• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Abstract
 Table of Contents
 List of Tables
 Chapter I: Introduction
 Chapter II: The analytical...
 Chapter III: Application of the...
 Chapter IV: Solution of the farm...
 Chapter V: Summary and conclus...
 Bibliography
 Appendix






Title: Farm organization and resource fixity
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Title: Farm organization and resource fixity
Physical Description: Book
Language: English
Creator: Hildebrand, Peter E.
Affiliation: Michigan State University -- Department of Agricultural Economics
Publisher: Michigan State University
Publication Date: 1959
 Subjects
Subject: Farming   ( lcsh )
Agriculture   ( lcsh )
Farm life   ( lcsh )
University of Florida.   ( lcsh )
Spatial Coverage: North America -- United States of America -- Illinois
North America -- United States of America -- Florida
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General Note: "Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY"
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Resource Identifier: oclc - 12543677

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Abstract
        Page iii
        Page iv
        Page v
    Table of Contents
        Page vi
    List of Tables
        Page vii
        Page viii
    Chapter I: Introduction
        Page 1
        Page 2
        The nature of fixed resources
            Page 3
        The effect of predetermined resource fixities without regard to MVP
            Page 4
        Endogenous determination of resource fixity
            Page 5
            Page 6
        Some previous linear programming models incorporating various aspects of the problem
            Page 7
        The farm situation and credit supply function
            Page 8
            Page 9
        Thesis organization
            Page 10
    Chapter II: The analytical model
        Page 11
        The specialized equations
            Page 12
            Page 13
            Page 14
            Page 15
            Page 16
        The double purpose acquisition activities
            Page 17
        The credit activities
            Page 18
        The cash coefficients
            Page 19
            Page 20
            Page 21
            Page 22
        Specialization and diversification and the effect of a single fixed resource on the solution
            Page 23
            Page 24
        Discrete investment levels
            Page 25
            Page 26
            Page 27
            Page 28
    Chapter III: Application of the model
        Page 29
        Crop productions
            Page 29
        Milk production
            Page 30
        Derivaton of the technical matrix and restrictions
            Page 31
        Acquisition and salvage
            Page 32
        The range of possible solutions
            Page 33
            Page 34
    Chapter IV: Solution of the farm model
        Page 35
        The initial optimum solution
            Page 35
            Page 36
            Page 37
            Page 38
            Page 39
            Page 40
            Page 41
            Page 42
        The discrete investment series
            Page 43
            Page 44
            Page 45
            Page 46
            Page 47
            Page 48
            Page 49
            Page 50
            Page 51
            Page 52
            Page 53
        The final farm organization
            Page 54
            Page 55
            Page 56
    Chapter V: Summary and conclusions
        Page 57
        Application of the model
            Page 57
            Page 58
            Page 59
            Page 60
        The empirical results
            Page 61
            Page 62
        Further study indicated
            Page 63
            Page 64
    Bibliography
        Page 65
        Page 66
        Page 67
    Appendix
        Page 68-a
        Appendix A: Resource fixity and discrete investment levels
            Page 68
            Page 69
            Page 70
        Appendix B: Tables 1 to 19
            Page 71-a
            Page 71
            Page 72
            Page 73
            Page 74
            Page 75
            Page 76
            Page 77
            Page 78
            Page 79
            Page 80
            Page 81
            Page 82
            Page 83
            Page 84
            Page 85
            Page 86
            Page 87
            Page 88
            Page 89
Full Text







FriM ORGANIZATION A1N R M ECE FIITY: MODIFICATIONS


OF THE LINEAR PROGRAMMING MODEL


By


Peter E. Hildebrand


Submitted to the School for Advanced Graduate Studies
of Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of


DOCTOR OF PHILOSOPHY


Department of Agricultural Economics


1959












ACKNOWED GMET


The author wishes to express his sincere gratitude and appreciation
to the following people, all of whom played important roles in the writ-
ing of this thesis.

Dr. Glenn L. Johnson, who served as the chairman of the authors
guidance committee. His inspiration made graduate work and the writing
of a thesis an enjoyable experience rather than a burdensome task,

Dr. Dean E. McKee, who assumed the chairmanship responsibility for
the final stages of the thesis after the original chairman began his
sabbatical leave. His help in the construction of the model, while
serving as an informal member of the committee, was invaluable.

Dr. L. L. Bqger, for his part in furnishing financial assistance
during the writing of the thesis.

Dr. E. L. Baum, Chief, Agricultural Economics. Branch, Tennessee
Valley Authority for furnishing the funds for computation on the IBM
704 Computer at Oak Ridge, Tennessee.

Glenn O-Neal, Agricultural Economics Branch, Tennessee Valley
Authority for his invaluable help in readying the model for computation,

C. R. Hoglund who seemed a never ending source of data. Without
his help, the thesis would have been delayed many long months,

Frank Dvorak who furnished much of the technical data and provided
many provocative arguments which improved the model.

The secretaries and staff of both Michigan State University and
the Tennessee Valley Anthority who were involved, for their unselfish
assistance and for the late dinner hours sometimes made necessary by
the time factor.

And, perhaps most of all, it was the author' s wife, Joyce, who
made the completion of this thesis easier.


ii












TRBK famrlzTITr AND RxofI [T Y: AiM :


OF THE LINEAR PROGRAMMING MDEL



By


Peter E. Hildebrand


AN ABSTRACT






Submitted to the School for Advanced Graduate Studies
of Michigan State University of Agriculture and
Applied Science in partial fulfillment 6f
the requirements for the degree of


DOCTOR OF. PHILOSOPHY


Department of Agricultural Economics


Year 1959


Approved


C. V-1A .


M1DIFICATIONS











ABSTRACT


In this thesis, the standard formulation of the linear programming

model is modified so that the productive resources of the firm are fixed

endogenously rather than being arbitrarily fixed at a predetermined

level. A resource is fixed for the firm if the acquisition price of

another unit is greater than or equal to its marginal value productivity,

which in turn is greater than or equal to its salvage value to the firm.

Resource fixity in this model is subject to the above condition, the

credit supply function of the firm, the initial level of the resource

and the level of technology considered available to the firm.

In addition to the model, and in the absence of precise discrete

programming procedures, a rule is devised for obtaining discrete invest-

meat levels for the resources acquired or sold in the solution. The

rule is based on the concept of fixed assets incorporated in the model.

In the application of the model to a firm, the problem of varying

the stock of durable resources and allocating the annual flow of their

services is encountered because the objective of the analysis is to

determine an optimum organization of the firm which maximizes annual

net revezne. The acquisition and salvage values of the annual flow of

services from a resource are regarded as the annual cost of ownership

of the stock. The annual cost of ownership of a durable stock is the

sum of the annual depreciation, interest, repairs and taxes on the

res curce.










The model is applied to a 160 acre South-central Michigan farm

which is initially organized as a dairy farm with 32 cows and their

replacements, a 32 stanchion barn meeting grade A market requirements

and a full line of crop machinery. The model is sufficiently flexible

to consider the following range of possible solutions: 1) selling the

farm, investing the capital at 4 per cent interest and obtaining off

farm employment; 2) a generalized dairy farm similar to the initial

organization; 3) a milk-factory type of organization with all the feed

purchased and 4) a cash crop farm with no dairy. Expansion of the firm

is limited by the credit supply function of the farmer and a reasonable

limit to the amount of land available for purchase.

The prices on items which can be purchased are 1958 prices uni-

formly inflated by 10 per cent. The prices received are $3.90 per

hundredweight for milk, $0.90 per bushel for corn and $17.50 per ton

for hay.

The final farm organization obtained from the model and the appli-

cation of the rule for discrete investment levels, is a 320 acre cash

crop farm with 13 acres of oats, 39 acres of hay and 216 acres of corn

on the 268 tillable acres. The dairy was unable to compete with the

cash crop alternative so the dairy herd was sold,

The model is constructed under the assumptions of static economic

theory. As such, it does not consider the functions of management,

situations of risk and uncertainty, nor formal and informal insurance

schemes.










TABLE OF CONTENTS


CHAPTER Page

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

The Nature of Fixed Resources.... .................... 3
The Effect of Predetermined Resource Fixities Without
Regard to MVP............,........................ 4
Endogenous Determination of Resource Fixity.,......*.... 5
Some Previous Linear Programming Models Incorporating
Various Aspects of the Problem.... ..............,. 7
The Farm Situation and Credit Supply Function..... ..... 8
Thesis Organization.....1........,. ......0........... 10

II THE ANALYTICAL MODEL....................................... 11

The Specialized Equations............... ... ........... 1.2
The Double Purpose Acquisition Activities............... 17
The Credit Activities............ .... ........... ...... 18
The Cash Coefficients........................... ....... 19
Specialization and Diversification and the Effect of a
Single Fixed Resource on the Solution............... 23
Discrete Investment Levels..........,,..,.,.......... 25

III APPLICATION OF THE MODEL............................. ..., 29

Crop Production....... .... .......... .,............... 29
Milk Production...... ............................... 30
Derivation of the Technical Matrix and Restrictions..., 31
Acquisition and Salvage....... ........... .......... 32
The Range of Possible Solutions...... ................ 33

IV SOLUTION OF THE FARM MeIL................ .............. .... 35

The Initial Optinm Solution. ,..... ............ .... 35
The Discrete Investment Series.............. ,......., h3
The Fintl Farm Organization............,......,,,....... 54

V SUMiMARYX AND 00NCGUSIOMS...........................t.,...,. 57

Application of the Model ................................ 57
The Empirical Results...............................,, 61
Further Study Indicated............6,. ............... 63

BIBLIOCGAPHY...................................................... 65

APPENDICES........................................................ 68










LIST OF TABLES


TABLE Page

2.1 Cash Qoefficients for the Various Groups of Activities,.... 22

4.1 Original and Optimum Inventories ..*...... ..,... .. .... .. 36

4.2 Profit and Organization for 320 Acres and 360 Acres...,...., 45

4.3 Profit and Organization for 320 Acres with Four and Five
Tractors 0....... ...... ..... ........ ....*..* *.......... 48

4. Profit and Organization for 320 Acres, Four Tractors, With
and Without a.Forage Chopper................. .. ..... 49

4.5 Profit and Organization for 320.Acres, Four Tractors, One
Chopper and Two and Three Gorn Pickers............,,....... 51

4.6 Complete Inventory ghanget Original Organization to Final
Farm Plan... .........,.......... .,...........,......... $3

.47 Comparison of Profit: Optimum Solution and Final Farm Plan. 55

4.8 Disposable Income, Final Farm Plan..................... 56
B.1 Crop Activity Titles and Profit Coefficients.............. 71

B.2 Dairy Activity Titles and Profit Coefficients, Per Cow...... 72

B.3 Acquisition, Credit and Salvage Activity Titles and Profit
Coefficients........................... .... ... ..... 74

B.L4 Initial Optimum Solution...................... ..... 75

B .5 Optimum Soltiona-320 Acres...,........... .....,. ,...., 77

B.6 Optimum Solution--320 Acres, 4 Tractors.................. 78

B.7 Optimum Solution--320 Acres, 4 Tractors, 1 Chopper.....*..., 79

B.8 Optimum Solution--320 Acres, 4 Tractors, 1 Chopper, 3 Corn
Pickers................,........................ ..,... 80

B.9 Optimum Solution--Final Farm Plan.. ..............,,........ 81

B.10 Purchasable Assets: Price' Credit Terms and Depreciation... 82


vii









IF TABLES--continmed


]


LIST O

TABLE

B .11

B.12

B.13

B.l

3.15

B.16

B .17

B.18


B.19


Page

83

8h

85

85

86

86

87


88


89


viii


Cost of Machinery Repair ...................................

Fertilizer ApplUcation and Crop Yield Estimates....., ......

Time Reqgirements for Field Operaticons.....................

NtMber of Field Working Days Per Month...........,..... ....

Dairy and Crop Cash Qosts,................... ...........,

Dairy Labor Requirenmets...................*** ..

Rations and Production for the Milking Herd, Per Cow,,......

Rations in Hay Equivalents and Corn Equivalents Per Cow Per
Year, Includes Replaements................. ...............

An Kcample of the Comnptatiol of Machine and Power
Restrictions ........ ...................................***











CHAPTER I


INTRODUCTION


When the conventional linear programming problem is fornmlated

with fixed restraints, the level at which the resources of the firm

are fixed are of primary concern because these restrictions indicate

the boundaries of the solution to the organizational problem of the

firm. The linear nature of the profit function of the linear programming

problem would indicate infinite production in the absence. of these

resource limitations,

To predetermine a set of fixed resources for any firm usually

builds into the optimal solution a certain amount of unrealism. Many

of the assets of a firm are not fixed in an economic sense, i.e., when

the marginal value product lies between acquisition and salvage values.

A farm firm is constantly adjusting many of the factors of production

which are normally considered fixed in the usual formulation of the

linear programming model for analyzing the resource allocation problems

of the firm. Land is one of the most commonly fixed resources in pro-

gramming an optimal operation of a farm. Many farmers, however, rent,

buy and sell parts of farms or whole farms and recombine their land

holdings. An important consideration in determining the optimum

organization of a farm is to find the right amount of land to combine

with the other factors. Similarly, all other factors are subject to











acquisition and salvage and should be considered so in determining an

optimum farm organization. In addition to the ability of the manager,

important limits to farm size and organization involve the amount of

funds over which the manager can gain control and some reasonable limit

to the area in which land can be purchased.

A procedure allowing for variations in the initial asset structure

of the firm, therefore, is the principal goal of this thesis--i.e., to

determine a process whereby the resource restrictions in a linear

program become endogenously determined, The procedure involves the use

of increasing factor supply functions--primarily, that of the supply

of credit--and a differential between acquisition and salvage prices of

the factors. The approach involves essentially an increasing cost

function for credit.

A problem which always exists in the interpretation of the results

of a linear program involves the assumption of infinite divisibility of

factors and products. Infinite divisibility is particularly a problem

when considering investments in non-divisible assets such as tractors,

silos, milking parlors and buildings. Some non-divisible assets such

as tractors can be rented by time period and using such a method is

satisfactory in certain problems, However, when investment in buildings

and silos, etc. is being considered, renting in small,units is undesir-

able or even impossible as a solution. An arbitrary rule for dealing

with indivisibility in investments is developed and used in the thesis.










The Nature of Fixed Resources

In the most simple sense, fixed resources are those which cannot

be or are not varied in quantity. In an economic sense, fixed resources

are those which it does not pay to vary, i.e., those resources for

which acquisition price is greater than or equal to marginal value

product which is, in turn, greater than or equal to salvage value.

In some cases, resources appear to be physically fixed. This could be

the case for an old building, possibly constructed of stone or blocks

or even of wood. It would appear that regardless of the MVP of such a

bWilding, assuming it to be very low, it would never pay to salvage it.

This is an indication of a negative salvage value where a cost, greater

than sale value, is involved in removing the building from the farm,

Since it is not rational to produce where an MVP is negative, the

building is, indeed, a fixed factor, even if it is not used at all,

If the returns from the use of the land on which the building stands

plus the sale value of the materials is greater than the cost of salvag-

ing plus the MVP of the building, it would, of course, be salvaged.

A factor is not fixed, then, if (1) the costs of removing it are ex-

ceeded by the sum of expected revenues occurring as a result of its

salvage, or (2) the costs of acquiring it are exceeded by the sum of

expected revenues occurring as a result of obtaining it It is this

principle which is used in constructing the model for this thesis.

Another form of fixity which may be effective are institutional

restrictions. Acreage allotments may limit production of a given crop

even though the MVP's of the factors in producing the crop exceed their










marginal factor cost. Using wheat as an example, a combine may be

fixed because no more than one is needed, even though its MVP may be

greater than its MFC. The amount of credit which any firm can extend

to an individual may also be limited by institutional restrictions,

It is this type of restriction which partially determines the supply

of credit available to a farmer.


The Effect of Predetermined Resource Fixities Without Regard to MVP

If a specific farm or "typical" farm is used as a basis for a

linear programming problem, and the given resources are fixed at the

initial levels, two types of error are likely to exist. A resource

fixed in abundant amounts can be utilized to the point where its MVP

drops to zero, indicating that salvage price is considered to be zero

when it actually is greater than zero. The other extreme is a resource

fixed in short supply. In this case, the MVP of the resource may be

mrch higher than the MFC of another unit.

Both bases lead to a less than optimum allocation of resources.

A factor fixed in abundance will cause the program to select inefficient

technologies with respect to that factor. For example if labor is

fixed in large amounts, labor saving technology becomes unimportant.

Similarly, highly restricted factors will impose artificial require-

meats for technology favoring efficient use of this factor. If adjust-

ment in factor quantity cannot be based upon the productivity of the

factor, when, in fact no real barriers to adjustment exist, less

desirable solutions will result.










The solution of a linear programming problem imputes values to the

fixed resources. These values are the MVP of the resource to the firm-

the amount of income which the firm would gain or lose by buying or

selling, respectively, one unit of the resource. If the resources are

artificially fixed, the imputed value would be unreasonable if that

value were greater than acquisition price or less than salvage value.

The true value of a factor to a firm is never less than its salvage

value since the firm could realize at least this amount if it disposed

of thp1factor in the market. Similarly, if the productivity is greater

than cost of acquisition (MFC) the firm would gain by purchasing and

using more of the asset.

A further undesirable characteristic of using fixed quantities of

resources in optimizing a farm organization is that the stock of

capital and credit is not converted into resources, but is used only for

cash expenses for the completely variable or non-durable factors (factors

for which cost of acquisition equals salvage value). In actuality, the

stock of funds available to the firm is convertible into stock resources

as well as factors comprising the list of expenses.


EM~pguous Determination of Resource Fixity

A linear programming model incorporating the endogenous determin-

ation of resource fixity requires acquisition and salvage activities

for all durable resources. The acquisition and salvage of durable

assets presents a stock-flow problem since the use value of the asset

during a time period is derived from the flow of services available










from the stock of the resource on hand. Short term profit maximization

would undoubtedly involve the sales of all owned resources during the

first time period. Therefore, it is essential that the stock price be

appropriately distributed over the series of time periods during which

its services would be available so that the costs from buying, and

returns from selling, correspond to the time period involved in the

flow of resources.

The costs of acquiring an additional unit of a durable asset for

a one year period are the annual depreciation, interest, repairs and

taxes. The sum of these four items rather than the market price is

the animal marginal factor cost to the firm of acquiring the asset.

The corresponding annual salvage value to the firm of selling the asset

is the sum of the depreciation, interest, repairs and taxes based on

the salvage price of the asset at time of sale.

The MFC of a factor produced on the farm is the marginal cost of

production to the firm, or the market price of the last unit delivered

to the farm whichever is lower. So long as the WC is lower than the

coat of purchasing the marginal unit, it will pay the firm to produce

the factor if more is desired. When EC exceeds the cost of the marginal

unit in the market, it will pay the firm to purchase the factor.

The imputed value of resources given in a model incorporating

endogenous fixities will ecqal (1) annual cost of acquisition for all



LFor a fuller discussion of the pricing problem see footnote 1 on
page 19.










resources increased in quantity, (2) annual salvage value for all

resources decreased in quantity, or (3) the annual value in use for all

resources fixed at the original quantity and neither purchased nor sold.

$Thns all durable assets in this model receive an imputed value based

on the annual flow of services from it.


Se2me Prfrvis Ina r Proir Wg ng iMode. Incorporating Various Aspectg

of the problem.

MaNy programming projects have been reported in the various.

Journals. Most of them follow the standard pattern with but slight

variation. Two models which have been reported in the Journal of Farm

Economics, while not closely related to the model developed here,

incorporate some of the aspects of the problem under consideration.
i
Victor E. Smith has constructed a model which incorporates a

price differential between acquisition and salvage values for some

factors and products. He incorporates cash and credit into a lump sum

to which is added, in one model, the proceeds from hay sales. These

funds are used to purchase feeder stock, protein supplement and corn

but not labor nor shelter which, in addition to funds, are considered

as fixed resources. In his second model the buying and selling prices

of hay and corn are differentiated.



IVictor E. Omith, "Perfect vs. Discontinuous Input Markets,"
Journal of Farm Boonomics, Vol. 37 (August, 1955), p. 538.










Loftsgard and Heady develop a model to obtain a solution over a

series of years, ". .. with the optimum for any one year depending on

the optimum in other years, on the availability of and returns on

capital in other years, on the need for household consumption at
2
different points in time, etc." This model is of more interest as.a

suggested extension of the model developed in this thesis than as an

explicit aspect of it and will be discussed in this respect in a later

section. In their model, however, account is taken of investments

added to the initial inventory of durable goods and includes expendi-

tures for depreciation, taxes and insurance. They do not, however,

include the problem of endogenous determination of resource fixity.


The Farm Situation and Credit Supply Functions

The farm to be programmed is a "typical" central Michigan dairy

farm located on moderately productive soils (with Miami as the major

soil series) containing 160 acres of which 132 are tillable. Included

are a full line of equipment with a PTO forage chopper, two field

tractors and one "chore" tractor, and a one row corn picker plus a 180

ton upright silo, a 32 stanchion barn which meets Grade A market

requirements and 32 cows and their replacements. The silo is equipped

with an unloader, but feeding is not automatic. It is considered that

the milking routine is set up for average efficiency but the farmer is


2Laurel D. Loftagard and Earl 0. Heady, "Application of Dynamic
Progrtmaing Mtels for Optimam Farm and Home Plans,' Journal of Farm
Zconozia, Vol. 41 (February, 1959), p. 51.

SIbid., p. 51.










capable of managing a highly efficient organization including automatic

silage feeders and either a walk-through or a herringbone parlor.

Possible investments include new machinery of the same type already

on the farm, additional upright silos or bunker silos, either a walk-

through or herringbone milking parlor, additional bulk tanks, more cows

and replacements, and automatic silage feeding bunks in the case of

upright silos. Feeding from a bunker silo is on a self-feeding basis

for efficient operation and the investment includes movable feeding

gates for this purpose. In order to keep the farm an entity, that is,

not spread over too wide an area, 480 acres is the maximum amount of

land considered available for purchase. No limit is placed on the

amount of the other resources which can be purchased except that imposed

by the availability of spendable funds.

The debt-asset structure of the farm includes a total asset value

of 445,090 with an estimated net worth of $36,000 and a debt of $9,090.

The assets are $7,545 in machinery, $10,545 in cattle plus $3,000 in a

bulk tank and $24,000 in land valued at $150 per acre. All initial

debt was considered as land mortgage at 5.5 percent interest. The total

amount of land mortgage available is 45 percent of current market value,

$2f0 per acre, or $18,000. Deducting the mortgage outstanding leaves

$8.,91Q-of land mortgage available.

In addition to the land mortgage available, credit is available

for purchasing the additional 480 acres of land, A 5,5 percent land

mortgage is available for up to 160 acres, requiring a down payment

of 55 percent. Two land contracts are considered available.










One contract requires 6 percent interest, the other 7 percent; both

require only 10 percent down payment, Each contract can be used for

as MDUIh a 160 a=Os purchased in 40, 80 and 120 acre units. A chattel

mortgage is available for $10#545 which is half the value of the chattels

and carries a 6.5 percent interest charge. The credit supply function

also includes $20,000 at 13 percent from machinery dealers and $14,000

at 9.4 percent from a silo dealer. Real estate credit is payable over

a 20 year period and all other sources of credit must be repaid in

3 years. Interest is charged annually.


Thesis Organization

First (Chapter II) the analytical model is presented and discussed,

In Chapter III the problems of applying the model to the farm situation

are discussed. The initial optimal solution, the succeeding solutions

of the discrete investment series and the final farm organization are

presented in Chapter IV. To simplify the material presented in the

text, most of the technical data and results are listed in the Tables

of Appendix B beginning on page 71.











CHAPTER II


THE ANALYTICAL MODEL


Many equations and activities in the model are of standard form,

i.e., the type usually used in a resource allocation model as applied

to a farm firm, and should require no clarification other than-descrip-

tion. Labor from April to October inclusive is divided into monthly

periods. November through March labor is considered one resource.

Tractor services, measured in hours, are divided into the same monthly

periods as labor. Machinery services are on a monthly basis and their

availability is specifically taken into account only for those months

in which they are required--there are no equations for equipment

Service during months when that service is not required. The unit for

measuring machinery service is the number of acres which can be covered

by that machine in an eight hour day, accounting for the number of days

each month the land can be worked.

Since the unit of measure for the capacity of milking parlors is

commonly time per cow, the services from the parlors are measured in

100 hour units. All other dairy equipment is measured on a per cow

and replacement basis. Land is measured in tillable acres and all

monetary equations are in $100 units. The crops produced on the farm

are transferred into crop equations so that they either. can be sold or

fed to the dairy stock. In contrast, the milk production activities

account for the sale of milk, since milk is not an input for other

activities.











In constructing the model it was found necessary to include several

specialized equations to handle satisfactorily, the investment activi-

ties. The asset aQquisition and credit activities also require

explanation since they contain some aspects peculiar to the model,

Table 2.1 on page 22 should help clarify the following narrative,


The fpeWialized EQuations

Some difficulty is encountered in explaining the three sets of

specialized equations individually since there is a degree of relation-

ship between them. However, as explaining them jointly would probably

create confusion, they are explained individually, with some of the

coefficients being more fully interpreted later in the chapter.

1. The "Suad Eqaation. The name of this equation is unimportant

and is not closely related to its function. The equation essentially

states that the sum of the annual net revenue of the firm must be at

least as great as the sum of all annual commitments which must be met

if the farm is to remain solvent. Symbolically, omitting the variables:

< R > < A C. The annual commitments of the firm include those which

accrue within the solution as well as any previous commitments the

farmer has made or must pay such as taxes, debt repayment, depreciation

and family living expenses. For convenience, let the sum of the initial

annual commitments be called K. The equation then reads: < NR > < A C + K.

The K becomes the restriction or bi value: < NR < AnC > K.

To remove the inequality from the last equation a slack activity

with the appropriate coefficient must be added.










< NR < A K

< NR < AC S + Sp K


In these equations, Ss is the regular slack coefficient. A positive

slack coefficient, S nmst be added to complete the identity matrix

used as the first solution in solving the problem by the simplex

procedure. However, the positive slack activity, corresponding to the

coefficient Sp, is artificial and should be prevented from entering

the final solution. This artificial activity, therefore, requires an

appropriate penalty coefficient in the objective function.

2. The Credit Source Restrictions (CSR). The model contains four

of these equations, one for machinery dealer credit (CSRID), one for

silo dealer credit (OSRSD), and one each for land mortgage (-CSRLM) and
1
land contracts (CSRLG). These equations are related to the acquisition

of machinery, silos and land respectively, and state that no more of

the particular source of credit is available than is generated by the

purchase of that particular asset. For example, machinery dealer credit

is not available unless, in fact, a piece of machinery has been pur-

chased. The CSR for machinery dealers will serve as an example to

explain the formulation of the equations.

It is necessary to pay 25 percent of the price (P) of a piece of

machinery as down payment (Dp). Thus, machinery dealer credit cannot

exceed 75 percent of the value of machinery purchased. It is important


aThe abbreviations are used in Table 2.1 on page 22.










to note that purchase of machinery does not force the use of dealer

credit. The purchase can be made wholly with cash. The equation, then,

is:

Dealer credit available (DCA) < P Dp

or DCA (B-Dp) 0

and removing the inequality:

DCA (P-Dp) + S 0

The DCA coefficient is part of the dealer credit acquisition

activity and the P-Dp coefficients are in the machinery acquisition

activities. The negative sign preceding P-Dp indicates that machinery

acquisition increases the amount of credit available from this source

by the amount of the coefficient. Since the initial restriction or b

value is zero, no credit from this source is available unless machinery

is purchased. The other CSR equations are exact duplicates of the

BRMD equation explained above except that the value of the down payment

varies for each.

T. The Cash Equations. The model contains two cash equations,

he first (Cash 1) is similar to the standard capital equation found

in most programming models, with one exception. All funds acquired

through the credit transactions are transferred into this restriction.

Every credit acquisition activity increases the available supply of

capital as expressed in the Cash 1 equation. In addition, all

transactions and activities requiring cash draw the full amount involved

from this equation. The cash expenses for the production activities










are drawn from this equation as well as the full purchase price of all

assets acquired.

The sales of assets increase the supply of funds since they will

be sold at the beginning of the year, but the sale of products does

not increase the amount of funds in Cash 1. Crop sales revenue is

received after most of the expense for the farm has accrued. It would

be unrealistic to add this income to cash to be used in its own

production. An exception would be milk income which is generally

received in monthly checks. In order to be realistic in adding this

income to cash, it would be necessary to consider the capital restrictions

by months. To consider monthly capital restrictions would involve a

large amount of complication in the cash transfer and utilization

activities. For this reason, income from milk production is not added

to cash available for operation and asset purchase.

The second cash equation (Cash 2) concerns the minimum down pay-

ment required for any transaction, The acquisition activities involv-

ing all items which can be purchased with direct credit (machinery,

silos, land) contain the down payment required, as a coefficient in

this equation. The firm must have at least this much cash available

before the purchase can be made. Since this equation involves only

the actual cash available and not the total amount of funds, as does

Cash 1, the credit activities such as land contracts which do not

transfer cash, do not transfer funds into Cash 2. This is the major

difference between the two cash equations. Cash 1 involves the total

amount of funds the farmer has to work with including the full amount











of credit acquired from machinery dealers, silo dealers, from land

mortgages and contracts. The Cash 2 equation considers only the actual

cash the farmer has to work with. This amount of cash includes cash

on hand and cash received from land and chattel mortgages only.

In effect, the Cash 2 equation states that the money balance or cash

on hand must be at least as great as the minimum amount necessary for

purchase of the asset.

The minimum amount necessary for purchase of an asset is not always

a down payment. Consider a banker silo for example. The materials

come from various sources, most of which do not offer credit plans.

The usual procedure would be for a farmer to acquire a loan from some

source either on his land or chattels and make cash purchases of the

necessary material and labor. In this case, the coefficient in the

Gash 2 equation is equal to that in the Cash 1 equation. And repeating,

funds for purchases of this type are available from land mortgage and

chattel mortgage acquisition activities.

One further aspect of the cash equations should be mentioned.

Depreciation accrues to the firm as the products are sold. Since

storable crops frequently are sold during the year following production,

depreciation can accumulate at any time during the year. As an arbitrary

choice, half the depreciation is added to the cash account at the outset.

This makes it necessary to add half the annual depreciation of an asset

to cash at the time of purchase, which is assumed to be at the first of

the year. Similarly, half the depreciation must be removed from cash

if the asset is sold. Therefore, for all depreciable assets, the full










coefficient for the Cash 1 equation in the acquisition activities is

price minus one-half the depreciation (P-1/2D). The corresponding co-

efficient for salvage activities is one-half of the depreciation minus

the salvage value (1/2D-Vs).


The Double Purpose Acquisition Activities

Two methods exist for incorporating the asset acquisition activi-

ties into the model. The first, and less desirable involves, for each

asset, one activity for cash purchases and one for purchases with direct

credit. This would be necessary if only one cash equation were used

since the two types of purchases require different amounts of cash.

The addition of the second cash equation reduces the number of

activities needed by requiring only one acquisition activity for each

asset. A single acquisition activity contains the coefficients for

both cash equations and simultaneously handles both types of purchase,

A direct credit purchase enters the solution only if one of the direct

credit acquisition activities enters. If no-direct credit acquisition

activity has entered, all funds in both cash equations are derived

only from cash on hand plus cash loan activities. Therefore, if none

of the direct credit acquisition activities has entered, all purchases

are on a cash basis and only the Gash 1 equation would be effectively

limiting.

The extent of direct credit purchases which are made depends on

the level at which the pertinent credit acquisition activities enter

the solution. To this extent, funds are added to Cash 1 and not to











Cash 2, and both equations can then become effectively limiting.

Thus, the type of purchase made, with cash or with direct credit, is

independent of the acquisition activity and one activity serves a

double purpose.


The Credit Activities

There are three types of credit acquisition activities in the

model:, mortgages, dealer credit and land contracts. Land-mortgages

are divided into two categories depending on use. A mortgage is avail-

able on the land owned by the farmer at 5.5 percent interest. This is

one of the credit activities which transfers funds to both of the cash

equations described above. The other land mortgage is available for

purchase of up to 160 acres, the purchased land being the collateral.

Since this latter activity does not transfer the actual funds to the

farmer, only the Cash 1 equation is credited with the amount of the

mortgage when the activity enters the solution. The land contract

acquisition activities have the same effect on the cash equations as

the second type of land mortgage activity since funds are not transferred

directly to the farmer. A chattel mortgage acquisition activity is

available and transfers funds into both cash equations. The two dealer

credit acquisition activities, machinery dealer and silo dealer, affect

the restriction of only the Cash 1 equation,

One additional credit activity should be described. This is the

land mortgage repayment activity. The activity enters the solution

only if the firm goes out of business, sells its assets and repays its










debts. Since no other debts exist at the outset, no other debt repay-

ment activity need be considered. Funds are drawn from both cash

equations if debt repayment is included in the solution.


The Cash Coefficients

The annual MVP of an asset mnst exceed the annual cost of owner-

ship of one more unit of that asset (MFC) in order for the. purchase of

another unit to be profitable. The annual cost of ownership includes

depreciation (D), interest (i), repair (R) and taxes (T). These items

are, in effect, the cost of the annual flow of services from the asset.

The sum of these items aust be charged against the acquisition of an
1
asset as the MFC of obtaining another unit.

In this model, only the depreciation and taxes are charged directly

against the acquisition activity for crop machinery; that is, appear

in the profit equation as a cost coefficient, Repairs are charged as

expenses in the crop producing activities since they are primarily a


The MVP and MFC can be in units of either a stock or a flow so
long as both are in the same unit. To convert the MVP of a flow unit
to the MVP of a stock unit, naltiply the MVP by the number of flow
units per unit of stock. The consequences of this relationship are
explored in a later chapter.
The annual MFC of a stock unit is not the total market price of
the resource divided by the number of years: use. A durable asset
which has a life greater than one year, need not return its full market
price in one year to be profitable to acquire. In contrast, the MFC of
a unit of a non-durable item, which is expended within the year, is its
market price--the equivalent of the annual cost of ownership of a
durable asset. Since the annual cost of ownership of a durable asset
is composed of depreciation, interest, taxes and repairs, these items
comprise the annual MFC of a durable.










function of use. This cost is then reflected in the profit equation

as crop producing cost. Charging repairs in this manner has the effect

of reducing the direct annual MFC of the machine, but sinmltaneously,

it increases the indirect cost by increasing the cost of producing the

crop. Thus, indirectly, the MFC is unchanged. The annual expenses or

"repair" charge on the livestock, i.e., veterinarian fees, breeding fees,

etc., is similarly charged against the milk producing activities.

Repairs on silos, buildings and dairy equipment are included with

depreciation and taxes in the profit equation for acquisition activities.

All interest costs are handled through the credit acquisition

activities. The initial cash on hand has an opportunity cost of four

percent through the cash salvage activity. Capital used for production

or asset purchase must bear a return greater than four percent before

cash will be so used. When the initial cash on hand is exhausted,

more can be acquired at 5.5 percent through the land mortgage acquisi-

tion activity. Therefore, the MVP of the asset purchased mast be at

least as large as the total of repairs, depreciation, taxes, and the

interest charge, the latter being a cost coefficient in the profit

equation for the credit acquisition activity. The profit equation

coefficient for machinery sales activities reflects the savings to the

firm of not owning the asset. That is, the depreciation plus taxes

which are saved by not owning the machine.

The coefficients in the profit equation for the crop producing

activities are cost figures equal to the cash expenses (CE) for non-

durable items plus repairs on the durable assets. This same coefficient










is in both cash equations for these activities. The profit coefficients

for the milk producing activities are gross revenue minus cash expense.

The cash expenses appear in the cash equations. The profit coefficients

for the crop sales activities are the gross revenues received from the

sales since all costs have been deducted elsewhere in the program,

The sum equation accounts for changes in net revenue and annual

commitments. The revenue increasing activities-milk production, crop

sales, debt repayment and asset salvage-have the same coefficient in

the sum equation as in the profit equation with a positive sign.

Asset acquisition activities increase annual commitments and thus bear

a negative coefficient in the sum equatifon Here, again, the co-

efficient is the same as in the profit equation as is the case for the

coefficients in the crop producing activities which also have a negative

sigt The annual commitment acquired upon the acquisition of credit

includes not only the interest, but also the annual repayment of

capital (J ). The coefficient in the sum equation for the credit

acgiisitioa activities, therefore, is the sum of interest plus capital

repayment and bears a negative sign since it is an annual commitment.

The coefficients for the cash equations have been explained elsewhere.




-Debt repayment actually is a cost decreasing activity, but the
net effect is the same as a revemne increasing activity,





TEABL 2.1
L^


CASH, 0OseFIGBI I, MOR. THB VATRIOS MpPa Ao A ISr.lTI'ib


Activities Land Credit Credit Credit
aq. Credit Credit Credit acq. acq. repay-
cash Land acq. acq. acq. land banks meant Crop Milk
Equations or acq. Machy. laid land machy. and (Chattel Machy. land pro- pro-
mort. contract acq. mort. cont. dealer mart mort,) sales, mort. duction duction

Profit -T -T -(D+T) -i -i -i -i -i (D+T) i -(CAt.R) NR
Cash 1 (e ) P P P-1/2D -100 -100 -100 -100 -100 1/2D-V 100 CE + R CE
Cash 2 (C ') 5P .10o .25--D -100 -100 1/2D-Vs 100 CE + R CE
Sum -T -T -(D+T) -(i+g) -(i+Cg) -(iCR) -(i+CR) -(iCR) D+T i+CR CE + R NR
Land mort.
avail. 100 -100
Land cont.
avail. 100
Dealer credit
avail. 100
Bank credit
avail 100
CSLM -4UP 100
CSRMD -.75P 100
OCSRL r .90P 100
Land and mort.
avail. 1,Q.











Specialization and Diversification and the Effect of a Single Fixed

Resource on the Solution.
most farmers choose as their principal or main enterprise--
around which to develop farming programs--an enterprise which has
high and sustained marginal returns; they then produce this
product with their fixed investment as long as marginal returns to
the variable inputs exceed those obtainable from other enterprises,
They add to such a crop (or livestock) other enterprises which
will employ unused resources equally advantageously at the margin.
If they are interested only in monetary returns, this process of
Expansion is continued until marginal returns are equal for all
enterprises. it is obvious that the existence of complemen-
tary (and, hence, multified farms) depends upon the production
relationships existing for the variable factors of production,
given the fixed investments in each enterprise. if a high
proportion of the inputs used in the production of the various
products, is fixed, complementarity is likely to exist. If a small
proportion of the inputs used in the production of the various
products is fixed, then complementarity is less likely to exist,1

The basic assumption of this model, concerning initial resource

fixity, is that the supply schedule for spendable funds is the only

fixed resource. All other resources, except land to some degree, are

variable and thus present no limit to production. The program, there-

fore, emphasizes, much as the farmer described in the above passage,

the single most profitable activity relative to the use of spendable

funds. The magnitude of this activity will expand to the point where

the cost of obtaining additional factors of production, a function of

the increasing cost of credit, exceeds the marginal value productivity

of the factors in this one activity or to the limit of a resource, the

MVP for which lies between acquisition and salvage values and is,


'Lawrence A. Bradford and Glenn L. Johnson, Farm Management Analis
(New York: John Wiley and Sons, Inc., 1953), pp. 171-172.











therefore fixed. This process of enterprise expansion can create idle

services from some of the resources during the months in which they

are not used. Such idle services might be used profitably in other

enterprises or activities. In effect, these idle services have become

fixed for the firm as a by-product of the expansion in resources to

produce the most profitable product (activity).

An increase in the proportion of services which are thus fixed,

tends to create seasonal complementarity (sometimes called supple-

mentarity) between enterprises as expressed in the quoted passage above.

Therefore, the program, as would the farmer, selects the next most

profitable activity (enterprise) to make fuller use of the endogenously

fixed stock of resources. Thus, it can be seen that specialization is

not a by product of a single, fixed resource if provision is made for

determining fixity endogenously. Unused services from endogenously

determined fixed levels can make diversification a profitable alterna-

tive just as can unused services from predetermined resource fixities.

In a mechanical sense, it would appear that with only one resource

initially fixed, only one production activity could enter the solution

since in a standard linear programming model, when a resource becomes

limiting, the slack activity becomes zero and a production activity

enters the solution to the limit of the scarce resource. In the model

presented in this thesis, a production activity can, but need not

enter the solution when a non-money resource becomes limiting. If the

productivity of the factor is such that more of the asset should be










purchased, an acquisition activity will replace the slack activity.

Therefore, a production process or activity may not be obtained in the

solution to replace a slack resource activity unless one of the re-

sources is just exactly used up and no more acquired, i.e., the resource

has been endogenously fixed at the initial level. However, since

spendable funds are limited in amount, at least one production activity

will enter so long as the solution indicates any production at all

(the other possibility would be to sell out). Other possibilities for

production processes to enter into the solution would be when any of

the specialized equations (cash 2, sum or one of the CSR's) is an exact

equality and the slack activity drops out. Thus, if it is profitable

for the firm to diversify, the program, mechanically, is capable of

arriving at such a solution.


Discrete Investment Levels

An ever present problem of linear programming evolves from the

assumption of infinite divisibility. This problem is particularly

difficult when considering investments in expensive durable items,

since the purchase of a complete unit is essential. In this model an

arbitrary method has been incorporated as one possible way of handling

the problem.

The problem is to find the most profitable discrete level of

investment for the important investment items. This is equivalent to

the most profitable discrete level at which an asset should be fixed,

Thus, the method evolved depends upon the concept of resource fixity,










An asset is fixed to the firm if its MVP lies between, or is

equal to, its acquisition and salvage values. The greater the differ-

ential between the acquisition and salvage values, the more subject

the asset is to fixity because the MVP will have to change by a greater

magnitude before it lies outside these boundaries. It is also true

that the MVP of a fixed asset will vary as the quantities of the vari-

able factors used with it vary,

It is a reasonable approach to determine the level of fixity for

assets individually, beginning with the one most subject to fixity.

The variations of the other assets will be less likely to cause the

MVP of the fixed asset to shift beyond the bounds of fixity if the one

with the greatest differential between acquisition and salvage values

is the first to be fixed in the solution,

The method, then, for determining discrete investment levels is

first to obtain an optimal solution with all assets assumed to be

infinitely divisible. Choose from among the assets in which investment

occurred, the one most subject to fixity. This particular asset is

then fixed for the farm at the next higher and next lower discrete

level by changing the initial restrictions by the amount of the co-

efficients in the acquisition activity multiplied by the level of the

activity for each case and removing the acquisition and salvage activi-

ties for the asset from the matrix. This process, however, may result

in negative values for the restrictions in some equations, particularly

the cash equations, so that manipulation of some other activity levels

may be necessary to increase the negative values to some non-negative











or zero level. When this process is completed, the program is rerun

twice, once for each investment level. After adjusting the profit

values for each solution to account for the different investment levels,

the solution for which the largest profit was obtained indicates the

most profitable discrete investment level of the asset in question.

The process is then repeated as often as desired, each time using the
i
new set of restrictions derived from the previous trial solution,

Figure 1 should help explain the procedure described above. In

Figure 1, ACGK is a portion of the MFC curve for spendable funds and

the point E represents the MVP of dollars invested for the optimum

solution. To the left of E, the MVP of cash would be no lower than DE,

and to the right, no greater than EF. The line DEF, therefore, repre-

sents the extreme range of the MVP of cash on either side of the opti-

mum value, E. The initial optimal solution indicates the use of OP

dollars of inputs including an investment in 2.4 tractors with a

revenue of OREP or greater. The problem is to determine whether an

investment in two or in three tractors is more profitable.

If investment is fixed at two tractors, revenue will be no less

than the area ORDN, the area lying under the MVP curve. The net cost

of moving from 2.4 to 2 tractors is BDEC, the loss in net revenue.

Net revenue, of course, is < MVP- MFC or BDEC between 2 and 2.4

tractors. In moving from 2,. to 3 tractors, the net cost is EGHF, the


lIt should be emphasized that this method of determining dis-
creteness leaves much to be desired. See Appendix A for a more complete
discussion of the effect on resource fixity from using this method.










amount by which the change in cost exceeds the change in revenue. The

alternative chosen is the one having the lower net cost--two tractors

would be chosen if the relationships were as in Figure 1.

The difficulty is in determining the magnitude of the net cost

areas BDEC and EGHF. The effect of forcing an investment in either

two or three tractors can change the proportions in which the enter-

prises as well as the inputs are combined. This can cause a shift in

either or both the MVP and MFC such that it is impossible to pre-

determine, without computing the two programs, the most profitable

level of investment for the asset under consideration.



$
Product
Cost
G H K F
MFC


-------------- MP

A Bi G

I I



0 1 2 2,1 3tr
SM N P Q tractors
Sinputs


Figure 1











CHAPTER III


APPLICATION OF TE MODEL


The model was applied to a "typical" central Michigan dairy farm

situation for which several alternative organizations were considered.

The "typical" aspects of the farm refer to the initial resource base

including type of land, amount and kind of machinery, size of herd and

livestock facilities. The manager was considered to be above average

in capabilities for obtaining higher than average crop and milk yields

and able to use the most efficient type dairy facilities in use at the

present time. The dairy farms of Michigan are presently undergoing a

technological change, increasing labor efficiency particularly for the

milking chores and herd management. Therefore, it is not unreasonable

to consider such possibilities for a man on an average dairy farm,


Crop Production

In all, 33 crop producing activities are included in the model,

involving three crops--corn, oats and alfalfa. The oats and alfalfa

are considered as one crop with one-fourth of each acre devoted to

oats, for a nurse crop, and three-fourths to alfalfa. The proportion

of corn in the rotation is independent at all levels. The solution

could involve continuous corn, no corn, or any amount in between.

For each crop, three fertilizer levels are included, the lowest level











CHAPTER III


APPLICATION OF TE MODEL


The model was applied to a "typical" central Michigan dairy farm

situation for which several alternative organizations were considered.

The "typical" aspects of the farm refer to the initial resource base

including type of land, amount and kind of machinery, size of herd and

livestock facilities. The manager was considered to be above average

in capabilities for obtaining higher than average crop and milk yields

and able to use the most efficient type dairy facilities in use at the

present time. The dairy farms of Michigan are presently undergoing a

technological change, increasing labor efficiency particularly for the

milking chores and herd management. Therefore, it is not unreasonable

to consider such possibilities for a man on an average dairy farm,


Crop Production

In all, 33 crop producing activities are included in the model,

involving three crops--corn, oats and alfalfa. The oats and alfalfa

are considered as one crop with one-fourth of each acre devoted to

oats, for a nurse crop, and three-fourths to alfalfa. The proportion

of corn in the rotation is independent at all levels. The solution

could involve continuous corn, no corn, or any amount in between.

For each crop, three fertilizer levels are included, the lowest level










being about equivalent to the general level of application currently in

practice. Consequently, the higher fertilizer levels are concurrent
1
with above average management practices.

Silage is an important component of the rations for dairy cattle.

It is desirable, therefore, to include in a dairy farm program, various

amounts of both hay and corn which can be cut for silage. The amount

of corn cut for silage varies by 20 percent intervals from zero to

one-fifth, to two-fifths, up to 100 percent. The oats are all cut

for silage in each oat-hay activity, with the combined oat-hay crop

being cut for silage at the rate of one-fourth (oats only) two-fifths,

three-fifths, four-fifths and 100 percent. Thus, there are six corn

production activities and five oat-hay activities each having three

levels of fertilizer application, or a total of 33 crop production

activities.


Milk Production

Initially, the farm is equipped with a 32 stall grade A stanchion

milking barn and a 500 gallon bulk tank. Milking is done by machine,

but the milk is carried to the bulk tank. Grain is fed on an individual

basis from a cart. Silage feeding is accomplished with an automatic


'The low and medium fertilizer application levels are taken (with
slight.modification) from: C. R. Hoglund and R. L. Cook, Higher Profits
FroL. Fertier r and Improved Practices, Agricultural Economics Mimeo
5, Michigan State University Agricultural Experiment Station and Soil
science Department, Revised October, 1956. The high application levels
are a current revision of the same publication by Hoglund, Cook, John
luttay and L. S. Robertson.











silo unloader in the upright silo but without automatic auger feed

bunks. The labor efficient operation of the stanchion system includes

an automatic feeder for silage and a pipe line milking system. If the

herd were expanded or more silage fed, additional investments could

include another upright silo or bunker silo. Three stanchion systems

are considered as alternatives in the model: the present system with

"average" labor efficiency; a labor efficient system with upright silos;

and a labor efficient system with additional investment in one or more

bunker silos.

Two milking parlors are included--a double three walk-through

parlor and a double six herringbone system. For each type, combinations

for (1) "average" efficiency with upright silos, (2) efficient opera-

tions with upright silo and (3) efficient operations with bunker silos

are included. In addition, for each of the nine different systems,

nine rations with varying proportions of hay and silage and varying

levels of grain are used. There are three proportions of hay and silage

with three grain levels for each. Milk production increases from

.10,000 pounds to 10,500 pounds and 11,000 pounds depending on the

amount of grain in the ration. In all, the model contains 81 different

milk production activities.


Derivation of the Technical Matrix and Restrictions

Technical production data for a specific area are always difficult

to obtain. The sources of data used in this thesis are primarily pub-

lished bulletins and articles and unpublished reports of the Michigan










Agricultural Experiment Station. Where specific data were not avail-

able, "best-estimates" were obtained from staff members working in

that field. Tables summarizing the data used are presented in

Appendix B.

The restrictions for all crop machinery except tractors are com-

puted for the number of acres which can be covered in an eight-hour

day including time loss for repairs, lubrication and turning. An esti-

mate of the number of days per month during which field conditions are

suitable for field work was used to obtain the total number of acres

which could be covered per month for each operation. Tractor services

are based on an eight hour day and are considered available the same

number of days per month for which field conditions are satisfactory.

The data used in the computations are in Appendix B.

The capacity of the milking equipment was figured in hours for 16

hours a day, 365 days a year. This would make possible a specialized

"milk factory" operation. Since the milk production activities are

on a per cow basis, the coefficients are the number of hours per cow

per year, milking at the rate of 46 cows per hour for the most efficient

parlor organisation. The feeding equipment is on a per cow basis, so

that the coefficients are one.


Acquisition and Salvage

All the crop producing machinery can be bought or sold. A dif-

ferential between acquisition and salvage prices makes it unprofitable

to buy and sell the same piece of machinery. Land, too, can be bought.











or sold. If the original acreage is sold, the mortgage on it must be

repaid. The acquisition of a new milking parlor includes the disposal

of the old stanchion barn. Buildings and facilities which are not

included in the initial resource base cannot be sold so no salvage

activity exists for these items, In addition, more cows and replace-

ments, jointly, can be purchased, or any proportion of the herd sold.

Hired labor can be acquired by the month for cropping operations

and summer milking for the months of April through October. Any labor

acquired during the off season would be for milking, so the months of

November through March are grouped together. In case no dairy is

included in the solution, the farmer has the opportunity of off-farm

employment of his labor during the slack months of November through

March. The opportunity cost of the farmer's own labor during the

summer months is the possibility of employment a specified number of

days every month up to full time off-farm employment.


The Range of Possible Solutions

First, it is possible for the farmer to sell out completely,

invest the resulting cash at 4 percent, and obtain full time off-farm

employment. The earnings from off-farm employment will satisfy the

family living requirements and thus, the sum equation, since all other

annual commitments will be cancelled. It is also possible to have a

complete milk factory with all inputs acquired. It is possible to

purchase all labor, feed and equipment necessary to run this type of

operation. The third possible extreme is to keep the farm but sell







34


the dairy equipment and herd and end up with a cash crop farm. It is

not necessary for the crops to be sold through the dairy herd.

Given these extremes and the assumptions of linear programming,

it is evident that any combination of the limited number of altern-

atives considered, represents a possible solution.












CHAPTER IV


SOLUTION OF THE FARM MDDEL


The initial optimal solution obtained from this model is unique

to linear programming in that the quantity of all resources can be

varied should it be profitable to do so. Consequently, the model

allows the determination not only of the optimum combination of enter-

prises, but also the optimum combination of the factors of production

subject to the limitation on funds, the initial asset structure, the

acquisition and salvage values of the assets, product prices and the

input-output relationships. Since the principal limit to enterprise

organization and size results from the increasing cost of obtaining

funds, the solution is optimal with respect primarily, to spendable

funds. In addition, the imputed values of the resources are a function

of their acquisition and salvage values, their use opportunities and

their initial level on the farm, rather than being a function of an

arbitrarily set and rigidly fixed limitation on the amount available

to the farm.


The Initial Optimal Solution

The initial assumptions made in formulating the model result in

an optimum organization consisting of a 337.2 acre cash crop farm

containing 282.7 acres of continuous corn, of which 12 acres are cut

for silage and sold out of the field, with the remainder sold as grain.












CHAPTER IV


SOLUTION OF THE FARM MDDEL


The initial optimal solution obtained from this model is unique

to linear programming in that the quantity of all resources can be

varied should it be profitable to do so. Consequently, the model

allows the determination not only of the optimum combination of enter-

prises, but also the optimum combination of the factors of production

subject to the limitation on funds, the initial asset structure, the

acquisition and salvage values of the assets, product prices and the

input-output relationships. Since the principal limit to enterprise

organization and size results from the increasing cost of obtaining

funds, the solution is optimal with respect primarily, to spendable

funds. In addition, the imputed values of the resources are a function

of their acquisition and salvage values, their use opportunities and

their initial level on the farm, rather than being a function of an

arbitrarily set and rigidly fixed limitation on the amount available

to the farm.


The Initial Optimal Solution

The initial assumptions made in formulating the model result in

an optimum organization consisting of a 337.2 acre cash crop farm

containing 282.7 acres of continuous corn, of which 12 acres are cut

for silage and sold out of the field, with the remainder sold as grain.










This organization involves the purchase of 177.2 acres of. land, of

which 85 percent is assumed to be tillable, and the complete disposal

of the dairy enterprise. Although somewhat unrealistic, it is more

profitable for the farmer to take advantage of full-time off-farm


employment and hire the necessary farm labor.


Table 4.l shows the


change in inventory between the initial farm assets and those of the

optimum organization.


TABLE h.l


ORIGINAL AND OPTIMUM INVwTORIES


Item Initial Purchased Sold Optimum
Inventory

Land, total acres 160 177.2 337.2
Land, tillable acres 132 150.7 282.7
Dairy cows 32 32 O
Dairy heifers 11 11 0
Dairy calves 13 13 0
Fiel4. tractors 2 3.0 5
Plows 1 1.6 2,6
Disc, drill 1 1 0
Disc, planter 1 1.1 2.1
Cultivator, sprayer 1 0,7 1.7
Mower, rake i 1 O
Wagons 2 4.8 6.8
Chopper 1 0.8 0.2
Fertilizer spreader 1 1.0 0
Corn pickers 1 2.4 3.4
Bulk tank, 1 1 o


1In at least one case, this has actually occurred on a Michigan
farm. In general, however, this is an undesirable course of action
since it leaves the farm without an active manager when only monthly
laber is hired. Wire the hired labor on a full time or tenant basis,
of course, the organization would not be unrealistic nor necessarily
undesirable. Obtaining such a result in the solution is a consequence
of the static nature of the analysis. The opportunity cost of full
time off farm employment is s~fficient~yy igh that, since management is
not considered a necessary resource, the services of the manager are
sod~i off the farm.











After deducting cash expenses, taxes, depreciation and interest

for new debt, but excluding interest on the owned assets and capital

repayments to retire the debt, profit for the optimum solution is

$8610.1 De0ct~ig the off farm income of $4W00 leaves a farm profit

of $4310. Farm profit includes a return to owned assets. If the owned

capital is charged a 6.5 percent interest rate, which is the highest

rate paid for credit, the remaining amount is $2412.

Adding the off farm income to the $2412 above gives the labor

income for the farm. Labor income is $6912. If the family spends

only the minimum amount for consumption, $3200, then $3712 is available

from labor income to retire the debt. The annual capital repayment

contracted upon the acquisition of the debt is'S3635. By paying this

amount in full, the family has available for consumption, in addition
2
to the minimum $3200, the amount of $77.

To organize the optimum farm requires a full mortgage on the owned

land and a chattel mortgage on all equipment. In addition, 160 acres

is purchased with a 6 percent land contract and an additional 17.2

acres with a mortgage after meeting the down payment requirements.

The total annual interest and capital repayment commitment which the

farm must meet is $7320. In addition to the credit acquired, cash was

increased $8837 by the sale of assets.

'This is the value which is maximized in the objective function.
For purposes of comparing profit from the various solutions, only those
items stated above are deducted from gross income. This figure could
be called return for family labor and owned capital..
I2t is, of course, possible for the family to spend for consumption
the interest on owned assets and depreciation, in addition to labor
income.










The values imputed to the resources and farm produced crops are

of major interest from both an empirical and a theoretical point of

view. As one would expect on a cash crop farm where the crops are not

sold through livestock, the value of the crops are the prices received

by the farmer--90 cents per bushel of corn and $17.50 per ton hay

equivalent of silage. Similarly, the imputed value of assets sold

should be equal to their salvage value.

The salvage value of a unit of service from a durable asset is

equal to the savings in depreciation, taxes and interest all based upon

the salvage value of the durable stock. For example, the depreciation

and taxes per cow and replacements as a unit are $42.39. The interest

charged at the highest rate (6.5 percent) on the net salvage price of

$139.22 is $9.05. The Delta J value or imputed value of the cow and

replacements unit is $52.07 which is very near the total of taxes,

depreciation and interests, $51,44.. The imputed value of one unit of

service from the disc, drill asset is 80 cents. The salvage value of

the service unit is 79 cents. The corresponding values for the forage

chopper, which was only partially sold, are $3.52 and $3,47 respectively.

3The term Delta J.stands for the imputed value of the activities.
The values imputed to the slack activities are the MVPts of the resources,
An accumulated round-off error, accounting for the difference between the
Delta J and salvage value is to be expected when working with a large
number of equations and activities, especially with the high degree of
interaction expressed in this model.
2The MVPts of the resources are expressed in terms of the units in
which they are measured. In the cow and replacements example above, both
the salvage activity and the resource are measured in the same unit. In
contrast, machinery salvage is measured in terms of a stock but the resource
in terms of a flow of services. (As a consequence, such resources are
varied in terms of a flow rather than in terms of a stock,) Therefore, it
is necessary to divide the salvage value of such an asset by the number of
units of the flow service derived from it to put it in the units in which
the inputed value is measured.










The acquisition cost of a unit of flow service from an asset is

the sum of the annual cost of depreciation, interest and taxes of the

stock divided by the number of flow units, This cost is computed in

the same way as was the salvage value for assets sold. The imputed

value and cost of acquisition respectively for three acquired resources

are: for May plow services, $.34 and $.29; the services for the disc

and corn planter, $.67 and $.63; and an hour of June labor, $l.iI. and

$1.13. A listing of the imputed values of the resources for each

solution appears in Appendix B and are further discussed in a later

section.

The values imputed to non basis or excluded activities indicate

the decrease which would occur in profit if that activity were forced
1
into the solution. This information makes possible the determination

of the relative profitability (in a more strict sense, unprofitability)

of those activities not in the solution. Several aspects of the excluded

activities are worthy of note.

Considering first, the corn activities in which all the corn is

picked for grain, the activity having the heaviest level of fertili-

zation entered the solution, The reduction in profit from using the

medium level of fertilizer would have been $19.60 an acre, determined

from the Delta J value of the activity. Using the lightest application

of fertilizer considered in the program would have reduced profit by

$44.12 per acre. The same relationship is true for all the corn


INon basis activities are the activities which do not enter into
the final solution.










activities. That is, the heavier the application of fertilizer, the

less would be the reduction in profit or, stated alternatively, the

greater the increase in profit, from incorporating that activity in

the solution. Within the corn activities using a high level of

fertilization, the reduction in profit from increasing the amount of

silage would be $3.24 per acre if 40 percent were so harvested, $4.78

if 60 percent, and $6.40 and $8.04, respectively, for 80 and 100 per-

cent silage per acre.

No hay producing activities entered the solution. The least

reduction in profit from forcing hay into the solution ($1.88 per acre

of hay) would have resulted from the most highly fertilized hay of

which anly the oat nurse crop was chopped for silage. Here, again,

the increasing reduction in profit from decreasing the level of

fertilization is evident as well as from increasing the amount of

silage per acre.

By varying the level of fertilizer within a crop activity series

with the proportion of silage held constant, the change in profit due

to changing the fertilizer can be determined. For example, consider

the corn activities in which 40 percent of the acreage.was chopped and

60 percent picked. The imputed values of the activities at the three

fertilizer levels were: low, $21,20; medium, $10.88 and high, $3.26.

Since these figures indicate the loss in profit, the difference between

low and medium, and between medium and high indicate the increase in

profit from heavier application of fertilizer. The gain in profit

from low to medium is $1.32 and from medium to high is $7.62, Plotting










these values on a graph with dollars of fertilizer on the horizontal

axis, illustrates the decreasing returns as more fertilizer is applied.


Gain $ 11
10



8

7

6

1

0
8 9 10 11 12
Dollars of Fertilizer per acre
(Corn)

Figure 4.1


Since in the imputed values, all costs are accounted for, the

values plotted in Figure 4.1 are changes in net revenue or profit and

can be defined as gain. Maximum profit is equivalent to zero gain.

Therefore, it appears that even though higher level fertilizer appli-

cations were used in this study than currently in common practice, even

hijger applications walld be profitable. The total cost of fertilizer

applied to corn at the three levels was: $8,32, $10.-2 and $12.92.

The total cost of fertilizer applied to hay at the three levels

was $3.0O, $6.54 and $9.32. The corresponding imputed values for hay

with only the oats cut for silage are $21.94, $11.28 and $1.88.










In Figure 4.2, the gain obtained from increased fertilizer application

is plotted. Here, again, it appears that heavier rates of fertilizer

would be profitable.


Gain 12

11

10

9

8

7

1


4 5 6 7 8 9

Dollars of Fertilizer per acre
(Hay)

Figure 4.2

With only two points on the gain function, it is not possible to

determine the most profitable level of fertilizer to use. However,

the closer gain is to zero, the closer the rate of application to the

maximum profit point. Given the information available, it appears that

the rate of fertilizer application on corn is nearer to the optimum

than the rate on hay -

The magnitude of the Delta J values for the milk producing activi-

ties indicate that dairying, under the conditions set forth in the

assumptions, is a poor alternative compared to cash cropping if con-

tinuous corn is possible. The least unprofitable type of dairy











enterprise, a highly labor efficient herringbone system, would have

reduced profit by $2224 if one cow were milked. Throughout all three

milking systems, efficiency in labor utilization has a marked effect

on profitability, but there is only a slight profit differential between

upright silos and bunker silos. In choosing between the types of milk-

ing parlors, the double six herringbone has a slight advantage over

the double three walk-through, but investing in either would be con-

siderably more profitable (less unprofitable) than using the stanchion

arrangement already on the farm.


The Discrete Investment Series

Had a dairy enterprise been included in the solution, the important

assets for which to determine discrete investment levels would have been

the milking parlor and the silos. These are items with a high acquisi-

tion cost and, because of their permanent nature, a relatively low

salvage value.

On a cash crop farm, it is important to determine the size of the

farm, the number of tractors, and the amounts of other expensive

machinery. In addition to determining the level of land and tractor

investments, solutions were obtained to determine whether or not to

sell the forage chopper and to find the most profitable number of corn

pickers for the farm.

Fixing the level of any asset for the farm, will decrease the

value of the objective functia..from the previous solution in which

the asset level was not fixed. Each successive solution, therefore,










for which more and more of the assets are fixed will have a lower

profit than the previous solution. That is, the solutions for a

resource fixed at the next higher and next lower discrete levels, will

both exhibit less profit than did the previous solution. The choice

of which discrete level of investment to use depends on the 'relative

profitability between the two levels being programmed.

Forty acres was considered as the most reasonable discrete level

of land investment. Forty acre plots are generally available while an

area as small as 20 acres is not. To restrict purchase to 80 acres

puts an unreasonable demand on farm size. The initial solution indi-

cated an investment in an additional 177,2 acres or 337.2 total farm

acres. Land investment programs were computed, therefore, for 320 and

360 total acres or for an additional investment in 160 and 200 acres.

'the optimum organization and profit for both conditions is given in

Table 4.2 on the following page.

The 320 acre farm incorporates 268 acres of continuous corn and

no hay. Twelve acres of corn is chopped for silage using the services

of 0.17 chopper. An additional 2.2 corn pickers are acquired to pick

2.56 acres of corn,. and the acquisition of 2.7 tractors increases the

stock of tractor services to 4.7 tractors. The addition of 40 acres,

giving rise to the 360 acre farm, makes hay production a profitable

alternative by decreasing the necessary investment in specialized corn


it should be pointed out that the higher profits received from
prior solutions are based on infinite divisibility of factors and
product and as such, are only illusionary.










TABLE 4.2
PROFIT AND ORGANIZATION FOR 320 AiRES AND 360 ACRES


Description 320 360
Total Acres Total Acres

Tillable acres 268 302
Tractors, beginning inventory 2 2
Tractors acquired 2.7 2.0
Tractors, ending inventory 4.7 4,0
Choppers, beginning inventory 1,0 1,0
Choppers sold 0,83 0,53
Choppers, ending inventory 0.17 0.47
Corn pliers, begLnning inventory 1,0 1.0
Corn ptbkers acquired 2.20 1.84
Corn pickers, ending inventory 3.20 2.84
Acres in hay, high fert., oats for silage 0 74.8
Acres in corn, high fert., 1/5 for silage 60.0 1.4
Acres in corn, high fert., all picked 208.0 225.8
Total acres, picked corn 256.0 227.0
Profit, nearest dollar $8345.00 $7639.00
Profit differential +706


equipment. The production of 74.8 acres of hay restricts corn pro-

duction to 227.2 acres. With fewer acres in corn, a smaller tractor

investment is required since the use of tractor services is spread more

evenly throughout the year. Since all the hay is chopped as well as

the oat silage, more chopper services are retained on the larger farm.

Profit comparison between the alternative organizations, however,

favors the smaller farm. Consequently, succeeding programs are based

on 320 acres.

The MY~ts of most resources were reduced only slightly, comparing

the 320 apre farm with the initial optimal solution. As would be

expected, however, the MVP of land increased (from $20.72 per acre to










$22.11 per acre) when it was fixed at the 320 acre level. Cash, which

in the initial optimum was worth $7.42 per $100, is worth $6,50 per

$100 on the 320 acre farm. This occurs as a result of the limitation

on land, which causes some 6.5 per cent credit not to be used.

In figure 4.3, the segmented curve labeled AB'CD'EF represents,

again, a portion of the MFt of dollars to the firm and the line MVP

indicates the MVP of spendable funds in the initial optimum solution.


Returns to
Dollars


135 E F


7.4% --- -- VI _

6 -% D
III
I
A jB

I I
0 $i4,759 $19,289 Spendable Funds

Figure 4.3


Spendable funds, here, includes cash, owned land mortgage and chattel

mortgage, but not land contract funds nor land mortgage on purchased

land. In the optimal solution, a total of $19,289 of spendable funds

was used. This amount includes all the 6.5 percent credit available.

In the 320 acre organization, the land limitation forced down the MVP

of spendable funds so that not all the 6.5 percent credit is exhausted.










Were the MVP of spendable funds greater, an additional $4530 of 6.5

credit could be acquired.

The 320 acre organization indicated an optimum of 4.7 tractors,

Programs were computed to determine the most profitable alternative

between 4 and 5 tractors. The results appear in Table 4.3.

It is of interest to note the effect -on organization from fixing

the number of tractors at levels higher and lower than the optimum

number in the previous 320 acre solution, Restricting the number of

tractors to four has the expected effect of placing a premium on their

services, and as a result, more intensive use of these services through

time is required. Although hay is a less profitable crop than is corn,

it is profitable to more fully utilize these tractor services than to

specialize in the production of corn. Specialized corn production

makes less efficient use of the relatively scarce tractor services than

does the more diversified previous solution.

The farm organized around five tractors is a sharp contrast to

the one for which tractors are a more limiting resource. On the five

tractor farm, tractor services are relatively abundant. As a conse-

qaence, intensification of their use is not a prerequisite to a

profitable farm organization, as is the case where tractor services

are relatively scarce, Because tractor resources are fixed at a high

level on the second (five tractor) farm, specialization is a profitable

alternative.

IThe comparison of these two programs with reference to the effect
of tractor limitation on organization is a good example of the effect
on the ultimate outcome from predetermining the level of resource fixity.










Although the second farm specializes in a relatively more profit-

able crop, the added expense of the additional tractor is sufficient

to reduce profit below that for the four tractor farm organization.

Since the four tractor farm is more profitable, it is this organization

which was chosen for further investigation in accordance with the rule

developed for this purpose, In an actual planning situation, however,

the profit differential is sufficiently small that other alternatives

should be considered.


TABLE 4.3

PROFIT AND ORGANIZATION FOR 320 AGRES WITH 4 AND 5 TRACTORS


Description Four Tractors Five Tractors


Tillable acres 268 268
Tractors 4 5
Choppers, beginning inventory 1 1
Choppers sold 0,8 1
Choppers, ending inventory 0.2 0
Corn pickers, beginning inventory 1 1
Corn pickers acquired 1.82 2.35
Corn pickers, ending inventory 2,82 3.35
Acres in hay, high fert.-, oats for silage 2.80 0
Acres in corn, high fert,, 1/5 for silage 71.1 0
Acres in corn, high fert., all picked 168.9 268
Total acres, picked corn 225.8 268
Profit, nearest dollar $8228.00 $8088,00
Profit differential +140


The qUestion of whether or not to sell the forage chopper is the

next to be determined. The 4 tractor optimum indicated salvage of 0,8

of the chopper, using only 0.2 to harvest 28 acres of hay and 14.2

acres of corn silage. If the chopper is completely sold, only ear corn










car be raised since both the hay and corn silage activities require

the services from the chopper and no provision is made for hiring

custom work on the farm. If the chopper is not sold, one would expect

a more diversified farm plan to make fuller utilization of this fixed,

specialized piece of equipment. In some respects, therefore, the

effects of selling or keeping the chopper are more important to the

farm organization than determining the level of fixity for the re-

sources with a more general use.


TABLE .h
PROFIT AND ORGAIZATION FOR 320 ACGRE, 4 TRACTORS,
WITH AND WITHOUT-A FORAGE CHOPPER.


Description Without With
Chopper Chopper

Tillable acres 268 268
Tractors 4 4
Chopper 0 1
Corn picker, beginning inventory 1 1
Corn pickers acquired 1,8 1.4
Corn pickers, ending inventory 2.8 2.U
Acres in hay, high fert., oats for silage 0 28.0
Acres in corn, high fert,, 1/5 for silage 0 240.0
Acres in corn, high fert., all picked 225.6 0
Total acres, picked corn 225.6 192.0
Profit, nearest dollar $6270.00 $8047,00
Profit differential +1777



As expected, the forage chopper has a marked effect on farm

organization. With no chopper, all the corn must be picked. The

limitation on October tractor services prevents more than 225..6 acres

of corn from being harvested as ear corn. Consequently, 42.4 tillable










acres on the farm must remain idle--an unprofitable alternative.

On the other hand, having the chopper available on the farm leads to

a diversified organization which fully utilizes all available tillable

acres. With the price restriction still holding for corn pickers, it

becomes profitable to more fully utilize the chopper and reduce the

investment in the corn pickers, so more hay and corn silage is pro-

duced relative to the amount of ear corn than was the case in all

previous solutions.

These two solutions, again, provide a good example of the effect

of predetermined resource fixity. With no chopper available to the

farm, land was used to the point where its MVP dropped to zero. Were

land not fixed in this particular problem, some would be sold--the

amount sold stopping at the point where its MVP reaches salvage value.

In this example, the value, of land in Use is less than its value in

salvage. Since land has a positive slavage value, it is unrealistic

to value it at zero,

The final factor of production to be set at a discrete level in

the investment series are corn pickers. Table 4U. shows the organi-.

zation and profit for the two levels of investment.

Varying the amount of corn picker services available has less

effect on organization than when the chopper was varied. The limitation

of corn pickers in the first, 2 pickers, solution restricts the amount



1In this case, the consequences of fixing the farm size at 320
acres, when 42.4 tillable acres remain idle, are plainly evident.










TABLE 4.5

PROFIT AND ORGANIZATION OF 320 AGRES, 4 TRACTORS, 1 CHOPPER
AND 2 AND 3 CORN PICKMRS

Two Three
Description Corn Pickers Corn Pickers

Tillable acres 268 268
Tractors 4 U
Chopper 1 1
Corn pickers 2 3
Acres in hay, high fert,, oats for silage 68 28
Acres in corn, high fert., 1/5 for silage 200 240
Acres in corn, high fert., all picked 0 0
Total acres, picked corn 160 192
Profit, nearest dollar $7337 $7708
Profit differential +$371


of corn which can be harvested by this method and as a consequence,

more hay is produced. It is interesting to note that although the

organization for the 3 picker solution is the same as for the previous

solution with a chopper fixed, the Investment in the additional corn

picker reduces profit by $339.

The pattern of VPts of the various resources throughout the -

investment series helps explain the effect of fixing resources arbi-

trarily at various levels, In the two land investment problems, when

land was fixed at 320 acres, tillable acres had a value in use of $22,11,

but for the 360 acre farm where land was more abundant, the MVP of

tillable acres dropped to $10.28 which is $8.39 below salvage value.

Because the other resources were combined with a greater amount of

land on the 360 acre farm, their MVP's increased relative to those for

the 320 acre organization.










The MP of tillable acres decreases to $16,04. when the number of

tractors is fixed at four, but increases to $34.78 when five tractors

are available. Thus, it can be seen that in linear programming, as

in other computational procedures, the MVP of one fixed resource

increases as the amount of another resource is increased.

The value of the services from the forage chopper and the corn

picker remains constant as tractors are varied from four to five,

This is to be expected because in both cases, some of the chopper is

sold and some corn pickers acquired. The value of the flow unit of

the chopper is its salvage value and the MVP of the corn picker is

equal to its annual acquisition cost. The MVP of tractor services for

any given month, however, varies, depending upon the proportions of

crops produced. A change in the proportions of crops changes the

tractor requirements and thus their MVP.

The application of the model and the discrete investment rule to

the original farm situation has resulted in a farm organization con-

sisting of a 320 acre cash crop farm with h field tractors, 1 chore

tractor, a forage chopper and 3 corn pickers. In addition, for the

final farm organization, the remaining factors were fixed at the

following levels: 2 plows, 2 discs, 1 drill, 2 corn planters,

2 cultivators and sprayers, 1 mower and rake, 5 wagons and 1 fertilizer

spreader. Table 4.6 shows the complete change in farm inventory from

the original organization to the final farm plan, including discrete

investment levels for all assets.










TABLE 4.6


COMPLETE INVENTORY CHANGE
ORIGINAL ORGANIZATION TO FINAL FARM PLAN


Orijilnal Inventory FinaInvento Change In
Description Amount Value Amount Value1 Value


Land, total acres

Machinery and Equipment
Tractors
Plows
Discs
Corn planters
Cultivators
Grain drills
Mowers
Rakes
Choppers
Wagons
Fertilizer spreaders
Corn pickers
Sprayers
Truck
Silo filler
Bulk tank


160


2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1


Total


Dairy Cattle
Cows
Yearling heifers
Heifers calves

Total
Total farm investment


$24,000 320 $60,000 $36,000


$2,400
100
150
180
75
350
180
220
1200
600
220
700
100
620
45o0
3,000

$10,545


$7,680
1,760


145, 9
$h4,090


$7,968
321
467
382
329
296
1-42
162
1,018
1,425
195
3,292
364
558
405
.0


$5,568
221
317
202
254
-54
-38
-58
-182
825
-25
2,592
264
-62
-hS
-3.000


$17,324 $6,779


0
$77,324


-$7,680
-1,760


-$10h,2
$32,234


10riginal inventory value plus additional imnestment
units) minus depreciation on all units.
a~ncludes improvements.


(price x number of











The Final Farm Organization

The initial solution derived from the model is an optimum solution

under the assumption of complete divisibility. Succeeding solutions

derived from the investment series are not optimum in the strict sense.

The 320 acre farm organization with other factors variable is optimum

only in the sense that it is more profitable than the 360 acre altern-

ative. (Of course, given the 320 acres, the remaining factors and

products are optimum,) A major weakness of the rule for determining

discrete investments is that the previously fixed resources may

actually be fixed at the wrong level as more resource fixation occurs,

That is, additional resource fixation may have a sufficient effect

upon the MVP of previously fixed resources, that the excluded altern-

ative, or even an alternative not tested, may lead to higher profits.

If the MVP of land drops so low for the last solution that at least

40 acres could be sold before the MVP increased to the salvage value,

it would indicate that given the resource fixation of succeeding solu-
1
tions, too much land was acquired in the original investment solution.

The change in acreage accounts for the greatest amount of change

in inventory value. Although the additional acreage was priced at

$250 per acre, the inventory value is $225, the net price the farmer

would receive were he to sell it. For inventory purposes, the original

land is valued at $10 per acre. Placing a value of $225 per acre on

this land would have the effect of increasing the original net worth


1Refer to pages 49-50 for such a solution,


J ~ CII I I










of the farmer Net worth, when the original farm is valued at the

lower price is $36,000. Increasing the value of the land would

increase net worth to $48,000. Either valuation will have no effect

on the change in the value of inventory nor in the change in net worth,

TABLE 4.7

GOMPARISON OF PROFIT:
OPTIMTM SOLUTION AND FINAL FARM PLAN


SOptimum Final Farm Loss Involved
Description Solution Elan in Obtaining
Discrete Solu-
tion


Profit $8,810 $6,796 $2,014
Labor income 6,912 4,828 2,084
Available for capital repayment 3,712 1,628 2,084
Needed for full capital repayment 3,635 2,58 --

IFor a definition of the income categories, see page 37.

In Table 4.7, a comparison is made between comparable profit

figures for the initial optimal solution and the solution derived from

the investment series--the final farm plan. The third column in Table

4.7 shows the loss in profit due to fixing the assets at discrete levels.
In the final farm solution, labor income is $4828. In addition

to this amount, the family also has available for consumption or

investment (disposable income) the interest on owned assets and asset

depreciation. Final asset value is $77,324 and the total debt is

$59,242. Interest, at 6.5 percent, on the difference is $1175, and
depreciation on the assets is $2729. However, half the depreciation










has already been added to cash (see page 16). The disposable income

obtained by adding interest and half the depreciation to labor income

is $7,367. These figures are summarized in Table 4.8.

TABLE 4.8

DISPOSABLE INCOME, FINAL FARM PLAN


Description Amount

Labor income $4,828
Interest on owned assets 1,175
One-half depreciation 1,364

Disposable income $7,367



It remains to examine the capital accumulation side of the business.

The difference between final total asset value and total debt is

$18,082. This is the net worth of the farmer at the end of the year if

none of the debt is retired. Should the family so choose, a maximum

of $4,167 of the debt could be retired from disposable income if only

the minimum $3,200 was used for family consumption. If this course of

action were followed, net worth, at the end of the year would be $22,249.

Therefore, depending upon the use of disposable income, net worth at

the end of the year would be between $18,082 and $22,249.











CHAPTER V


SUMMARY AND CONCLUSIONS


Application of the Model

The model developed in this thesis actually is composed of two

parts. The first part, which is the principal development of the

thesis is the mathematical model dealing with the endogenous determin-

ation of fixed resources. The second deals with the discrete invest-

ment levels and is more a rule than a model. The range of application

of the mathematical model is as wide as the use of linear programming

for solving maximization and minimization problems involving resources

which, in fact, are subject to variation. The modifications in the

linear programming model made in this thesis would not be necessary

nor especially useful where resources are rigidly fixed.

The model is particularly useful in a business which has resources

as variable as does farming. It is capable of handling the very

important resource allocation problems facing farmers today--such

problems as diversification, specialization and vertical integration.

An asset structure fixed at the initial levels and proportions, pre-

determines the outcome of an optimizing problem in a very real sense.

The importance of scarce resources is unrealistically emphasized where

the opportunity for further investment actually exists. A model with

predetermined resource levels also has more of a tendency toward a

more diversified, solution than will this more general model. A model











CHAPTER V


SUMMARY AND CONCLUSIONS


Application of the Model

The model developed in this thesis actually is composed of two

parts. The first part, which is the principal development of the

thesis is the mathematical model dealing with the endogenous determin-

ation of fixed resources. The second deals with the discrete invest-

ment levels and is more a rule than a model. The range of application

of the mathematical model is as wide as the use of linear programming

for solving maximization and minimization problems involving resources

which, in fact, are subject to variation. The modifications in the

linear programming model made in this thesis would not be necessary

nor especially useful where resources are rigidly fixed.

The model is particularly useful in a business which has resources

as variable as does farming. It is capable of handling the very

important resource allocation problems facing farmers today--such

problems as diversification, specialization and vertical integration.

An asset structure fixed at the initial levels and proportions, pre-

determines the outcome of an optimizing problem in a very real sense.

The importance of scarce resources is unrealistically emphasized where

the opportunity for further investment actually exists. A model with

predetermined resource levels also has more of a tendency toward a

more diversified, solution than will this more general model. A model











in which resources are variable, is not forced to search for employ-

ment for factors of production having a very low or zero productivity.

It is much more realistic to dispose of such resources which in turn

will free funds for the expansion of the more productive enterprises.

At the same time, this model does not overemphasize specialization

which would be an equally undesirable result.

The alternative enterprises considered in the standard programming

model are, by necessity, restricted by the group of resources con-

sidered fixed. In the more general model developed here, this is not

the case. The entire initial set of assets can be disposed of and an

entirely new type of business brought into being if such alternatives

are specified in the model. However, the initial set of resources in

this general model, does influence the outcome of the program. This is

the case because the initial assets will not be sold so long as their

value in use is greater than their salvage value. Therefore, their

value in use, when combined with the other initial resources, or

additional acquired resources, must have an MVP less than their salvage

value before the initial resources would be exchanged for another set

of resources--a new type of business being organized--or sold and the

capital invested outside the organization.

It should not be inferred from the above statements that all the

analysis problems of a firm have been solved with the conception of

this model. The model still contains many of the problems organic to

linear programming and as such has many of its shortcomings. An attempt










to alleviate one of these shortcomings resulted in the rule creating

the discrete investment series described in the text.

The results obtained from any linear program are limited to the

particular alternatives and activities included in the model. The

determination of the combination of factors within each production

activity is exogenous to the model itself and as such, must be dealt

with independently. Erroneous factor combinations within the activi-

ties result in erroneous conclusions from the model.

In addition to the regular problems encountered in linear pro-

gramming, this model is oversimplified and lacks realism concerning

the budgeting and accounting techniques used. Depreciation and income

(particularly dairy income) accruing through the year are not adequately

handled nor are problems concerning the stock and flow characteristics

of resources. The stock-flow problem is of major concern. The acquisi-

tion and salvage of resources involve units of stock such as tractors,

buildings and machinery. The productivity of the stock, however, is

measured in terms of the flow of services from that resource. As a

result, the differential between acquisition and salvage values is,

operationally, a function of the unit of service, and as a consequence,

the buying and selling of resources, due to the nature of linear

programming, is a function of the flow unit of the resource rather than

of the unit of stock. This characteristic reduces the fixation re-

strictions for resources and thus creates a tendency toward more vari-

ability than actually exists. In the absence of a fully discrete

programming model, where activities enter only in discrete units, the











infinite divisibility assumption of programming will continue to be

a problem.

Further, the model is constructed under static economic assump-

tions. In the static framework, reference is not made to the manage-

ment function nor to the interrelationships between the firm and

household. The model assumes profit maximization as the only moti-

vation for production. At the same time, enterprises which are dis-

tasteful or undesirable to the manager may simply be excluded as a

possibility in the problem. The only management decisions beyond

profit maximization considered in the model are the alternative enter-

prises acceptable to the manager, including minimum and maximum size

restrictions.

The lack of risk and uncertainty considerations is another charac-

teristic of the static economic assumptions under which the model is

constructed. The input-output relationships are considered to be single

valued. The effect of diminished crop yields or prices on the liquidity

of the firm and status of the family are not taken into consideration.

Its static nature precludes risk discounts and informal insurance

schemes.

A major inconvenience of the model concerns the complex nature of

it, which tends to create great size. To completely analyze a diversi-

fied farm organization, requires at best a large and unwieldly-program

matrix. Adding the complex of asset buying and selling activities and

capital transfer activities as well as the specialized equations,

compounds the size of the matrix involved. A complete programming











analysis including the features of this model, will invariably require

the services of a large electronic computer, i.e. one with a large

memory system.


The Epirical Results

The optimal solution to the model indicates that, under the con-

citions set forth in the problem, a cash crop farm is more profitable

in the Central Michigan area than is a dairy farm even if the dairy

utilizes the most labor efficient type of operation now in practice.

It would be unwise to make recommendations from these results without

further study, for several reasons. The crop yields considered in the

application correspond to a very high degree of management skill--it

would require a very good manager to obtain the results indicated by

the most productive crop activities. Secondly, under exceptional

management, milk yields may be greater than the maximum of 11,000 pounds

considered in the model. An individual who was a very good dairy

farmer, but lacked this ability in producing crops, may well find the

profit situation reversed from the optimal solution.

The assumptions made, relative to labor, have an important effect

on the outcome of the problem. The problem assumes off farm employment

is available only a specified number of days every month for each of

the two time periods. During the cropping season, this assumption

makes it profitable to hire all necessary labor, so that the farmer's

labor is fully employed throughout the period. Were monthly off farm

labor employment available, it would have been profitable to accept










off farm employment only during slack months, hiring labor only in

excess of that supplied by the farmer during the rush seasons.

The fact that alternative employment is considered available off

the farm during the winter months, has an influence upon the profit-

ability of dairying. If the farmers labor were not utilized off the

farm during these months, the opportunity cost of dairying may be

sufficiently great that this enterprise would enter the optimum solu-

tion.

The method of handling income from the dairy enterprise quite

probably has an important influence on the outcome. If the monthly

milk checks were reflected in the cash account, less cash would need

to be borrowed outside the firm. Since cash in the initial optimum

solution has a marginal value product of $7.42 per $100, the addition

of the milk income to the cash account each month may have been

sufficient to cpuse the dairy enterprise to enter the solution,

Price considerations should also be taken into account before

making recommendations on the basis of the results of the program.

While both the crops and the milk were conservatively priced, the

relationship between the two has an important bearing on the outcome

of the problem.

The optimum cropping program, itself, should receive special

scrutiny. Since the initial assumptions were organized around a dairy

farm, the possibilities of a larger variety of crops was not considered.

This is perhaps, the most serious restriction of the results. In making

the initial assumptions, the possibility of forming a cash crop farm











as a solution was desirable, but since the farm was a dairy farm, more

emphasis was put on dairy organization than on the organization of a

cash crop farm.


Further Study Indicated

The model as applied in this thesis, considers investment, organi-

zation and operation only for a one year period. Obviously, the optimum

program the following year could not be a duplicate of the first year s

solution. It would be highly desirable to incorporate the features of

this model with the model developed by Loftsgard and Heady and referred

to earlier in the introduction. Their model makes use of dated vari-

ables and arrives at an optimum solution through time, but does not

consider the investment alternatives made possible by the incorporation

of a model considering endogenously determined resource fixities. The

combination of the two models should produce a much more realistic

answer than either is able to product alone.

Further work is required on the stock-flow problem, which, as

indicated previously, is not sufficiently handled by this model. Two

problem areas exist with respect to this problem, One concerns the

use of assets over time and the corresponding investment plan through

time. The other concerns the effect on the fixity restrictions caused

by imputing productivity values to flows rather than to stocks.

The application of linear programming to dynamic economics is

worthy of further study. Price and resource mapping are examples of

previous work in this area. The mapping technique, sometimes called







64


parametric programming, considers the effects of changes in prices and

resources on farm organization. An important problem, which has as

yet not been solved, is programming in terms of risk and uncertainty

using distributed coefficients.











BIBLIOGRAPHY

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London, 1957.

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Botts, Ralph R., Amortization of Loans, Its Application to Farm Problems,
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Bowlen, Bernard and Heady, Earl 0., Optimum Combinations of Competitive
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Gandler, Wilfred, "A Modified Simplex Solution for Linear Programming
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Hoglund, C. R. and Wright, K. T., Reducing Dairy Costs on Michigan
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APPENDICES











APPENDIX A


Resource Fixity and Discrete Investment Levels
(Text reference: pp, 25-26)

First, consider the case of a resource which is acquired (positive

investment). In the optimum solution, the MVP of the resource will

equal its acquisition value. Assuming some fractional acquisition level

in the optimum solution, the rule for obtaining discreteness will be

applied.

For the discrete level in which the fraction is dropped (next

lower discrete level), one would expect the MVP to be greater than in

the optimal solution since a smaller amount of the resource is combined

with at least as great an amount of the other resources. Immediately,

then, the resource in question is no longer economically fixed (MVP> Ga),

But at this lower discrete level, the second asset to be fixed in dis-

crete units will, in all probability, itself be at a fractional amount.

Fixing the second asset at a lower level will generally decrease the

MVP of the first resource, and, conversely, fixing the second asset at

the next higher level will further increase the MVP of the first asset

considered. Thus, if all succeeding assets are fixed at the next

higher discrete level, the MVP of the first will, in general, continue

to increase, diverging more and more from its acquisition cost. At

some point, it may become profitable to acquire an additional full unit

of the first resource.











In the case when the first resource is initially fixed at the

next higher discrete level, its MVP will decrease relative to that in

the initial optimam solution. If, in the new solution, the MVP> Va,

there is no problem-the resource remains fixed. Should the MVP become

less than the value of salvage and continue to decrease as more assets

are fixed at discrete levels, it may become profitable, at some point,

to salvage one full unit of the first resource.

The argument in favor of using this method to deal with indivisi-

bility could be based on attaching equal probabilities to all values

taken by the MVP of one resource as others are fixed at discrete levels.

Given this assumption, the greater the differential between acquisition

and salvage values, the greater the probability of the MVP of the

resources fixed at discrete levels, falling between these values and

the resource actually being economically fixed in the final solution.

It is quite evident, however, that the distribution of the values

of the MVP of a resource when fixing other resources at discrete levels

is not a uniform distribution. It seems much less likely that either

of the extreme cases discussed above will occur than that some inter-

mediate point will be reached. Thus, one would expect a distribution

more like the normal distribution with a mean near or equal to the

acquisition price. If the MVP values are normally distributed about

the acquisition price, then it is equally likely that the final MVP

will be greater than the acquisition price as below acquisition price.

In this case, too, however, the greater the differential between







70


acquisition and salvage values, the more likely the asset will be

economically fixed in the final solution.



























APPENDIX B











TABLE B.1

CROP ACTIVITY TITLE AND PROFIT COEFFICIENB


D.scriptton Profit or Cj
Number Crop Unit '-Cut for Silage Fertilizer Level Coefficient
S Dollars


Corn
Corn
Corn
Corri
Corn
Corn
Gorn
Corn
Corn
Gor=
Corn
Corn
Gorn
Corn
Corn
Gorn
Gorn
Corn
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay


100
80
60
LO
20
0
100
80
60
40

0
100
80
60

0
0
only
plus
plus
plus
plus
only
plus
plus
plus
plus
only
plus
plus
plus
plus


Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre


High
High
High
High
High
High
Medium
Medium
Medium
Medium
Medium
Medium
Low
Low
Low
Low
Low
Low
High
High
High
High
High
Medium
Medium
Medium
Medium
Medium
Low
Low
Low
Low
Low


o.o00
38.00
35,90
33-90
30.4O
29,80
36,70
34.80
32.90
31,00
29,10
27.20
34.60
32.70
30.80
28,90
27.00
25.20
32.20
32,20
32,20
32.20
32.20
29,50
29,50
29.50
29.50
29.50
26.30
26,30
26.30
26.30
26,30


Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats
Oats


3/20 hay
7/20 hay
11/20 hay
15/20 hay

3/20 hay
7/20 hay
11/20 hay
15/20 hay

3/20 hay
7/20 hay
11/20 hay
15/20 hay











TABLE B.2

DAIRY ACTIVITY TITLE AND PROFIT COEFFICIENTS, PER COW#


D!ecription Profit or
Labor Cj Go-
Number Ration No. Parlor Type Efficiency Level Silo Type efficient
Dol ars


Stanehion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Srtanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough


Average
Average
Average
Average
Average
Average
Average
Average
Average
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Average
Average
Average
Average
Average
Average
Average
Average
Average
Efficient
Efficient
Efficient
.Efficient


Contimned


Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Tpright


399.50
379.50
360.50
399.50
379.50
360.50
399,50
379.50
360.50
399,50
379.50
360.50
399,50
379.50
360,50
399.50
379.50
360,50
399.50
379.50
360,50
399,50
379.50
360.50
399.50
379,50
360.50
399.50
379.50
360.50
399.50
379.50
360,50
399.50
379.50
360,50
399.50
379.50
360.50
399.50










TABLE B.2-Contine ad

Stesription Profit or
Labor Cj Co-
Number Ration No. Parlor Type Efficiency Level Silo Type efficient
Dollars


74
75
76
77
78
79
80
81
82
83
84
8$
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
111


Walkthrough
Walkthrough
WalkthroUgi
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrou gh
Walkthrough
Walkthrough
Walkthrough
Herringbone
Herringbone
Herringbone
Herringbane
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone
Herringbone


Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Average
Average
Average
Average
Average
Average
Average
Average
Average
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient
Efficient


Upright
Upright
Upright
Upright
Upright
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Upright
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker
Bunker


379.50
360.50
399.50
379,50
360,50
399,50
379,50
360.50
399,50
379,50
360,50
399,50
379,50
360,50
399,50
379.50
360,50
399.50
379,50
360,50
399.50
379,50
360,50
399,50
379,50
360,50
399,50
379,50
360.50
399,50
370,50
360,50
399,50
379,50
360.50
399.50
379,50
360.50
399.50
379.50
360.50


--










TABLE B,3


ACGQIBITION, CREDIT AND SALVAGE ACTIVITY TITLES AND
PROFIT GOEFF1IIENTS


Profit or C
Number Description Goeffic ient


115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
1h2
143
144
115
216
147
148
149
150
151
152


Continued


Acquisition, Upright silo 284.82
Acquisition, Bunker silo 714.00
Acquisition, Herringbone parlor 1087.25
Acquisition, Walkthrough parlor 703,69
Acquisition, Automatic feed bunk 164.01
Acquisition, Tractor 356,70
Acquisition, Plow 18.63
Acquisition, Disc, drill 88,37
Acquisition, Disc, planter 48.22
Acquisition, Cultivator, sprayer 55,21
Acquisition, Chopper 279.31
Acquisition, Wagon 33.82
Acquisition, Mower, rake 98.81
Acquisition, Fertilizer spreader 26.10
Acquisition, Corn picker 156.31
Acquisition, Bulk tank 173.25
Acquisition, Loafing area, per cow 66,00
Acquisition, Cow and replacements 42.39
Acquisition, Non-auto silage feed bunk, per cow 8.12
Acquisition, Hay storage and feeding, per cow 33.00
Acquisition, Corn, 100 bushels 95.00
Acquisition, Hay, 10 tons 225.00
Acquisition, April labor, 260 hours 350.00
Acquisition, May labor, 260 hours 350.00
Acquisition, June labor, 260 hours 350.00
Acquisition, JUly labor, 260 hours 350.00
Acquisition, August labor, 260 hours 350.00
Acquisition, September labor, 260 hours 350.00
Acquisition, October labor, 260 hours 350,00
Acquisition, November to March labor, 1300 hours 1750.00
Land acquisition, cash and mortgage, 10 acres 12.50
Land acquisition, contract, 10 acres 12.50
Credit acquisition, land and mortgage, $100 5.50
Credit acquisition, 6% land contract, $100 6.00
Credit acquisition, 7% land contract, $100 7.00
Credit acquisition, land mortgage, $100 5.50
Credit acquisition, chattel mortgage, $100 6.50
Credit acquisition,. silo dealer, $100 9,40









TABLE B .3--ontinued


Profit or CG
NUdmber Description Coefficientt

153 Credit acquisition, machinery dealer, $100 13.00
154 Salvage, tractor 356.70
155 Se4vage, plow 18.63
156 Salvage, disc, drill 88.37
157 Salvage, disc, planter 48,22
158 Salvage, cultivator, sprayer 55.21
159 Salvage, chopper 279,31
160 Salvage, wagon 33.82
161 Salvage, mower, rake 98.81
162 Salvage, fertilizer spreader 26.10
163 Salvage, corn picker 156.31
164 Salvage, cow and replacements .2.39
165 Salvage, corn, 100 bushels 90.00
166 Salvage, hay, 10 tons 175.00
167 Salvage, land, 10 acres 12.50
168 Salvage, summer labor, 14 days 175.00
169 Salvage, winter labor, 10 days 125.00
170 Salvage, cash, $1000' 0.00
171 Salvage, bulk tank 173.25
172 Credit repayment, $1000 55.00
1.73 Positive unit vector, sum equation, penalty 4444.00
174 Negative unit vector, sum equation 0.00
1751 Salvage hay equipment


IAll hay equipment was combined for the final computations, The set
includes the disc and drill, mower and rake, and the fertilizer
spreader.




TABLE .4,


INITIAL OPTIMJM SOLUTION
[ I J r l .. i i r r 1a
'Orani atXi. andl~ ted Values -
Organiz~ataia Selected Iputed Vaties
Activity No. Unit Amutint ResoUirce i M.,,,,,. .Activity No. Delta J


5
6
156
161
159
162
164
171
168
169
165
166
138
139
142
143
129
120
123
126
124
121
146
1J45
Unised
Used
Unused
Unzsed


Acres
Acres
One each
One each
One unit
One unit
One unit
One unit
2 days/month
100 hours
100 bushels
10 tons
260 hours
do
do
do
One unit
do
do
do
do
do
10 acres
do
$100
do
do
do


60.00
227.20
1.00
1,00
0.83
1,00
32.00
1.00
15.00
15.00
243.60
6.00
2.17
1.35
0.26
2.77
2.38
3.00
1,06
4.77
0.74
1,62
16.00
1.72
0.00
0.00
0.00
360.00


Disc, drill
May plow
Disc, planter
Cultivator, sprayer
Mower, rake
Fertilizer, spreader
Sept. chopper
Oct. tractor
Oct. wagon
Corn picker
Corn
Hay
April labor
May labor
June labor
July labor
Aug. labor
Sept. labor
Oct. labor
N-M labor
Herringbone capacity
Auto bunk capacity
Cow, replacements
Cash 1
5.5% credit
. 6% land contract
6..5% credit
Bulk tank capacity
Land


AC1
1 ho
AC
do
do
do
dd
1 he
AC
do
10 b
1 to
1 he
do
do
do
do
do
do
100
do
per
unit
$100
do
do
do
gal
T.A.


$ 0.80
uar 0,34
0.67
0.62
0.44
0.16
3, 52
ar 5.02
1.42
3.30
>U 9.00
nl 17.50
Ur 0.72
1.44
1.44
1.44
1.44
1.44
1.44
hrs 134.28
30.08
cow 2,80
52.00
7.42
1,92
0,46
0.92
0.78
2 20,72


cash
5.5 credit
6.5% credit
7% credit


4
1
12
7
18
13
19
23
24
28
29
33
34
42
43
51
52
60
61
69
70
78
79
87
88
96
97
105
106
114.
117
1L8
132


$ 3.26
8,04
9,80
12.52
22,06
19,76
1.88
9.48
11.28
17.44
21.94
26.48
5918.00
5950.00
3464.o00
3494.00
3484,00
3506.00
3978.00
4008,00
2452 .o
2482.00
2472,00
2494,00
3590,00
3620,00
2224.00
2254.00
2244.00
2266,00
0.00
1144.00
13.5h


-- --


---- --------------- ---- --~--- -- -- -- -- ----------- ---------
Idnrrcrs nms~r~~r




. TABLE B 5


OPTIMJM SQWAIONy. 320. ACRES

A tiity Oj zatioo a.. :3.e.Desta
Or aizasbion; Le l eeolt2 f Imuted Yalues
Activity No. Unit Amcabt escf Uc~T Activity No. Delta J


Acres
do
One each
do
One unit
do
do


5
6
156
161
159
162
164
171
168
169
165
166
138
139
142
14-3
129
120
123
126
124
121
Unused
Unused
Unused


t


60.00
208.00
1.00
1.00
0.83
1,00
32..00
1,00
15.00
15.00
230,40
6.00
2.17
1.28
0.26
2.62
2.20
2.67
0.96
4.40
0.65
1.48
0.00
0.00
45.30


'Acres coverable. billable acres.


do
2 days/month
100 hours
100 bu
10 tons
260 hours
do
do
do
One unit
do
do
do
do
do
$100
credit do
credit do


Dise, drill
May plow
Disc, planter
Cultivator, sprayer
Mower, rake
Fertilizer spreader
Sept, chopper
Oct, tractor
Oct. wagon
Corn picker
Corn
Hay
April labor
May labor
June labor
July labor
Aug. labor
Sept. labor
Oct. labor
N-M labor
HB capacity
Auto bunk capacity
Cow and replacement
Gash 1
5.5% credit
6% land contract
6:5% credit
Bulk tank capacity
Land


AG:l
1 hour
AC
do
do
do
do
1 hour
AC
do
10 bu
1 ton
1 hour
do
do
do
do
do
do
100 hrs,
do
Per cow
Unit
$100
do
do
do
Gal.
T.A.


cash
5.5%
6.5%


$ 0.79
0.00
0.63
0,58
0.44
0.16
3.47
4.76
1.36
3.13
9,00
17.50
1.43
1,143
1.43
0.72
1.43
1.43
1.43
133.12
0.00
0.00
51.44
6.50
1.00
0,00
0.00
0.73
22.11


4
1
12
7
18
13
19
23
24
28
29
33
34
42
43
51
52
60
61
69
70
78
79
87
88
96
97
105
106
114
117
118
132


$ 3.23
7,96
9.83
12,66
22,10
20.02
2,52
9,63
11,98
17.74
22.71
26.95
5865,00
5896.00
3428.00
3459.00
3428,00
3459.00
3941.00
3972.00
2425.00
2456.00
2425.00
2456.00
3536,00
3567.00
2186,00
2217,00
2186,00
2217.00
1673.46
1090.80
11.21









TABLE B.6


OPTIMJM SOLUTION, 320 ACRES, 4 TRACTORS

Orazaization and Imputed Values
Activity Orgi a.tion' Selected Imputed Values
Number ilt ou Resource Unit MVP


51 Acres
61 do
191 do
175 Set
159 One unit
137 260 hours
138 do
139 do
140 do
141 do
142 do
113 do
129 One Unit
.23 do
126 do
124 do
121 do
Unused cash $100
Unused 5.5%
credit do
Unused 6.5%
credit do


Hay equipment AC
May tractor 1 hour
May plow AC
Disc, planter do
Cultivator, sprayer do
Sept, chopper do
Oct., wagon AC
Corn picker do
Labor 1 hour
Cash 1 $100
5.5% credit do
6.5% credit do
Land T.A.


.71.1
168.9
28.0
0.8
0.80
0.05
1.85
1.55
0,07
0.40
0.31
2.31
1.82
0.75
3.66
0.48
1.22
0.00


0.00

55.19


sellingg of
solutions.


0.99
6.55
0.32
0,63
0,58
3.47
1.35
3.13
1.43
6,5
1.00
0,00
20.12


crops is combined with this activity in this and succeeding


- -- --










IABLE B.7


OPTIMM SOLUTION--320 ACRES, 4 TRACTOBB, 1 CHOPPER

,Or.arYstion, a d Impute PValues
Activity No. 'iavtation i- iected mput Values
Unit Amount Reaource Unit .MVP


5
6
19
175
137
138
139
14i
141
142
143
129
123
126
124
121
Unsed cash
Used 5.5%
credit .
Umsied 6.5%
credit


Acres
do
do
Set
260 hours
do
do
do
do
do
do
One Unit
do
do
-do
do
$100


do


20.0
O,0
28.0
0.8
0.05
1.85
1.55
0.07
0.40
1,03
1.96
1.4
0.75
2.80
O .48
1.22
0.00

0.00

69.18


Hay equipment
May tractor
May plow
Disc, planter
Cultivator, sprayer
Sept, chopper
Oct. wagon
Corn picker
Labor
Cash 1
5,5% credit
6.5% credit.
Land


AC 0.99
1 hour 7,69
*AC 0.32
do 0.63
do 0,58
do 0,00
do 1.35
do 3.13
1 hour 1,.3
$100 6.50
do 1.00
do 0.00
Til. acre 20,12










TBLB B.8

QPTIMM S0LUTION--320 AGCE, L TRASTORG, 1 CHOPPER, 3 CORN PCIKEWR


.Prigazation a Imputed Valuea
UOrfanzation Selected Ipted Values
Activity No.Unit Amoult Resource Unit MVP
i + .+ Lj ~ $ : I .+ t I ,IJ I l


5 Acres
6 do
19 do
175 Set
137 260 hours
138 .do
139 do
140 do
i11 do
1U2 do
143 do
123 One unit
126 do
124 do
121 do
Unrsed cash $100
United 5.5%
credit do
umtsed 6.5%
credit do


240.00
0.00
28.00
0.80
0.05
1.85
1.55
0.07
0,40
1.03
1.96
0.75
2.80
0.48
1,22
0.00

0.00

60 .9


Hay equipment AC
May tractor 1
May plow AG
Disc, planter do
Cultivator, sprayer do
Sept. chopper do
Oct. vagon do
Corn picker do
Labor 1
Cash 1 $1
5.5% credit do
6.5% credit do
Land


hour


hour
30


0.99
8,94
8.9h
0.32
0.63
0.58
0.00
1,35
0.00
1.43
6.50
1,00
0.00
20.12


- --- -










TABLE B.9

OPTIMM SOLUTION, FINAL FARM PLAN


Organization and Imputed Values
Organization Selected Imputed Values
Activity No. Unit uAmont Resource Unit MVP

5 Acres 80.00 Hay equipment AG 0.00
6 do 136.00 May tractor 1 hour 0.00
19 do 52.00 May plow AG 17.84
137 260 hours 0.09 Disc, planter do 0.00
138 do 1,66 Cultivator, sprayer do 0.00
139 do 1.78 Sept, chopper do 0.00
140 do 0.13 October wagon do 0.85
141 do 0.75 Corn pLcker do 0.00
1h2 do 0.34 Labor 1 hour 1,43
143 do 2.04 Gash $100 6,50
Unused caah $100 0.00 5.5% credit do 1.00
Unsaed 5.5 6,5% credit do 0.00
credit do 0.00 Land Til. acre 22.11
Unused 6.5%
credit do 53.03




TMBLE B,10


PURCiSAMA" AS8TS
FPS3aSJ uIT T2t^B. .HD DEPgIABC TIGMN

I70,11 -P yme nt
Including Credit Annual Annual
Asset Description Price- Credit Fee Balance Terms Payment Depreciation2
Dollars. Dollars Dollars Years $/$100 Dollars
Tractor, 2-3 plow 3480 874 2610 3 42.51 348,00
Plow, 2 x 14" 257 68 193 3 do 18.00
Disc, drill 1153 292 865 3 do 84,50
Corn planter, disc, 2 row 613 157 460 3 do 46.69
Cultivator, sprayer, 2 row 625 160 469 3 do 53.65
Chopper, PTO, Silo filler 2725 685 2044 3 do 272.50
Wagon 330 86 248 3 do 33.00
Mower, side rake, 71 1125 285 8U4 3 do 96,00
Fertilizer spreader, 10l 360 94 270 3 do 25.20
Corn picker, pull type,.1 row 1525 385 1143 3 do 152.50
Upright silo, 201x60t, complete 6669 3169 3500 3 39.76 284.823
Bunker silo, 6x30x130, complete 5100 00 -- -- 714.003
Bulk tank, 500 gal. 3300 829 2475 3 42.51 165.00
Double 3 Walkthrough, complete 6175 3775 2400 3 do 688,254
Double 6 Herringbone, complete 9359 5527 3832 3 do 1063,854
Loafing area for 10 cows 800 800 -- -- 64.00
Hay storage, feeding, 10 cows 400 00 -- -- 32.004
Feed bunk, non auto, 10 cows 50 50 8.004
Feed bunk, auto, 10 cows 852 -- -- 161,884
Cow and replacements 332 332 -- --- 41,56
Land, cash purchase, 10 acres 2500 .2500 -- -- --
Land, mortgage, 10 acres 2500 1375 1125 20 8.0 --
Land, 6% contract, 10 acres 2500 250 2250 20 8,70
Land, 7% contract, 10 acres 2500 250 2250 20 940 --
Prices were obtained from various dealers. Dealer prices were then increased uniformly by 10%.
2Depreciatiac rates from: Nielson, James M., Application of the Budget Method in Farm Planning,
unpublished Ph. D. Thesis, Harvard University, Cambridge, Massachusetts, 1953.
31ncludes repairs, taxes, insurance.
*Includes repairs.







83


TABLE B.11

osr OF 1NGHINERY REPAIR


Machine Repairs as Percent of
Machine Gost1

Tractor 7
Plow 5
Disc 4
Sworn planter 3
Cultivator 3
Drill 3
Chopper 7
Wagons 5
Side rake 2
Fertilizer spreader 3
Corn picker 7
Sprayer 10
Mower 5
Silo filler 7


IData from: Nielson, James M., op. cit.










TABLE B,12

FERTILIZER APPLICATION AND CROP YIELD ESTIMATES


Oat Hay Hay Corn Corn
Item Siage Silage Grain Silage

Fertilizer (low)
5-20-10 200 lbs 210 Ibs. 210 Ibs,
0-20-20 60 lbs 60 Ibs,
Yield 5.0 tons 2.5 tons 7.5 tons 60 bu. 10.6 tons

Fertilizer (Ined.)
5-20-10 300 lbs 250 250
0-20-20 200 Ibs, 200 Ibs,
-idedresa, N 40 Ibs. O0 Ibs.
Yield 8.0 tons 3.4 tons 10.2 tons 76 bu, 12.5 tons

Fertilizer (high)
5-20-10 400 lbs 300 Ibs. 300 lbs
9-20-20 300 lbs 300 Ibs
gidedress, N 30 Iba. 80 Ibs 80 Ibs
Yield 8.5 tons 4.2 tons 12,6 tons 90 bu. 15 tons


'Data modified from: Hogltnd, G. R., and Cook, R. L,, Hi her-Profits
s gj er and, proved Practices, Agricultural Economics Mimeo
545, Michigan State University Agricultural Experiment Station and Soil
Science Department, East Lansing, October, 1956. The high roles and
yields are from unpublished data by the same authors,










TABLE B.13


TIME REQUIR'MIESs FOR FIELD


OPERATIONS


Acrea per Hours per Acres per
Operation Hour Aere 8 Hour Day

Plow 0.90 1,11 7.2
Disc 2.80 0.36 22,4
Drill 3.50 0.29 28,0
Plant corn 1.90 0.53 15.2
Cultivate 2,40 0.42 19.2
pray weeds 2.50 0.40 20.0
Pick corn 0.75. 1,33 6.0
Mow hay 2.0 0.50 16.0
Rake hay 1.9 0.53 15.2
Chop hay 1.1 0.91 8.8
Chop corn 0.8 1.25 6.4
Spread fertilizer 1.5 0.67 12.0


'Primarily from: American society of Agricultural Engineers,
Agricultural Engineers Yearbook, 2nd Edition, 1955, p. 89,

tBLE B .14
1
NUMBER OF FIE~D WORKIG DAYS PER MONTH


Month Days

April 12
May 15
June 18
July 20
August 21
September 17
October 15


'Data from unpublished sources.









TABLE B.15

DAIRY AND GRAC CASH COSTS


Item Unit Amount

Crops
Fuel and oil Per hour tractor time $ 0.70
Alfalfa seed Bushel. 25.00
Oat seed Bushel 1.45
Corn aeed Bushel 12.50
Fertilizer
5-20-10 Ton 79,20
0-20-20 Ton 47.55
45-0-0 Ton 118.00
Weed spray Per acre 3.00

Dairy
Vet, breeding,
elec., etc. Per head 20.00
Milk for calves Per head 4.00
Bedding Per head 24.00


'Data from various unpublished sources.


TABLE B.16
1
DAIRY LABOR R3QRIREMETS1

Parlor Level of Type of Minutes per
Type Sfficiency .Silo Day per Cow2

Stanchion average Upright 17.76
Stanchion efficient Upright 10.56
Stanchion efficient Bunker 10.56
alkthrough average Upright 12.06
WkaLthrough efficient Upright 7.50
Walkthrough efficient Bunker 7.50
Herringbone average Upright 10.92
Herringbone efficient Upright 6,90
Herringbone efficient Bunker 6.90

IPrimarily from: Hoglund, C. R., Boyd, J. S. and Snyder, W. W. "Herring-
bone and Other Milking Systems," aartarly Bulletin, Michigan Agricul-
tural Erperiment Station, Michigan State University, East Lansing, Vol.
41, No. w (February, 1959) and Hoglund, C. R. and Wright, K. T., Reduci2
Dairy (osts .on Michigan Farms, Michigan State University Agricultural
Experiment Station Special Bulletin 376, East Lansing, Nay, 1952.
21ncludes care of the entire herd.




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