry is characterized by
increasing returns to size. The capacity of each type of
meatpacking plant located in a supply region and the total
capacity in each region are shown in Table 5.8. The cost of
making hamburger is estimated to be 23% of the cost of
slaughtering and fabricating. (See Appendix B Table B.7 for
further details.)
Transfer activities in the model move the live cattle
up through the vertical sector and between the supply
regions. Transportation costs, shrinkage due to death loss,
interregional weight adjustments, and a processor to retail
marketing margin are all accounted for in the transfer
activities.
The cost of transporting live animals from one supply
region to another are shown in Tables 5.9 and 5.10 and the
costs of transporting hamburger, roasts and steaks from
supply to demand regions are shown in Table 5.11. The costs
of transporting live animals between supply regions were
estimated by Kennedy and updated by Disney. They are based
on distance traveled and the weight of the animal being
transported (see Appendix B Table B.8).

TABLE 5.8 SIZE AND NUMBER OF MEATPACKING PLANTS
Region
125,000
250,000
500,000
750,000
1,000,000
1,300,000
Total
Southeast
14
-
-
-
-
-
1,750,000
Midwest
-
5
14
6
2
3
18,650,000
Southwest
-
7
1
2
1
1
6,050,000
Plains
-
1
6
-
1
-
4,250,000
West
18
-
-
-
-
-
2,250,000
Total
32
13
21
8
4
4
30,289,000
Source: Faminow and Sarhan, 1983.
137

138
TABLE 5.9 TRANSPORTATION COSTS FOR CULLS, CALVES, AND
STOCKERED CATTLE.
Origin/
Destination Year- 1 1/2
Region Culls Calves lings Years
$/hd-
Southeast
Southeast
2.541
1.257
1.882
2.492
Midwest
34.833
17.237
25.796
34.156
Southwest
31.445
15.561
23.287
30.834
Plains
43.197
21.376
31.990
42.358
Midwest
Southeast
37.500
18.511
27.070
35.430
Midwest
4.103
2.026
2.962
3.877
Southwest
27.014
13.335
19.500
25.523
Plains
14.932
7.371
10.779
14.107
Southwest
Southeast
32.343
14.015
21.742
29.289
Midwest
28.423
12.317
19.107
25.739
Southwest
4.792
2.076
3.221
4.339
West
46.391
20.103
31.185
42.010
Plains
20.255
8.777
13.616
18.342
West
Southwest
52.109
22.597
34.303
45.738
West
6.253
2.712
4.116
5.489
Plains
44.466
19.283
29.272
39.030
Plains
Southeast
47.788
21.228
31.842
42.210
Midwest
15.344
6.816
10.224
13.553
Southwest
21.786
9.678
14.516
19.243
West
38.535
17.118
25.677
34.037
Plains
5.856
2.601
3.902
5.173

139
TABLE 5.10 TRANSPORTATION COSTS FOR FED BEEF BY REGION.
Origin/
Destination
Region
900 1,100 1,200 1,300
$/head-
Southeast
Southeast
2.608
3.189
3.479
3.769
Midwest
35.748
43.710
47.691
51.672
Southwest
32.271
39.459
43.053
46.646
Plains
44.332
54.206
59.143
64.080
Midwest
Southeast
37.022
44.984
48.965
52.946
Midwest
4.051
4.922
5.358
5.793
Southwest
26.670
32.405
35.273
38.140
Plains
14.741
17.912
19.497
21.082
Southwest
Southeast
30.726
37.914
41.328
45.101
Midwest
27.002
33.318
36.318
39.634
Southwest
4.552
5.617
6.123
6.682
West
44.072
54.381
59.278
64.690
Plains
19,243
23,744
25,882
28,245
West
Southwest
47.916
58.806
63.162
69.696
West
5.750
7.057
7.579
8.364
Plains
40.888
50.181
53.898
59.474
Plains
Southeast
44.184
54.058
58.995
63.932
Midwest
14.187
17.357
18.942
20.527
Southwest
20.143
24.644
26.895
29.145
West
35.629
43.591
47.572
51.553
Plains
5.415
6.625
7.230
7.835

140
TABLE 5.11 TRANSPORT COST BOXED BEEF FROM SUPPLY TO DEMAND
REGIONS.
Destination/
Origin Ham-
Region Roast Steak burger
$/cwt
Northeast
Southeast
3.017
3.017
3.017
Midwest
3.547
3.547
3.547
Southwest
4.311
4.311
4.311
Plains
4.098
4.098
4.098
South
Southeast
1.733
1.733
1.733
Midwest
2.835
2.835
2.835
Southwest
2.318
2.318
2.318
West
4.674
4.674
4.674
Plains
3.283
3.283
3.283
Midwest
Midwest
1.843
1.843
1.843
Southwest
3.254
3.254
3.254
Plains
2.752
2.752
2.752
West
Midwest
3.085
3.085
3.085
Southwest
2.981
2.981
2.981
West
2.182
2.182
2.182
Plains
2.225
2.225
2.225

141
The costs of transporting hamburger steaks and roasts
were estimated by Ward and Farris (1989) (see Appendix B
Table B.9). The cost per mile of transporting the retail
cuts declines as the distance traveled increases. Levels of
live animal shrinkage during transfer from one production
stage to another and from one supply region to another are
shown in Table 5.12. The shrinkage on the shipment of
hamburger, roasts and steaks from supply to demand regions
is set at .04%.
An interregional weight adjustment is used to account
for the cost incurred of keeping an animal for a longer or
shorter period of time in a production activity because it
is larger or smaller than the beginning weight for that
animal. At the slaughter-processing stage it adjusts the
costs incurred because the quantity of primal cuts produced
is greater or less than typical in a region depending on
whether the live animal coming in is heavier or lighter than
the typical animal slaughtered in that supply region. It is
possible for this to occur because there are differences in
weights of animals at the same stage of production between
supply regions (see Table 5.13). Thus, when cattle are
shipped from one region to another it may be necessary to
keep the animal in the production activity for a longer or
shorter period of time depending on whether it is heavier or
lighter than the beginning weight for cattle used in the
production activity in the region to which it is shipped.

142
TABLE 5.12 SHRINKAGE OF LIVE CATTLE DURING TRANSFER BETWEEN
PRODUCTION
STAGES AND
SUPPLY REGIONS
Region
Southeast
Midwest
Southwest
West
Plains
Southeast
.964
.913
.928
.890
.908
Midwest
.965
.922
.900
.943
Southwest
.959
.904
.932
West
.945
.912
Plains
.959
Southeast
.965
.928
.931
.900
.926
Midwest
.964
.932
.912
.936
Southwest
.945
.926
.934
West
.945
.928
Plains
.945
Note: Shrinkage includes death loss in transit which is .04% for
nonfed cattle and .05% for fed cattle.
aNonfed cattle includes calves, Stockers, and culls.
bFed cattle includes 900 lb-1300 lb cattle shipped from feed
lots.

TABLE 5.13 WEIGHT OF LIVE CATTLE
Fed
Nonfed
Year- 1 1/2
Region 900 lb 1,100 lb 1,200 lb 1,300 lb lings years Calves Culls
cwt
Southeast
8.98
10.98
11.98
12.98
6.48
8.58
4.33
8.75
Midwest
9.30
11.30
12.30
13.30
6.80
8.90
4.65
9.42
Southwest
8.55
10.55
11.50
12.55
6.05
8.15
3.90
9.00
West
8.80
10.80
11.60
12.80
6.30
8.40
4.15
9.57
Plains
8.95
10.95
11.95
12.95
6.45
8.55
4.30
9.68
CO

144
The adjustment is necessary because the costs of the pro¬
duction activities are based on the typical beginning and
ending weight of the cattle in a particular region.
The marketing margin accounts for costs incurred at
the distributing stage. The margins used are shown in Table
5.14. They are not based on production budgets for distri¬
bution activities, but on the differences between the aver¬
age retail price for hamburger, roasts and steaks in each of
the demand regions and the shadow price for the sales activ¬
ity constraint in the solution of the linear programming
formulation of the model. The linear programming formula¬
tion of this model was obtained by fixing both the retail
price and quantity demanded of roasts, steaks, and hamburger
at the average level observed in the data set used to estim¬
ate the demand system.
A major portion of beef is consumed away from the
home. In order to account for this in the model the level
of away from home consumption in each region was fixed at a
predetermined level. The levels of away from home consump¬
tion are reported in Table 5.15. The levels were estimated
by using the LP formulation of the model where prices for
beef were fixed. In the first step the level of household
consumption in each region was fixed at the mean of the data
used in the demand system estimation. In the second step
household consumption was not fixed so that production was
only constrained by the size of the cow herd. Then the

145
TABLE 5.14 MARKETING MARGIN ON RETAIL CUTS IN DEMAND
REGIONS.
Ham-
Region burger Roast Steak
$ /cwt
Northeast
0.59
84.16
119.96
Midwest
1.46
77.94
36.53
South
8.20
91.78
0.77
West
9.10
104.38
85.48

146
TABLE 5.15. ANNUAL AWAY FROM HOME CONSUMPTION
Ham-
Region Roast Steak burger
(000,000 cwt)
Midwest
1.4934
1.8864
4.4801
West
1.0278
1.6929
3.3253
Northeast
1.5296
1.7382
3.6850
South
1.7957
3.4916
4.6887

147
total quantity of beef produced in the first step was
subtracted from the total quantity of beef produced in the
second step. This is the estimate of total away from home
consumption. The total quantity of beef consumed away from
home was distributed to the various regions based on each
regions share of total population. Finally, each regions
away from home consumption of beef was allocated among the
beef cuts according to each cuts share of total beef
consumption in the respective regions.
The level of beef imported was set at 1,446.34 million
lbs. This represents the average level of beef imported
from 1982-1986 (USDA, 1989). Since the U.S. is a net
importer of hamburger all beef is imported as hamburger in
the model. In addition, hamburger imports were restricted
to the South and West demand regions. No beef is permitted
to be exported during the base version of the model.

CHAPTER 6
BASE RESULTS AND SIMULATIONS
In this chapter the base results obtained from the
optimization model and the results of four simulations are
reported. The base solution is reported in detail while
only results for variables of interest are reported in the
simulations.
The Base Run
The maximum level of net social benefit (NSB) is
-8.81 x 10"11. The sign of this variable is unexpected as
one would expect the optimal value of NSB to be positive at
its maximum point. The negative sign is most likely caused
by the different scales used to measure the areas under the
demand curves and the areas under the supply curves. The
demand functions use a logarithmic scale while costs are
measured using the normal scale of measure. Thus, the area
under the supply curves have a much greater magnitude than
the area underneath the demand curve. Given that the main
purpose of the objective function is to permit the
constrained optimization model to simulate behavior in the
beef sector there is no particular interest in the value of
NSB. However, for welfare analysis it might be better to
148

149
have both the areas under the demand and supply curves
measured on the same scale.
The optimal level of household consumption and retail
prices are reported in Tables 6.1, 6.2 and 6.3. Note should
be taken that the level of consumption reported reflects the
level consumed for one month. The levels of the variables
reported in these tables are consistent with the levels for
quantity consumed and prices reported in the data set used
to estimate the demand system.
The quantity of roast, steak and hamburger produced in
each region and the amount transported from the supply
regions to the demand regions are reported in Tables 6.4 and
6.5. The results show that the Midwest, Southwest and the
Plains regions are the major suppliers of fresh beef. The
dominance of the Midwest region over the rest is mainly due
to the fact that it possesses the largest slaughtering
capacity. The Midwest supplies all four of the demand
regions. Both the Southeast and the Southwest supply all of
the beef they produce to the South demand region. The West
supplies beef only to the West while the Plains region sup¬
plies beef to the West and to the Northeast.
The quantity of weaned calves and beef culls produced
and the transfer of calves to the other stages of production
are reported in Tables 6.6-6.7. The quantity of calves
produced is fixed as the size of the breeding herd and the
calving rate have been set exogenously. The calves produced

150
TABLE 6.1. HOUSEHOLD CONSUMPTION OF BEEF.
Region
Ham-
Roast Steak burger Total
(lbs/month)
Midwest
1.579
1.988
4.327
7.894
West
1.269
1.984
4.075
7.328
Northeast
1.771
1.930
3.970
7.671
South
1.514
2.865
3.861
8.240
Average
1.058
2.192
4.058
7.783
TABLE 6.2. REGIONAL CONSUMPTION OF BEEF.
Ham-
Region Roast Steak burger Total
(000,000
lbs/month)
Midwest
37.864
47.682
103.770
189.316
West
26.299
41.095
84.417
151.811
Northeast
39.419
42.972
88.381
170.772
South
46.230
87.490
117.900
251.620
Total
149.812
219.239
394.468
763.519
TABLE 6.3. PRICE OF BEEF IN DEMAND REGIONS.
Region
Roast
Steak
Ham¬
burger
Midwest
West
Northeast
South
( $/lb)
2.262 2.716 1.650
2.547 3.243 1.732
2.345 3.603 1.659
2.418 2.355 1.732

151
TABLE 6.4.
QUANTITY OF BEEF PRODUCED.
Region
Roast Steak
Ham¬
burger
Total
(000,000 cwt)
Southeast
0.132
0.159
0.814
1.101
Midwest
16.142
26.125
34.479
76.746
Southwest
4.184
5.046
6.686
15.916
West
0.394
0.472
2.425
3.291
Plains
3.963
4.779
6.690
15.432
Total
24.816
36.581
51.094
112.486
TABLE 6.5. QUANTITY OF BEEF CUTS SHIPPED.
Region
Roast Steak Hamburger
Southeast.South®
Midwest.Midwest
Midwest.West
Midwest.Northeast
Midwest.South
Southwest.South
West.West
Plains.West
Plains.Northeast
(cwt)
132,336 158,512 814,378
6,288,590
7,925
-
1,648
6,520,685
7,182
3,332,484
9,368
4,184,496
5,045
394,082
472
3,963,931
4,779
229
17,637,460
972
-
183
8,195,359
850
8,645,746
967
6,686,815
033
2,425,123
363
6,690,781
indicates the region shipped from and the region shipped
to.

152
TABLE 6.6. WEANED CALVES AND CULLS PRODUCED.
Region
Cull
Calf
(Head)
Southeast
Midwest
Southwest
West
Plains
708,520
1,564,248
1,090,656
349,305
791,424
4,180,268
6,815,652
5,725,944
1,171,201
3,066,768
TABLE 6.7. CALVES TRANSFERRED TO STOCKER AND FINISHING
STAGE.
Region
Feedlot
Stocker
(Head)
Southeast.Southwest
Midwest.Midwest
Southwest.Southwest
Southwest.Plains
West.Plains
Plains.Plains
4,180,268
6,815,652
2,748,956
2,976,987
1,171,201
3,066,768
0
0
0
0
0
0

153
in the Southeast are transferred to the finishing stage in
the Southwest. The Southwest in turn transfers a portion of
the calves it produces to the finishing stage in the Plains
region. All the calves produced in the Midwest and Plains
regions are transferred to the finishing stage in their
respective regions while the calves produced in the West are
transferred to the finishing stage in the Plains region.
The movement of calves from the Southeast to the Southwest
and from the Southwest to the Plains is typical of the
observed pattern of feeder calf movements between supply
regions (Ward, 1979).
In none of the supply regions are calves placed in the
stocker activity before they are transferred to the finish¬
ing stage. This does not correspond to common practice in
the beef sector. The primary reason why the stockering
stage is not used in the model is that the cost of gain in
the feedlot for stockered cattle is much higher than the
cost of gain on feedlot for calves placed directly on the
feedlot. This makes it uneconomical to stocker calves.
This result indicates that the budgets for finishing
stockered cattle need to be evaluated to determine whether
the costs associated with these activities are too high.
The quantity of fed beef produced and the transfer of
fed beef to the slaughtering-processing stage are reported
in Tables 6.8-6.10. Only the Plains, Midwest and Southwest
regions produce fed beef. The Plains region is the largest

154
TABLE 6.8. CATTLE USED IN THE FEEDLOT.
Region
Calf
—(Head)—
Midwest
6,577,104
Southwest
6,515,537
Plains
6,783,719
Total
19,876,360
TABLE 6.9. FED CATTLE PRODUCED.
Region
900 lb
1,100 lb
Total
Midwest
Southwest
Plains
Total
6,783,719
6,783,719
(Head)
6,577,104
6,515,537
13,692,641
6,577,104
6,515,537
6,783,719
19,876,360
TABLE 6.10. FINISHED CATTLE
SHIPPED TO SLAUGHTER
•
Region
900 lb
1,100 lb
Midwest.Midwest
Southwest.Midwest
Southwest.Southwest
Plains.Midwest
Plains.Plains
^ nuauj
3,789,792
2,993,926
6,577,104
3,870,034
2,645,502

155
producer of fed beef and feeds them out at 900 lbs. Both
the Midwest and the Southwest regions finish cattle at 1,100
lbs. The average weight of the cattle finished in the model
is 1,033 lbs.
Both the Southwest and Plains regions transfer more
than half of their fed cattle to the Midwest region to be
slaughtered. The Midwest region slaughters all the fed beef
it produces.
The transfer of beef culls to slaughter is reported in
Table 6.11. The Southeast region retains a portion of its
beef culls for slaughter and transfers the remainder to the
Midwest and Southwest regions. The Southwest also retains a
portion of its beef culls and transfers the remainder to the
Plains regions. However, it remains a net importer of beef
culls. The Midwest, Plains and West regions do not transfer
any beef culls out of their respective regions.
The quantity of dairy culls transferred between
regions is reported in Table 6.12. All the available dairy
culls are utilized in the model. There are no transfers of
dairy culls between regions.
The quantity of cattle slaughtered is reported in
Table 6.13. The Midwest region slaughters the most cattle.
It slaughters 900 lb. and 1,100 lb. fed cattle and culls.
The Southwest region slaughters 1,100 lb. fed cattle and
culls and the Plains region slaughters 900 lb. fed cattle

156
TABLE 6.11. BEEF CULLS SHIPPED TO SLAUGHTER.
Region
Cull
—(Head)—
Southeast.Southeast
Southeast.Midwest
Southeast.Southwest
Midwest.Midwest
Southwest.Southwest
Southwest.Plains
West.West
Plains.Plains
13,612
158,920
535,986
1,564,248
636,618
454,037
349,305
791,424
TABLE 6.12. DAIRY CULLS
SHIPPED TO SLAUGHTER.
Region
Cull
—(Head)—
Southeast.Southeast
Midwest.Midwest
Southwest.Southwest
West.West
Plains.Plains
331,200
2,332,600
200,300
608,400
122,900
TABLE 6.13. CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb
Cull
Total
\ ntsciu.)
Southeast
__
332,399
332,399
Midwest
3,547,246
9,947,200
3,905,552
17,399,998
Southwest
-
2,500,000
1,300,000
3,800,000
West
-
—
905,031
905,031
Plains
2,829,260
-
1,300,000
4,129,260
Total
6,376,506
12,447,200
7,742,982
26,566,688

157
and culls. The Southeast and West regions slaughter only
culls. The average weight of cattle slaughtered in the
model is 1,015 lbs. This compares to an average weight of
1,093 lbs. reported from 1983-87 (USDA, 1989).
The quantity of fabricated cuts produced in each
region and their allocation to roast, steak, and hamburger
production are reported in Tables 6.14-6.16. Each region
uses the full amount of lean and medium trim available. In
the Midwest region roast is also used in the production of
hamburger. This result reflects the growing importance of
hamburger in household expenditures for beef and the
declining importance of roasts.
The quantity of hamburger imported into the West and
South is reported in Table 6.17. Considerably more ham¬
burger is imported into the West than into the South.
Scenarios
The use of the model to simulate sector response to
changes in economic conditions raises a question concerning
the limitations placed on the model's ability to portray the
sector's behavior because the size of the breeding herd has
been fixed. It is true that by fixing the size of the
breeding herd the manner in which the sector can respond is
limited by the fact that the size of the breeding herd
cannot be increased.
There are four factors, however, which when taken into
account suggest that fixing the size of the breeding herd

TABLE 6.14. PRIMAL CUTS PRODUCED
Region
Roast
Steak
Lean Trim
Medium
Trim
Fat and
Bone
( UWL J
Southeast
132,336
158,512
770,751
43,627
349,019
Midwest
21,656,720
26,125,240
18,640,440
10,323,160
29,679,390
Southwest
4,184,496
5,045,967
4,725,463
1,961,351
6,021,471
West
394,082
472,033
2,295,206
129,917
1,039,338
Plains
3,963,931
4,779,363
4,843,690
1,847,090
5,797,834

159
TABLE 6.15. PRIMAL CUTS ALLOCATED TO HAMBURGER.
Region
Roast
Medium
Lean Trim Trim
Southeast
Midwest
Southwest
West
Plains
5,514,962
—(cwt)
770,751
18,640,440
4,725,463
2,295,206
4,843,690
43,627
10,323,160
1,961,351
129,917
1,847,090
TABLE 6.16. PRIMAL CUTS ALLOCATED TO RETAIL.
Region
Roast
Steak
(cwt)
Southeast
Midwest
Southwest
West
Plains
132,336
16,141,760
4,184,496
394,082
3,963,931
158,512
26,125,240
5,045,967
472,033
4,779,363
TABLE 6.17. QUANTITY OF HAMBURGER IMPORTED.
Region
Hamburger
—(cwt)
West
11,127,200
South
3,336,201

160
is not unreasonably restrictive, at least in the medium run.
First, changing the number of calves produced is not the
only way for beef production to be increased or decreased.
It can also be increased or decreased by adjusting the size
of the cattle produced. The decline in the size of cattle
produced during the last decade suggests that the sector has
responded to declining demand for beef by doing just that.
Second, the model is structured so that all calves produced
do not need to be utilized if they are not needed. Third,
while the number of calves and culls produced is fixed the
total cost of producing them is not fixed in the model but
varies with the number of calves or culls actually used.
Furthermore the calves and culls are priced into the model
at market prices. Fourth, due to the long lag period
involved to expand the size of the cow herd the sector
cannot adjust cow numbers instantaneously so that in the
medium run, say five years, a fixed breeding herd may better
reflect the sector's response to changing conditions than a
breeding herd that is endogenously determined. Thus, one
can see that by fixing the size of the breeding herd that
costs of producing beef are not unduly distorted and that,
in the medium, run the ability of the sector to increase or
decrease production is not unduly restricted.

161
Scenario 1
In the first scenario the quantity of poultry consumed
is increased to reflect projected levels of poultry consump¬
tion five years from now. The new level of poultry consump¬
tion was determined by taking the current level of poultry
consumption in the base model and using the average rate of
growth in poultry production from 1980-86 to project out
five years.
From 1980-86 chicken production increased by an annual
rate of 2.3% (USDA, 1989). This projects to an increase in
chicken consumption of 11.5% over a period of five years.
During this same time period turkey consumption increased at
an annual rate of 4.2%. This rate projects to an increase
in the level of turkey consumption over a five-year period
of 21%. Based on these projections the levels of whole
chicken and chicken parts consumption in the model were
increased by 12%, while the level of other poultry consump¬
tion in the model was increased by 21%.
Given the negative sign on the poultry parameters in
the beef demand equations an increase in the quantity of
poultry consumed will cause the price of all the beef
products to decrease. The decrease in the price of beef
will in turn reduce profits to producers and cause the
quantity of beef produced to decline. Thus, the increase in
poultry consumption shifts the beef demand equations inward.
The inward shift in the demand for beef, especially in the

162
case of roasts, is tempered by the cross-quantity effects
between the beef products.
The new equilibrium level of household consumption is
shown in Table 6.18. The increase in poultry consumed
causes the level of all beef products to fall as shown in
Table 6.19. The decline in consumption on an annual basis
is greatest for hamburger (0.873 lbs.), followed by steak
(0.707 lbs.) and then by roasts (0.248 lbs.).
The pattern of decline in consumption levels of roast,
steak and hamburger differs among the demand regions. In
the West, steak declined by 4.3%, hamburger by 1.5%, and
roasts by 1.0% (see Table 6.20). The pattern of decline was
similar in the Midwest but to a somewhat lesser extent. In
the Northeast region it was hamburger which declined the
most, then steak and then roasts, while in the South the
order was reversed as roasts declined the most followed by
steak and then hamburger.
The decline in household consumption of beef trans¬
lated into a decline in the quantity of beef produced of
181.7 million lbs. The quantity of beef produced, the
amount transported from each supply region to the demand
regions and the change in the value of these variables
obtained under Scenario 1 compared to their values in the
base run are shown in Tables 6.21-6.26. Total production of
roast declined by 27.34 million lbs., steak by 69.94 million
lbs. and hamburger by 81.93 million lbs. On a total weight

163
TABLE 6.18. SCENARIO Is HOUSEHOLD CONSUMPTION OF BEEF.
Region
Roast
Steak
Ham¬
burger
Midwest 1.557
West 1.257
Northeast 1.769
South 1.469
(lbs/month)
1.934 4.258
1.897 4.014
1.881 3.842
2.819 3.828
TABLE 6.19. SCENARIO 1: CHANGE IN HOUSEHOLD CONSUMPTION OF
BEEF.
Ham-
Region Roast Steak burger Total
â– ( lbs/year)-
Midwest
-0.264
-0.648
-0.828
-1.740
West
-0.144
-1.040
-0.732
-1.916
Northeast
-0.024
-0.588
-1.536
-2.148
South
-0.540
-0.522
-0.396
-1.488
Average
-0.243
-0.707
-0.873
-1.823
TABLE 6.20.
SCENARIO Is
PERCENTAGE
CHANGE IN HOUSEHOLD
CONSUMPTION
OF BEEF.
Ham-
Region
Roast
Steak
burger
Total
(*)
Midwest
-1.4
-2.7
-1.6
-1.8
West
-1.0
-4.3
-1.5
-2.2
Northeast
-0.1
-2.5
-3.2
-3.3
South
-3.0
-1.6
-0.9
-1.9
Average
-1.3
i
NJ
•
-1.8
-2.0

164
TABLE 6.21. SCENARIO 1: QUANTITY OF BEEF PRODUCED.
Region
Roast
Steak
Ham¬
burger
Total
[UUU/UUU CWL j
Southeast
0.1271
0.1523
0.7822
1.0616
Midwest
15.9070
25.4720
33.6940
75.0730
Southwest
4.1845
5.0460
6.6868
15.9173
West
3.9408
0.4720
2.4251
6.8379
Plains
3.9307
4.7392
6.6597
15.3296
Total
28.0901
35.8815
50.2478
114.2194
TABLE 6.22.
SCENARIO Is
PRODUCED.
CHANGE IN
QUANTITY OF
BEEF
Ham-
Region
Roast
Steak
burger
Total
/ n n n
nnn i \
(UUU
,UUU IDS)
Southeast
-0.490
-0.670
-3.180
-4.34
Midwest
-23.500
-65.300
-78.500
-167.300
Southwest
0.000
0.000
0.000
0.000
West
0.000
0.000
0.000
0.000
Plains
-3.320
-4.020
-3.110
-10.450
Total
-27.340
-69.945
-81.931
-181.700
TABLE 6.23.
SCENARIO 1: PERCENTAGE
BEEF PRODUCED.
CHANGE IN QUANTITY
OF
Ham-
Region
Roast
Steak
burger Total
(*)
Southeast
-4.0
-4.0
-4.0
-4.0
Midwest
-1.5
-2.5
-2.3
-2.2
Southwest
0.0
0.0
0.0
0.0
West
0.0
0.0
0.0
0.0
Plains
-0.8
-0.8
-0.5
-0.7
Total
-1.1
-1.9
-1.6
-1.6

165
TABLE 6.24. SCENARIO 1: QUANTITY BEEF SHIPPED.
Region
Roast
Steak
Hamburger
(cwt)
Southeast.South
127,112
152,255
782,228
Midwest.Midwest
6,223,570
7,763,104
17,430,960
Midwest.West
-
1,463,834
-
Midwest.Northeast
6,516,026
7,045,634
7,868,366
Midwest.South
3,167,711
9,199,442
8,394,997
Southwest.South
4,184,496
5,045,967
6,686,815
West.West
394,082
472,033
2,425,123
Plains.West
3,930,685
4,739,233
-
Plains.Northeast
-
-
6,659,731
TABLE 6.25. SCENARIO 1: CHANGE IN QUANTITY OF BEEF
SHIPPED.
Region
Roast Steak Hamburger
Southeast.South
-5,224
(cwt)
-6,257
-32,150
Midwest.Midwest
-65,019
-162,214
-206,500
Midwest.West
-
-185,137
-
Midwest.Northeast
-4,658
-136,549
-326,993
Midwest.South
-164,773
-169,407
-250,748
Southwest.South
0
0
0
West.West
0
0
0
Plains.West
-33,246
-40,129
-
Plains.Northeast
-
-
-31,049

166
TABLE 6.26.
SCENARIO 1:
BEEF SHIPPED
PERCENTAGE
•
CHANGE IN
QUANTITY OF
Region
Roast
Steak
Ham¬
burger
(%)
Southeast.South
i
•
o
-4.0
-4.0
Midwest.Midwest
-1.0
-2.0
-1.2
Midwest.West
-
-11.2
-
Midwest.Northeast
o
•
o
-1.9
-4.0
Midwest.South
-4.9
-1.8
-2.9
Southwest.South
0.0
o
•
o
0.0
West.West
0.0
o
•
o
0.0
Plains.West
-0.8
-0.8
-
Plains.Northeast
-
-
-0.5

167
basis the quantity of beef produced declined the most in the
Midwest, then the Plains and then the Southeast. There was
no change in the quantity of beef produced in either the
Southwest or the West regions. In terms of percentages, the
Southeast was the region hardest hit by the decline in the
levels of beef consumption as its production of beef
declined by 4%.
The pattern of shipments of beef from the supply
regions to the demand regions remain unchanged. The great¬
est decline in shipments occurred in the amount shipped from
the Midwest to the West (see Tables 6.25 and 6.26). The
level of hamburger imported into the West declined by 1.4%
but the level imported into the South increased by 4.6%
(Table 6.27) .
The number of cattle slaughtered in each region under
Scenario 1 and the change number of cattle slaughtered from
the base are reported in Tables 6.28 and 6.29. The decline
in quantity of beef produced does not translate directly
into a decline in the number of cattle slaughtered. While
the Midwest region had the greatest decline in quantity of
beef produced there was no decline in the number of cattle
slaughtered. This implies that the average weight of cattle
slaughtered in the Midwest region declined which in turn
implies that the average weight of finished cattle has
declined.

168
TABLE 6.27.
SCENARIO 1: QUANTITY
OF HAMBURGER IMPORTED.
Region
Hamburger
Change
(cwt) —
—(cwt)— (%)
West
South
10,974,970
3,488,434
-152,230 -1.4
+152,233 -4.7
TABLE 6.28.
SCENARIO 1:
CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb Cull
Total
(Head)
Southeast
-
—
319,276
319,276
Midwest
5,198,476
8,283,542
3,917,981
17,399,999
Southwest
-
2,500,000
1,300,000
3,800,000
West
-
—
905,031
905,031
Plains
2,801,524
-
1,300,000
4,101,524
Total
8,000,000
10,783,542
7,742,288
26,525830
TABLE 6.29.
SCENARIO 1:
CHANGE IN CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb Cull Total
(Head)
Southeast
-
—
-13,123
13,123
Midwest
1,642,230
-1,663,658
12,427
-9,001
Southwest
—
0
0
0
West
—
0
0
Plains
-27,736
-
0
-27,736
Total
1,614,494
-1,663,658
695
-23,614

169
The number of cattle finished, their weight, and the
change in quantity finished are shown in Tables 6.30 and
6.31. The total number of cattle finished declined by
50,200 head. This represents less than 0.3% of the quantity
finished in the base model. However, while the decline
nationally is insignificant there were major changes in the
quantity of cattle finished in the Southwest and Plains
regions. The level of cattle finished in the Southwest
dropped 1.785 million head or by 27.4%. while the number of
cattle finished in the Plains region increased by 1.7348
million head or 25.5%. This shift in level of cattle
finished in the supply regions caused the average weight of
finished cattle to drop from 1,033 lbs. in the base to 1,014
lbs. This is because cattle are finished at a weight of 900
lbs. in the Plains and a weight of 1,100 lbs. in the South¬
west .
Table 6.32 gives the weight of finished cattle shipped
to slaughter. As shown in Table 6.33 the quantity of 1,100
lb. fed cattle shipped to the Midwest from the Southwest
declined by 1.785 million head while the quantity of 900 lb.
fed cattle shipped from the Plains to the Midwest increased
by 1.764 million. This result explains how the Midwest
region can have a decline in the quantity of beef produced
and yet have no decline in the number of cattle slaughtered.
The number of weaned calves utilized in each supply
region did not change (see Table 6.34) even though the

170
TABLE 6.30.
SCENARIO Is FED CATTLE PRODUCED.
Region
900 lb
1,100 lb
(Head)
Midwest
—
6,577,104
Southwest
—
4,730,495
Plains
8,518,504
-
TABLE 6.31.
SCENARIO 1
: CHANGE IN CATTLE
FINISHED
i.
900 lb
1.100 lb
Total
Region
Head
Per¬
cent
Head
Per¬
cent
Head
Per¬
cent
(000,000)
(000,000)
(000,000)
Midwest
Southwest
Plains
1.734
25.5
0.000
-1.785
0.0
-27.4
0.000
-1.785
1.734
0.0
-27.4
25.5
Total
1.734
25.5
-1.785
-27.0
-0.050
-0.3

171
TABLE 6.32. SCENARIO 1: FINISHED CATTLE SHIPPED TO
SLAUGHGHTER.
Region 900 lb 1,100 lb
Midwest.Midwest
Southwest.Midwest
Southwest.Southwest
Plains.Midwest
Plains.Plains
(Head)
5,553,927
2,964,576
6,577,104
2,084,993
2,645,502
TABLE 6.33. SCENARIO Is CHANGE IN NUMBER OF FINISHED
CATTLE SHIPPED TO SLAUGHTER.
Region
900 lb
1.100 lb
Head
Per¬
cent
Head
Per¬
cent
Midwest.Midwest
Southwest.Midwest
Southwest.Southwest
Plains.Midwest 1,764,135
Plains.Plains -29,350
0 0.0
-1,785,041 -46.1
0 0.0
46.5
-1.0

172
TABLE 6.34. SCENARIO Is CALVES SHIPPED TO FEEDLOT.
Region
Calves
Chancre
Head
Per¬
cent
Southeast.Southwest
4,180,268
0
o
•
o
Midwest.Midwest
6,815,652
0
o
•
o
Southwest.Southwest
887,598
-1,861,357
-67.7
Southwest.Plains
4,838,345
1,861,357
+62.5
West.Plains
1,171,201
0
o
•
o
Plains.Plains
3,066,768
0
o
•
o
Total
20,959,834
0
o
•
o

173
number of cattle finished declined. The reduction in the
number of cattle finished occurred because there were less
calves retained in the Southwest than during the base run
and the quantity of calves shipped from the Southwest to the
Plains region was increased by 1.861 million. However,
there is a higher rate of shrink (mainly due to death loss
in transit) for cattle shipped from the Southwest to the
Plains than from those retained in the Southwest.
What do these changes occurring in the weights of
cattle imply about the impact of increased levels of poultry
consumption on returns to beef producers? At a national
level the implication is that there will not be a whole lot
of change. The reduction in the level of beef produced only
amounts to a 1% change in the level of production compared
to the base model. At a regional level, however, the
results indicate that meat processors in the Southeast
suffer some losses as the level of their production is cut
back by 4%. The hardest hit segment of the beef sector will
be feedlot operators in the Southwest region where produc¬
tion declines by 27.4%.
Scenario 2
In Scenario 2, the level of poultry consumed is
increased by 40%. This is approximately the percentage by

174
which the level of poultry consumption increased from
1975-1985 (USDA, 1987). Hopefully, the results will provide
some insight into what has occurred in the pattern of meat
consumption during this period. If the decline in the price
of poultry relative to the price of beef is the reason per
capita level of beef consumed has decreased then the
increase in the level of poultry consumption by 40% should
cause the quantity of beef consumed as determined by the
model to decline by the same amount as the level of beef
consumption declined from 1975-1985. If the levels of beef
consumption obtained from the model do not decline by this
amount then this provides an indication that the decline in
the consumption of beef is due to other factors such as a
change in preferences or change in income.
The level of household consumption of beef and the
change which has incurred in its level from the base model
are shown in Tables 6.35-6.37. The per capita level of beef
consumption declined on an annual basis by an average of
1.93 lbs. This figure was derived by dividing the average
total decline in beef consumption by 2.5, the average
household size, and then multiplying this amount by 12, the
number of months in the year. This represents a 5.2%
decline in the level of beef consumed which is approximately
one-half of the amount by which beef declined from 1975-
1985.

175
TABLE 6.35.
SCENARIO 2:
HOUSEHOLD
CONSUMPTION OF
BEEF.
Region
Roast
Steak
Ham¬
burger
Total
Midwest
1.490
(lbs/month)
1.901 4.103
7.494
West
1.233
1.803
3.884
6.920
Northeast
1.762
1.827
3.594
7.183
South
1.379
2.780
3.772
7.931
Average
1.466
2.078
3.838
7.382
TABLE 6.36.
SCENARIO 2:
BEEF.
CHANGE IN
HOUSEHOLD CONSUMPTION OF
Ham-
Region
Roast
Steak
burger
Total
^XDS/montnj
Midwest
-0.089
-0.087
-0.224
-0.400
West
-0.036
-0.181
-0.191
-0.408
Northeast
-0.009
-0.103
-0.376
-0.488
South
-0.135
-0.085
-0.089
-0.309
Average
-0.067
-0.114
-0.220
-0.401
TABLE 6.37.
SCENARIO 2:
CONSUMPTION
PERCENTAGE CHANGE IN !
OF BEEF.
HOUSEHOLD
Ham-
Region
Roast
Steak
burger
Total
( %)
Midwest
-5.60
-4.4
-5.2
-5.1
West
-2.8
-9.1
-4.7
-5.6
Northeast
-0.5
-5.3
-9.5
-6.4
South
-8.9
-3.0
-2.3
-3.8
Average
-0.067
-0.114
-0.220
-5.2

176
This result indicates that the decline in per capita
levels of beef consumption observed during the 1975-1985
time period was due in part to a decline in the price of
chicken relative to the price of beef. However, it also
indicates that the decline in beef consumption was not due
solely to the decline in the price of poultry. Close to 50%
of the decline in beef consumption was caused by other fac¬
tors such as a shift in consumers preferences.
The increase in poultry consumption has also led to a
decrease in the price of roasts, steaks, and hamburger (see
Table 6.38). The decline in the price of beef is less than
1%. This also indicates that the decline in beef consump¬
tion is due to factors other than a decline in the price of
poultry. The price of beef in real terms has declined more
than this amount. Thus, factors other than prices of sub¬
stitute goods must have caused the demand for beef to shift
inward.
The quantity of beef produced and the change in the
quantity of beef produced under this scenario from the base
level are reported in Tables 6.39-6.41. All the supply
regions, except for the Plains region, produce less beef
than produced before. The greatest reductions in beef
production occur in the Southeast (60.0%) and the West
(65.5%). The increase in the level of beef production in
the Plains region is a continuation of the process noted on
in Scenario 1 where the number of 900 lb. fed cattle

177
TABLE 6.38.
SCENARIO 2: PRICE OF BEEF IN DEMAND REGIONS.
Region
Ham-
Roast Steak burger
Midwest
($/lb)
2.253 2.698 1.644
West
2.538 3.225 1.725
Northeast
2.336 3.584 1.652
South
2.409 2.337 1.725

178
TABLE 6.39. SCENARIO 2: QUANTITY PROCESSED MEAT PRODUCED.
Region Roast Steak Hamburger Total
(000,000 cwt)
Southeast
0.053
0.063
0.326
0.442
Midwest
15.415
24.992
32.812
74.219
Southwest
4.184
5.046
6.686
15.917
West
0.143
0.172
0.884
1.200
Plains
4.121
4.969
6.837
15.927
Total
23.917
35.241
48.546
107.710
TABLE 6.40.
SCENARIO 2:
PRODUCED.
CHANGE IN
QUANTITY PROCESSEE
1 MEAT
Ham-
Region
Roast
Steak
burger
Total
/ f\r\n
( U U U t
UUU UWL)
Southeast
-0.079
-0.095
-0.488
-0.659
Midwest
-0.727
-1.330
-0.667
-2.570
Southwest
0.000
0.000
0.000
0.000
West
-0.250
-0.299
-1.540
-2.091
Plains
0.157
0.189
0.146
0.496
Total
-0.899
-1.340
-2.547
-4.776
TABLE 6.41.
SCENARIO 2:
PRODUCED.
PERCENTAGE
CHANGE IN
QUANTITY BEEF
Ham-
Region
Roast
Steak
burger
Total
(*)
Southeast
-59.8
-59.7
-60.0
-60.0
Midwest
-4.4
-4.3
-2.0
-3.3
Southwest
0.0
0.0
0.0
0.0
West
-63.5
-63.3
-62.8
-65.5
Plains
4.0
4.0
2.2
3.2
Total
-3.6
-3.7
-5.0
-4.2

179
produced has increased and the level of 1,100 lb. fed cattle
produced has decreased in response to a decrease in the
demand for beef. The Plains region has a comparative
advantage over both the Midwest and the Southwest in the
production of 900 lb. fed cattle. Consequently, while
cattle production has declined in the Southwest region some
40.4% it has increased in the Plains region by 37.8% (see
Tables 6.42-6.44). For the country as a whole, the quantity
of cattle finished as a result of the increase in poultry
consumption dropped by 74,222 head. This amounts to a
reduction in the number of feeder cattle of less than 1%.
The total amount of cattle slaughtered under this
scenario declined by 643,000 head (see Tables 6.45-6.47).
The reduction is due mostly to a net reduction in the
quantity of culls slaughtered of 585,483 head.
Scenario 3
In Scenario 3 the level of hamburger imports is
increased in order to determine its impact on domestic
producers. Beef imports into this country are currently
subject to quotas. However, the U.S government as part of
its trade negotiations is arguing for a removal of all
government subsidies to agricultural products. As a result
imports of beef may not be subject to quotas in the near
future.
In the base run the level of imported hamburger was
fixed at 1.446 billion lbs. From 1983-1987 imports of beef

180
TABLE 6.42.
SCENARIO 2: FED
CATTLE PRODUCED.
Region
900 lb
1,100 lb
Total
Midwest
Southwest
Plains
Total
9,345,746
9,345,746
[ncjuu)
6,577,104
3,879,288
10,456,392
6,577,104
3,879,288
9,345,746
19,802,138
TABLE 6.43.
SCENARIO 2: CHANGE
IN FED CATTLE
PRODUCED.
Region
900 lb
1,100 lb
Total
y UUU f UUU JlCaU J
Midwest
0.000
0.000
Southwest
—
-2.636
-2.636
Plains
2.562
-
2.562
Total
2.562
-2.636
-0.074
TABLE 6.44.
SCENARIO 2:
PRODUCED
PERCENTAGE CHANGE IN
FED CATTLE
Region
900
lb 1,100 lb
Total
(*)
Midwest
_
0.0
0.0
Southwest
—
-40.4
-40.4
Plains
37.8
-
37.8
Total
37.8
-19.3
•<*
•
o
l

181
TABLE 6.45. SCENARIO 2: CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb
Cull
Total
( IlCQQ )
Southeast
133,074
133,074
Midwest
5,815,450
7,490,217
4,094,332
17,399,999
Southwest
—
2,500,000
1,300,000
3,800,000
West
—
—
330,093
330,093
Plains
2,960,361
-
1,300,000
4,260,361
Total
8,775,811
9,990,217
7,157,499
25,923,527
TABLE 6.46.
SCENARIO 2:
CHANGE IN
CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb
Cull
Total
/ nnn
( UUU r
uuu neaaj
Southeast
-0.199
-0.199
Midwest
2.268
-2.457
0.189
0.000
Southwest
—
0.000
0.000
0.000
West
—
—
-0.575
-0.575
Plains
0.131
-
0.000
0.131
Total
2.399
-2.457
-0.585
-0.643
TABLE 6.47.
SCENARIO 2:
SLAUGHTERED.
PERCENTAGE
CHANGE IN CATTLE
Region
900 lb
1,100 lb
Cull
Total
(*)
Southeast
_
_
-60.0
-60.0
Midwest
64.0
-24.7
4.8
0.0
Southwest
—
0.0
0.0
0.0
West
—
—
-63.5
-63.5
Plains
4.6
-
0.0
3.2
Total
37.6
-19.7
-7.5
-2.4

182
increased by 16% from 1.415 billion lbs. to 1.643 billion
lbs. (USDA, 1989). In this scenario the level of hamburger
imported is increased by 16%.
An increase in the level of imported hamburger will
cause the price of hamburger to decline because it is
cheaper than domestically produced hamburger. The decline
in the price of hamburger will cause the level of hamburger,
consumed by households to increase. From the parameter
values on the estimated demand systems it is known that an
increase in the quantity of hamburger consumed will cause
the price of both steak and roast to decline. The decline
in the price of roasts and steaks will in turn cause house¬
holds to increase their level of consumption of steaks and
roasts. Thus, it is possible that the loss of hamburger
sales to imported hamburger will be offset by increased
consumption of roasts and steak. However, the ability of
producers to substitute away from hamburger production and
increase production of steaks and roasts is limited by the
fact that steaks and roasts are only available from a
carcass in a fixed proportion.
The impact of a 16% increase in imports of hamburger
on the level of household consumption of beef is shown in
Tables 6.48-6.50. As expected the quantity of hamburger
consumed increased as did the consumption of roasts. How¬
ever, the consumption of steak decreased. Total consumption
of beef increased on average by 0.032 lbs. per month.

183
TABLE 6.48. SCENARIO 3: HOUSEHOLD CONSUMPTION OF BEEF.
Region
Ham-
Roast Steak burger Total
(lbs)
Midwest
1.596
1.946
4.395
7.937
West
1.273
1.955
4.130
7.358
Northeast
1.784
1.914
4.010
7.708
South
1.524
2.827
3.906
8.257
Average
1.544
2.161
4.110
7.815
TABLE 6.49.
SCENARIO 3:
CHANGE IN HOUSEHOLD CONSUMPTION OF
BEEF.
Ham-
Region
Roast
Steak
burger
Total
(lbs)
Midwest
0.017
-0.042
0.068
0.043
West
0.004
-0.029
0.055
0.030
Northeast
0.013
-0.016
0.040
0.037
South
0.010
-0.038
0.045
0.017
Average
0.011
-0.031
0.052
0.032
TABLE 6.50.
SCENARIO 3:
PERCENTAGE CHANGE IN HOUSEHOLD
CONSUMPTION-
OF BEEF.
Ham-
Region
Roast
Steak
burger
Total
/ & \
(%)
Midwest
1.0
-2.1
1.6
0.5
West
0.3
-1.5
1.3
0.4
Northeast
0.8
-0.8
1.0
0.5
South
0.7
-1.3
1.2
0.2
Average
0.7
-1.4
1.3
0.4

184
The increased levels of imported hamburger caused the
price of hamburger and roasts to decline, but caused the
price of steak to increase (see Tables 6.51 and 6.52). The
increase in the price of steak explains why steak consump¬
tion declined.
The level of beef produced under Scenario 3 is
reported in Table 6.53. In terms of aggregate beef pro¬
duction, the increase in imports caused production to
decline by 203.4 million lbs. (see Table 6.54). This
represents a 1.8% reduction from the base level of pro¬
duction (see Table 6.55). While the total reduction in beef
production is small the effect on regional production varied
dramatically. In the Southeast and the West output of beef
declined by 57% and 50% respectively. In the Plains region,
however, output increased by 4%.
The 1.8% decline in beef production led to a decline
in the number of cattle slaughtered of 466,635 (see Tables
6.56 and 6.57). This amounts to 1.7% reduction in the
quantity of cattle slaughtered in the base run. As occurred
in the poultry scenarios the composition of the slaughter
cattle was altered. The number of 900 lb. cattle slaught¬
ered increased by 348,999 head (5.5%) and the number of
1,100 lb. cattle slaughtered declined by 355,908 head (2.9%)
(see Tables 6.57 and 6.58).
The quantity of cattle finished and the change in
quantity finished from the quantity finished in the base

185
TABLE 6.51. SCENARO 3: RETAIL PRICE OF BEEF.
Region
Roast
Steak
Ham¬
burger
V v / )
Midwest
2.255
2.728
1.643
West
2.545
3.255
1.725
Northeast
2.337
3.614
1.652
South
2.411
2.367
1.725
TABLE 6.52.
SCENARO 3: CHANGE
IN RETAIL PRICE
OF BEEF.
Ham-
Region
Roast
Steak
burger
( v / )
Midwest
-0.007
0.012
-0.007
West
-0.002
0.012
-0.007
Northeast
-0.008
0.011
-0.007
South
-0.007
0.012
-0.007

TABLE 6.53. SCENARIO 3: QUANTITY BEEF PRODUCED
Region
Roast
Steak
Hamburger
Total
^U U UfUUU CWu|
—
Southeast
0.057
0.069
0.354
0.480
Midwest
16.344
25.812
34.174
76.330
Southwest
4.184
5.046
6.686
15.916
West
0.198
0.237
1.219
1.654
Plains
4.168
5.026
6.881
13.075
Total
24.952
36.190
49.317
110.455
TABLE 6.54.
SCENARIO 3 J
CHANGE IN
BEEF PRODUCED.
Ham-
Region
Roast
Steak
burger
Total
/nnn
“(UUU/
UUU CWL f —
South
-0.074
-0.090
-0.460
-0.624
Midwest
0.202
-0.313
-0.305
-0.416
Southwest
0.000
0.000
0.000
0.000
West
-0.196
-0.235
-1.205
-1.636
Plains
0.204
0.247
0.191
0.642
Total
0.136
-0.391
-1.779
-2.034
TABLE 6.55.
SCENARIO 3:
PERCENTAGE
CHANGE IN BEEF
PRODUCED.
Ham-
Region
Roast
Steak
burger
Total
(*)
Southeast
-56.0
-57.0
-57.0
-56.8
Midwest
1.0
-1.0
-1.0
-0.5
Southwest
0.0
0.0
0.0
0.0
West
-50.0
-50.0
-50.0
-50.0
Plains
5.0
5.0
2.9
4.1
Total
0.5
-1.0
-3.5
i
H*
•
00

187
TABLE 6.56. SCENARIO 3: CATTLE SLAUGHTERED.
Region
900 lb
1,100 lb
Cull
Total
\ncauf
Southeast
_
_
144,826
144,826
Midwest
3,725,505
9,591,292
4,083,202
17,399,999
Southwest
—
2,500,000
1,300,000
3,800,000
West
—
—
455,229
455,229
Plains
3,000,000
-
1,300,000
4,300,000
Total
6,725,505
12,094,292
7,283,257
25,955,373
TABLE 6.57.
SCENARIO 3:
CHANGE IN CATTLE SLAUGHTERED
•
Region
900 lb
1,100 lb
Cull
Total
/non non
(UUU f UUU
neau)
Southeast
__
-0.187
-0.187
Midwest
0.178
-0.356
0.178
0.000
Southwest
—
0.000
0.000
0.000
West
—
—
-0.450
-0.450
Plains
0.171
-
0.000
0.171
Total
0.350
-0.356
-0.460
-0.467
TABLE 6.58.
SCENARIO 3:
SLAUGHTERED.
PERCENTAGE CHANGE IN CATTLE
Region
900 lb
1,100 lb
Cull
Total
/non nnn
(UUUfUUU
IlBciQ ) ' "
Southeast
_
-56.0
-56.0
Midwest
o
•
in
-4.0
4.0
0.0
Southwest
—
0.0
0.0
0.0
West
—
_
-50.0
-50.0
Plains
6.0
-
0.0
6.0
Total
5.5
1
to
•
-5.9
-1.7

188
model are shown in Tables 6.59-6.61. The total number of
cattle finished declined by only 10,752 head (<0.1%).
However, the number of cattle finished in the Southwest
declined by 318,876 head (58.0%), while in the Plains
region the number of cattle finished increased by 371,124
head (5.5%). As was the case with the composition of
slaughter cattle the composition of fed cattle changed as
the cattle in the Plains region were finished at 900 lbs.
and the cattle in the Southwest were finished at 1,100 lbs.
Thus, as the demand for feeder cattle decreases the cattle
are fed out at lighter weights.
The disposition of the imported hamburger is shown in
Table 6.62. The West's imports of hamburger increased by
11.6% and the level of the South's imports of hamburger
increased by 23.4%. Despite the disparity in the percent¬
age increase in imports the increase in imports in terms of
weight was allocated evenly between the two regions.
Scenario 4
In the fourth scenario the impact of increased levels
of beef exports on beef producers is examined. Historic¬
ally, beef exports have not been large in comparison to
total domestic production. In 1977 for example, exports of
beef accounted for less than 0.5% of total U.S. beef pro¬
duction (USDA, 1989). However, during the last decade
(1977-1987) beef exports have increased substantially and
prospects for even greater expansion of beef exports are

189
TABLE 6.59.
SCENARIO 3: FED
CATTLE PRODUCED.
Region
900 lb
1,100 lb
Total
(Head)
Midwest
6,577,104
6,577,104
Southwest
—
6,133,661
6,133,661
Plains
7,154,843
-
7,154,843
Total
7,154,843
12,107,765
19,107,765
TABLE 6.60.
SCENARIO 3 s CHANGE
IN FED CATTLE
PRODUCED.
Region
900 lb
1,100 lb
Total
/ r\nn nnn \
| UUU / UUU iICqQ j
Midwest
0.000
0.000
Southwest
—
-0.382
-0.382
Plains
0.371
-
0.371
Total
0.371
-0.382
-0.011
TABLE 6.61.
SCENARIO 3: PERCENTAGE CHANGE IN
PRODUCED.
FED CATTLE
Region
900 lb
1,100 lb
Total
(*)
Midwest
__
0.0
0.0
Southwest
—
-5.8
-5.8
Plains
5.5
-
5.5
Total
5.5
to
•
<-0.1
TABLE 6.62.
SCENARIO 3: QUANTITY
OF HAMBURGER IMPORTED.
Region
Hamburger
Change
—(cwt)—
—(cwt)—
(%)
West
South
12,422,220
4,355,319
1,295,020
1,019,118
11.6
23.4

190
good. From 1977-1982 exports of beef doubled from 91.5
million lbs. to 188.9 million lbs. They nearly tripled
again from 1982-1987 as they rose from 188.9 million lbs. to
465.1 million lbs. As a result of this expansion, exports
of beef accounted for 2% of total production in 1987,
causing beef producers to view increasing the level of beef
exports as a means of offsetting loss of market share in
domestic markets.
In order to look at the impact of increased levels of
beef exports on household consumption of beef and on beef
producers the model is altered to include the export of beef
as a production activity. The demand for beef exports can
be incorporated in two ways: (1) fixing the level of beef
exported at a predetermined level or (2) using an export
demand equation. For the analysis undertaken here the level
of beef exports was fixed at a level of 1,395.3 million lbs.
This represents three times the level of beef exports in
1987. In addition beef exports were limited to steaks and
roasts as the U.S. is a net exporter of steaks and roasts
and a net importer of hamburger.
The model, as presently set up is limited by the fact
that the size of the breeding herd is fixed at a prede¬
termined level rather than being endogenously determined
within the model. As a consequence an increase in the level
of beef exported cannot be met by increasing the number of
cattle available but only through reducing domestic con-

191
sumption or increasing the size of cattle slaughtered or
both. Given the slow response time involved in expanding
beef production this limitation may not be too severe.
The increase in level of beef causes the overall
demand for beef to increase. This result will in turn cause
the domestic price of beef to increase as the amount of beef
available in domestic markets is reduced. It will also
cause beef producers to expand production in response to
both the increased level of beef exports and the rise in
domestic beef prices. Because the size of the breeding herd
is fixed the quantity of beef produced can only be increased
by increasing the weight of the cattle being produced.
Thus, producers in supply regions with a comparative
advantage in finishing higher weight cattle will see
production increase while producers in other regions should
see their level of production decline.
The level of household consumption of beef due to the
increase in beef exports and the change which has occurred
in these consumption levels from their base levels are
reported in Tables 6.63-6.65. As expected the level of
household consumption of beef declined as a result of an
increase of beef exports. In this case the 6% increase in
exports led to an average decline in beef consumption of
0.583 lbs. per month. This represents a 7.5% decline in
beef consumption from the base level.

192
TABLE 6.63. SCENARIO 4: HOUSEHOLD CONSUMPTION OF BEEF.
Region
Ham-
Roast Steak burger Total
â– (lbs/month)-
Midwest
1.615
1.475
4.227
7.317
West
1.237
1.603
3.968
6.808
Northeast
1.747
1.693
3.699
7.139
South
1.477
2.298
3.762
7.537
Average
1.519
1.767
3.914
7.200
TABLE 6.64.
SCENARIO 4:
CHANGE IN
HOUSEHOLD CONSUMPTION OF
BEEF.
Heim-
Region
Roast
Steak
burger
Total
^ / niuii uu )
Midwest
0.036
-0.513
-0.100
-0.577
West
-0.032
-0.381
-0.107
-0.520
Northeast
-0.024
-0.237
-0.271
-0.532
South
-0.037
-0.567
-0.099
-0.703
Average
-0.014
-0.425
-0.144
-0.583
TABLE 6.65.
SCENARIO 4;
PERCENTAGE
CHANGE IN HOUSEHOLD
CONSUMPTION
OF BEEF.
Ham-
Region
Roast
Steak
burger
Total
(*)
Midwest
2.3
-25.8
-2.3
-7.3
West
-2.5
-19.2
-2.6
-7.1
Northeast
-1.4
-12.3
-6.8
-6.9
South
-2.4
-19.8
-2.6
-8.5
Average
-1.0
-19.4
-3.5
-7.5

193
The greatest decline occurred in the consumption of
steak which dropped 19.4%. The consumption of hamburger
declined even though exports of hamburger were not
permitted. In fact, the decline in hamburger consumption
was greater than the decline in consumption of roasts on
both an absolute and a percentage basis.
On a regional basis the decline in steak consumption
was greatest in the Midwest and lowest in the Northeast.
The consumption of roasts actually increased in the Midwest.
The decline in the consumption of hamburger was greatest in
the Northeast and least in the Midwest.
Changes in the level of beef production are reported
in Tables 6.66-6.68. The 6% increase in beef exports led to
a 6% increase in the quantity of beef produced. This
implies that the multiplier on the change in beef production
due to a change in beef exported is one. Thus, the increase
in export demand did not cause the domestic price of beef to
increase high enough to cause domestic consumption of beef
to decline enough to offset the impact of the increase
export demand on beef production.
The production of roast increased the most, 23.5%
while the overall level of hamburger production decreased by
3.3%. The production of beef increased the most in the
Plains region, 409.62 million lbs. followed by the Midwest
375.9 million lbs. The level of production in the West was

194
TABLE 6.66. SCENARIO 4: QUANTITY OF BEEF PRODUCED.
Ham-
Region Roast Steak burger Total
(000,000 cwt)
Southeast
0.093
0.111
0.570
0.774
Midwest
21.103
27.691
31.701
80.505
Southwest
3.471
4.182
7.471
15.124
West
0.394
0.472
2.425
3.291
Plains
5.577
6.728
7.224
19.528
Total
30.637
39.1835
49.3912
119.222
TABLE 6.67. SCENARIO 4: CHANGE IN QUANTITY OF BEEF
PRODUCED.
Region
Southeast
Midwest
Southwest
West
Plains
Total
Roast
-0.039
4.961
-0.714
0.0
1.613
5.821
Ham-
Steak burger Total
(000,000 cwt
-0.048 -0
1.566 -2
-0.864 0
0.0 0
1.949 0
2.606 -1
244
-0.327
778
3.759
784
-0.791
0
0.0
533
4.096
703
6.736
TABLE 6.68. SCENARIO 4: PERCENTAGE CHANGE IN QUANTITY OF
BEEF PRODUCED.
Region
Roast
Steak
Ham¬
burger
Total
-(%)•
Southeast
-29.8
-30.2
-30.0
-29.7
Midwest
30.7
6.0
-8.1
5.0
Southwest
-17.1
-17.1
11.7
-5.0
West
0.0
0.0
0.0
0.0
Plains
40.7
40.8
8.0
26.7
Total
23.5
7.1
-3.3
6.0

195
unchanged while the level of beef production in the South¬
west and Southeast regions actually declined.
The increase in beef production observed in the Plains
and Midwest regions was due to a change in the size of
cattle slaughtered in these regions (Tables 6.69-6.70). The
Plains and Midwest regions no longer slaughter 900 lb.
cattle but only 1,100 lb. cattle and culls.
The change in size of cattle slaughtered reflects
changes observed in the size of cattle finished (Tables
6.71-6.72). While the number of cattle finished increased
less than 0.5% the number of cattle finished at 1,100 lbs.
increased by 50.1% while the number of cattle finished at
900 lbs. declined by 100.0%. As a result of this shift to
heavier finishing weight the number of cattle finished in
the Southwest increased by 43.8% while the number finished
in the Plains region decreased by 40.9%. Thus the feedlot
operators in the Southwest benefit from an increase in beef
exports while feedlot operators in the Plains region lose.

196
TABLE 6.69. SCENARIO 4: QUANTITY CATTLE SLAUGHTERED.
Region
lf100 lb
Cull
Total
(neaaj ~
Southeast
—
232,712
232,712
Midwest
13,639,540
3,760,458
17,399,998
Southwest
1,821,134
1,978,865
3,799,999
West
—
905,031
905,031
Plains
3,423,163
876,836
4,299,999
Total
18,883,837
7,753,902
26,637,739
TABLE 6.70.
SCENARIO 4:
SLAUGHTERED.
CHANGE IN QUANTITY CATTLE
Region
900 lb
1,100 lb
Cull
Total
( nG3.Q)
Southeast
-
-99,687
-99,687
-
Midwest
-3,547,246
3,692,340
-145,094
0
Southwest
-
-678,866
678,865
0
West
-
0
0
0
Plains
-2,829,260
3,423,163
-423,164
170,739
Total
-6,376,506
6,436,637
10,920
71,052

197
TABLE 6.71 SCENARIO 4: CATTLE FINISHED.
Region
1,100 lb
—(Head)
Midwest
6,577,104
Southwest
9,370,469
Plains
4,009,166
Total
19,956,739
TABLE 6.72 SCENARIO 4: CHANGE IN CATTLE FINISHED.
Region
900 lb
1,100 lb
Total
( rieclQ ) ■ “
Midwest
0
0
Southwest
—
2,854,932
2,854,932
Plains
-6,783,719
4,009,166
-2,774,553
Total
-6,783,719
6,864,098
80,379
TABLE 6.73
SCENARIO 4: PERCENTAGE
CHANGE IN CATTLE
FINISHED.
Region
900 lb
1,100 lb
Total
( s)
Midwest
0.0
0.0
Southwest
—
43.8
43.8
Plains
-100.0
N/A
-40.9
Total
-100.0
50.1
0.4

CHAPTER 7
SUMMARY AND CONCLUSIONS
The structure of the beef sub-sector is dynamic,
responding to technological innovations in beef production
and changes in household meat consumption patterns. It is
important to be able to determine the impact of these
changes in the economic environment on the structure of the
sector so that both producers and government agencies can
anticipate these changes and develop responses.
The purpose of this research was to develop a mathe¬
matical programming model of the U.S. beef sector which
incorporates regional differences in production, endogenous
price determination and interdependence of demand for meats.
A linear activity analysis model is used to represent the
beef production system at the regional level. The activity
analysis model is integrated with a system of inverse demand
equations for hamburger, steak and roasts. Thus, the model
incorporates endogenous determination of prices, interde¬
pendence among meat products in the demand for meats, and
regional representation of beef production.
The integration of systems of demand equations into
mathematical programming model is problematic both in
regards to satisfying mathematical conditions and to
operationalizing the theoretical model. The theoretical
198

199
problems associated with incorporating demand systems into
programming models are well known. However, the operational
difficulties are not as well known due to the fact that the
difficulties in overcoming the theoretical problems have
limited the application of this methodology.
One theoretical problem, known as the integrability
problem, is that demand systems derived from economic theory
do not have mathematical properties which satisfy the
mathematical conditions of the programming model. Solutions
to the integrability problem developed until recently have
either been computationally intractable or inadequate in
their representation of the demand structure.
The methodology used in this dissertation solves the
integrability problem by using a compensated demand system
in place of an uncompensated system in the formulation of
the problem. The properties of the compensated demand
system satisfy the integrability conditions. When consumer
demand equations are used, this methodology represents an
approximation to the true solution.
The structure of the demand for beef and other fresh
meats was represented in the model by deriving an inverse
demand system from a distance function similar in form to
the cost function used by Deaton and Muelbauer to derive
their AIDS model. The compensated system was approximated
by holding the quantity index constant. The U.S. was
divided into four demand regions and a demand system

200
estimated for each region. The demand systems contained
eight meat commodities: hamburger, roast, steak, pork, whole
chicken, chicken parts, other poultry, and other meat. The
main component of other poultry is turkey. Household
monthly expenditures on each of the eight commodities at the
regional level were derived from the BLS' CES from 1982-
1986. Price indexes were derived from a separate data set .
provided by the BLS.
Two major problems were encountered in the integrating
of the demand system with the activity analysis model.
These were (1) the demand systems did not satisfy the
convexity conditions globally and (2) there was a gap
between the retail prices being generated by the demand
system and the costs of production coming out of the
activity analysis model.
This problem was handled by restricting the range in
quantity space over which the search for the solution can
occur and adjusting the magnitude of the own-quantity
parameters in the demand system by a small scaler value.
The gap between the retail price and the costs of
production coming from the activity analysis model is known
as the marketing margin. The problem of representing the
marketing margin was handled by fixing the marketing margin
at a fixed level under all scenarios.
The regional activity analysis models of the beef
production system were developed from production budgets.

201
The exception was at the cow-calf stage where market prices
for weaned calves and beef culls were used to represent
costs of production incurred by producers at this stage.
This approach resulted in the size of the breeding herd
being fixed.
Four different scenarios to simulate sector responses
to various changes in economic environment were run. The
first two scenarios looked at the changes which would occur
due to increases in the level of poultry consumption. The
third scenario examined the impact of increased levels of
beef imports on the beef sector and the fourth scenario
dealt with changes in sector due to increased levels of beef
exports.
In Scenario 1 the level of poultry consumption was
increased by the amount which poultry consumption increased
from 1982-1987. The increase in poultry consumption caused
both retail prices and household consumption to fall,
slaughter weight to decline, and the number of cattle
finished to decrease in the Southwest and increase in the
Plains.
In Scenario 2 the level of poultry consumed was
increased by 40%. This reflects the amount by which per
capita consumption of poultry increased from 1975-1985. The
decline in the consumption of beef in this scenario is
approximately one-half of the amount by which the consump¬
tion of beef declined during the 1975-1985 time period.

202
This indicated that the decline in beef per capita con¬
sumption of beef during this time period was not completely
caused by change in demand but was due to other factors,
such as a shift away from beef in consumers' preferences for
meat.
In Scenario 3 the level of hamburger imported into the
U.S. was increased by 16%, the amount by which beef imports
will increase if current trends continue. The increase in
beef imports led to a decline in beef production of 1.8%.
and a decline in the number of cattle slaughtered of 1.7%.
The regional impacts were much greater as beef production
declined by 57% in the Southeast and 50% in the West, but
actually increased by 4% in the Plains region.
In Scenario 4 the quantity of beef exported was set at
a level which reflects a 6% increase in the level of beef
exported from present levels of exports. While the increase
in beef exports caused U.S. domestic consumption of beef to
decline, the production of beef increased by 6%. Thus,
whatever losses occurred in production due to a decline in
domestic consumption, as a result of a higher domestic price
of beef, were offset by the increased export demand. In
addition the increase in beef exports caused the size of
finished cattle produced to increase, the number of cattle
finished in the Plains to decrease and the number of cattle
finished to decline in the Southwest.

203
Conclusions
In conclusion, all of the major objectives of this
dissertation were fulfilled. A price endogenous spatial
equilibrium model of the U.S. beef sector was successfully
operationalized. This involved the development of an
activity analysis model of the production system for beef,
the derivation of an inverse demand system for meat based on
the AIDS model, the estimation of the demand system at the
regional level, and the integration of the regional demand
systems with the activity analysis model.
The results of the base run of the model conformed
with observed phenomena in the beef sector. The level of
production and their location are as observed in the beef
sector. The exception to this is the lack of utilization of
stockering activities. This outcome is believed to be a
result of an over-estimation of the costs of finishing
stockered cattle. The model was run under four different
scenarios and behaved as expected.
The model was solved using GAMS. GAMS facilitated
both the formulation of the model and in its documentation.
It was especially useful as an aid in representation of the
model mathematically. GAMS also facilitated in the develop¬
ment of a portable model. The model is easily solved on a
386 personal computer, taking approximately 20 minutes per
run. It also permitted the model to be run at both the
University of Florida and at the USDA with little

204
difficulty. Also, the manner in which GAMS documents the
model makes it readily comprehensible to individuals not
involved in writing of the program for the model.
With respect to the results from alternative scenarios
which are analyzed, several conclusions can be drawn. One
conclusion to be drawn from the scenarios is that predicted
changes in levels of production are greater in the individ¬
ual regions and in individual stages of production than the
changes occurring in country as a whole. For example, as a
result of an increase in the beef imports the level of beef
produced in the U.S. declined by 1.8%. However, the pro¬
duction of beef in the Southeast and the West declined by
56.8% and 50%, respectively, with no change occurring in the
Midwest or West. The impact of increased beef imports also
has varying impacts on producers in the different stages of
production. While no change occurred in the number of
cattle slaughtered in the Southwest the number of cattle
finished in the Southwest declined by 5%. This result
occurred despite the fact that U.S. production of finished
cattle declined by less than 0.1%. This result demonstrates
that by simply looking at aggregate production levels can
lead to misleading conclusions concerning the impact of
changes in the economic environment on participants in the
sector. Adjustments in the sector do not fall evenly across
regions.

205
Another conclusion to be drawn from this research is
that the beef industry should concentrate on two things to
recapture lost market share. The industry should continue
its efforts to change consumers' preferences for beef
through introduction of new beef products or advertising.
The industry, however, should also concentrate on reducing
costs of production. This might be accomplished through
technological innovation, such as cattle which are genet¬
ically engineered to be more efficient at converting feed to
gain or reorganization of structure of sector so that a
single operator has control over several stages of produc¬
tion which has occurred in poultry and pork sectors. This
two-pronged approach is recommended because the results of
the analysis suggest that the reduction in consumption of
beef is due to both a change in consumers' preferences for
beef and a decline in the relative price of poultry to beef.
This research also indicates that a significant
increase in the level of beef exports is another way for the
sector to offset decrease in production due to the decline
in domestic consumption of beef. However, the ability of
the sector to expand exports is contingent on the opening up
of markets in Japan and the Europe and on the ability of
U.S. producers to compete in these markets with producers
from the rest of the world. While there is great potential
in the opening up of these markets due to the high standard
of living enjoyed by consumers in these countries, the

206
attitude of consumers towards beef in these countries is
likely to be similar to those held by consumers in the U.S.
In addition, with the opening up of agricultural markets,
producers of beef in the U.S. will not be shielded from
competition with producers around the world. These
observations suggest that the industry needs concentrate on
developing products which satisfy consumers' needs and
reducing costs of production in order to realize the
potential of the opportunities provided by the opening up of
these markets.
Limitations of Model
The analysis conducted by using this model is limited
by the fact that the size of the breeding herd is fixed and
not endogenously determined. Thus, the sector cannot
respond to economic changes by changing the number of calves
and culls produced. As a consequence the reaction of the
production system to change is not as fluid as it might be.
The model is structured so that all the weaned calves
produced do not have to be utilized by the production
system. Thus, the fixing of the size of the cow herd may be
limiting under scenarios in which beef production is expand¬
ing. On the other hand, the adjustment of the number cattle
pushed through the production system is not the only manner
in which the sector has of increasing or decreasing produc¬
tion of beef. It can also increase and decrease production
by adjusting the size of the cattle being slaughtered.

207
Thus, the response of the sector is not completely-
constrained by fixing the size of the cow herd.
Another limitation of this study is the manner in
which the marketing margins are handled. The method used is
purely ad hoc and is not consistent with the manner in which
the marketing margin is believed to change. In a single
commodity market, under the assumption of perfect compe¬
tition, the marketing margin represents the costs associated
in marketing the product. In a multi-commodity framework,
however, the marketing margin also includes producer rents
in addition to marketing costs. It is the producer rents
which increase or decrease in response to changes in market
conditions which cause the marketing margin to rise or fall,
thereby buffering cattle producers from changes in supply
and demand.
This research is also limited by the inability of the
demand functions used to satisfy convexity conditions
globally. In order to adapt the estimated demand systems
for use in the model the commodity space had to be
restricted and some of the parameters on the demand
functions needed to be adjusted. This is a common problem
for all demand systems using flexible functional forms, not
just this case in particular. This is because flexible
functional forms only have local properties and because
convexity is not imposed during estimation.

208
Areas for Further Research
Since the size of the cattle herd is not endogenously
determined in the model one of the first areas of further
development of the model would be to make the size of the
breeding herd endogenous. It would then be interesting to
compare the results obtained with the size of the breeding
herd fixed to those obtained when size of the breeding herd
can vary.
The results from the import and export scenarios
indicate that more effort needs to be placed in incorp¬
orating the import and export demand for beef. Currently,
the levels of beef imports and exports a fixed at a speci¬
fied level. In order to gain a better understanding of the
industry's competitiveness with producers in other nations
the demand for beef imports and exports should be endogen¬
ously determined. This could be accomplished by estimating
import and export demand functions or by increasing the
number of production and demand regions in the model to
reflect overseas markets.
Finally, it would be interesting to include a poultry
production model with the beef production model. This could
be used to analyze the impact on both sectors of changes in
the cost of feed and energy as well as technological inno¬
vations, such as genetic engineering.

appendices

APPENDIX A
The number of households sampled in one month repre¬
sents one-third of the total population and the number
sampled in one quarter represents the total population. The
formula used calculate regional household expenditures is
AE(s,m,t)= 3*Days(t)/7*^W( j , s,t)*E(j,s,m,t)/3*^jW(j,s,t)
where AE(s,m,l,l) represents the expenditure per household
in region s on commodity m in month t; W(j,s,t) is the
sample weight attached to the household j in region s in
month t; and E(j,s,m,t,l) represents the expenditure of
household j in region s on food item m in month t.
Days(t)/7 converts weekly expenditure to monthly
expenditure. Multiplying weighted expenditures for one
month by 3 gives a representation for the total population.
3*£W(jfSft) represents the amount of observations for the
total population. If the decision-making process used to
define the choice set does not reflect the consumer's
decision making process then the choice set is not properly
defined and the demand system does not represent consumer's
preferences appropriately.
210

211
For the formulas used to compute the missing prices
see Table A.l.

212
Table A.l. FORMULAS USED TO COMPUTE IMPUTED PRICES
Factor
Commodities
Poultry
USA
<
n
.00939 + .36489 Plag +.229935 PbtOMt.
South
Pw =
.004496 + .459131 Plag +.134901 Pbraa8t
West
II
»
(U
.00357 + .349183 Plag +.231541 Pbraa8t;
Midwest
Plega
= .915635 + .055394 Pw + .258423 Pbraa8t
Beef
Steak
Pw =
2.171608 + .457926 Pusa - .02892 Pna +
.730283 P^ - .87934 Psoutb
Ground beef
Pusa
= -.2464 + 7.1493 Pne - 2.68675 P„ -
1.68078 Pgouth - 1.62809 Pw08t
Roast
P
* usa
= -.01535 + .216136 Pna - .369562 P„, -
.281286 P90Utb - 1.62809 Pwa8t
Pork
Ham
P
* usa
= .298427 Pna - .255562 P^, - .31477 PBOUtb -
.127058 Pwa8t

APPENDIX B

214
TABLE B.l. NUMBER OF CATTLE BY REGION, 1984-1988.
Region
Year
Beef
Cows
Milk
Cows
Total
Percent
Beef of
Total
Region
Percent
of U.S.
Total
Northeast
1984
360
000
2,114
2,473
14.5
1.0
1985
339
2,096
2,434
13.9
1.0
1986
335
2,128
2,463
13.6
1.0
1987
374
2,009
2,383
15.7
1.1
1988
369
1,921
2,290
16.1
1.1
Avg.
355
2,054
2,409
14.8
1.0
Southeast
1984
6,733
2,436
9,169
72.3
18.0
1985
7,371
1,347
8,718
84.5
20.8
1986
7,076
1,380
8,456
83.7
21.0
1987
7,278
1,281
8,559
85.0
21.5
1988
6,968
1,248
8,216
84.8
21.1
Avg.
7,085
1,538
8,624
82.3
20.5
Southwest
1984
9,789
621
10,410
94.0
26.1
1985
9,163
595
9,758
93.9
25.9
1986
9,057
873
9,930
91.2
26.9
1987
8,773
586
9,359
93.7
26.0
1988
8,662
607
9,269
93.5
26.3
Avg.
9,089
656
9,745
93.3
26.2
Midwest
1984
12,167
5,113
17,280
70.4
32.5
1985
11,465
4,962
16,427
69.8
32.4
1986
10,925
5,140
16,065
68.0
32.5
1987
10,761
4,814
15,575
69.1
31.9
1988
10,548
4,699
15,247
69.2
32.0
Avg.
11,173
4,946
16,119
69.3
32.2

215
TABLE B.1.—Continued
Region
Year
Beef
Cows
Milk
Cows
Total
Region
Percent
Beef of
Total
Percent
of U.S.
Total
000
Plains
West
U.S.
1984
5,334
535
5,869
90.9
14.2
1985
4,914
525
5,439
90.3
13.9
1986
5,334
541
5,875
90.8
15.9
1987
4,606
515
5,121
89.9
13.6
1988
4,544
508
5,052
89.9
13.8
1984
2,237
1,290
3,527
63.4
6.0
1985
2,134
1,294
3,428
62.2
6.0
1986
2,039
1,368
3,407
59.8
6.1
1987
1,988
1,297
3,285
60.5
5.9
1988
1,877
1,324
3,201
58.6
5.7
Avg.
2,055
1,315
3,370
60.9
5.9
1984
37,494
11,109
48,603
77.1
100.0
1985
35,370
10,805
46,175
76.6
100.0
1986
33,633
11,177
44,810
75.1
100.0
1987
33,779
10,502
44,281
76.3
100.0
1988
32,958
10,307
43,265
76.2
100.0
Avg.
34,647
10,780
45,427
76.3
100.0
Source: USDA (1989)

TABLE B.2 COST OF PRODUCING CULLS AND CALVES
Region
Calves
Culls
$/cwt
Southeast
59.32
39.65
Midwest
65.29
44.34
Southwest
63.34
42.68
West
58.64
43.27
Plains
65.38
42.34
Source: USDA (1989).

217
TABLE B.3
COSTS INCURRED AT THE
STOCKERING STAGE
Region
Type
Cost
Year¬
lings
1 1/2
years
$/head
Southeast
Variable
70.99
166.76
Fixed
15.80
35.10
Midwest
Variable
69.74
163.86
Fixed
19.84
49.60
Southwest
Variable
71.73
168.51
Fixed
14.76
36.91
West
Variable
72.01
169.24
Fixed
20.03
60.08
Plains
Variable
70.80
166.41
Fixed
16.88
42.18
Source: Disney (1989).
Formulas used to calculate the average cost (AC) of
stockering activities on a per head basis are shown below.
Southeast:
Midwest:
Southwest:
West:
Plains:
AC = 1.050 (Variable + Fixed)
AC = 1.046 (Variable + Fixed)
AC = 1.050 (Variable + Fixed)
AC = 1.197 (Variable + Fixed)
AC = 1.197 (Variable + Fixed)

TABLE B.4.
COST OF PRODUCTION ACTIVITIES AT THE FINISHING STAGE.
Fed Nonfed
Region
Type
of Cost
Calf to
900 lbs
Calf to
1,100 lbs
Yearling
to
1,200 lbs
1 1/2
year to
1,300 lbs
Yearling
to
900 lbs
1 1/2
year to
1,100 lbs
Southeast
Variable
277.98
424.43
452.49
472.40
205.50
263.89
Fixed
29.44
42.79
35.75
28.90
16.20
16.26
Corn
46.00
70.20
69.20
63.30
31.40
37.10
Midwest
Variable
364.96
404.55
434.19
454.19
197.16
253.58
Fixed
27.76
40.37
33.72
25.25
15.36
15.35
Corn
46.00
70.20
69.20
63.30
31.40
37.10
Southwest
Variable
262.56
402.55
426.45
443.04
193.66
249.70
Fixed
19.18
27.86
23.27
18.81
10.55
17.72
Corn
46.00
70.20
69.20
63.30
31.40
37.10
West
Variable
306.54
468.43
482.55
520.00
220.43
290.48
Fixed
20.02
29.07
24.30
19.62
10.77
10.81
Corn
46.00
70.20
69.20
63.30
31.40
37.10
Plains
Variable
222.20
398.43
425.66
454.64
193.30
253.27
Fixed
19.60
18.46
23.78
19.21
11.00
11.04
Corn
46.00
70.20
69.20
63.30
31.40
37.10
Source:
Disney (1989)
•
Formulas used to calculate the average cost (AC) of finishing activities from Table B.4 are
shown below.
Southeast: AC=0.875*Variable+Fixed+0.16*Corn West: AC=0.875*Variable+Fixed+0.ll*Corn
Midwest: AC=0/875*Variable+Fixed+0.05*Corn Plains: AC=0.875*Variable+Fixed+0.05*Corn
Southwest: AC=0.875*Variable+Fixed+0.ll*Corn
218

219
TABLE B.5 CARCASS YIELD FROM LIVE
ANIMAL.
Item
Yield
900 lbs
.59
1,100 lbs
.61
1,200 lbs
.62
1,300 lbs
.63
Yearling
.52
1 1/2 year old
.54
Cull
.50
TABLE B.6 PRIMAL
CUT YIELD
FROM CARCASS.
Item
Fed
Nonfed
Cull
Roast
.227
.209
.091
Steak
.274
.251
.109
Lean trim
.101
.220
.530
Medium trim
. Ill
. 120
.030
Fat and bone
.287
.200
.240

220
TABLE B.7. PARAMETER ESTIMATES ON TRANSLOG COST FUNCTION
FOR SLAUGHTERING AND FABRICATING.
Item
a
b
c
Parameter
7.3165
0.4801
0.0409
Standard Error
0.1918
0.0480
0.0059
T-Statistic
38.1500
9.9970
6.9231
R2
0.9980
The equation estimated is:
ln(TC) = a + b*ln(q) + l/2*c*(ln(q)2) + e
where TC is the total cost of slaughtering the live animal
and fabricating into primal cuts and q equals the quantity
of cattle slaughtered per week.
The formula used to calculate the average cost (AC) of
slaughtering and fabricating is
AC = (exp(7.32 + 0.48*ln(Q/52) + 0.02*(ln(Q)2) )/Q
where AC is the average cost and Q is the slaughter plants
annual capacity.

221
TABLE B.8. DISTANCE BETWEEN SUPPLY REGIONS
South- Mid- South-
Region west west west West Plains
(miles)
Southeast
50
1090
986
-
-
Midwest
1090
50
830
-
425
Southwest
986
830
100
1352
600
West
-
-
1352
100
1150
Plains
_
425
600
1150
100
Source: Kennedy (1982); Disney (1989).
The cost of transporting live cattle were determined by
using the equations listed below.
For routes less than 1,000 miles:
$/cwt = 0.121*(0.7132 + 0.00181(miles))
$/head = ($/cwt) (cwt/head)
For routes greater than 1,000 miles:
$/cwt = 0.121*(0.7132 + 0.00165(miles))
$/head = ($/cwt) (cwt/head)

TABLE B.9. DISTANCES BETWEEN SUPPLY AND DEMAND REGIONS
Supply Center
Demand Center
Miles
West: Stockton, CA
West: San Francisco, CA -Denver,
South: Dallas, TX - Atlanta, GA
CO
363.75
2,237.80
Plains: Sterling, CO
West: San Francisco, CA -Denver,
South: Dallas, TX - Atlanta, GA
Midwest: Chicago, IL
Northeast: New York, NY
CO
864.75
1,342.40
871.00
1,646.00
Southwest: Lubbock, TX
West: San Francisco, CA -Denver,
South: Dallas, TX -Atlanta, GA
CO
1,209.75
552.84
Midwest: Chicago, IL
Northeast: New York, NY
1,134.00
1,795.00
Midwest: Sioux City, IA
West: San Francisco, CA -Denver,
South: Dallas, TX -Atlanta, GA
Midwest: Chicago, IL
Northeast: New York, NY
CO
1,288.75
974.56
1,300.00
1,446.00
Southeast: Montgomery, AL
South: Dallas, TX -Atlanta, GA
Northeast: New York, NY
1,007.00
306.60
Source: Kennedy (1982).
The distances for the West and South demand regions represent the weighted average of
the distance between the supply center and the individual cities. The weights used are
the demand region's population accounted for by the sub-region for which the individual
city acts as the demand center.
Transportation costs were calculated using the following formula:
$/cwt = 0.7589 + 0.00258(miles) - (3.35xl07) (miles)2
Source: Ward and Farris.
222

APPENDIX C
GAMS PROGRAM
SOFFSYMLIST OFFSYMXREF
$ title US BEEF MODEL
•«»*#**«***** MESSAGES ««t**t***#tf*t*«**#**tt*»***##ff*»#t#t***fft*
Sontext
ATTENTION: THIS NEEDS TO BE GIVEN STARTING VALUES
AND BOUNDS OH VARIABLES BEFORE RUNNING.
—Dairy culls from the northeast have been included In the
midwest region.
—The values of the own quantity parameters on the regional demand
have been adjusted by +.0025 (+.0001 in the West) to permit the equations
to be negative seal-definite over the range of quantities permitted.
—The quantites of exogenous meat products consumed have been placed at
the minimum value observed over the data set.
Sofftext
•flflff DIMENSIONS OF SUPPLY VARIABLES USED IN MODEL ffffffff
SETS
U0 CLASS OF COW SUPPLIED
/ FB9, FB11, PB12, FB13, NFB1, NFB1-5, Cull/
U1 CLASSES SLAUGHTERED CARCASSES
/ FB9, FB11, FB12, FB13, NFB1, NFB1-5, Cull/
U2 TYPES OF FABRICATED CUTS
/ROAST, STEAK, LNTRM, MDTRM, F-T/
K1 PRODUCTION PROCESSES AT SLAUGHTER PLANT
/ FB9, FB11, FB12, FB13, NFB1, NFB1-5, Cull/
K2 PRODUCTION PROCESSES AT FABRICATION STAGE
/ FB9, FBI1, FB12, FB13, NFB1, NFB1-5, Cull/
L SLAUGHTER PLANTS
/PL1+PL5/
EXX FOREIGN DEMAND REGIONS
/EXX1 + EXX5 /
SR DOMESTIC SUPPLY REGIONS
/SB, MW, SW, W, PL/
3RD SUPPLY REGIONS FOR DAIRY HERD CULLS
/NNE,SE,SW,MW,W,PL/
IM FORGEIN SUPPLY REGIONS
/IMPORTS/
H HAMBURGER ROWS
/Min MINIMUM PAT CONTENT
Max MAXIMUM FAT CONTENT/
SRL(SR,L) NO. OF PLANTS IN EACH REGION
/ SE.PL1
MW. (PL1+PL5)
SW. (PL1+PL5)
W.PL1
PL.(PL1*PL3) /
PC(U0,K1) PRODUCTION COMBINATIONS
/FB9.FB9
FB11.FB11
FB12.FB12
FB13.FB13
NFB1.NFB1
NFB1-5.NFB1-5
Cull.Cull /
$lines 11
SRLPC(SR,L,U0,K1) SRL U PC
/SE.PL1 .(FB9.PB9,FB11.FB11,FB12.FB12,FB13.FB13,
NFB1.NFB1,NFB1-5.NFB1-5,Cull.Cull)
MW.(PL1+PL5).(FB9.FB9,FB11.FB11,FB12.FB12,FB13.FB13,
NFBl.NFBl,NFBl-5.NFBl-5,Cull.Cull)
SW.(PL1+PL5).(FB9.FB9,FB11.FB11,FB12.FB12,FB13.FB13,
NFBl.NFBl,NFBl-5.NFBl-5,Cull.Cull)
W .PL1 .(FB9.FB9,FB11.FB11,FB12.FB12,FB13.FB13,
NFBl.NFBl,NFBl-5.NFBl-5,Cull.Cull)
PL.(PL1+PL3).(FB9.FB9,FB11.FB11,FB12.FB12,FB13.FB13,
NFBl.NFBl,NFBl-5.NFBl-5,Cull.Cull) /
RTL (SR, L, U2) PRIMAL CUTS TO BE SENT TO RETAIL OR TO MAKE HAMBURGER
/SE . PL 1.(ROAST, STEAK )
MW.(PL1+PL5).(ROAST,STEAK)
SW. (PL1+PL5) . (ROAST,STEAK)
W .PLl.(ROAST,STEAK)
PL.(PL1+PL3) .(ROAST,STEAK) /
223

/
HB(U2) PRIMAL CUTS USED TO MAKE HAMBURGER
/ROAST, STEAK, MDTRM , LHTRM
SRLHB(SR,L,U2) SRL U PRIMAL CUTS USED TO MAKE HAMBURGER
/ SB . PL 1.(ROAST, STEAK, MDTRM, LHTRM )
MW. (PL1*PL5) . (ROAST, STEAK, MDTRM, LHTRM)
SW. (PL1*PL5). (ROAST,STEAK,MDTRM,LMTRM)
W ,PL1.(ROAST,STEAK,MDTRM,LHTRM)
PL.(PL1*PL3) .(ROAST,STEAK,MDTRM,LMTRM) /
ALIAS(UO,VO)
ALIAS (SR, SRR)
LIVE AHIMAL VARIABLE DIMEHSIOHS
SETS
US CLASS OF AHIMAL COW HO FROM DAIRY
/CULL /
U6 CLASS OF AHIMAL PRODUCED AT COW-CALF STAGE
/ CALF, CULL /
U7 CLASS OF AHIMAL PRODUCED AT STOCKER STAGE
/ HFB1, HFB1-5 /
U8 CLASS OF AHIMAL PLACED OH FEED LOT
/ CALF, HFB1, NFB1-5 /
U9 CLASS OF AHIMAL PRODUCED OH FEED LOT
/ FB9, FB11*FB13 /
U10 CLASS OF AHIMAL USED AT SLAUGHTER PLANT
/ FB9, FB11*FB13, KFB1, NFB5, CULL /
K6 PRODUCTION PROCESSES AT COW-CALF STAGE COW-CALF
/ BREED /
K7 PRODUCTION PROCESSES AT STOCKER STAGE STOCKER
/ NFB1, NFB1-5 /
KB PRODUCTION PROCESSES AT FINISHING STAGE FEED LOT
/ FB9, FB11*FB13, NFB1-FB9, NFB2-FB11 /
PC7(U7,K7) NOHFED PRODUCTIOH COMBIHATIOHS
/ NFB1.NFB1, NEBI—5.NFB1-5 /
PC8(U8,K8) PRODUCTION COMBIHATIONS
/ CALF.(FB9,FB11)
NFB1.(HFB1-FB9.FB12)
NFB1-5.(NFB2-FB1I,FB13) /
PC88(U9,K8) PRODUCTION COMBINATIONS
/FB9.(FB9,NFB1-FB9)
FB11.(FB11,NFB2-FB11)
FB12.FB12
FB13.FB13 /
I TYPES OF PRODUCTION COSTS
/VAR, FIXED, CORN /
D3RL (SRR, SR, L) SUPPLY REGION AND PLANT COMBINATIONS
/ (SE,MW, SW) .SE.PL1
(SB,MW,SW,PL) -MW.(PL1*PL5)
(SE,MW,SW,PL,W).SW.(PL1*PL5)
(SW,PL,W) .W.PL1
(MW,SW,PL,W) .PL.(PL1*PL3) /
DSRLD(SRD,SR,L) DAIRY SUPPLY AND PLANT COMBINATIONS
/(SB,MW,SW) .SE.PLl
(SE,MW,SW,PL) .MW.(PL1*PL5)
(SE,MW,SW,PL,W).SW.(PL1*PL5)
(SW,PL,W) .W.PL1
(MW,SW,PL,W) .PL.(PL1*PL3) /
ALIAS(U6,V6)
Seject
*»**
******** SUPPLY PARAMETERS **«
******** The data in this section is organized according to #**
******** the production stages found in the beef sector. It ***
******** starts with the cow-calf stage then the stocker stage, ***
******** the finishing stage, and finally the slaughter/processing ***
******** stage. For the most part the quantity parameters are *#*
******** first then the cost parameters. ***
‘f**********************************************************************
PARAMETER
* NNE . CULL
PARAMETER
DAIRY (SRD,U5)
/SB.CULL
MW.CULL
SW.CULL
W.CULL
PL. CULL
772.0
CSTDA(SRD,U5)
/SB.CULL
MW.CULL
SW.CULL
REGION (THSND HD)
SUPPLY OF DAIRY CALLS BY
331200
2332600
200300
608400
122900
COST OF DAIRY CULLS BY SUPPLY REGION (DOL PER CWT)
39.65
44.34
42.68

225
42.34
43.27 /
40.27
AVERAGE WEIGHT DAIRY CULL BY REGION (CWT)
8.75
9.42
9.00
9.57
9.68 /
W.CULL
PL.CULL
*NNE.(SE,MW,SW,W,PL).CULL
PARAMETER DARYVT( 3RD ,U5 )
/SB. CULL
MW.CULL
SW.CULL
W.CULL
PL.CULL
•NNE.CULL 9.50
PARAMETER RD(SRD,U5) COST OF DAIRY CULLS TO SLAUGHTER (DOL PER HD);
RD (SRD,U5)-DARYWT(3RD,U5) *CSTOA( SRD,U5) ;
DISPLAY RD;
COW-CALF STAGE
ttlttltittttttt
ttttittttttittt
PARAMETER
Z5(SR,K6)
COWS fcHEIFERS
THAT HAVE CALVED BY
REGION
(HD)
/SE.BREED
7.0852E+06
MW.BREED
11.1732E+06
SW.BREED
9.0888E+06
W.BREED
2.05474E+06
PL.BREED
4.9464E+06
/
PARAMETER C6(SR,K6)
BREEDING STOCK
PER UNIT OF COW-CALF PROCESS (HD)
/ (SE,MW,SW
,W,PL) .BREED
1 /
TABLE D6(SR,U6,K6) CULLS C CALVES PER UNIT OF COW-CALF PROCESS
(HD)
CALF.BREED
CULL.BREED
SB
.59
.10
MW
.61
.14
sw
.63
.12
w
.57
.17
PL
.62
.16
Paranatar
cd6(er,k6)
bub culls and
calves available In
region;
cd6(er,k6)>
aua(u6, z5(»r.
*6)*d6(sr,u6,k6))/7;
Display cd6;
TABLE DC(SR,U6) THE
WEIGHT COMING
FROM COW-CALF STAGE
(CWT PER HEAD)
CALF
CULL
SB
4.33
8.75
MW
4.65
9.42
SW
3.90
9.00
W
4.15
9.57
PL
4.30
9.60
TABLE R6A(SR,U6) COST
OF PRODUCING
CULLS AND CALVES (DOLLARS PER CWT)
CALF
CULL
SB
59.32
39.65
MW
65.29
44.34
SW
63.34
42.68
W
58.64
43.27
PL
65.38
42.34
PARAMETER
R6(3R,U6)
COST COW-CALF
STAGE (DOLLARS PER HD);
R6(SR,
U6)-R6A(SR,U6)
*DC(SR,U6);
DISPLAY R6;
Seject
•Ittttttttttt
‘tttttttitt
THE STOCKER STAGE
PARAMETER
C7(SR,U6,K7)
CALVES USED PER UNIT
STOCKERING PROCESS (HD)
/ (SE, MW, SW, W,
PL).CALF.(NFB1.NFB1-5)
1 /
display c7
PARAMETER
D7(SR,U7,K7)
NFB £ NFB1-5 PRODUCED
PER UNIT
STOCKERING PROCESS
D7(SR,U7,K7)
-1 $PC7(U7,K7);
DISPLAY D7
TABLE DS(SR,U7) THE WEIGHT COMING FROM STOCKER STAGE
(CWT PER HEAD)
NFB1
NFB1-5
SE
6.48
0.58
MW
6.80
8.90
SW
6.05
8.15
w
6.30
8.40
PL
6.45
8.55
TABLE R7A(SR,I,K7)
COST DATA FOR
NFB1
STOCKER STAGE (DOLLARS PER HEAD)
NPB1-5
SE.VAR
70.99
166.76
SE.FIXED
15.80
35.10
MW.VAR
69.74
163.86
MW.FIXED
19.84
49.60
SW.VAR
71.73
168.51
SW.FIXED
14.76
36.91
W. VAR
72.01
169.24
W.FIXED
20.03
60.08
PL.VAR
70.80
166.41
PL.FIXED
16.88
42.18

PARAMETER R7(SR,K7) COST FORAGE FED STOCKER (DOLLARS PER HD);
R7('SE',K7)- 1.05* SUM(I, R7A( 'SE', I ,K7)) ;
R7('KW',K7)« 1.046*3UM(I, R7A('MW',I,K7));
R7('SW',K7)« 1.05* SUM(I, R7A('SW',I,K7));
R7('W', K7)- 1.197*SUM(I, R7A('W' ,I,K7));
R7(’PL',K7)« 1.197*SUM(I, R7A( 'PL' ,I,X7) );
DISPLAY R7;
Saject
•fftttftffftffft THE FIWISHIHG STAGE ft#
*ffff#######ff##### ft#####
TABLE DAA(SR,U9) THE WEIGHT LEAVING THE FEED LOT (CWT PER HEAD)
FB9
FB11
FB12
FB13
SB
8.98
10.98
11.98
12.98
MW
9.30
11.30
12.30
13.30
SW
8.55
10.55
11.50
12.55
W
8.80
10.80
11.60
12.80
PL
8.95
10.95
11.95
12.95
PARAMETER C8(SR,U8,K8) CALF,NPB tNPBl-5 USED PER UNIT FINISHING PROCESS (HD)
C8(SR,U8,K8)«1 SPC8(U8,K8);
DISPLAY C8;
PARAMETER D8(SR,U9,K8) FINISHED CATTLE PER UNIT OF FINISHING PROCESS (HD);
D8(SR,U9,K8)-1 SPC88(U9,K8);
DISPLAY D8;
TABLE R8A(SR,I,K8)
COST DATA FOR
FINISHING IN A
FEEDLOT
(DOLLARS PER
FB9
FB11
FB12
FB13
SB.VAR
277.98
424.43
452.49
472.40
SB.FIXED
29.44
42.79
35.75
28.90
SB.CORN
46
70.2
69.2
63.3
MW.VAR
264.96
404.55
434.19
454.19
MW.FIXED
27.76
40.37
33.72
25.25
MW.CORN
46
70.2
69.2
63.3
SW.VAR
262.56
402.55
426.45
443.04
SW.FIXED
19.18
27.86
23.27
18.81
SW. CORN
46
70.2
69.2
63.3
W. VAR
306.54
468.43
482.55
520.00
W.FIXED
20.02
29.07
24.3
19.62
W.CORN
46
70.2
69.2
63.3
PL.VAR
222.20
398.43
425.66
454.64
PL.FIXED
19.6
28.46
23.78
19.21
PL.CORN
46.00
70.20
69.20
63.30
♦
NFB1-FB9
NFB2-FB11
SB.VAR
205.50
263.89
SB.FIXED
16.2
16.26
SB.CORN
31.4
37.10
MW.VAR
197.17
253.58
MW.FIXED
15.36
15.35
MW.CORN
31.4
37.1
SW. VAR
193.66
249.70
SW.FIXED
10.55
17.72
SW. CORN
31.4
37.1
W. VAR
220.43
290.48
W. FIXED
10.77
10.81
W.CORN
31.4
37.1
PL.VAR
193.30
253.27
PL.FIXED
11.0
11.04
PL.CORN
31.4
37.1
PARAMETER R8(SR,K8) COST FINISHING IN A FEEDLOT (DOLLARS PER HD);
R8('SB',K8)«0.875*(R8A('SE'('VAR',K8)
+R8A('SE','FIXED',K8))
+0.16*(R8A( 'SE', 'CORN' ,K8));
R8( 'MW' ,K8)=0.875* (R8A( 'MW' , 'VAR' ,K8)
♦ R8A( 'MW', 'FIXED' ,K8))
+0.05*(R8A('MW','CORN',K8));
R8('SW',K8)«0.875*(R8A('SW','VAR',K8)
+R8A('SW','FIXED',K8))
♦ 0.11*(R8A('SW','CORN',K8));
R8( 'W',K8)«0.875*(R8A('W','VAR',K8)
+R8A('W','FIXED',K8))
+0.11*(R8A('W','CORN',K8));
R8('PL',K8)“0.875*(R8A('PL','VAR',K8)
+R8A('PL','FIXED',K8))
+ 0.05*(R8A('PL','CORN',K8)) ;

#**####«*##*##*
##*#f«•#!**#
#*t#f If tttMf f #
DISPLAY R8;
Sejoct
•t«*f*#*f**f«##l
*l*#*t*t*«*t SLAUGHTER t PROCESSING STAGE
*t*t«»#tt«!ttt*f
PARAMETER C1(SR,L,U0,K1) TYPE OF CARCASS USED IN KILL-CHILL (HEAD);
C1(SR,L,U0,K1)-1 $SRLPC(SR,L,U0,K1);
DISPLAY Cl;
PARAMETER D1A(SR,L,U0,KI) OUTPUT FROM KILL-CHILL (HEAD);
D1A(SR,L,U0,K1)-1 SSRLPC(SR,L,U0,K1);
display dla;
PARAMETER CAPCTY(3R,L)
NO. AND SIZE OF SLAUGHTER PLANTS BY REGION (HD)
/SE.pll
125000
MW.pll
250000
MW.pl2
500000
MW. pl3
750000
MW. pl4
1000000
MW.plS
1300000
SW.pll
250000
SW.pl2
500000
3W.pl3
750000
SW.pli
1000000
SW.pl5
1300000
W.pll
125000
PL.PL1
250000
PL.pl2
500000
PL.PL3
1000000
TCAPCTY ( SR, L )
TOTAL SLAUGHTER
/SE.pll
1750000
MW.pll
1250000
MW.pl2
7000000
MW.pl3
4500000
MW.pl4
2000000
MW.pl5
3900000
SW.pll
1750000
SW.pl2
500000
3W.pl3
1500000
SW.pl4
1000000
sw.pis
1300000
W.pll
2250000
PL.PL1
250000
PL.pl2
3000000
PL.PL3
1300000
PARAMETER C10(SR,K1) THE WEIGHT ENTERING THE MEATPACKING PLANT;
C10(SR, 'FB9')=DAA(SR, 'FB9') ;
C10(SR, 'FB11')=DAA(SR, 'FB11') ;
C10(SR,'FB12')=DAA(SR,'FB12');
CIO(SR. 'FB13' )=DAA(SR, 'FB13') ;
CIO(SR,'NFB1')-DS(SR,'NFB1');
C10(SR,'NFBl-5')=DS(SR,'NFB1-5');
C10(SR,'CULL')-DC(SR,'CULL');
DISPLAY CIO;
TABLE DA(SR,K1) THE WEIGHT COMING FROM FINISHING STAGE (CWT PER HEAD)
FB9
FB11
FB12
FB13
HFB1
NFBl-5
CULL
SE
8.98
10.98
11.98
12.98
6.48
8.58
8.75
MW
9.30
11.30
12.30
13.30
6.80
8.90
9.42
SW
8.55
10.55
11.50
12.55
6.05
8.15 -
9.00
W
8.80
10.80
11.60
12.80
6.30
8.40
9.57
PL
8.95
10.95
11.95
12.95
6.45
8.55
9.68
PARAMETER KILL(Kl) carcass yield from live animal (percentage)
/ FB9 .59
FB11 .61
FB12 .62
FB13 .63
NFB1 .52
NFB1-5 .54
Cull .50 /
PARAMETER D1(SR,K1) THE CARCAS WGHT (CWT PER HEAD);
D1(SR,K1)= KILL(K1)*DA(SR,K1);
DISPLAY Dl;
TABLE CUTOUT(U2,K1) primal cuts percentage of carcass
ROAST
(FB9,FB11,FB12,FB13)
.227
(HFB1,NFBl-5)
.209
Cull
.091
STEAK
.274
.251
.109
LNTRM
.101
.22
.53
MDTRM
• 111
.12
.03
F-T
.287
.2
.24

PARAMETER D2(SR,U2,K1) WEIGHT OF FABRICATED CUTS (CWT);
D2(SR,U2,Kl)-CUTOUT(U2,Kl)*Dl(SR,Kl);
DISPLAY D2;
PARAMETER C2(SR,L,U0,K1) CARCASS USED PER UHIT FABRICATION (HEAD);
C2(SR,L,U0,K1)-1 $SRLPC(SR,L,U0,K1);
display c2;
PARAMETER A3(SR,H,U2) FAT CONTENT OF PRIMAL CUTS;
A3 (SR, 'MIN', 'ROAST')- -.20;
A3(SR, 'MAX', 'ROAST')- .20;
A3(SR,'MIN','STEAK')- -.20;
A3 (SR,'MAX','STEAK')- .20;
A3 (SR, 'MIN' , 'LHTRM' )â–  -.15;
A3(SR, 'MAX', 'LNTRM' )â–  .15;
A3 (SR, 'MIN' , 'MDTRM' )â–  -.50;
A3 (SR,'MAX','MDTRM')- .50)
PARAMETER C3(SR,U2) LEVEL USED IN HAMBURGER MANUFACTURE (CWT);
C3(SR,U2)-1 $HB(U2);
display c3;
PARAMETER FAT(SR,H) PERCENT FAT REQUIREMENT OF HAMBURGER;
FAT (SR, 'MIN') —.15 ;
FAT (SR, 'MAX' )- .27 ;
•DISPLAY FAT;
*»#### COSTS OF PRODUCTION
PARAMETER SIHT(SR,L) Intercept; on cost function for slaughter;
SINT(SR,L)- 7.32 $SRL(SR,L);
PARAMETER 3B1(SR,L) linear tarn coefflcent on cost function;
SB1(SR,L)« .48 $SRL(SR,L);
PARAMETER SC1(SR,L) Quadratic tern coefficient on cost function;
SCl(SR,L)-.02 $SRL(SR,L);
PARAMETER R1(SR,L) AVERAGE COST OF SLAUGHTERING LIVB ANIMAL (DOLLARS PER HD)
R1(SR,L)“( (EXP(SINT(SR,L)
♦ SB 1 (SR, L) * LOG (capcty (SR, L) / 5 2)
+ (SC1(SR,L) )*SQR(LOG(capcty(SR,L)/52))) )/(capcty(SR,L)/52))
$SRL(SR,L);
DISPLAY Rl;
PARAMETER R3(SR,L) COST OF MAKING HAMBURGER (DOL PER CWT);
R3(SR,L)s.234*Rl(SR,L) / (sum (hi, klll(kl)*da(sr,kl))/7);
DISPLAY R3;
Seject
*tl*»#«** THE DEMAND PARAMETERS **««*#*«
*######## This section contains the parameters for the demand t#fftft
•ttttftl# equations for the domestic markets and the price l#ft#tt#
•Mlflll# received by domestic producers in foreign markets. ftfft*tt
SETS U3 TYPES OF PROCESSED CUTS
/HMBRGR, ROAST, STEAK/
U4 OTHER MEAT CONSUMED BY HOUSEHOLD (EXOGENOUS)
/PORK, OTHMEAT, CHICKENW, CHICKENP, OTHPOULT/
DR DOMESTIC DEMAND REGIONS
/NNE, S, MW, W /
IMPRTS(U3) TABLE CUTS IMPORTED
/HMBRGR/
IMPRTDMND(IM,DR,U3) THE DEMAND MARKETS TO WHICH IMPORTS ARE SHIPPED
/IMPORTS.(S,W).HMBRGR /
ALIAS(U3,V3)
TABLE BBFIMPRT(IM,U3) BASE LEVEL BEEF AVAILABLE FROM IMPORT REGIONS (CWT)
HMBRGR ROAST STEAK
IMPORTS 14.4634B+06
PARAMETER BPIMPRT ( IM, U3) BEEF AVAILABLE FROM IMPORT REGIONS (CWT);
BFIMPRT( IM, U3 ) -1 • BBFIMPRT (IM, U3 ) ;
PARAMETER RF(IM,U3) COST OF FOREIN BEEF (DOL PER CWT)
/ IMPORTS.HMBRGR 90.2 /

TABLE
BII(U3,DR) THE MATRIX OP CWB-QUARTITT EFFECTS
KNE 3 MM W
HMBRQR
ROAST
STEAK
.13946
.084251
.12838
.13608
.082355
.12413
.15571
.080141
.12447
.13521
.044852
.136
TABLE BIJ(U3,V3,DR) THE MATRIX 07 CROSS-QUANTITY EFFECTS
NHE S MW W
HMBRGR.ROAST -.01365 -.01556 -.01716 -.00189
ROAST.STEAK -.02393 -.OHIO -.01699 -.00681
STEAK. HMBRGR -.01644 -.02965 -.02902 -.03135
TABLE CIJ(U3,U4,DR) THE MATRIX OF FIXED CR08S-QUANTITY EFFECTS
PORK.NNE
OTHMBAT.NNE
CHICKKEW.HKE
CHICKENP.NNE
OTHPOULT•NHE
HMBRGR
-.04072
-.02928
-.00934
-.02118
-.00633
ROAST
-.02033
-.01288
-.00471
-.00251
-.00373
STEAK
-.03357
-.02066
-.00866
-.01462
-.00798
♦
PORK.S
OTHMEAT. S
CHICKENW.8
CHICKENP.S
OTHPOULT.S
HMBRGR
-.04121
-.02983
-.00667
-.00562
-.00505
ROAST
-.02122
-.01529
-.00990
-.00312
-.00365
STEAK
-.03297
-.02618
-.00310
-.01681
-.00182
♦
PORK.MW
OTHMEAT.MW
CHICKENW.MW
CHICKENP. MW
OTHPOULT.MW
HMBRGR
-.05532
-.02727
-.00840
-.01176
-.00429
ROAST
-.02047
-.00897
-.00655
-.00598
-.00150
STEAK
-.03283
-.02328
-.00564
-.01066
-.00354
♦
PORK.W
OTHMEAT.W
CHICKENW.W
CHICKENP .W
OTHPOULT. W
HMBRGR
-.04208
-.03337
-.00754
-.01237
-.00647
ROAST
-.01752
-.00952
-.00101
-.00485
-.00312
STEAK
-.04588
-.02180
-.00683
-.01308
-.01011
PARAMETER A(DR,U3) VALUES OF INTERCEPTS
/NKB. HMBRGR
NNE.ROAST
NHE.STEAK
S.HMBRGR
S.ROAST
S.STEAK
MW.HMBRGR
MW.ROAST
MW.STEAK
W.HMBRGR
W.ROAST
W.STEAK
0.10712
0.14033
0.21690
0.12131
0.15366
0.17795
0.10896
0.14678
0.19817
0.13559
0.14481
0.23876
B(DR,U3) VALUE OF PARAMETER ON QUANTITY INDEX
/NNE.HMBRGR
.01019
KNE.ROAST
-.00039
NNE.STEAK
-.00043
S.HMBRGR
-.02012
3.ROAST
-.00645
S.STEAK
-.01463
MW.HMBRGR
.01050
MW.ROAST
.00537
MW.STEAK
.00457
W.HMBRGR
.00377
W.ROAST
-.01690
W.STEAK
-.00360 /
t,U4) QUANTITY
CONSUMED OF
/NNE. PORK
2.515
NNE.OTHMEAT
2.207
NNE.CHICKENW
0.977
NNE.CHICKENP
0.941
NNE.OTHPOULT
0.495
S.PORK
3.321
S. OTHMEAT
1.714
S.CHICKENW
1.593
S.CHICKENP
0.560
S.OTHPOULT
0.407
MW.PORK
2.963
MW.OTHMEAT
2.404
MW.CHICKENW
1.235
MW.CHICKENP
0.793
MW.OTHPOULT
0.212
W.PORK
2.806
W.OTHMEAT
1.997
W.CHICKENW
0.748
W.CHICKENP
0.467
W.OTHPOULT
0.375

PARAMETER Y0M(DR,U4) ADJUSTED LEVEL EXOGENOUS MEAT PRODUCT (LBS);
YOM(DR, 'PORK' )-l*YM(DR, 'PORK') ;
YOM(DR, 'OTHMEAT' )-l*YM(DR, 'OTHMEAT' ) ;
YQM(DR, 'CHICXENW')-1*YM(DR,'CHICKEHW');
YOM( DR, 'CHICKEHP')-1*YM(DR,'CHICKENP');
YOM(DR, 'OTHPOULT' )*1*YM(DR,'OTHPOULT' ) ;
PARAMETER EX(DR) TOTAL EXPENDITURE ON MEAT
/NNE 25.606
S 26.649
MW 27.938
W 28.963 /
QI(DR) QUANTITY INDEX
/ NNE .59412
S .7602
MW .82731
W .76248 /
P(DR) POPULATION
/ NNE 5.5650949E+07
S 7.6352485E+07
MW 5.9955417E+07
W 5.1790655E+07 /
PARAMETER
PA(DR) POPULATION ADJUSTMENT PARAMETER;
PA(DR)-P(DR)/(2.5);
DISPLAY PA;
PARAMETER
REX(DR) TOTAL REGIONAL EXPENDITURE;
REX(DR)-EX(DR)*PA(DR);
PARAMETER
RYOM(DR,U4) TOTAL REGIONAL CONSUMPTION OF EXOGENOUS MEATS
RYOM( DR, U4)-YOM ( DR, U4) *PA (DR ) ;
PARAMETER
ROM(DR,U3) OTHERMEAT CONSTANT;
ROM(DR,U3)-SUM(U4, CIJ(U3,U4,DR) *LOG(RYOM(DR,U4))) ;
DISPLAY ROM;
PARAMETER
DINTC(DR,U3) INTERCEPT ON DEMAND EQUATIONS;
DINTC('mw','roast')-ROM('mw','roast')—B('mw','roast')*QI( 'mw')
♦.8*A('mw','roast');
DINTC('mw','steak')-ROM('mw','steak')-B('mw','steak')*QI('mw')
+.85«A('mw','steak');
DINTC('mw','hmbrgr')-ROM('mw','hmbrgr')—B( 'mw','hmbrgr')*QI('mw')
♦.9*A('mw','hmbrgr');
DINTC( 'w', 'roaBt')=R0M( 'w', ' roast' )-B( 'w', 'roast') *QI( 'w')
♦.765*A('w','roast');
DINTC( 'w', 'steak' )»ROM( 'w', 'steak') —B( 'w' , 'steak') *QI( 'w')
♦.88*A('w','steak');
DINTC('w','hmbrgr')«RQM('w','hmbrgr')—B('w','hmbrgr')*QI('w')
t.92*A( 'w','hmbrgr');
DINTC('nne','roast')*ROM('nne','roast')—B('nne','roast')*QI('nne')
♦.94*A('nne','roast');
DINTC('nne','steak')>ROM('nne','steak')—B( 'nne','steak')*QI('nne')
•H.02*A( 'nne', 'steak');
DINTC('nne', 'hmbrgr' )>ROM( 'nne', 'hmbrgr' )-B( 'nne', 'hmbrgr' )*QI( 'nne'
♦.95*A('nne','hmbrgr');
DINTC('s','roast')«R0M('s','roast')-B('s','roast')*QI('s')
*.78*A('s','roast');
DINTC ('s', 'steak' )-ROM( 's', 'steak' )-B( ' s',' steak' ) *QI( ' s')
♦.87*A('s','steak');
DINTC('s','hmbrgr')-R0M('s','hmbrgr')-B('s','hmbrgr')»QI( 's')
+.87 *A('s','hmbrgr');
DISPLAY DINTC;
TABLE PEX(EXX,U3) PRICE POR BOXED CUTS IN FOREIGN MARKETS
HMBRGR ROAST STEAK
EXX1 260 360
EXX2
EXX3
EXX4
EXX5
TABLE RIC(DR,U3) AWAY FROM HOME CONSUMPTION (CWT)
HMBRGR
ROAST
STEAK
NNE
3.685E+06
1.5296E+06
1.7382E+06
S
4.6887E+06
1.7957E+06
3.4916E+06
MW
4.4801E+06
1.4934E+06
1.8864E+06
W
3.3253E + 06
1.0278E+06
1.6929B+06
Seject

* Iff Itlllttlttltlif If tf If tltltttlltttf ##i*tti#ttf ttlf ItlltitIHf If ttttl#
*##### THE TRANSPORTATION PARAMETERS (Includes shrinkage due ######
•Ilfft to transport, distances and cost per hd) ######
•flfftfffffffflffffffftflfffffffffffffftfffftfffffffffffftfffffffffffflf
TABLE SHR6 (SRR,SR) SHRINKAGE OF CALVES & NON-FED BEEF BETWEEN REGIONS (HD)
SE
MW
SW W
PL
SB
.964
.913
.928 .89
.908
MW
.913
.965
.922 .90
.943
SW
.928
.922
.959 .904
.932
w
.89
.90
.904 .945
.912
PL
.908
.943
.932 .912
.959
TABLE SHED (3RD, SR) SHRINKAGE DAIRY CULLS BETWEEN REGIONS (HD)
SB
MW
SW
W
PL
SB
.964
.913
.928
.89
.908
MW
.913
.965
.922
.90
.943
SW
.928
.922
.959
.904
.932
W
.89
.90
.904
.945
.912
PL
.908
.943
.932
.912
.959
NNE
TABLE SHR(SRR,SR,U9) SHRINKAGE OF FED BEEF TO SLAUGHTER (HD)
SB.(FB9,FB11*FB13) MW.(FB9,FB11*FB13) SW.(FB9,FB11*FBI3)
SB
.965
.928
.931
MW
.928
.964
.932
SW
.931
.932
.945
W
.90
.912
.926
PL
.926
.936
.934
♦ W.
,(FB9,FB11*FB13)
PL.(FB9,PB11
*FB13)
SE
.90
.926
MW
.912
.936
SW
.926
.934
W
.945
.928
PL
.928
.945
TABLE
DST (SRR, SR) 1
3EEF:
DISTANCE BETWEEN SUPPLY
REGIOl
SE
MW
SW
PL
W
SE
50
1090
986
MW
1090
50
830
425
SW
986
830
100
600
1352
PL
425
600
100
1150
W
1352
1150
100
TABLE DSTD(SRD,SR) DAIRY: DISTANCE BETWEEN SUPPLY REGIONS (MILES)
SE
MW
SW
PL
w
SE
50
1090
986
MW
1090
50
830
425
SW
986
830
100
600
1352
PL
425
600
100
1150
W
1352
1150
100
TABLE RATBC(U6,
SRR,SR)
TRANSPORT COSTS
BEEF
CALVES i
SE
MW
SW
W
PL
(CULL,CALF) .SE
.24
3.29
2.97
4.08
(CULL,CALF).MW
3.29
.36
2.37
1.31
(CULL, CALF ).SW
2.97
2.61
.44
4.26
1.86
(CULL,CALF).W
4.50
.54
3.84
(CULL,CALF) .PL
4.08
1.31
1.86
3.29
.50
PARAMETER TCC(SRR,SR,U6) ADJ. TRANS. COSTS CALVES & CULLS (DOL PER HD);
TCC(SRR,SR,U6)-1.21*RATEC(U6,SRR,SR)*DC(SRR,U6);
DISPLAY TCC;
TABLE RATES(U7,SRR,SR) TRANSPORT COSTS NON-FED BEEF (DOL PER CWT)
(NFB1,NFB1—5).SE
(NFB1 ,NFB1—5 ) .MW
(NFB1,NFB1—5).SW
(NFB1,NFB1-5).W
(NFB1,NFB1-5).PL
SE
MW
SW
W
PL
.24
3.29
2.97
4.08
3.29
.36
2.37
1.31
2.97
2.61
.44
4.26
1.86
4.50
.54
3.84
4.08
1.31
1.86
3.29
.50
,U7) ADJ.
TRANS
. COSTS
NON-FED
BEEF (DOL
,U7)*1.21
•RATES(U7,SRR,
SR)*DS(SRR,U7);
SR) TRANSPORT COSTS OF FED ANIMALS (DOL
SB
MW
SW
W
PL
.24
3.29
2.97
4.08
3.29
.36
2.37
1.31
2.97
2.61
.44
4.26
1.86
4.50
.54
3.84
4.08
1.31
1.86
3.29
.50
DISPLAY TS;
TABLE RATEF(U9,SRR,SR)
(FB9,FB11*FB13).SE
(FB9,FB11*FB13).MW
(FB9,FB11*FB13).SW
(FB9,FBU*FB13).W
(FB9,FB11*FB13).PL
PARAMETER TF(SRR, SR, U9) ADJ. TRANS. COSTS FED BEEF (DOL PER HD);
TF(SRR,SR,U9)“1.21*RATEF(U9,SRR,SR)*DAA(SRR,U9);

232
DISPLAY TF;
TABLE RATED(U5,SRD,SR)
TRANSPORT COSTS OF DAIRY CULLS (DOL PER CWT)
SE
MW
SW
W
PL
CULL.SE
.24
3.29
2.97
4.08
CULL.MW
3.29
.36
2.37
1.31
CULL.SW
2.97
2.61
.44
4.26
1.86
CULL.W
4.50
.54
3.84
CULL.PL
4.08
1.31
1.86
3.29
.50
PARAMETER TD(SRD,SR,U5) ADJ. TRANS. DAIRY CULLS (DOL PER HD);
TD(SRD,3R,U5)«1.21*RATED(U5,SRD,SR)*DARYWT(SRD,U5);
DISPLAY TD;
TABLE SHRDD(SR,DR) SHRINKAGE FINAL PRODUCTS BETWEEN REGIONS (HD)
NNE
MW
S
w
SB
.996
.996
MW
.996
.996
.996
SW
.996
.996
.996
.996
W
.996
.996
.996
PL
.996
.996
.996
.996
TABLE
DD(DR,SR)
DI8TAHCB
BETWEEN SUPPLY AND
DEMAND REGIONS
SB
MW
SW
PL
W
NNB
1007
1300
1795
1646
S
307
975
553
1342
2224
MW
446
1134
871
W
1289
1210
865
364
PARAMETER T3(DR,SR,U3) TRANSPORT COST BOXED BF TO DMAND REGIONS (CWT);
T3(DR,SR,U3) $DD(DR,8R)-0.7589+.00258*DD(DR,SR)-(3.35E-07)*SQR(DD(DR,SR));
DISPLAY T3;
TABLE TFI(DR, IM,U3) TRANSPORT COST; IMPORTS (DOLLARS PER CWT)
IMPORTS. HMBRGR
NNB
S 90.2
MW
W 90.2
TABLE MRGI(DR,IM,U3) MARKETING MARGIN IMPORTS (DOLLARS PER CWT)
HMBRGR ROAST STEAK
NNE. IMPORTS
S. IMPORTS 60
MW. IMPORTS
W. IMPORTS 60
TABLE T2(SR,EXX,U3) TRANSPORT COST BOXED CUTS TO FOREIGN MARKETS (CWT)
(EXX1*EXX5) .HMBRGR (EXX1*EXX5 ).(ROAST, STEAK)
SE
MW
SW
W
PL
*»«#*«»ffttH*t END OF TRANSPORT SECTION ttf«Iflttft#**fII#tt*##*ll«
* #l#titt##t#tf ttIMitif Miff f f Iff f Mi##f If tittttllfif tttttlffttf f t##4##Mif #
'tlfltflttltt#* WEIGHT ADJUSTMENT SECTION IlfIfftttfttt*«*tt#f«ft***#
$offmargin ontext
The section below calculates the adjustment to production costs In order to
account for dlfferrences In the starting weights of live animals In a production
activity In a region due to differences In weights between regions of origin.
For example, at the cow-calf stage weaned calves In the midwest region weigh 465
lbs.
while weaned calves in the southeast only weigh 435 lb. The budget for producing
a 900 lb fed animal in the midwest is based on a starting weight for weaned calves
of 465 lbs. If a weaned calf from the southeast is shipped to the midwest for
finishing then the cost of producing a 900 lb slaughter animal has to be adjusted
upwards to account for the increased lenght of time the southeast calf needs to
be
fed to reach market weight. The adjustment In production costs are calculated by
determining the cost of gain in the midwest for bring a weaned calf up to 900 lbs.
Then the difference between the weights of weaned calves in the southeast and the
midwest is multiplied by this rate of gain to determine the cost of bring the calf
from the southeast up to the starting weight of midwest calves. The adjustment
cost
is divided by the weight of the 900 fed animal to put it into a per head
adjustment.
The adjustment cost is then added onto the cost of transporting weaned calves
from thesoutheast to the midwest.
Jofftext
PARAMETER CLFWT(SR) WEIGHT OF WEANED CALF IN SUPPLY REGIONS;
CLFWT(SR)=DC(SR, 'CALF' ) ;
PARAMETER WTDC(SR,SRR,U6) D IFF. IN WGHTS OF CALVES £ CULLS BETWEEN REG. (CWT);
WTDC('SE', 'SE',U6)=DC( 'SE',U6)-DC( 'SE',U6);
WTDC( 'SE' , 'MW',U6)-DC( 'MW',U6)-DC( 'SE',U6);

WTDC( 'SE' , 'SW' ,U6)-DC( 'SW' ,U6)-DC( 'SE' ,U6);
WTDC( 'SE', 'W',U6)-DC( 'W' ,U6)-DC( 'SB' ,U6);
WTDC('SE', 'PL',U6)-DC( 'PL',U6)-DC( 'SB' ,U6);
WTDC( 'MW' , 'SE' ,U6)-DC( 'SE' ,U6)-DC( 'MW' ,U6) ;
WTDC( 'MW', 'MW' ,U6)-DC( 'MW' ,U6)-DC( 'MW' ,U6) ;
WTDC('MW','SW',U6)-DC( 'SW' ,U6)-DC< 'MW' ,U6);
WTDC( 'MW', 'W' ,U6)-DC( 'W' ,U6)-DC( 'MW' ,U6) ;
WTDC( 'MW', 'PL' ,U6)«DC( 'PL' ,U6)-DC( 'MW' ,U6);
WTDC( 'SW', 'SB' ,U6)-DC( 'SE' ,U6)-DC( 'SW' ,U6);
WTDC('SW','MW',U6)-DC('MW',06)-DC('SW',U6);
WTDC( 'SW' , 'SW' ,U6)-DC( 'SW' ,U6)-DC( 'SW' ,U6) ;
WTDC( 'SW', 'W' ,U6)-DC( 'W' ,U6)-DC( 'SW' ,U6);
WTDC('SW', 'PL',U6)-DC( 'PL',U6)-DC( 'SW' ,U6);
WTDC('W', 'SB',U6)«DC< 'SB',U6)-DC( 'W' ,U6);
WTDC{ 'W', 'MW',U6)-DC( 'MW',U6)-DC( 'W' ,U6);
WTDC( 'W', 'SW' ,U6)-DC( 'SW',U6)—DC( 'W' ,U6);
WTDC( 'W', ’W',U6)-DC( 'W',U6)-DC( 'W',U6);
WTDC( 'W', 'PL',U6)-DC( 'PL',U6)-DC( 'W',U6);
WTDC( 'PL', 'SB' ,U6)«DC( 'SE',U6)-DC( 'PL' ,U6);
WTDC( 'PL', 'MW' ,U6)-DC{ 'MW' ,U6)-DC( 'PL' ,U6);
WTDC('PL', 'SW',U6)-DC( 'SW' ,U6)-DC( 'PL' ,U6);
WTDC( 'PL', 'W',U6)-DC( 'W',U6)-DC( 'PL' ,U6);
WTDC( 'PL','PL',U6)«DC< 'PL' ,U6)-DC( 'PL' ,U6);
display vrtdc;
*»***««* COW-CALF TO STOCKER STAGE IXIilllltltlll
PARAMETER WT67(SR) WEIGHT GAINED FROM CALF TO NFB1 (CWT);
WT67 (SR)”DS(SR, 'NFB1' )-DC(SR, 'CALF');
DISPLAY WT67;
PARAMETER G7(SR) COST OF GAIN AT STOCKER STAGE (DOL PER CWT);
G7(SR)-R7(SR, 'NFB1' ) /WT67 ( SR) ;
DISPLAY G7;
PARAMETER ADJ(SR,SRR) COST OF AJUSTMENT (DOL PER HD);
ADJ(SR,SRR)«WTDC(SR,SRR, 'CALF')»G7(SRR);
display adj;
*»ff»«»f COW-CALF TO FINISH STAGE «#«*#*#*##*«**#
PARAMETER WT68(SR) WBIGHT GAINED FROM CALF TO FINISHING (CWT);
WT68(SR)-DAA(SR, 'FB9') -CLFWT(SR) ;
DISPLAY WT68;
PARAMETER G68(SR) COST OF CALF GAIN AT FINISHING STAGE (DOL PER CWT);
G68(SR)-R8(SR,'FB9')/WT68(SR) ;
DISPLAY G68;
PARAMETER ADJCF( SR, SRR) COST OF AJUSTMENT CALF TO FEEDLOT (DOL PER HD);
ADJCF(SR,SRR)*VTTDC(SR,SRR, 'CALF') *G68( SRR) ;
DISPLAY ADJCF;
*t***f#« STOCKER TO FINISH STAGE **«lftt*f#**««*
PARAMETER NFBWT(SR,U7) WEIGHT OF NFB IN SUPPLY REGIONS;
NFBWT (SR, U7)-DS (SR, U7 ) ;
PARAMETER WTDS( SR,SRR,U7) DIFFERENCES IN WGHTS OF NFB BETWEEN REGIONS (CWT)
WTDS( 'SE', 'SE' ,U7)-DS( 'SE' ,U7)-DS( 'SB' ,U7);
WTDS( 'SE', 'MW',U7)-DS( 'MW' ,U7)-DS( 'SE' ,U7);
WTDS( 'SE', 'SW',U7)-DS( 'SW' ,U7)-DS( 'SE' ,U7);
WTDS ( 'SE','W',U7)=DS( 'W' ,U7 ) -DS( 'SE', U7) ;
WTDS('SE', 'PL',U7)-DS( 'PL' ,U7)-DS( 'SE' ,U7);
WTDS( 'MW' , 'SE' ,U7)»DS( 'SE' ,U7)-DS( 'MW' ,U7);
WTDS( 'MW', 'MW' ,U7)-=DS( 'MW' ,U7)-DS( 'MW' ,U7);
WTDS( 'MW', 'SW',U7) =DS( 'SW' ,U7)-DS( 'MW' ,U7);
WTDS( 'MW', 'W' ,U7)=DS( 'W' ,U7) -DS( 'MW' ,U7 ) ;
WTDS( 'MW', 'PL',U7)-DS( 'PL',U7)-DS( 'MW' ,U7);
WTDS( 'SW', 'SB',U7)«DS( 'SE' ,U7)-DS( 'SW',U7);
WTDS( 'SW', 'MW' ,U7)=DS( 'MW' ,U7)-DS( 'SW' ,U7);
WTDS( 'SW', 'SW' ,U7)-DS( 'SW' ,U7)-DS( 'SW',U7);
WTDS('SW', 'W',U7)»DS('W',U7)-DS('SW',U7);
WTDS( 'SW','PL',U7)=DS( 'PL',U7)-DS( 'SW',U7);
WTDS ( 'W', ' SE ' ,U7 ) *DS ( 'SE',U7)-DS( 'W' ,U7);
WTDS('W', 'MW',U7)=DS( 'MW',U7)-DS( 'W' ,U7);
WTDS( 'W', 'SW' ,U7)-DS( 'SW' ,U7)-DS( 'W' ,U7);
WTDS( 'W', 'W',U7)*DS( 'W' ,U7)-DS( 'W' ,U7);
WTDS( 'W','PL',U7)=DS('PL',U7)-DS('W',U7);
WTDS( 'PL', 'SE' ,U7)=DS( 'SE' ,U7)-DS( 'PL' ,U7);
WTDS('PL', 'MW' ,U7)=DS( 'MW' ,U7)-DS( 'PL' ,U7);
WTDS( 'PL', 'SW' ,U7)-DS( 'SW' ,U7)-DS( 'PL' ,U7);
WTDS('PL', 'W',U7) =DS( 'W' ,U7)-DS( 'PL' ,U7);
WTDS( 'PL', 'PL' ,U7)=DS( 'PL' ,U7)-DS( 'PL' ,U7);
DISPLAY WTDS;
PARAMETER WT78(SR,U7) WEIGHT GAINED FROM STOCKER TO FINISHING (CWT);
WT78(SR, 'NFB1' )-DAA(SR, 'FB9' ) -DS(SR, 'NFB 1' ) ;

WT78(SR,'NFB1-5')-DAA(3R,'FB11')-DS(SR,'NFB1-5');
DISPLAY WT78;
PARAMETER G78(SR,U7) COST OF GAIN AT FINISHING STAGE (DOL PER CWT);
G78(SR,'NFB1')-R8(SR,'NFB1-FB9')/WT78(SR,'NFB1');
G78(SR, 'NFB1-5' )-R8(SR, 'NFB2-FB11' ) /WT78(SR, 'NFB1-5') ;
DISPLAY G78;
PARAMETER ADJSF(SR,SRR,U7) COST OF AJUSTMENT (DOL PER HD);
ADJSF (SR, SRR, U7) -WTDS (SR, SRR,U7 ) *G78 (SRR, U7) ;
DISPLAY ADJSF;
*********************** NFB S FB TO SLAUGHTER tf****************************
PARAMETER WTDFB(8R,SRR,U9) DIFF. IN WGHTS OF FED SLGHTR ANIMALS BETWEEN REG.;
WTDFB( 'SB', 'SE',U9)-DAA( 'SB',U9)-DAA( 'SB',U9);
WTDFB('SE', 'MW',U9)-DAA( 'MW' ,U9)-DAA( 'SE' ,U9);
WTDFB( 'SB', 'SW' ,U9)-DAA( 'SW' ,U9)-DAA( 'SE' ,U9);
WTDFB('SE','W',U9)-DAA('W',U9)-DAA('SE',U9);
WTDFB('SE', 'PL',U9)-DAA('PL',U9)-DAA('SE',U9);
WTDFB( 'MW', 'SE' ,U9)-DAA( 'SE' ,U9)-DAA( 'MW' ,U9) ;
WTDFB( 'MW' , 'MW' ,U9)-DAA( 'MW' ,U9)-DAA< 'MW' ,U9);
WTDFB('MW','SW',U9)-DAA('SW',U9)-DAA('MW',U9) ;
WTDFB( 'MW', 'W',U9)-DAA( 'W' ,U9)-DAA< 'MW' ,U9);
WTDFB( 'MW','PL',U9)-DAA('PL',U9)-DAA( 'MW',U9);
WTDFB( 'SW', 'SE',U9)-DAA('SB',U9)-DAA('SW',U9);
WTDFB('SW','MW',U9)-DAA<'MW',U9)-DAA('SW',U9);
WTDFB( 'SW', 'SW',U9)-DAA('SW',U9)-DAA( 'SW',U9);
WTDFB( 'SW' , 'W' ,U9)-DAA< 'W' ,U9)-DAA( 'SW',U9);
WTDFB('SW','PL',U9)-DAA('PL',U9)-DAA('SW',U9);
WTDFB('W', 'SE',U9)-DAA( 'SE' ,U9)-DAA( 'W' ,U9);
WTDFB('W','MW',U9)-DAA('MW',U9)-DAA('W',U9) ;
WTDFB( 'W', 'SW' ,U9)-DAA< 'SW',U9)-DAA( 'W' ,U9);
WTDFB('W','W',U9)-DAA('W',U9)-DAA('W',U9);
WTDFB('W','PL',U9)-DAA('PL',U9)-DAA<'W',U9);
WTDFB('PL','SE',U9)-DAA('SE',U9)-DAA('PL',U9);
WTDFB ( 'PL','MW',U9)-DAA( 'MW',U9)-DAA('PL ' , U9) ;
WTDFB ( 'PL', 'SW' ,U9)-DAA( 'SW',U9)-DAA( 'PL',U9);
WTDFB{'PL','W',U9)-DAA('W',U9)-DAA('PL',U9);
WTDFB('PL','PL',U9)-DAA('PL',U9)-DAA('PL',U9);
DISPLAY WTDFB;
PARAMETER ADJSLF( SR,SRR,L, U9) COST OF AJUSTMENT (DOL PER HD);
ADJSLF(SR,SRR,L,U9)-(WTDFB(SR,SRR,U9)/DAA(SRR,U9) )«R1(SRR,L);
DISPLAY ADJSLF;
PARAMETER ADJSLS(SR,SRR,L,U7) COST ADJUSTMENT NFB TO SLAUGHTER (DOL PER HD) ;
ADJSLS (SR, SRR, L , U7 ) “WTDS ( SR, SRR, U7 )/DS (SRR, U7 ) *R1 ( SRR, L) ;
DISPLAY ADJSLS;
PARAMETER ADJSLC ( SR, SRR, L, U6) COST OF ADJUSTMENT CULL TO SLAUGHTER (D PER HD);
ADJSLC ( SR, SRR, L, ' CULL' ) =WTDC( SR, SRR, ' CULL' ) /DC ( SRR, 'CULL' )*R1(SRR,L);
DISPLAY ADJSLC;
*##111111#### DAIRY CULL ADJUSTMENT <#*#t((***tt*t*f*##«*ttf******
PARAMETER WTDD(SRD,SR,U5) DIFF. IN WGHTS OF DAIRY CULLS BETWEEN REG.;
WTDD( 'SE' , ' SB ' ,U5 ) *»DARYWT( ’ SE ' , U5 ) -DARYWT( 'SE' ,U5);
WTDD('SE','MW',U5)»DAHYWT( 'MW', U5 )-DARYWT( 'SE',U5);
WTDD ( ' SE ' , ' SW' , U5 )-DARYWT( ' SW ' , U5 )-DARYWT ( ' SE ' , U5 ) ;
WTDD( 'SE' , 'W',U5)-DARYWT( 'W' ,U5)-DARYWT( 'SE' ,U5);
WTDD( 'SE', 'PL',U5)=DARYWT( 'PL', U5 )-DARYWT ( 'SB' ,U5);
WTDD( 'MW', 'SE',U5)-DARYWT('SE',U5)-DARYWT( 'MW' ,U5);
WTDD( 'MW' , 'MW' ,U5)-DARYWT( 'MW' ,U5)-DARYWT( 'MW' ,U5) ;
WTDD( 'MW', 'SW' , U5 ) -DARYWT ( 'SW',U5)-DARYWT ( 'MW' ,U5);
WTDD( 'MW' , 'W' , U5 ) —DARYWT ( ' W ' , U5 ) -DARYWT ( 'MW' ,U5) ;
WTDD( 'MW','PL',U5)-DARYWT( 'PL ' ,U5 )-DARYWT ( 'MW',U5);
WTDD( 'SW', 'SE' ,U5)-DARYWT( 'SE ' ,U5 )-DARYWT ( 'SW' ,U5);
WTDD( 'SW' , 'MW' , U5 )—DARYWT ( 'MW' ,U5)-DARYWT( 'SW',U5);
WTDD( 'SW', ' SW',U5)-DARYWT ( 'SW', U5 )-DARYWT ( 'SW' ,U5);
WTDD( 'SW' , 'W',U5 )-DARYWT( 'W' ,U5)-DARYWT( 'SW' ,U5) ;
WTDD( 'SW', ' PL', U5 )-DARYWT ('PL',U5)-DARYWT ( 'SW',U5);
WTDD( 'W' , 'SE' ,U5 )-DARYWT( 'SE' ,U5)-DARYWT( 'W' ,U5) ;
WTDD( 'W' , 'MW' ,U5 )-DARYWT( 'MW' , U5 ) -DARYWT( 'W' ,U5) ;
WTDD( 'W' , 'SW' , U5 ) -DARYWT ( 'SW' , U5 ) -DARYWT ( 'W' ,U5) ;
WTDD( 'W' , 'W' ,U5)-DARYWT( 'W' ,U5)-DARYWT( 'W' ,U5) ;
WTDD('W', 'PL' ,U5)-DARYWT('PL' ,U5)-DARYWT( 'W' ,U5);
WTDD('PL','SE',U5)-DARYWT('SE',U5)-DARYWT('PL',U5);
WTDD ( 'PL' , 'MW' , U5 ) -DARYWT ( 'MW' , U5 ) -DARYWT ( 'PL' ,U5);
WTDD( 'PL' , 'SW' ,U5)-DARYWT( 'SW' ,U5)-DARYWT( 'PL' ,U5);
WTDD( 'PL', 'W' ,U5)=DARYWT( 'W', U5 )-DARYWT( 'PL' ,U5 ) ;
WTDD( 'PL', ' PL',U5)-DARYWT ('PL',U5)-DARYWT ('PL' ,U5);
DISPLAY WTDD;
PARAMETER ADJSLD(SRD,SR,L,U5) COST OF ADJ. DAIRY CULL TO SLAUGHTER (D PER HD);
ADJSLD(SRD,SR,L, 'CULL' )-WTDD(3RD ,SR, 'CULL' ) /DARYWT(SRD, 'CULL' ) *R1 (SR,L)
$DSTD(SRD,SR);

DISPLAY ADJSLD
* ###litt#f#fflt#t#f>#t#lf#tfftf#fl*#fifi#fil#f##i##if##titf#t##t####t
*1flit parameters used to calculate starting values
Table bfcnamptn(dr,u3) MONTHLY HOUSEHOLD CONSUMPTION (lbs.)
HMBRGR
ROAST
STEAK
NNE
4.204
1.738
1.988
S
3.890
1.513
2.89
MW
4.65
1.53
1.999
W
4.022
1.266
2.069
PARAMETER BEEF(DR,U3) regional consumption of beef (cwt.);
BEEF(DR,U3)-PA(dr)*bfcnsmptn(dr,u3);
DISPLAY BEEF;
TABLE PRICE)DR,U3) Retail Price of Beef (DOLLARS PER LB.)
hmbrgr
roast
steak
nne
1.614
2.344
3.541
s
1.724
2.414
2.343
raw
1.605
2.264
2.689
w
1.733
2.546
3.196
DISPLAY PRICE;
•»tt«*«*l**f END OF DATA SECTION tf*«fIffl##fIfIf# Soffmargln ontext
*#########################################################################
*ff##lffftff Display of Combined Parameters #«ttt#t##1111(4*###
parameter ppn(sr) NO. OF PLANTS IN EACH REGION
/
SE
MW
SW
W
PL
parameter check)sr,dr,u3,kl) cost of supplying regions;
check(sr,dr,'roast',kl) $dd(dr,sr) » t3(dr,sr,'roast')
♦(sum(l,rl(sr,l))/ppn(sr))
•CUTOUT('roast',X1)/D2(SR,'roast',K1);
check)sr,dr,'steak',kl) $dd(dr,sr) - t3(dr,sr,'steak')
♦(sum(1,rl(sr,1))/ppn(sr))
•CUTOUT('steak',K1)/D2(SR,'steak',XI);
display check;
parameter costfsl(sr,srr,l,u9) cost of slghtmg fed beef by region of origin;
costfsi(sr,srr,1,u9) $dsr1(sr,srr,1)«
tf(sr,srr,u9)+adjslf(sr,arr,1,u9)+rl(srr,1);
display costfsl;
parameter costffl(sr,srr,u8,k8) cost of finishing fed beef by region of origin
costffl(sr,srr,'calf','fb9') Sdst(sr,srr)-
tcc(sr,srr,'calf')+adjcf(sr,srr)♦r8(srr,'fb9');
display costffl;
parameter cststck(sr,srr,u6,k7) cost of finishing fed beef by region of origin
cststck(Br,srr,'calf','nfbl') $dst(sr,srr)»
tcc(sr,srr,'calf')+adj(sr,srr)+r7(srr,'nfbl');
display cststck;
Sofftaxt
parameter tcl(sr) total cost of producing non-fed beef 1200 (per head);
tcl(sr)-r6(sr,'calf')+r7(sr,'nfbl')*r8(sr,'fbl2')+rl(ar,'pll');
parameter tc2(sr) total cost of producing non-fed beef 900 (per head);
tc2(sr)~r6(sr,'calf')+r7(sr,'nfbl')+r8(sr,'nfbl-fb9')trl(sr,'pll');
parameter tc5(sr) total coBt of producing non-fed beef 1100 (per head);
tc5(sr)-r6(sr,'calf')+r7(sr,'nfbl-5')+r8(sr,'nfb2-fbll')+rl(sr,'pll')
parameter tc3(sr) total cost of producing fed beef 1100 (per head);
tc3(sr)-r6(sr,'calf')+rB(sr,'fbll')+rl(sr,'pll');
parameter tc4(sr) total cost of producing fed beef 900 (per head);
tc4(sr)»r6(sr,'calf')+r8(sr,'fb9')+rl(sr,'pll');
parameter
parameter
parameter
parameter
parameter
tcwl(sr)
tcwlj sr )<
tew2(sr)
tcw2(sr)!
tcw5(sr)
tcw5 (sr):
tcw3(sr)
tew 3(sr) i
tcw4(Br)
tcw4(sr)'
total
'teller
total
'tc2(sr
total
â– tc5(sr
total
'tc3 (sr
total
â– tc4(sr
cost of
)/dl(sr,‘
cost of
)/dl(sr,'
cost of
)/dl(sr,
cost of
)/dl(sr,'
cost of
)/dl(sr.
producing
fbl2');
producing
fb9');
producing
fbll');
producing
fbll');
producing
fb9');
non-fed beef 1200 (per cwt);
non-fed beef 900 (per cwt);
non-fed beef 1100 (per cwt);
fed beef 1100 (per cwt);
fed beef 900 (per cwt);
display tel;
display tc2;
display tc3;
display tc4;
display tcwl;
display tcw2;
display tcw3;
display tcw4;

236
POSITIVE VARIABLES
* TRANSPORTATION
XX ( SRR,SR,U6) CALVES SHIPPED TO STOCKER (HD)
XXC(SRR,SR,U6) CALVES SHIPPED TO FEEDLOT (HD)
XXS(SRR,SR,U7) STOCKERS SHIPPED TO FEEDLOT (HD)
XXXC(SRR,SR,L,U6) BEEF CULLS SHIPPED TO SLAUGHTER( HD)
XXXS(SRR,SR,L,U7) NOH-FED SHIPPED TO SLAUGHTER (HD)
XXXF(SRR,SR,L,U9) FINISHED ANIMALS SHIPPED (HD)
XXXD(SRD,SR,L,U6) DAIRY CULLS SHIPPED (HD)
XF(IM,DR,U3) QUANTITY OF FOREIGN HAMBURGER SHIPPED (CViT)
X2(SR,EXX,U3) QUANTITY OF BOXED BEEF SHIPPED OVERSEAS (CWT)
X(SR,DR,U3) QUANTITY OF FINAL PRODUCT SHIPPED (CWT)
PRODUCTION PROCESSES
Q6 (SR, K6 ) QUANTITY OF LIVE ANIMALS SUPPLIED
Q7(SR, K7) HEAD STOCKERED
Q8(SR,K8) HEAD FINISHED
Q1(SR,L,K1) HEAD SLAUGHTERED
Q1A(SR,L) HEAD OF CATTLE SLAUGHTERED IN PLANT L
Q2(SR/K2) LEVEL OF FABRICATION PROCESS UTILIZED
Q3(SR,L,U2) LEVEL OF HAMBURGER PROCESS USED (CWT)
(HD)
PRODUCTS USED AND
ZD ( SRD , U 5)
Z5(SR,K6)
Z6(SR,U6)
Z77(SR,U6)
Z7(SR,U7)
Z8FL ( SR, U8 )
Z8(SR,U9)
ZO(SR,L,UO)
Z1(SR,L,U2,K1)
ZLH(SR,L,U2)
Z1R(SR,L,U2)
Z(SR,U3)
Y(DR,U3)
AHY(DR,U3)
BFEXPRT(EXX,U3)
PRODUCED
DAIRY CULLS SUPPLIED TO SLAUGHTER (HD)
BREEDING STOCK AVAILABLE (HD)
WEANED CALVES AND CULLS PRODUCED (HD)
WEANED ANIMALS STOCKERED (HD)
STOCKERED ANIMALS PRODUCED BY PRODUCTION ACTIVITY (HD)
CATTLE USED IN THE FEEDLOT (HD)
FED ANIMALS PRODUCED BY PRODUCTION ACTIVITY (HD)
ANIMALS SUPPLIED USED IN SLAUGHTER (HD)
QUANTITY OF FAB CUTS PRODUCED (CWT).
PRIMAL CUTS USED FOR HAMBURGER (CWT)
PRIMAL CUTS ALLOCATED TO RETAIL (CWT)
QUANT PROCESSED MEAT PRODUCED
MONTHLY HOUSEHOLD CONSUMPTION OF BEEF (LBS)
ANNUAL AWAY FROM HOME CONSUMPTION (CWT)
FOREIGN CONSUMPTION OF BEEF (CWT)
FREE VARIABLES
NSB NET SOCIAL BENEFIT (VALUE OF LINE INTERGRAL)
NSR NET SOCIAL REVENUE (VALUE OF LP OBJECTIVE FUNCTION);
EQUATIONS
*lfl DAIRYCULLS ( SRD )
DAIRYTRANS {SRD )
BRDNGSTCX(SR,K6)
LIVESPPLY(SR,U6)
TRANCULL6 (SR)
TRANCALF6 (SR)
CCTOSTK(SRR)
CCUSEDSTK(SR)
PLACESTCKfSR,U7)
TRANSFER71 (SR )
TRANSFER72 ( SR)
CCSTCK1(SRR)
CCSTCK2 ( SRR)
CCSTCK3 ( SRR )
LVANUSEFL(SR,U8)
FINISHFL(SR,U9)
DEFEINITIONS *««««*«I«»««««»«««tfIt####I#########
DAIRY CULLS SUPPLY CONSTRAINT
DAIRY CULL SHIPMENTS TO SLAUGHTER
AVAIALBILTY OF BREEDING STOCK
PRODUCTION OF CULLS £CALVES
CULL SHIPMENTS TO OTHER STAGE
WEANED CALF SHIPMENTS TO OTHER STAGE
WEANED CALVES SHIPPED IN TO STOCKER STAGE
WEANED CALVBS UTILIED IN STOCKER STAGE
PRODUCTION OF STOCKERS
YEARLING SHIPMENTS TO FEEDLOT £ SLAUGHTER
LONG YEARLING SHIPMENTS TO FEEDLOT £ SLAUGHTER
CALVES SHIPMENTS INTO FINISHING STAGE
YEARLING SHIPMENTS INTO FINISHING STAGE
LONG YEARLING SHIPMENTS INTO FINISHING STAGE
LIVE ANIMALS UTILIZATION IN FINISHING STAGE
FED BEEF PRODUCTION
TRANSFERS (SR, U9)
TOSLGHT1(SRR,L)
TOSLGHT2(SRR,L)
TOSLGHT3(SRR,L)
TOSLGHT4(SRR,L)
T0SLGHT5 (SRR, L)
TOSLGHT6(SRR,L)
TOSLGHT7 (SRR, L)
SHIPMENTS OF FED BEFF TO SLAUGHTER
FED SHIPMENTS INTO THE SLAUGHTER STAGE (900)
FED SHIPMENTS INTO THE SLAUGHTER STAGE (1100)
FED SHIPMENTS INTO THE SLAUGHTER STAGE (1200)
FED SHIPMENTS INTO THE SLAUGHTER STAGE (1300)
NON-FED SHIPMENTS INTO THE SLAUGHTER STAGE (YEARLING)
NON-FED SHIPMENTS INTO THE SLAUGHTER STAGE (1.5 YEARS)
CULL SHIPMENTS INTO THE SLAUGHTER STAGE
*####!### SLAUGHTER DEFINITIONS
INTERMED1(SR,L,U0)
FABRICAT (SR, L, U2, K1)
PLNTAGG ( SR, L )
PLCPCTY ( SR, L)
ALLOCFAB (SR, L , U2 )
RSTRTL (SR)
STXRTL(SR)
INTERMED 3 (SR , L , U2 )
HAMBURGER (SR)
FATMINM( SR,L)
FATMAXM (SR, L )
SLAUGHTER:
SLAUGHTER:
CAPACITY:
CAPACITY:
TRANSFER:
TRANSFER:
TRANSFER:
PROCESSING
PROCESSING
PROCESSING
PROCESSING
LIVE ANIMAL USAGE
PRIMAL CUTS PRODUCED
HEAD CATTLE SLAUGHTERED IN PLANT L
CAPACITY PLANT L
ALLOCATION OF CUTS TO HB AND RETAIL
AGGREGATION OF ROAST TO REGION SALE
AGGREGATION OF STEAK TO REGION SALE
USE OF PRIMAL CUTS TO MAKE HB
MAKING HAMBURGER
MINIMUM FAT CONTENT HAMBURGER
MAXIMUM FAT CONTENT HAMBURGER

SALE ( SR, U3 )
EXTRNSPRT(EXX,U3)
IMTRNSPRT(IM,U3)
CNSMPTH(DRrU3)
AHCNSMPTN(DR,U3)
WLFR1
TRANSFER: SALE OF TABLE CUTS £ HAMBURGER
TRANSPORTATION: FOREIGN BEEF EXPORT BALANCE
TRANSPORTATION: FOREIGN BEEF IMPORT BALANCE
PURCHASE OF RETAIL CUTS BY CONSUMERS
AWAY FROM HOME CONSUMPTION RESTRICTION
NET SOCIAL WELFARE;
•DAIRY
DAIRYCULLS(SRD). . -DAIRY(SRDCULL') +ZD(SRD, 'CULL' )-L-0;
DAIHYTRANS(SRD).. -ZD (SRD, 'CULL')
♦ 8UM( (SR,L)SDSRLD(SRD,SR,L) , XXXD(SRD,SR,L, 'CULL' ) )
-L-0;
•COW-CALF
BRDNGSTCK(SR,K6).. -Z5(SR,K6) ♦ C6(SR,K6)*Q6(SR,K6)
-L-0;
LIVESPPLY(SR,U6)■• Z6(SR,U6)-SUM(K6, D6(SR,U6,K6)*Q6(SR,K6))
-B-0;
TRANCULL6(SR).. -Z6(SR,'CULL')
♦ SUM( (SRR, L) $DSRL ( SR, SRR , L ) , XXXC(SR,SRR,L, 'CULL'))
-L-0;
TRANCALF6(SR).. -Z6(SR,'CALF')
♦8UM(SRR SDST (SR, SRR) , XX( SR, SRR, ' CALF ' ) )
♦ SUMfSRR $DST (SR, SRR) , XXC(SR,SRR,'CALF') )
-L-0;
•STOCKER
CCTOSTK(SRR) .. -3UM(SR $DST( SR, SRR) , SHR6( SR,SRR) *XX( SR,SRR, ' CALF' ) )
+ Z77(SRR,'CALF')
-L-0;
CCUSEDSTK(SR)..
-Z77(SR, 'CALF' )+SUM(K7, C7(SR, 'CALF' ,X7) *Q7 (SR,K7))
-B-0;
PLACESTCX(SR,U7)
TRANSFER71(SR).•
TRANSFER72(SR)..
•FEEDLOT
CCSTCK1 (SRR) • .
CCSTCK2(SRR)..
CCSTCK3 (SRR) . •
Z7(SR,U7)-SUM(K7, D7(SR,U7,K7)*Q7(SR,K7))
-B-0;
-Z7(SR,'NFB1')
+SUM(SRR SDST(SR,SRR) , XXS(SR,SRR, 'NFB1' ) )
♦SUM((SRR,L) SDSRL(SR,SRR,L), XXXS(SR,SRR,L,'NFB1'))
-L-0;
-Z7(SR,'NFB1-5')
♦ SUMfSRR SDST( SR, SRR) , XXS (SR, SRR, ' NFB1-5 ' ) )
♦SUM((SRR,L) SDSRL(SR,SRR,L), XXXS(SR,SRR,L,'NFB1-5'))
-L-0;
-SUM(SR SDST( SR, SRR) , SHR6 (SR, SRR) «XXC( SR, SRR, ' CALF' ) )
+Z8FL(SRR,'CALF')
-L-0;
-SUM(SR SDST(SR,SRR), SHR6(SR,SRR)• XXS(SR,SRR,'NFB1'))
♦Z8FL(SRR,'NFB1')
-L-0;
-SUM(SR SDST(SR,SRR) , SHR6(SR,SRR) * XXS(SR,SRR,'NFB1-5 ' ) )
+Z8FL(SRR,'NFB1-5')
-L-0;
LVANUSEFL(SR,U8)..
FINISHFL(SR,U9).•
TRANSFER8(SR,U9)..
-Z8FL(SR,U8)+SUM(K8, C8(SR,U8,K8)*Q8(SR,K8))
-B-0;
-SUM(K8, D8(SR,U9,K8)*Q8(SR,K8))
♦Z8(SR,U9)
-B-0;
-Z8(SR,U9)
+SUM((SRR,L) SDSRL(SR,SRR,L), XXXF(SR,SRR,L,U9))
-L-0;
•SLAUGHTER-PROCESSING
TOSLGHT1(SRR,L) $SRL(SRR,L)..
-SUM(SR SDSRL(SR,SRR,L), SHR(SR,SRR,'FB9')*XXXF(SR,SRR,L,'FB9'))
+Z0(SRR,L,'FB9')
-L-0;
TOSLGBT2(SRR,L) SSRL(SRR,L)..
-SUM( SR SDSRL(SR,SRR,L), SHR( SR, SRR, 'FB11' ) *XXXF( SR, SRR,L, 'FB11' ) )
♦ZO(SRR,L,'FB11')
-L-0;
TOSLGHT3(SRR,L) $SRL(SRR,L)..
-SUM(SR SDSRL(SR,SRR,L),
+Z0(SRR,L,'FB12')
-L-0;
TOSLGHT4(SRR,L) $SRL(SRR,L)..
SHR( SR, SRR, 'FB12 ' ) *XXXF( SR, SRR,L, 'FB12' ) )

238
-SUM(SR $DSRL(SR,SRR,L), SHR(SR,SRR,'FB13') *XXXF(SR,SRR,L, 'FB13 ' ) )
+Z0(SRR,L,'FB13')
-L-0;
TOSLGHT5(SRR,L) $SRL(SRR,L)..
-SUM(SR $DSRL(SR,SRR,L), SHR6(SR,SRR) *XXXS(SR,SRR,L, 'NFB1' ))
♦Z0(SRR,L,'NFB1')
-L-0;
T0SLGHT6(SRR,L) SSR1(SRR,L)..
-SUM(SR $DSRL(SR,SRR,L), SHR6(SR,SRR) *XXXS(SR,SRR,L, 'NPB1-5 ' ) )
+Z0(SRR,L,'NFBl-5')
-L-0;
T0SLGHT7(SRR,L) $SRL(8RR,L) • •
-SUM(SR $DSRL( SR,SRR,L), SHR6 (SR,SRR) *XXXC(SR, SRR,L, 'CULL' ) )
-SUM(3RD $DSRLD(SRD,SRR,L), SHRD(SRD,SRR)*XXXD(SRD,SRR,L,'CULL') )
+Z0(SRR,L,'CULL')
-L-0;
INTERMED1(SR,L,U0) $SRL(SR,L).. -ZO(SR,L,UO)
♦ SUM(K1 $SRLPC(SR,L,U0,K1), C1(SR,L,U0,K1)*Q1(SR,L,K1))
-B-0;
FABRICATOR,L,U2,K1) $SRL(ur,l).. Z1(SR,L,U2,K1)
-D2(SR,U2,K1)*Q1(SR,L,K1)
-B-0;
PLNTAGG(SR,L) SSRL(SR,L)., *SUM(K1, Q1(SR,L,K1)) -QlA(SR,L)-E-0;
PLCPCTY(SR,L) $SRL (SR,L) • • Q1A( SR,L)-TCAPCTY( SR,L)-L-0;
ALLOCFAB(SR,L,U2) SSRLHB(SR,L,U2). . -SUM(K1 SSRLHB(SR,L,U2), Z1(SR,L,U2,K1))
♦ Z1R(SR,L,U2) $RTL (SR,L,U2)+ Z1H(SR,L,U2) SSRLHB(SR,L,U2)
-L-0;
RSTRTL(SR) • . -SUM(L SSRL(SR,L), Z1R(SR,L,'ROAST') )*Z(SR,'ROAST')-B-0;
STKRTL(SR) • • -SUM(L $SRL(SR,L), ZlR(SR,L,'STEAK'))+Z(SR,'STEAK')-B-0;
INTERMBD3(SR,L,U2) SSRLHB(SR,L,U2).. -Z1H(SR,L,U2)
♦C3(SR,U2)*Q3(SR,L,U2)
-B-0;
HAMBURGER ( SR) . . Z ( SR, ' 5MBRGR ' ) -SUM ( ( L, U2 ) SSRLHB(SR,L,U2) , Q3(SR,L,U2))
-B-0;
FATMINM(SR,L)., SUM(U2 $SRLHB(SR,L,U2), A3(SR,'MIN',U2)*Q3(SR,L,U2))
-FAT(SR, 'MIN' )*Z(SR, 'HMBRGR' )-L-0;
FATMAXM(SR,L) . - SUM(U2 SSRLHB ( SR, L,U2 ) , A3( SR,'MAX',U2 ) *<23 (SR,L,U2) )
-FAT(SR, 'MAX' )*Z(SR, 'HMBRGR' )-L-0;
SALB(SR,U3).. -Z(SR,U3) +SUM(DR $DD(DR,SR), X(SR,DR,U3))
* SUMfEXX ST2(SR,EXX,U3), X2(SR,EXX,U3))=L=0;
EXTRNSPRT(EXX,U3) $PKX(KXX,U3 ) . . -SUM(SR $PEX(EXX,U3 ) , X2 (SR,EXX,U3 ) )
+ BPEXPRT(EXX,U3)
-L-0;
IMTR5SPRT( IM,U3 ) . • SUM(DR SIMPRTDMHD( IM,DR,U3 ) , XF( IM,DR,U3 ) )
-BFIMPRT( IM, U3)
-L-0 ;
CNSMPTN (DR, U3 ) . . -SUM(IM SIMPRTDMHD( IM, DR, U3 ) , XF(IM,DR,U3) )
-3UM(SR $DD(DR,SR), .96*X(SR,DR,U3))
♦ ( 12/100)*Y(DR,U3)+AHY(DR,U3)-L-0;
AHCNSMPTN (DR, U3).. AHY (DR, U3) -E-RIC (DR, U3) ;
•OBJECTIVE FUNCTION FOR FIXED PRICE MODEL
WLFR1..
SUM((DR,U3), PRICE(DR,U3)*12*Y(DR,U3))
♦SUM((DR,U3), 100*PRICE(DR,U3)*AHY(DR,U3))
*SUM( (EXX, U3 ) SPEX( EXX, U3 ) , PEX( EXX, U3 ) *BFEXPRT( EXX, U3 ) )
-SUM((SR,L,K1)SSRL(SR,L), R1(SR,L)*Q1(SR,L,K1))
-SUM( ( SR, L , U2 ) SSRLHB( SR,L, U2 ) , R3 ( SR, L) * -SUM((SRD,U5), RD(SRD,U5)*ZD(SRD,U5))
-SUM((SR,U6), R6(SR,U6)*Z6(SR,U6))
-SUM((SR,K7), R7(SR,K7)*Q7(SR,K7))
-SUM((SR,K8), R8(SR,K8)*Q8(SR,K8))
-SUM( (SRR,SR)SDST(SRR,SR) , (TCC( SRR,SR, ' CALF ' )+ADJ( SRR, SR) )
•XX(SRR,SR,'CALF'))
-SUM( (SRR,SR)SDST(SRR,SR) , (TCC(SRR,SR, 'CALF ' ) »ADJCF(SRR,SR) )
•XXC(SRR,SR,'CALF'))
-SUM( ( SRR, SR, U7 ) $DST( SRR, SR) , (TS (SRR, SR, U7 )+ADJSF ( SRR, SR,U7 ) )
*XXS(SRR,SR,U7))
-SUM( (SRR,SR,L)SDSRL(SRR,SR,L), (TCC(SRR,SR, 'CULL' )+ADJSLC(SRR,SR,L, 'CULL'))
*XXXC(SRR,SR,L, 'CULL' ) )
-SUM( ( SRR, SR,L,U7 ) SDSRL ( SRR,SR,L) , (TS (SRR, SR,U7 ) ♦ADJSLS ( SRR, SR, L,U7 ) )

*XXXS(SRR,SR,L,U7))
-SUM( (SRR,SR,L,U9)$DSRL(SRR,SR,L) , (TP(SRH, SR,U9) +ADJSLF( SRR,SR,L,U9) )
*XXXF( SRR, SR.L/J9 ) )
-8UM( (SRD,SR,L)$8RL(SR,L), (TD(SRD,SR, 'CULL' )+ADJSLD(SRD,SR,L, 'CULL')}
*XXXD(SRD,SR,L, 'CULL' ) )
-SUM((IM,DR,U3) SIMPRTDMHD(IM,DR,U3) , (TFI {DR, IM,U3 ) +MRGI(DR, IM,U3) )
*X7(IM,DR,U3))
-SUM( ( SR,EXX,U3) 3T2 (SR,EXX, U3), T2(SR,EXX,U3) *X2(SR,EXX,U3))
-SUM( (SR,DR,U3), T3(DR,SR,U3)*X(SR,DR,U3) J-E-NSR;
MODEL USBEEF1 /
BOUNDS ON VARIABLES
DAIRYCULLS
DAIRYTRANS
BRDNGSTCK
LIVESPPLY
TRANCULL6
TRAHCALF6
CCTOSTK
CCUSEDSTK
PLACKSTCK
TRAHSPER71
TRANSFER7 2
CCSTCK1
CCSTCK2
CCSTCX3
LVANUSEFL
FIHISHFL
TRANSFERS
TQSLGHT1
TOSLGHT2
TOSLGHT3
TOSLGHT4
TOSLGHT5
TOSLGHT6
TOSLCHT7
INTERMED1
F ABRI CAT
PLHTAOG
PLCPCTY
ALLOCFAB
RSTRTL
STKRTL
INTERMED3
HAMBURGER
FATMINM
FATMAXM
SALE
EXTRNSPRT
IMTRNSPRT
CNSMPTN
AHCNSMPTN
WLFR1 /;
Y.LO( 'MW' , 'HMBRGR' )â– 
Y.LO('MW','ROAST')-
Y.LO( 'MW' , 'STEAK' )-
Y.UP( 'MW' , 'HMBRGR' )-
Y. UP ( ' MW', ' ROAST ' ) -
Y.UP('MW','STEAK')—
Y.LO('NNE','HMBRGR')
Y.LO( 'NNB' , 'ROAST' )-
Y.LO( 'NNE', 'STEAK' )-
Y.UP('NNE','HMBRGR')
Y.UP( 'NNE' , 'ROAST' )-
Y.UP( 'NNE' , 'STEAK' )-
Y.LO<'S','HMBRGR')-
Y.LO('S','ROAST')-
Y.LO('S','STEAK')=
Y.UP( 'S' , 'HMBRGR' )-
Y.UP('S','ROAST')—
Y.UP('S','STEAK')=
Y.LO('W','HMBRGR')-
Y.LO('W','ROAST')-
Y.LO('W','STEAK')=
Y . UP ( ' W ' , ' HMBRGR ' ) —
Y . UP ( ' W ' , ' ROAST ' ) —
Y.UP('W', 'STEAK')
4.65*PA('MW');
1.53*PA('MW');
1.999*PA('MW');
4.65*PA('MW');
1.53*PA('MW');
1.999*PA('MW');
4.204*PA('NNE' )
1.738»PA<'NNE')
1.988*PA('NNE')
4.204*PA('NNE')
1.73B*PA('NNE')
1.988*PA('NNE')
3.89*PA('S');
1.513«PA('S');
2.89*PA( 'S');
3.89*PA('S');
513*PA('S');
89*PA('S');
022*PA('W');
266*PA('W');
069*PA('W');
022«PA('W');
266*PA('W');
069*PA('W');
BFEXPRT.LO( 'EXX1' , 'ROAST' )-. 43*9.302E + 04;
BFEXPRT.UP ( 'EXX1' , 'ROAST' )-. 43*9.302E+04;
BFEXPRT.LO( 'EXX1','STEAK')-. 57*9.302E+04;
BFEXPRT.UP( 'EXX1' , ' STEAK' )-. 57*9.302E+04;
X.UP( 'MW',DR,U3)-5000000000;
Z.UP('MW',U3)«500000000;

240
•OPTION NLP-MINOS5;
OPTION LIMCOL-O; OPTION LIMROW-O;
OPTION ITERLIM-10000?
OPTION RESLIM-40000;
OPTION SQLPRINT-off;
SOLVE USBEEF1 USING LP MAXIMIZING NSR;
varlaUu
AXXXC(SRR,SR,U6)
AXXXS (SRR, SR, U7 )
AXXXP(SRR,SR,U9)
AXXXD(SRD,SR,U6)
AX1(SRR,SR,U0)
BEEP CULLS SHIPPED TO SLAUGHTER( HD)
NON-FED SHIPPED TO SLAUGHTER (HD)
FINISHED ANIMALS SHIPPED (HD)
DAIRY CULLS SHIPPED (HD)
HEAD OF FINISHED CATTLE SHIPPED
AQ1(SR,K1) HEAD SLAUGHTERED
AQ3(SR,U2) LEVEL OF HAMBURGER PROCESS USED (CUT)
AZ0(3R,U0)
AZ1(SR,U2)
AZ1H(SR,U2)
AZ1R(SR,U2)
ANIMALS SLAUGHTERD (HD)
FAB CUTS PRODUCED (CWT).
PRIMAL CUTS ALLOCATED TO HAMBURGER (CWT)
PRIMAL CUTS ALLOCATED TO RETAIL (CWT);
AXXXC.1(SRR,SR,U6)
AXXXS.1(SRR,SR,U7)
AXXXF. 1 (SRR, 8R, U 9)
AXXXD. 1 (SRD, SR, U6)
AQ1.1(SR,K1)
AQ3.1(SR,U2)
AZ0.1(SR,U0)
AZ1.1(SR,U2)
AZ1H.1(SR,U2) -
AZ1R.1(SR,U2) -
“ sum(1 $dsrl(srr,sr,1), xxxc.1(srr,sr,1,u6));
- sum(l Sdsrl(srr,sr,l), xxxa.l(err,sr,1,u7) );
- aum(1 Sdarl(srr,sr,1), xxxf.1(arr,sr,1,u9));
- sum(l Sarl(sr,l), xxxd.1(ard,ar,1,u6));
* sua(l Ssrl(ar,l), ql.1(sr,1,XI));
sua(l $srl(sr,l), q3.1(»r,1,u2));
buh(1 Sarl(ar,1), zO.1(sr,1,u0));
aun((1,X1) Sarl(sr,l), zl.l(ar,l,u2,Xl))?
aun(l $arl(ar,l)> zlh.1(ar,1,u2));
aun(l $arl(ar,l)« zlr.l(ar,l,u2));
VARIABLES
RP(DR,U3) PRICE OF BEEF IN DEMAND REGIONS
PY(DR,U3) MONTHLY HOUSEHOLD CONSUMPTION OF BEEF (LBS);
TABLE MRGTST(DR,SR,U3)
NNE.(SE,MW, SW,PL)
MW. (MW,SW,PL)
3.(SE,MW,SW,PL, W)
W.(MW,SW,PL,W)
MARKETING MARGIN FOR CUTS
HMBRGR ROAST STEAK
0.59 84.16 119.96
1.46 77.94 36.53
8.20 91.78 0.77
9.10 104.38 85.48
FROM WHOLESALE TO RETAIL
PARAMETER MRG(DR, SR,U3) MARKETING MARGIN USED;
MRG (DR, SR, U3) =MRGTST (DR, SR, U3) ;
EQUATIONS WLFR2 NET SOCIAL WELFARE (PRICES ENDOGENOUS);
•OBJECTIVE FUNCTION FOR EXOGENOUS PRICE MODEL
WLFR2 • •
12«(REX('mw')*dintc('mw','hmbrgr')»LOG(Y('mw','hmbrgr'))
+REX('aw')«l/2*bli('hmbrgr','mw')*(log(y('mw','hmbrgr'))**2)
♦REX('mw')»dlnto('mw','roaat')*LOG(Y('mw','roaat'))
+REX('mw')*bij('hmbrgr','roaat','mw')*log(y('mw','hmbrgr'))*log(y('raw','roast'))
+REX('mw')»l/2*bll('roaat','mw')*(log(y('raw','roast'))**2)
• REX( 'raw' )*dlnto( 'raw',' stoaX') *LOG(Y( 'raw', 'steaX'))
+REX('mw')*bij('steaX','hmbrgr','raw')*log(y('raw','hmbrgr'))*log(y('raw','steaX'))
♦REX('mw')*bij('roaat','steaX','mw')*log(y('raw','roaat'))*log(y('raw','steaX'))
+REX( 'mw' )*l/2*bil( 'steaX', 'raw') • (log(y( 'mw', 'steaX' ) )**2)
+REX('nne')*dlntc('nne','hmbrgr')*LOG(Y('nne','hmbrgr'))
+REX('nne')*l/2*bli('hmbrgr','nne')»(log(y('nne','hmbrgr'))**2)
+REX('nne')»dintc('nne','roast')*LOG(Y('nne','roast'))
+REX('nne')*blj('hmbrgr','roast','nne')*log(y('nne','hmbrgr'))•
log(y('nne','roast'))
+REX('nne')*l/2*bii('roast','nne')*(log(y(’nna','roast'))**2)
+REX('nne')«dintel'nne','steaX')*LOG(Y('nne','steaX'))
+REX('nne')*blj('steaX','hmbrgr','nne')*log(y('nne','hmbrgr'))*
log(y('nne','steaX'))
+REX('nne' )*blj( 'roast','steaX','nne')*log(y('nne','roast'))*
log(y('nne','steaX'))
+REX( 'nne' )*l/2*bii('steaX','nne')*(log(y('nne','steaX'))**2)
+REX('s')*dintc( 's','hmbrgr')»LOG(Y('s','hmbrgr'))
+REX('s')*l/2*bii('hmbrgr','s')*(log(y('s','hmbrgr'))«*2)

♦ REX( 'B' )*dintc( 's', 'roast' )*LOG(Y( 's', 'roast'))
♦REX('s')*blj('habrgr','roast','s')*log(y('s','habrgr'))*log(y('s','roast'))
+REX( 's')*l/2*bli('roast','s')*(log(y('s','roast'))*«2)
♦REX( 's' )*dlntc( 's','steak')*LOG(Y( 's', 'steak'))
+REX('s') *bij ('steak','habrgr','s')«log(y('s','habrgr'))*log(y('s','steak'))
+REX('s')*bij('roast','steak','s')*log(y('s','roast'))*log(y('s','steak'))
+REX( 's')*l/2*bli('steak','s')*(log(y('s','steak'))**2)
+REX( 'w')*dlntc< 'w', 'habrgr' )*LOG(Y( 'v', 'habrgr'))
♦REX( 'w')*l/2*bil<'habrgr', 'w') * (log(y('w','habrgr'))*«2)
♦RKX('w')*dintc('v','roast')*LOG(Y('w','roast'))
♦RKX('w')*bij('habrgr', 'roast', 'w')»log(y('w','habrgr'))*log(y( 'w', 'roast'))
+RBX('w')*l/2*bil('roast','w')«(log(y('w','roast'))**2)
+REX( 'w')*dintc( 'w', 'steak')*LOG(Y( 'w', 'steak'))
+REX( 'w' )*bij ('steak', 'habrgr', 'w')*log(y( 'w', 'habrgr') )*log(y( 'w', 'steak'))
♦REX( 'w' )*bij ('roast', 'steak', 'w' )*log(y( 'w', 'roast')) *log(y( 'w', 'steak'))
+REX( 'w' )*l/2*bli('steak','w')*(log(y('w','steak'))*»2))
♦ ( SUM( (EXX,03)SPKX(EXX,U3) , PKX(EXX,U3 ) *BPEXPRT(EXX,U3 ) ) )
+SUM((DR,U3), 100*PRICE(DR,U3)*AHY(DR,U3))
-SUM((SRD,U5), RD(SRD,U5)*ZD(SRD,U5))
-SUH((SR,U6), R6(SR,U6)*Z6(SR,U6))
-SUM( (SR,K7 ) , R7(SR,K7)*Q7(SR,K7) )
-SUM( (SR,K8), R8(SR,K8)*Q8(SR,K8))
-SUM( (SR,L), R1(SR,L)*Q1A(SR,L))
-SUM((SR,L,U2,K1), R3(SR,L)*Q3(SR,L,U2))
-SUM( ( 8RR,SR) SDSTf SRR, SR) , (TCC(SRR,SR, 'CALF' )+*DJ(SRR,SR) )
*XX(SRR,3R, 'CALF' ) )
-SUM( (SRR,SR)SDST(SRR,SR), (TCC(SRR,SR, 'CALF ' )+ADJCF(SRR,SR) )
*XXC(SRR,SR,'CALF') )
-SUM( (SRR,SR,U7)SDST(SRR,SR), (TS(SRR,SR,U7)+ADJSF(SRR,SR,U7) )
"XXS(SRR,SR,U7))
-SUM( (SRR,SR,L)SDSRL(SRR,SR,L) , (TCC(SRR,SR,'CULL') tADJSLC(SRR,SR,L, 'CULL'))
*XXXC(SRR,SR,L, 'CULL'))
-SUM( ( SRR, SR, L, U7 ) $DSRL (SRR, SR,L) , (TS (SRR,SR,U7 ) +ADJSLS( SRR,SR,L, U7 ) )
•XXXS(SRR,SR,L,U7))
-SUM((SRR,SR,L,U9)SDSRL(SRR,SR,L), (TF(SRR,SR,U9)+ADJSLF(SRR,SR,L,U9))
*XXXF(SRR,SR,L,U9))
-SUM( (SRD,SR,L)SSRL(SR,L) , (TD ( 3RD , SR, 'CULL' ) *ADJSLD(SRD,SR,L, 'CULL' ) )
*XXXD (SRD, SR, L , 'CULL' ) )
-SUM( (IM,DR,U3) SIMPRTDWTO(IM,DR,U3), (TFI (DR, IM,U3 )+MRGI (DR, IM,U3 ) )
*XF(IM,DR,U3) )
-SUM( (SR,EXX,U3) $T2 ( SR, EXX,U3 ) , T2 (SR,EXX, U3 ) *X2 (SR,EXX,U3 ) )
-SUM( (SR,DR,U3), (T3 (DR,SR,U3) ♦MRG(DR,SR,U3)) *X(SR,DR,U3) )-E-NSB;
•BOUNDS OR VARIABLES
Y.LO( 'MW', 'habrgr' )"
2.8*pa('aw');
Y.LO('MW','roast')«
1.2*pa('aw');
Y.LO('MW','steak')»
1.475*pa('aw'
Y.UP('MW','habrgr')-
7.7*pa('aw');
Y.UP('MW','roast')-
2.75*pa( 'aw')
Y.UP('MW','steak')-
3.5*pa('aw');
Y.LO( 'NNB' , 'HMBRGR' )-
2.1*pa('nne')
Y.LO<'NNE','ROAST')»
1.0*pa('nne')
Y.LO('NNE','STEAK') =
-8*pa('nne');
Y.UP('NNE','HMBRGR')-
7.2*pa('nne')
Y.UP('NNE','ROAST') =
3.3*pa('nne')
Y.UP('NNE','STEAK') =
4.0*pa('nne')
Y.LO( 'S' , 'HMBRGR' )»
2.4*pa('s');
Y.LO('S','ROAST')»
•4*pa('s');
Y.LO('S','STEAK')»
1.4*pa('s');
Y.UP('S','HMBRGR')-
8.1*pa('s');
Y.UP('S','ROAST')-
4.0*pa('s');
Y.UP( 'S', 'STEAK' ) =
7.0*pa('s') ;
Y.LO( 'W', 'HMBRGR' ) =
2.3*pa<'w');
Y.LO( 'W', 'ROAST' ) =
0.4*pa('w');
Y.LO( 'W' , 'STEAK' )-
1.3*pa('w');
Y.UP('W','HMBRGR')»
7.0*pa('w');
Y.UPf'W', 'ROAST')»
2.75*pa('w') ;
Y.UP('W','STEAK')»
4.0*pa('w');
AHY.UP(DR,U3)=RIC(DR,U3);
AHY.LO(DR,U3)=RIC(DR,U3);
BFEXPRT.LO( 'EXX1' , 'ROAST' )». 43*9.302E + 04;
BFEXPRT.UPf 'EXX1', 'ROAST')«.43*9.302E+04;
BFEXPRT.LOI 'EXX1', 'STEAK' ) = . 57*9.302E+04;
BFEXPRT.UP( 'EXX1', 'STEAK') =.57*9.302E+04;
X.UP('MW',DR,U3)»5000000000;
Z.UP('MW',U3)-500000000;
Q1A.UP(SR,L)=100000000;

Zl.UP(SR,L,U2,K1)*1000000000;
Z1H.UP(SR,L,U2)*1000000000;
Z1R. UP (SR, L,U2)* 1000000000;
Q3.UP(SR,L,U2)-1000000000;
X.UP(SR,DR,U31-10000000000;
Sontext
option livaspply:3:l:l; display livaspply.a;
option placestck:3:l:l; display placastck.a;
option lvanusefl:3:l:l; display lvanusefl.n;
option finisbfl:3:l:l; display finisbfl.a;
option transfar8:3:Is 1; display transfers.â– ;
‘option toslgbtl:3:1:1;
‘option toslgbt2:3:l:l;
‘option toslgbt3:3:l:l;
‘option toalgbt4>3:l:l;
‘option toslgbtS:3:l:l;
•option toslgbt6:3:l:l;
‘option toslght7:3:l:l;
option lntanaadl:3:2:1;
•option fabrlcat:3:2:2;
Sofftaxt
display toslgbtl.
display toslgbt2.
display toslgbtl.a;
display toalgbt4.a;
display toslgbtS.a;
display toslgbt6.n;
display toalgbt7.n;
display intanssdl.a;
display fabricat.a;
RP.L(DR, 'HMBRGR')-(REX(DR)/Y.L(DR, 'HMBROR' ) )‘(DINTC(DR, 'HMBRGR' )
♦BII( 'HMBROR',DR)*LOG(Y.L(DR, 'HMBROR' ) )
+BIJ ( 'HMBROR', 'ROAST' ,DR) *LOG( Y.L(DR, 'ROAST') )
+BIJ('STEAK', 'HMBROR' ,DR)‘LOG( Y.L(DR, 'STEAK'))) ;
RP.LfDR, 'ROAST')-(REX(DR)/Y.L(DR, 'ROAST'))»(DINTC(DR, 'ROAST')
+BIJ( 'HMBROR' , 'ROAST' ,DR) *LOO( Y.L(DR, 'HMBRGR' ) )
♦BII< 'ROAST' ,DR)*LOG(Y.L(DR, 'ROAST' ) )
♦BIJ('ROAST','STEAK',DR)*LOG(Y.L(DR,'STEAK')));
RP.L(DR, 'STEAK')-(REX(DR) /Y.L( DR, 'STEAK') )*(DIHTC(DR, 'STEAK')
♦ BIJ( 'STEAK' , 'HMBROR' ,DR) *LOG( Y.L(DR, 'HMBRGR' ) )
+BIJ('ROAST','STEAK',DR)‘LOG(Y.L(DR,'ROAST'))
+BII ('STEAK' ,DR)‘LOO(Y.L(DR, 'STEAK')));
DISPLAY RP.L;
PY.L(dr,u3)-Y.L(dr,u3)/PA(dr);
display PY.L;
MODEL USBEEP2 /
DAIRYCULLS
DAIRYTRANS
BRDNGSTCK
LIVESPPLY
TRANCULL6
TRANCALE6
CCTOSTK
CCUSEDSTK
PLACESTCK
TRANSFER71
TRANS PER 7 2
CCSTCK1
CCSTCK2
CCSTCK3
LVANUSEPL
FINISHFL
TRANSFERS
TOSLGHT1
TOSLGHT2
TOSLGHT3
TOSLGHT4
TOSLGHT5
TOSLGHT6
TOSLGHT7
I«TERMED1
FABRICAT
PLNTAGG
PLCPCTY
ALLOCFAB
RSTRTL
STKRTL
INTERMED3
HAMBURGER
PATMINM
FATMAXM
SALE
EXTRNSPRT
IMTRNSPRT
CNSMPTN
AHCNSMPTN
WLFR2 /;
OPTION NLP-MI NOS 5 ;
OPTION LIMCOL-0; OPTION LIMROW-O

OPTION BRATIO-1;
OPTION ITERLIM-10000;
OPTION RESLIM>400000;
OPTION SOLPRINT-on;
SOLVE USBSKF2 US HQ NLP MAXIMIZING NSB;
AXXXC.1(SRR,SR,U6)
AXXXS. 1 (SRR, SR, U7 )
AXXXF.1(SRR,SR,U9)
AXXXD.1(SBD,SR,U6)
AQ1.1(SR,K1)
AQ3.1(SR,U2)
AZ0.1(SR,U0)
AZ1.1(SR,U2)
AZlfi.KSR.U2) -
AZ1R.1(SR,U2) -
* bub(1 $dsrl(srr,8r,l), xxxc.l( »rr,sr,l, u6));
“ sua(l Sdsrl(srr,sr,1), xxx>.1(arr,>r,1,u7));
- sua(l Sdsrl(arr,ar,l), xxxf.l(srr,sr,l,u9));
- sue(l $srl(sr,l), xxxd.lfard,ar,l,u6));
- sua(l Sarl(ar.l), ql.l(ar,l,kl));
sua(l $srl(ar,l), q3.1(ar,l,u2))}
sua(l $arl(ar.l), zO.1(ar,1,uO));
sua((l,kl) $srl(ar,l), zl.1(ar,l,u2,kl));
bub(1 Sarl(ar,l), zlh.1(ar,1,u2));
bub(1 Sarl(ar.l), zlr.l(ar,l,u2));
•Sontaxt
option llveapply:3:l:l;
option placaatck:3:l:l;
option lvanuaefl:3:l:l;
option flnl8hfl:3:l:l;
option tranafarB:3:1:1;
option to8lghtl:3:l:l;
option toslght2:3:l:l;
option toalgbt3:3:l:l;
option toslgbt4>3:Is 1;
option toalgbtS:3:1:1;
option toalgbt6:3:l:l;
option toslght7:3:l:l;
option intemedl:3:2:l;
option fabrlcat:3:2:2;
display
display
display
display
display
display
display
display
display
display
display
•display
display
display
display
display
display
display
display
display
display
display
•Sofftext
XX.L;
XXC.L;
XXS.L;
AXXXC.L;
AXXXS. L;
AXXXF.L;
AXXXD.L;
XP.L;
AQ1.1;
AQ3.1;
ZD.L;
ZS.L ;
Z6.L;
Z77.L;
Z7.L;
28FL.L;
Q8.L;
Z8.L;
AZO.L;
AZ1.L;
AZ1B.L;
AZ1R.L;
display livespply.m;
display placaatck.a;
display lvanusafl.ii;
display tlnlsbfl.ai;
display transfers.a;
display toslghtl.m;
display toslgbt2.a;
display toslgbt3.a;
display toalgbt4.m;
display toslgbt5.a;
display toslgbt6.a;
display toslght7.m;
display internedl.a;
display fabricat.o;
option X:3:2:l; display x.l;
option sale:3:l:l; display sale.a;
option cnsmptn:3:l:l; display cnsaptn.o;
•Sontext
RP.L(DR, 'HMBRGR' )“(RBX(DR) /Y.L(DR, 'HHBRGR' ) ) • (DINTC(DR, 'HMBRGR' )
+BII ( 'HMBRGR' , DR) *LOG( Y.L( DR, 'HMBRGR' ) )
+BIJ( 'HMBRGR' , 'ROAST' , DR) *LOG( Y. L( DR, 'ROAST' ) )
+BIJ( 'STEAK', 'HMBRGR' ,DR)*LOG(Y.L(DR, 'STEAK') ) )
RP.L(DR, 'ROAST') = (REX(DR)/Y.L(DR, 'ROAST'))• (DINTC( DR, 'ROAST')
♦ BIJ( 'HMBRGR' , 'ROAST' ,DR) *LOG( Y.L(DR, 'HMBRGR' ) )
+BII( 'ROAST' ,DR)*LOG(Y.L(DR, 'ROAST' ) )
♦ BIJ( 'ROAST', 'STEAK' ,DR)*LOG(Y.L(DR, 'STEAK' ) ) );
RP.L(DR, 'STEAK')-(REX(DR)/Y.L(DR, ' STEAK'))• (DINTC (DR, 'STEAK')
+BIJ( 'STEAK' , 'HMBRGR' ,DR) «LOG( Y.L(DR, 'HMBRGR' ) )
+BIJ( 'ROAST' , 'STEAK' ,DR) *LOG(Y.L(DR, 'ROAST' ) )
+BII( 'STEAK' ,DR)*LOG(Y.L(DR, 'STEAK' ) ) ) ;
display RP.L;
PY.L(dr,u3)=Y.L(dr,u3)/PA(dr);
display PY.L;
•Sofftext

APPENDIX D
THE EMPIRICAL COMPENSATED DEMAND SYSTEM
This section demonstrates how to obtain the empirical
compensated demand system from the estimated demand system.
The compensated demand system as derived from the distance
function is
wt = at + 2
j
Yij In q3 + UpiPJIq^1
(D.l)
where
U = -(aD + 2 a1*lnq1 + l/22t2 Yij lnq^nqj)/p^Iq^1 (D.2)
1 j
and the following parameter restrictions hold: 20^ = 1,
Si Yij - Sj yi:) — 2Pi — 0, and Yij = Yji*
In order to obtain the empirical compensated demand
system, it is necessary to set a value for upo in equation
D.l and hold it constant. This can be accomplished by
substituting
a(q) = aD + 2 ai*lnqi + 1/222 Yij Inqilnqj (D. 3)
1 ij
244

245
in equation D.2 and solving for upo. The resulting demand
equation is
Wi = Oi + 2 Ytj In q3 + (^Hq*Pl
j
(D.4)
where
= - a(q) /Ilqi Pi
(D • 5)

REFERENCES
Anderson, R.W. "Some Theory of Inverse Demand for Applied
Demand Analysis." Eur. Econ. Rev. 14(1980):281-90.
Baumes, H. "A Partial Equilibrium Sector Model of U.S.
Agriculture Open to Trade: A Domestic Agricultural and
Agricultural Trade Policy Analysis." Ph.D. Disser¬
tation, Purdue University, 1978.
Boykin, Calvin C., Henry C. Gilliam, and Ronald A.
Gustafson. Structural Characteristics of Beef Cattle
Raising in the United States. AER. No. 450, USDA,
Washington D.C., 1980.
Braschler, Curtis. "The Changing Demand Structure for Pork
and Beef in the 1970's: Implications for the 1980's."
South. J. Aar. Econ. 15( 1983): 105-110.
Buse, Reuben C. "Is the Structure Of the Demand for Food
Changing?" Food Demand Analysis: Implications for
Future Consumption. Eds. Oral Capps, Jr. and Benjamin
Senauer. Blacksburg, Virginia: Virginia Politechnical
Institute, 1986.
Capps, Oral, and J. Havlicek. "National and Regional
Household Demand for Meat, Poultry, and Seafood: A
Complete Systems Approach." Can. J. Aar. Econ.
32(1984):93-108.
Carnes, Richard. "Meatpacking and Prepared Meats Industry:
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BIOGRAPHICAL SKETCH
Mark A. Peters was born on July 31, 1956, in New
Kensington, Pennsylvania, where he spent a typical
childhood. After high school graduation from Willowbrook
Community High School, he studied political science at Lew
and Clark College in Portland, Oregon, where he received a
B.A. in 1979 . From 1979-1982, he served with the U.S. Peace
Corps in Jamaica on an integrated rural development project.
In August 1983, he entered the graduate program in food and
resource economics at the University of Florida where he
received an M.S. in 1987, and where he will receive a Ph.D.
in December 1990.
251

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
a
Thomas H. Spreen, Chair
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Jofrrí S. SHonkwiler
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
William G. Boggess d d
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
TimotljyG
Associate
Resource
. ipáylor
¿Professor of Food and
Economics

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Douglas G. Waldo
Associate Professor of Economics
This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December 1990
Dean, Caliege of Agriculture
-Si
:u?Ftu
Dean, Graduate School