Farm organization and resource fixity

A.E. 769

FARM ORGANIZATION AND RESOURCE FIXITY: MODIFICATIONS
OF THE LINEAR PROGRAMMING MODEL

By
Peter E. Hildebrand

Agricultural Economics Department
Michigan State University
East Lansing, Michigan

November 10, 1959

S0. c2b

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TABLE OF CONTENTS

CHAPTER Page

I INTRODUCTION,........ ......................................... ..

The Nature of Fixed Resources *.5.o..............,............
The Effect of Predetermined Resource Fixities Without Regard
to MVP ,**......6..........-.........-..................-0., 6
Endogenous Determination of Resource Fixity ................... 7
Some Previous Linear Programming Models Incorporating Various
Aspects of the Problem ..*.................................0 8
The Farm Situation and Credit Supply Function ................. 9
Thesis Organization ******.......**..* ..****.********..o****** 11

II THE ANALYTICAL MODEL *...........................0.............0 12

The Specialized Equations *..o.........................0....... 13
The Double Purpose Acquisition Activities .................... 17
The Credit Activities ..............*............,...........o 17
The Cash Coefficients *.........................0.............. 18
Specialization and Diversification and the Effect of a Single
Fixed Resource on the Solution ......................... 20
Discrete Investment Levels *2........................*......... 22

III APPLICATION OF THE MODEL ....,....,0...0......0...0 .............o 26

Crop Production .............................................. 26
Milk Production *................. *........................... 27
Derivation of the Technical Matrix and Restrictions ........... 28
Acquisition and Salvage ,......*,*...... .................... 28
The Range of Possible Solutions .2............................ 29

IV SOLUTION OF THE FARM MODEL .*......*........................... .0 30

The Initial Optimum Solution *.............. .... ..... ..... 30
The Discrete Investment Series ................................ 37
The Final Farm Organization *..,.o............oo..........0... 46

V SUM1ARY AND CONCLUSIONS ...........,..o....... ...*............... 49

Application of the Model 49................................. 9
The Empirical Results .**..*......,............. ........** ...* 52
Further Study Indicated **..................................... 03

BIBLIOGRAPHY .......................*............,.. .............o 55

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LIST OF TABLES

TABIE

r

2.1 Cash Coefficients for the Various Groups of Activities ,.........

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

U42 Profit and Organization for 320 Acres and 360 Acres ,..........

4,3 Profit and Organization for 320 Acres with Four and Five Tractors,

4.4 Profit and Organization for 320 Acres, Four Tractors, With and
Without a Forage Chopper *................* ....,...*..........**

4,5 Profit and Organization for 320 Acres, Four Tractors, One Chopper
and Two and Three Corn Pickers **...,.... ..e.e,............C.....*

4.6 Complete Inventory Change: Original Organization to Final Farm
Plan ..........................................................

L.7 Comparison of Profit: Optimum Solution and Final Farm Plan ......

4.8 Disposable Income, Final Farm Plan ..**..,.,.,...............

B,1 Crop Activity Titles and Profit Coefficients ...............

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

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

B,4 Initial Optimum Solution *.....................................

B.5 Optimum Solution--320 Acres ............... ....................

B.6 Optimum Solution-320 Acres, I Tractors .........................

B,7 Optimum Solution--320 Acres, U Tractors, 1 Chopper *..............
B,8 Optimum Solutionr-320 Acres, 4 Tractors, 1 Chopper, 3 Corn Pickers

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

B.10 Purchasable Assets: Price, Credit Terms and Depreciation ........

B.ll Cost of Machinery Repair .....................ee ...o....,...*..

B.12 Fertilizer Application and Crop Yield Estimates ...........*......

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LIST OF TABIES--continued

TABLE

B.13 Time Requirements for Field Operations .........................

B.14 Number of Field Working Days Per Month *.........................

B.1S Dairy and Crop Cash Costs ...................................

B.16 Dairy Labor Requirements ..................... .............. C

B.17 Rations and Production for the Milking Herd, Per Cow ,...........

B.18 Rations in Hay Equivalents and Corn Equivalents Per Cow Per Year,
Includes Replacements .......................

B.19 An Example of the Computation of Machine and Power Restrictions .

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CHAPTER I
INTRODUCTION

When the conventional linear programming problem is formulated with fixed

restraints, the level at which the resources of the/firm are fixed are of

primary concern because these restrictions indiqcte 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 programming 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

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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 undesirable 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 building, 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 salvaging plus the MWP of the building, it would, of

course, be salvaged. A factor is not fixed, then, if (1) the costs of removing

it are exceeded',.by ,thei a sm "bf expected revenues occurring as a result of its-

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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 much 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 requirements for technology favoring efficient

use of this factor. If adjustment 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.

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The solution of a linear programming problem nmputes 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 the factor 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.

Endogenous Determination of Resource Fixity

A linear programming model incorporating the endogenous determination 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.

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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 annual marginal factor

cost to the firm of acquiring the asset.1 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 MC is lower than the cost of purchasing the marginal

unit, it will pay the firm to produce the factor if more is desired. When MC

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 equal (1) annual cost of acquisition for all resources increased

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

or (3) the manual value in use for all resources fixed at the original quantity

and neither purchased nor sold. Thus, all durable assets in this model receive

an imputed value based on the annual flow of services from it.

Some Previous Linear Programming Models Incorporating Various Aspe'ots 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.

1 For a fuller discussion of the pricing problem see footnote 1 on page 18.

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.

Loftsgard and Heady2 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 different points in time, etc."3 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 expenditures 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 fall 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

1 Victor E. Smith, "Perfect vs. Discontinuous Input Markets," Journal of Farm
Economics. Vol. 37 (August, 1955), p. 538.
Laurel D. Loftsgard and Earl 0. Heady, "Application of Dynamic Programming
Models for Optimum Farm and Home Plans," Journal of Farm Economics, Vol. 41
(February, 1959), p. 51.
3 Ibid., p. 51.

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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

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 bunter silos, either a walk-through or herring-

bone 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 madxmum

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

$45,090 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, $250 per acre, or $18,000.

Deducting the mortgage outstanding leaves $8,910 of land mortgage available.
In addition to the land mortgage available, credit is available for pur-

chasing 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 much as 160 acres purchased in 40, 80 and 120 acre

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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 fazm 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 6).

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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 firms and

should require no clarification other than description. 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 activities. The

asset acquisition and credit activities also require explanation since they

contain some aspects peculiar to the model. Table 2.1 on page 19a should help

clarify the following narrative.

The Specialized Equations

Some difficulty is encountered in explaining the three sets of specialized

equations individually since there is a degree of relationship 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 "Sum" Equation. The name of this equation is unimpor ant 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: }NR _..AnC. 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 ~ AnC + K.

The K becomes the restriction or bi value: ,NR An3C g K.

To remove the inequality from the last equation a slack activity with the

appropriate coefficient must be added.

NR -AC S S K
-K
NR-m AC S + S =K

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

coefficient, S must be added to complete the identity matrix used as the

first solution in solving the problem by the simples 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.

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

these equations, one for machinery dealer credit (CSRMD), one for silo dealer

credit (CSRSD), and one each for land mortgage (CSRIM) and land contracts

(CSRLC).1 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 purchased. 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 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) e P- Dp

or DCA (P-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 bi value is zero, no credit from this source is available

unless machinery is purchased. The other CSR equations are exact duplicates of

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

varies for each.

1 The abbreviations are used in Table 2.1 on page 19a.

3, The Cash Equations. The model contains two cash equations. The 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 payment required

for any transaction. The acquisition activities involving 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

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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 bunker 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 Cash 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 drpreciation is

added to the cash account at the outset. This makes it necessary to add half the

apnual- 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 coefficient

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

(l/2D-Vs).

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The Double Purpose Acquisition Activities

Two methods exist for incorporating the asset acquisition activities 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 Cash 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 available 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

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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 repayment 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 must exceed the annual cost of ownership 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 must be charged

against the acquisition of an asset as the MFC of obtaining another unit.

SThe MWP 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, multiply 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.

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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 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 simultaneously, 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 w ill be so used. When the

initial cash on hand is exhausted, more can be acquired at 5.5 percent through

the land mortgage acquisition activity. Therefore, the MVP of the asset

purchased must 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

TABLE 2.1

CASH COEFFICIENTS FOR THE VARIOUS GROUPS OF ACTIVITIES

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

Profit -T -T -(D+T) -i -i -i -i -i (D+T) i -(CE+R) NR

Cash 1 P P P-/2D-100 -100 -100 -100 -100 1/2D-Vs 100 CE + R CE
Cash 2 .55P .10P .25-PD-100 -100 /2D-Vs 100 CE + R GE

Sum -T -T -(D+T) -(i+CR) -(i+CR) -(i+CR) -(i+CR) -(i+CR) D+T i+C GCE + R NR
Land mort.
avail, 100 -100
Land cont,
avail. 100
Dealer credit
avail, 100
Bank credit
avail, 100
CSRIM -45P 100
CSRMD -,75P 100
CSRIC -.90P 100
Land and mort.
avail, 100

-19a-

-20-

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.1 Asset acquisition activities increase

annual commitments and thus bear a negative coefficient in the sum equation.

Here, again, the coefficient 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 sign. The annual commitment acquired upon the acquisition of credit

includes not only the interest, but also the annual repayment of capital (CR).

The coefficient in the sum equation for the credit acquisition 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.

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
complementary (and, hence, multified farms) depends upon the production

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

-21-

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, therefore, 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, 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 ex-

pansion 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 supplementarity) 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

alternative just as can unused services from predetermined resource fixities,

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

-22-

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

resources 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 con-

sidering 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

-23-

discrete level at which an asset shoulI e. fixed. Thus the method evoUe4
depends upon the concept of resource fixity.
An asset is fixed to the firm if it# WP Ule between, or is equal to, its

acquisition and salvage values. The greater the differential between the

acquisition and salvage values, the more subject the asset is to fixity because

the VWP will have to change by a greater magnitude before it lies outside these
boundaries. It is also trne that the WP of a fixed asset will vary as the
quantities of the vaaLabk factors used with it vary.
It is a reasonable approach to determine the level of fixity for assets
individually, beginning with the cne most sub3ect to fixity. The variations of
the other assets EIl be 2ws lktely to eauae the MWP of the fixed asset to shift
beyond the bounds of Lrity t ,the one vdth the greatest differential between

acquisition w4 salvage vaees s9 t h Arst to be filed in the solution.
The method, thea for detefirtg discrete investment levels is first to

obtain an optimal solUtionz wit 4a1 assae4 asetue m to be infinitely divisible.

Choose frcm among the as~eta in *iM4 iaveiatst occurred, the one most subject to

fixity. This particular asset is the fraed for the farm at the next higher
and next lower discrete level ty eWaling t ia~tial restrictions by the amount
of the coefficients in the acq isitlon activity waltiplied by the level of the
activity for each case and reag5ra acqEM )a s4tlaga activities for
the asset from the matrix. t~iS process, however, Mt retSlt in negative values
for the restrictions la siore euatios, particularlyl the cas equations, so that
manipulation of some other i atiity levels &ay be neceaeary to increase the
negative values to sors Oaygive or sero le1wV WhSn this process is coart
pleted, the program is rer~a twdts, once for each investment level. After adjust-

ing the profit values for *aeh sobntiO to account fo the different investment
levels, the solution fo iwhbih 3 l eagesa 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 new set of restrictions

derived from the previous trial solution.1

Figure 1 should help explain the procedure desori~ed ahve. In Figure 1,

ACGK is a portion of the NF c ure 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 IE, and to the right, no greater than BF.

The line DEF, therefore, represents the extreme range of the MVf of cash on

either side of the optimum 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 MWP 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 2.4 to 3 tractors,

the net cost is EGHF, the 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 determine~ tgthe 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 whichh the enterprises 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 predetermine, without computing the two programs, the most

profitable level of investment for the asset under consideration

1 It should be emphasized that this method of determining discreteness leaves:
much to be desired. See Appendix A for a more complete discussion of the
effect on resource fixity from using this method.

Product
Cost

0

'' -5

A

1 2
M N

tractors
Sinput

Figure 1

.." .. .....-MVP2

-26-

CHAPTER III

APPLICATION OF THE 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 fam.

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 with

above average management practices.*

1 The low and medium fertilizer application levels are taken (with slight
modification) from: C.R. Hoglund and R.L. Cook, Higher Profits From
Fertilizer aid Improved Practices, Agricultural Economics Mimeo 545, Michigan
tate 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 Guttay and L.S. Robertson.

-27-

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 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 operations 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

Page 28
Missing
From
Original

-29-

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 replacements, jointly, can be purchased, or any proportion of the herd

sold.

Hired labor can be acquired by the month far 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

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 alternatives considered,

represents a possible solution.

-30-

CHAPTER IV

SOLUTION OF THE FARMU MODEL

The initial optimal solution obtained from this model is unique to linear

programing 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 enterprises, 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 enter-

prise 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.1 Table 4.i shows the change

1 In 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 labor is hired. Were 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 sufficiently high that, since management
is not considered a necessary resource, the services of the manager are sold off
the farm.

-31-
in inventory between the initial farm assets and those of the optimum organization.
TABIE 4L1

ORIGINAL AND OPTIMUM INVENTORIES

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 0
Dairy heifers 11 11 0
Dairy calves 13 13 0
Field 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 1 1 0
Wagons 2 4i8 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 0

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 $8810.1 Deducting the off

farm income of $4500 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 $3635. By paying this amount in full, the family has available for consumption,

1 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.

-32-

in addition 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.

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, $51.44.2 The imputed value

1 It is, of course, possible for the family to spend for consumption the
interest on owned assets and depreciation, in addition to labor income.

2 The term Delta J stands for the imputed value of the activities. The values
imputed to the slack activities are the MVP's 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.

-33-

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*1

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, $1.14 and $l.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 into the solution.2

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 corn is picked for

grain, the activity having the heaviest level of fertilization entered the

solution. The reduction in profit from using the medium level of fertilizer

1 The MVPrs 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 imputed value
is measured.
2Non basis activities are the activities which do not enter into the final
solution.

-34-

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

all the corn 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, $.478 if 60 percent, and $6.4O and $8.04, respectively, for 80

and 100 percent 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 only 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 applications of fertilizer. The

gain in profit from low to medium is $10.32 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.

11
Gain $

9
8

7
6

0 1 -
8 9 10 11 12
Dollars of Fertilizer per acre
Figure 4.1 (Corn)

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 applications were used in this study than

currently in common practice, even higher applications would be profitable.
The total cost of fertilizer applied to corn at the three levels was: $8.32,

$10.42 and $12.92.
The total cost of fertilizer applied to hay at the three levels was:

$3.40, $6.l5i and $9.32. The corresponding imputed values for hay with only
the oats cut for silage are $21.94, $11.94, $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

10

9
8

7

0
4i 6 7 8 9
Dollars of Fertilizer per acre

(Hay)

Figure U.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 activities

indicate that dairying, under the conditions set forth in the assumptions, is

a poor alternative compared to cash cropping if continuous corn is possible.
S 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

market effect on profitability, but there is only a slight profit differential

between upright silos and bunker silos. In choosing between the types of milking

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

three walk-through, but investing in either would be considerably more :- *

-37-

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 acquisition 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 function 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.1 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 indicated 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

1 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.

-38-

in 160 and 200 acres. The optimum organization and profit for both conditions

is given in Table .2.".

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 256 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 equipment. The production of 74.8 acres of hay restricts corn
TABLE 4.2

PROFIT AND ORGANIZATION FOR 320 ACRES AND 360 ACRES

Description

Tillable acres
Tractors, beginning inventory
Tractors acquired
Tractors, ending inventory
Choppers, beginning inventory
Choppers sold
Choppers, ending inventory
Corn pickers, beginning inventory
Corn pickers acquired
Corn pickers, ending inventory
Acres in hay, high fert., oats for silage
Acres in corn, high fert., 1/5 for silage
Acres in corn, high fert., all picker
Total acres, picked corn
Profit, nearest dollar
Profit differential

320
Total Acres

268
2
2.7
4.7
1,0
0.83
0.17
1.0
2.20
3.20
0
60.0
208.0
256.0
$8345.o0
+706

360
Total Acres

302
2
2.0
4.0
1.0
0.53
0.47
1.0
1.84
2.84
74,8
1.4
225.8
227.0
$7639.00

production to 227.2 acres. With fewer acres in corn, a smaller tractor invest-

ment 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,

-39-

succeeding programs are based on 320 acres.

The MVP's of most resources were reduced only slightly, comparing the 320

acre 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 percent credit not to be

used.

In Figure l.3, the segmented curve labeled ABOCD*EF represents, again, a

portion of the MFC of dollars to the firm and the line MVP indicates the MVP of

spendable funds in the initial optimum solution. Spendable funds, here, includes

Returns to
Dollars

SE F

C D
6, . D% i

A B

0 $14,759 $19,289 Spendable Funds

Figure l.3

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

-h0-

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 iL$430 of 6.5 credit could be

acquired.

The 320 acre organization indicated an optimum of U.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 pro-

fitable crop than is corn, it is profitable to more fully utilize these tractor

services than to specialize in the production of corn. Specialized corn pro-

duction 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 consequence, 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.1

1 The 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 predeterming the level of resource fixity,

-41-

Although the second farm specializes in a relatively more profitable crops

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.
TABIE 4.3

PROFIT AND ORGANIZATION FOR 320 ACRES 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 +i.40

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 can 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

-42-

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

organization than determining the level of fixity for the resources with a more

general use.
TABIE 4.4

PROFIT AND ORGANIZATION FOR 320 ACRES, 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 2.4
Acres in hay, high fert., oats for silage 0 28.0
Acres in corn, high fert., l/$ for silage 0 240.0
Acres in corn, high fert., all picked 22.56 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 amaaled effect on farm organization

With no chopper, all the corn must be picked. The limitation on October tractor

services prevents more than 22.56 acres of corn from being harvested as ear

corn. Consequently, 42.4 tillable acres on the farm must remain idle--an

unprofitable alternatively 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 produced relative to the

amount of ear corn than was the case in all previous solution.

In this case, the consequences of fixing the farm size at 320 acres, when
42.4 tillable acres remain idle, are plainly evident.

-43-

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*. ere 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 salvage value, it

is unrealistic to value it at zero.

The final factor of production to be set at a discrete level in the invest-

ment series are corn pickers. Table L.5 shows the organization 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 of corn which can be

harvested by this method and as a consequence, more hay is produced. It is
TABIE 4,5

PROFIT AND ORGANIZATION OF 320 ACRES, 4 TRACTORS, 1 CHOPPER
AND 2 AND 3 CORN PICKERS

Description Two Three
Corn Pickers Corn Pickers'

Tillable acres 268 268
Tractors 4 4
Chopper 1 1
Corn pickers 2 3
Acres in hay, high fert., oats for silage 68 28
Acres in corn high fert., 1/5 far 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

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 MVPls of the various resources throughout the investment

series helps explain the effect of fixing resources arbitrarily 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 MVP of tillable acres decreases to $16.0 when the number of tractors is

fixed at four, but increases to $31.78 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 consisting 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

Original Inventory Final Inventory Change In
Description Amount Value Amount -Value Value

Land, total acres2

160 $24,000

320 $60,000 $36,000

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

Total

Dairy Cattle
Cows
Yearling heifers
Heifers calves

Total

Total farm investment

$2,400
100
150
180
75
350
180
220
1200
600
220
700
100
620
1450
3,000

$7,680
1,760

$45,090

$7,968
321
467
382
329
296
142
162
1,018
1,425
195
3,292
364
558
405
0

$17,324

$5,568
221
317
202
254
-54
-38
-58
-182
825
-25
2,592
264
-62
-45
-3,000

$6,779

47,680
-1,760
-1,105

0 410.,5 5

$77,324 $32,234

Original inventory value plus additional investment
minus depreciation on all units.
2 Includes improvements.

(price x number of units)

-e -- ~- --------- --

-45-

-46-

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 alternative. (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 alternative, 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 solutions, too much land was acquired in the original

investment solution,1

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 $150 per

acre. Placing a value of $225 per acre on this land would have the effect of
increasing the original net worth 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

1 Refer to pages 42-43 for such a solution.

-47-

the change in the value of inventory nor in the change in net worth.
TABLE 1.7

COMPARISON OF PROFIT:
OPTIMUM SOLUTION AND FINAL FARM PLAN

Optimum Final Farm Loss Involved
Description Solution Plan in Obtaining
Discrete Solu-
tion

Profit $8,810 $6,796 $2,014
Labor income 6,912 828 2,084
Available for capital repayment 3,712 1,628 2,084
Needed for full capital repayment 3,635 2,548 -

1 For a definition of the income categories, see page 31.

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 Tab3e 4.8.

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

-48-

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. Therefcae, depending upon the use of disposable

income, net worth at the end of the year would be between 1l8,082 and $22,249.
TABIE ,8

DISPOSABLE INCOME, FINAL FARM PLAN

Description Amount

Labor income $4,828
Interest on owned assets 1,175

One-half depreciation l3j6&4

Disposable income $7,367

-49-

CHAPTER V

SUMMARY AND C(CCLUSI ONS

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 determination of fixed resources* The second

deals with the discrete investment 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, predetermines 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 employment 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 over-

emphasize specialization which would be an equally undesirable result.

-50-

The alternative enterprises considered in the standard programming model

are, by necessity, restricted by the group of resources considered 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 short-

comings 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 com-

binations within the activities result in erroneous conclusions from the model.

In addition to the regular problems encountered in linear programming,

this model is oversimplified and lacks realism concerning the budgeting and

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 stodk-flow

problem is of major concern. The acquisition 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 restrictions for resources and thus

creates a tendency toward more variability 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 assumptions. In

the static framework, reference is not made to the management function nor to

the interrelationships between the firm and household. The model assumes

profit maximization as the only motivation for production. At the same time,

enterprises which are distasteful 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 enterprises

acceptable to the manager, including minimum and maximum size restrictions.

The lack of risk and uncertainty considerations is another characteristic

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.

-52-

A major inconvenience of the model concerns the complex nature of it,

which tends to create great size. To completely analyze a diversified 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 Empirical Results

The optimal solution to the model indicates that, under the conditions

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 iho 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

-53-

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 profitability of dairying.

If the farmer's 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 solution.

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 cause 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, organization

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 variables 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 produce 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 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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American Society of Agricultural Engineers, Agricultural Engineers Yearbook,
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Black, John D., Clawson, M., Sayre, C, R., and Wilcox, W. W., Farm Management,
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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 Crops
at Particular Locations, Iowa State College Research Bulletin 426,
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Bradford, Lawrence A. and Johnson, Glenn L., Farm Management Analysis, John Wiley
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Hildebrand, Peter E., "The Linear Programming Approach in Farm Management
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Hillman, Donald, "Feeding Dairy Cows," Michigan State University Cooperative
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Hoglund, C. R., Esmay, M. L., Boyd, J. S. and Snyder, W. W., "Economics of
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Hoglund, C. R. and Wright, K. T., Reducing Dairy Costs on Michigan Farms,
Michigan State University Agricultural Experiment Station Special
Bulletin 376, East Lansing, May, 1952.

Jensen, Einar, Klein, John W., Rauchenstein, Emil, Woodward, T. E. and Smith,
Roy H., Input-Output Relationships in Milk Production, United States
Department of Agriculture Technical Bulletin No. 615, Washington, D. C.,
May, 1942.
Johnson, Glenn L., and Hardin, Lowell S., Economics of Forage Evaluation,
North Central Regional Publication No. hl, Purdue University Agricultural
Experiment Station, Lafayette, Indiana, April 1955.

Kuhn, H. W., and Tucker, A. W., J!Nonlinear Programming," Second Berkeley Symposium
on Mathematical Statistics and Probability. Neyman, J. ed., University of
California Press, Berkeley and Los Angeles, 1951, p. 481.

Loftgard, Laurel D. and Heady, Earl 0., "Application of Dynamic Programming
Models for Optimum Farm and Home Plans," Journal of Farm Economics, Vol. 41,
Number 1 (February, 1959), p. 51.
McKee, Dean E., "The Use of IBM for Linear Programming," Agricultural Economics
Mimeo A. Ec. 652, Michigan State University, East Lansing, June, 1956.

McKee, Dean E., Heady, Earl 0., and Scholl, J. M., Optimau Allocation of Resources
Between Pasture Improvement and Other Opportunities on Southern Iowa Farms,
Research Bulleti 435, Agricultural Experiment Station, Iowa State College,
Ames, Iowa, January, 1956.

Nielson, James M., Application of the Budget Method in Farm Planning, unpublished
Ph. D. Thesis, Harvard University, Cambridge, Massachusetts, 1953.

Peterson, G. A., "Selection of Maximum Profit Combinations of Livestock
Enterprises and Crop Rotations," Journal of Farm Economics, Vol. 37
(August, 1955),p. 546.
Smith, Victor E., "Perfect vs. Discontinuous Input Markets: A Linear Programming
Analysis," Journal of Farm Economics, Vol. 37, (August, 1955), p. 538.

Sutherland, J. G. and Bishop, C. E., Possibilities for Increasing Production
and Incomes on Small Commercial Farms, Southern Piedmont Area, North
Carolina, North Carolina Technical Bulletin No. 117, December, 1955.

Trant, Gerald I., Institutional Credit and the Efficiency of Selected Dairy
Farms, unpublished Ph. D. Thesis, Michigan State University, 1959.

APPENDICES

-58-

APPENDX 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 (PMVP>Ca). But at this lower discrete level, the

second asset to be fixed in discrete 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 con-

sidered, Thus, if all succeeding assets are fixed at the next higher discrete

level, the WVP 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 WMP will decrease relative to that in the initial optimum

solution. If, in the new solution, the MVP>Vs, there is no problem--the

resource remains flxed. Should the MWP 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,

-9-

The argument in favor of using this method to deal with indivisibility 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 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 intermediate 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 acquisition and

salvage values, the more likely the asset will be economically fixed in the

final solution.

APPENDIX B

-60-

TABLE B.1

CROP ACTIVITY TITLES AND PROFIT COEFFICIENTS

Description Profit or CJ
Number Crop Unit % Cut for Silage Fertiliser Level Coefficient
Dollars

Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay
Hay

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

100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
only
plus
plus
plus
plus
only
plus
plus
plus
plus
only
plus
plus
plus
plus

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

40.00
38.00
35.90
33.90
30.40
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

_ ~ _~_ __

-61-

TABIE B.2

DAIRY ACTIVITY TITLES AND PROFIT COEFFICIENTS, PER COW
.. ........... ... .. ......... ...- . .. ..o. .,o,
Description t or
Labor CJ Coefficient
Number Ration No. Parlor Type Efficiency level Silo Type Dollars

Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
Stanchion
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

Continued

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
Upright

399.50
379.50
360.50
399.50
379.50
360.50
399.50
379.50
360.50
399.50
379450
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

-62-

TABLE B.2--Continued
Description Profit or
Labor C Coefficient
Number Ration No# Parlor Type Efficiency Level Silo Type Dollars

74
75
76
77
78
79
80
81
82
83
84
85
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
114

Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Walkthrough
Herringbone
Herringbone
Herringbone
Herringbone
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

ACQUISITION, CREDIT AND SALVAGE ACTIVITY TITLES AND
PROFIT COEFFICIENTS

Profit or Cj
Number Description Coefficients

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
1140
141
142
143
144
145
146
147
148
l149
150
151
152

Acquisition, Upright silo
Acquisition, Bunker silo
Acquisition, Herringbone parlor
Acquisition, Walkthrough parlor
Acquisition, Automatic feed bunk
Acquisition, Tractor
Acquisition, Plow
Acquisition, Disc, drill
Acquisition, Disc, planter
Acquisition, Cultivator, sprayer
Acquisition, Chopper
Acquisition, Wagon
Acquisition, Mower, rake
acquisition, Fertilizer spreader
Acquisition, Corn picker
Acquisition, Bulk tank
Acquisition, Loafing area, per cow
Acquisition, Cow and replacements
Acquisition, Non-auto silage feed bunk, per cow
Acquisition, Hay storage and feeding, per cow
Acquisition, Corn, 100 bushels
Acquisition, Hay, 10 tons
Acquisition, April labor, 260 hours
Acquisition, May labor, 260 hours
Acquisition, June labor, 260 hours
Acquisition, July labor, 260 hours
Acquisition, August labor, 260 hours
Acquisition, September labor, 260 hours
Acquisition, October labor, 260 hours
Acquisition, November to March labor, 1300 hours
Land acquisition, cash and mortgage, 10 acres
Land acquisition, contract, 10 acres
Credit acquisition, land and mortgage, $100
Credit acquisition, 6% land contract, $100
Credit acquisition, 7% land contract, $100
Credit acquisition, land mortgage, $100
Credit acquisition, chattel mortgage, $100
Credit acquisition, silo dealer, $100

Continued

284.82
711.00
1087.25
703,69
164.01
356.70
18.63
88.37
48.22
55.21
279.31
33.82
98.81
26.10
156.31
173.25
66.00
42.39
8.12
33.00
95.00
225.00
350.00
350.00
350.00
350.00
350.00
350.00
350.00
1750.00
12.50
12.50
5.50
6.00
7.00
5.50
6.50
9.04

- ---

TABIE B.3-Continued

Profit or Cj
Number Description Coefficients

153 Credit acquisition, machinery dealer, $100 13.00
154 Salvage, tractor 356.70
155 Salvage, 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
1161 Salvage, mower, rake 98.81
162 Salvage, fertilizer spreader 26.10
163 Salvage, corn picker 156.31
164 Salvage, cow and replacements 42.39
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, l$000 40O00
171 Salvage, bulk tank 173,25
172 Credit repayment, $1000 55.00
173 Positive unit vector, sum equation, penalty 444I.00
174s Negative unit vector, sum equation 0.00
175 Salvage hay equipment

1 All hay equipment was combined for the final computations. The set includes
the disc and drill, mower and rake, and the fertilizer spreader.

TABIF B.4
INITIAL OPTIMUM SOLUTION

Organization and Imputed Values
Organization T Selected Imputed Values
Activity No. Unit Amount Resource Unit MVP 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
145
Unused cash;
Unused 5.5% credit
Unused 6.5% credit
Unused 7% credit

1 Acres coverable.

Acres
Acres
One each
One each
One unit
One unit
One unit
One unit
2 days/month
100 hours
100 bushels
10 tons
260 tons
do
do
do
One unit

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 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.2

$ 0.80
0.34
0.67
0.62
0.44
0.16
3.52
5.02
1.42
3.30
9.00
17.50
0.72
1.44
1.44
1.44
1.44
1.44
1.14
134.28
30.08
2.80
52.00
7.42
1.92
0.46
0.92
0.78
20.72

2 Tillable acres.

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

132
132

$ 3.26
8.04
9.80
12.52
22.06
19.76
1.88
9.48
11.28
17.44
21.94
26.,8 4
5918.00
5950.00
3464.oo
3494.00
31484.00
3506.00
3978.00
4008.00
2152.00
2482.00
2172.00
2494.00
3590.00
3620.00
2224,00
2254.00
2214400
2266.00
0.00
144.00
13.5h

w WLIWW . .

----------------

P I .

TABLE B.5
OPTIMUM SOLUTION, 320 ACRES

Organization and Imputed Values
Organization Selected Imputed Values
Activity No, Unit -Amount source Unit MVP Activity No. Delta J
5 Acres 60,00 Disc, drill AC1 $ 0.79 I $ 3.23

6
156
161
159
162
164
171
168
169
165
166
138
139
142
143
129
120
123
126
124
121
Unused cash
Unused 5.5% c
Unused 6.5% c

do
One each
do
One unit
do
do
do
2 days/month
100 hours
100 bu.
10 tons
260 hours
do
do
do
One unit
do
do
do
do
do
$100
do
do

208.00
1.00
1.00
0.83
1.00
32.00
1.00
15.oo
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

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
Cash 1
5.5% credit
6% land contract
6.5% credit
Bulk tank capacity
Land

1 ho
AC
do
do
do
do
1 ho
AC
do
10 b
1 to
1 ho
do
do
do
do
do
do
100
do
Per
Unit
; 100
do
do
do
Gal.
T.A.

ur 0.00
0.63
0.58
0.44
0.16
3.47
ur 4.76
1.36
3.13
u 9.00
n 17.50
ur 1.43
1.43
1.43
0.72
1.43
1.43
1.43
hrs. 133.12
0.00
cow 0.00
51.44
6.50
1.00
0.00
0,00
02 73
2 22.11

1 Acres co -able. 2 Tillable acres.

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
21i
117
118
132

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

:redit
*redit

- -

-67-

TABIE B.6

OPTIMUM SOLUTION, 320 ACRES, 4 TRACTORS

Organization and Imputed Values
Activity Organization uSelected Impted Vales
Number Unit Amount Resource Unit MVP

51
61
191
175
159
137
138
139
140
141
142
143
129
123
126
124
121
Unused cash
Unused 5.5%
credit
Unused 6.5%
credit

Acres
do

do
Set
One
260

unit
hours

do
do
do
do
do
do
One unit
do
do
do
do
$100

Hay equipment
May tractor
May plow
Disc, plaiter
Cultivator, sprayer
Sept. chopper
Oct., wagon
Corn picker
Labor
Cash 1
5.5% credit
6.5% credit
Land

71.1
168.9
28.0
0.8
0.60
0.05
1.85
1.55
0.07
o.4o
0.31

2.31
1.82
0.75
3.64
0.48
1.22
0.00

0.00

with this activity in this and succeeding solutions.

AC
1 hour
AC
do
do
do
AC
do
1 hour
$100
do
do
T.A.

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

c

1 Selling of crops is combined

-68-

TABLE B.7

OPTIMUM SOLUTION, 320 ACRES, 4 TRACTORS

Organization and Imputed Values
Activity Organization Selected Imputed Values
Number Unit Amount Resource Unit MVP

5 Acres 240.00 Hay equipment AC 0.99
6 do 0.0 May tractor 1 hour 7.69
19 do 28,0 May plow AC 0.32
175 Set 0.8 Disc, planter do 0.63
137 260 hours 0.05 Cultivator, sprayer do 0,58
138 do 1.85 Sept. chopper do 0.00
139 do 1.55 Oct. wagon do 1.35
140 do 0.07 Corn picker do 3.13
141 do 0.40 Labor 1 hour 1.43
142 do 1.03 Cash 1 $100 6.50
143 do 1.96 5.5% credit do 1.00
129 One unit 1.4 6.5% credit do 0.00
123 do 0.75 Land Til. acre 20.12
126 do 2.80
124 do 0.48
121 do 1.22
Unused cash $100 0.00
Unused 5.5%
credit do 0.00
Unused 6.5%
credit do 69.18

-69-

TABIE B.8

OPTIIUM SOLUTION--320 ACRES, 4 TRACTORS, 1 CHOPPER, 3 CORN PICKERS

Organization and Iuted Values
Sganization Selected Imputed Values
Activity No. Unit Amount Resource Unit VP

5 Acres 240.00 Hay equipment AC 0.99
6 do 0.00 May tractor 1 hour 8.94
19 do 28,00 May plow AC 0.32
175 Set 0.80 Disc, planter do 0.63
137 260 hours 0.05 Cultivator, sprayer do 0.58
138 do 1,85 Sept. chopper do 0.00
139 do 1.55 Oct. wagon do 1.35
140 do 0.07 Corn picker do 0.00
141 do 0.40 Labor 1 hour 1.43
142 do 1.03 Cash 1 $100 6.50
143 do 1.96 5.5 credit do 1.00
123 One unit 0.75 6.5% credit do 0.00
126 do 2.80 Land 20.12
124 do 0.48
121 do 1.22
Unused cash $100 0.00
Unused 5.5%
credit do 0.00
Unused 6.5%
credit do 60.49

-70-

TABIE B.9

OPTIMUM SOLUTION, FINAL FAPE PLAN

Organization and Imyuted Values
Organization Selected and Iuted Values
Activity No. Uit Amount Resource Unit MV

$ Acres 80.00 Hay equipment AC 0.00
6 do 136,00 May tractor 1 hour 0.00
19 do 52.00 May plow AC 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 picker do 0.00
142 do 0.34 Labor 1 hour 1.43
143 do 2.04 Cash $100 6.50
Unused cash $100 0.00 5.5% credit do 1.00
Unused 5.5 6.5% credit do 0.00
credit do 0.00 Land Til. acre 22.1
Unused 6.5%
credit do 53.03

TABIE B.10

PURCHASABIE ASSETS
PRICE, CREDIT TERMS AND DEPRECIATION

Down Payment
Including Credit Annual Annual
Asset Description Pricel 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 204i 3 do 272.50
Wagon 330 86 248 3 do 33.00
Mower, side rake, 7' 1125 285 844 3 do 96.00
Fertilizer spreader, 10' 360 94 270 3 do 25.20
Corn picker, pull type, 1 row 1525 385 1143 3 do 152.50
Upright silo, 20'x 60', complete 6669 3169 3500 3 39.76 284.823
Bunker silo, 6x30x130, complete 5100 5100 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 1063.85
Loafing area for 10 cows 800 800 6.0
Hay storage, feeding, 10 cows 400 400 32.004
Feed bunk, non auto, 10 cows 50 50 8
Feed bunk, auto, 10 cows 852 -- -- 161.88
Cow and replacements 332 332 156
Land, cash purchase, 10 acres 2900 2500 -
Land, mortgage, 10 acres 2500 1375 1125 20 8.40 -
Land, 6% contract, 10 acres 2500 250 2250 20 8.70
land, 7% contract, 30 acres 2500 250 2250 20 9.40

- Prices were obtained from various dealers. Dealer prices were then increased
2 Depreciation rates from: Nielson, James M., Application of the Budget Method
Ph.D. thesis, Harvard University, Cambridge, Massachusetts, 1953.
SIncludes repairs, taxes, insurance.
SIncludes repairs.

uniform y by 10%.
in Farm Planning, unpublished

-72-

TABLE B.11

COST OF MACHINERY REPAIR

Repairs as Percent of
Machine Machine Cost L

Tractor 7
Plow 5
Disc 4
Corn 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

1 Data from: Nielson, James M., op cit

-73-

TABIE B.12

FERTILIZER APPIaCATION AND CROP YIELD ESTIMATES1

Oat Hay Hay Corn Corn
Item Silage Silage Grain Silage

Fertilizer (low)
5-20-10 200 Ibs 210 Ibs. 210 Ibs.
0-20-20 60 Ibs 60 Ibs.
Yield 5.0 tone 2.5 tons 7.5 tons 60 bu. 10.6 tons

Fertilizer (med.)
5-20-10 300 Ibs 250 250
0-20-20 200 Ibs. 200 Ibs.
Sidedress, N 40 Ibs. 40 lbs.
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,
0-20-20 300 Ibs. 300 Ibs.
Sidedress, N 30 Ibs. 80 Ibs. 80 lbs.
Yield 8.5 tons 4.2 tons 12.6 tons 90 bu. I5 tons

1 Data modified from: Hoglund, C. R., and Cook, R. L., Higher Profits from:
Fertilizer and Iproved Practices. Agricultural Economics Eimeo 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.

-714-

TABIE B.13

TIME REQUIREMENTS FOR FIELD OPERATIONS1

Acres per Hours per Acres per
Operation Hour Acre 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
Spray 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

1 Primarily from: American Society of Agricultural Engineers, Agricultural
Engineers Yearbook, 2nd Edition, 1955, p. 89.

TABLE B.lh

NMER OF FIELD WORKING DAYS PER MONTH1

Month Days

April 12
May 15
June 18
July 20
August 21
September 17
October 15

1 Data from unpublished sources.

TABLE B.15

DAIRY AND CROP CASH COSTS1

Item Unit Amount

Crops
Fuel and oil Per hour tractor time $ 0.70
Alfalfa seed Bushel 25.00
Oat seed Bushel 1.45
Corn seed 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

1 Data from various unpublished sources.

TABIE B.16

DAIRY LABOR REQUIREMENTS1

Parlor Level of Type of Minutes per
Type Efficiency Silo Day per Cow2

Stanchion average Upright 17.76
Stanchion efficient Upright 10.56
Stanchion efficient Bunker 10.56
Walkthrough average Upright 12.06
Walkthrough efficient Upright 7.50
Walkthrough efficient Bunker 7.50
Herringbone average Upright 10.92
Herringbone efficient Upright 6.90
Herringbone efficient Bunker 6.90

1 Primarily from: Hoglund, C. R., Boyd, J. S. and Snyder, W. W. "Herringbone
and Other Milking Systems," Quarterly Bulletin, Michigan Agricultural Experiment
Station, Michigan State University, East Lansing, Vol. 41, No. w (February, 1959)
and Hoglund, C. R. and Wright, K. T., Reducing Dairy Costs on Michigan Farms
Michigan State University Agricultura Experiment Station Special Bulletin 376,
East Lansing, May, 1952.

2 Includes care of the entire herd.

TABIE B.17
RATIONS AND PRODUCTION FOR THE MILKiNG HERD, PER COW1

Silage Hay Corn
Per Per Per Per Per Per Total Production
Ration Day Year TDN Day Year TDN Day Year TDN TDN Per Year
NIumber Pounds ounounds P ds unds Pounds Pounds Pounds Pounds Pounds Pounds Pounds Pounds
1 50 18,300 3,600 10 3,650 1,825 6.8 2,470 1,975 7,400 11,000
2 50 18,300 3,600 10 3,650 1,825 5.7 2,090 1,675 7,100 10,500

3 50 18,300 3,600 10 3.650 1,825 4.7 1,720 1,375 6,800 10,000
4 40 14,600 2,920 12 4,380 2,190 7.8 2,860 2,290 7,400 11,000
5 40 14,600 2,920 12 4,380 2,190 6.8 2,490 1,990 7,100 10,500
asl
6 40 14,600 2,920 21 4,380 2,190 5.8 2,120 1,690 6,800 10,000 0

7 30 10,950 2,190 15 5,470 2,740 8.5 3,090 2,470 7,400 11,000
8 30 10,950 2,190 15 5,470 2,740 7.4 2,720 2,170 7,100 10,500

9 30 10,950 2,190 15 5,470 2,740 6.4 2,340 1,870 6,800 10,000

1 Modified from: Jensen, Einar, et al., Input-Output Relationships in Milk Production,United States
Department of Agriculture Technical Bulletin No. 815, Washington D. C., May, 1942

TABIE B.3

RATIONS IN HAY EQUIVALENTS AND CORN EQUIVALENTS

PER COW PER YEAR, INCLUDES REPLACEMENTS

Hay, Silage, by Total Grain, Grain, Total
Ration Silage, Cows Cows Replacements Roughage Cows Replacement Grain
Number Tons Tons HE Tons HE Ton Tons HE Bu CE Bu CE

1 9.15 3.05 1.82 2.00 6.87 t4.1 13.3 57.4
2 9.15 3.05 1.82 2.00 6.87 37.4 13.3 50.7
3 9.15 3.05 1.82 2.00 6.87 30.7 13.3 44.0
4 7.30 2.43 2.19 2.00 6.62 51.1 13.3 614.
5 7.30 2.43 2.19 2.00 6.62 44.5 13.3 57.8
6 7.30 2.43 2.19 2.00 6.62 37.9 13.3 51.2

7 5$.7 1.82 2.74 2.00 6.56 55.2 13.3 68.5
8 5.47 1.82 2.74 2,00 6.56 48.6 13.3 61.9
9 5.47 1.82 2.74 2.00 6.56 41.8 13.3 55.1

-78-

TABLE B.19

AN EXAMPLE OF THE COMPUTATION OF MACHINE
AND POWER RESTRICTIONS

1. April power restriction

(a) Plowing is the most limiting restriction
(b) One tractor can plow 7.2 acres per day
(c) Twelve field working days in April
(d) One tractor can plow a maximum of 86.6 acres in April.

2. April disc and drill restriction
(a) One tractor can disc (2.8)(8) = 22.4 acres per day
(b) One tractor can drill (3.5)(8) = 28.0 acres per day
(c) Set up a set of simultaneous equations where:
x number of days to disc
y = number of days to drill

We have x + y = 12
22.4x = 28.0 y

(d) Solving,

Disc 6.67 days
Drill 5.33 days

(e) Thus, one tractor can disc (6.67)(22.4) = 1h9 acres
and one tractor can drill (5.33)(28.0) = 149 acres.

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