- . * 1
l" l M
311.21
PM? . 3'4-
? .2 ,
1 #:1531256!“

‘ 4 1v 1
g" #153.“ 1
k .

“1
m .I ;
.' [“3“ “.fi
11,-4 “‘3"

.
n

3‘,” . . ‘L' , 1.... 1mm 33323; =,:'
x. @3531 $12.31; , ~; 4.: M1“):
.“Eud‘hl :13fo V . . I-i 5.. ‘. ~ ‘15:“:1‘“ 635:; .4, Mfififi‘fif“
94‘. 316323;; 1 . - Egg: M 32 5 "1

‘l.

... "15;; 7 1.}.
L 2:22
. .. W“. ‘3- 7 ’ -' 1‘ '
1%}; 3R%~L?1fiw% I W32 rug

-5\ II E‘t’:;, H ‘0; 1‘3“. 't‘r‘ 32;? \. {.c
6...; “L:
1"".3'135‘ .Efii“:
“2.23% 16...»..223.
“was". $3234.?- ‘
“m

. 1- 32:;
REM f ‘- km:::‘;1:m
wave“. we w.
. . 3.2-:
“13151:. 233.23% " Tc 3: 3‘14““:
"£32952 '1‘5 3‘ m 1212.“:
.1. - 1'. $31314: fifths“.-.
3333.138. Lfiflfl‘a duratfq} ‘x‘Ifon-u
' F). ‘:L-'»‘ ‘Knjc. av \ ‘2‘;
‘. ,. _ +51" fi‘ufw‘r '3‘
*Wififl {2:1 "'2" ’7-151; .4. :
. .' .: ’ 3.633.." 1;..1513-:~¢.~“~'x~1~ .L' ..
“~21 — ~“~ 22...: 22:3 '2?
. m. ”1.121. W213:6;3 3%.;
u. . 2". at? ' LA L‘s-"Eat
“‘22:“ 5‘“ ‘3;ch “*2
1212.123» ~
#5 a}. '1‘? we}
‘13.:- ,. k ..
43"”: «Edi?
- ,; 1. mm
,4; 2152‘
"L“ .3258;
.u-“lu 1‘ .33.

“‘3 ' "I .‘qz': ,
222‘

I.
W

, ‘11;- ,§.,.;:,L 1913-,“ . WK 1:.
Egg " "9E9 2.2225? EM“? ‘ Mfi‘

“2'1.
«73%
13211“

2:2

Lag; ML
” ‘2‘1‘:
X .56. I ‘
%{‘$}‘ "1:; RR“ 3'; ' fifi‘fih’
'\ 31‘1“ 1.333%; {111% ‘5‘ . Lg?! 1 _ ‘
«131‘ ”“1L 4:52? $49 “3*" 1.13m: ‘
q'gfixh .. «a; X: 1.5 .5; R . .
(. ‘3“th 31" ‘ “E“?

. ' 11 1 :-
Jae .3; L ‘3'
n- W1; ,‘
1.4.11.1" :31“ L1 j~“‘=.L 71 2‘7: 932’
”‘3‘; 4 ‘ "
;.

$335.?

.3231". . _

.‘
L 22%.
£353}. {‘3 ,3,

2’
'I‘

‘F ,
. 3'...
«:35,
J12 1 3‘:

Ar
“Fm.
-1

“v.1

Fe; '2‘- ‘i t E:

AA
.. 1-
ram

z
.‘;5:. 5
'5':

a .

:32—
3'...

--_.. a.
1"" a.
m. - .~ -235}:
1.22%; ' _ _-§{; (315;
. L'I ' _ ‘ n‘

: >12: .
(a):
M .._.
.5. (if
‘4 7":
55:23.2 '

w...
-
VanMQVW'

”fififis
-“§?§2~:~ 71:... [f v _..-.
«j. .. 22-2" 1‘“ ,2 -

2V... .
2235..“ -‘
35,233:

M - A- w..-
2:6":

"zest—- *
vii-:-

:
’3

:z'
;

.Ir;“'-‘ 1
. :niE’

:-

_ 4y...
.«vfl‘

“(Luigi -
- .3“,

.,

.2‘

. 37’

 

Egg: .2 _, ,. ‘ ‘ “.11 ' ,x-‘l-p " F‘
~:. Lw . =7 ‘ Z. .2
'27 222m-“ _ A 5‘ : X . gr
”3;” ‘ ' - ‘ L'T . 22?? 4:
v .~ : .3 ; v.9, A, .
49* ‘
4: -

9E_;’,." Z.

o 4148!

LIBRARY

Michigan State
University

    
     

This is to certify that the

thesis entitled

THE RELATIONSHIP BETWEEN
LAND VALUES AND FACTOR COSTS

presented by
Ghanbar Kooti
has been accepted towards fulfillment

of the requirements for

Ph.D. (199-99111 Ag. Econ.

jW 0&9qu

M314 professor

Date W30

0-7639

 

 

w:
25¢ per day per item
RETURNING LIBRARY MATERIALS:

‘ w. Place in book return to ream
"'3',” charge from circulation recov

fl-|\\\\ ’IL

Iu~
"‘ In

 

 

 

 

THE RELATIONSHIP BETWEEN
LAND VALUES AND FACTOR COSTS

By

Ghanbar Kooti

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1980

ABSTRACT

THE RELATIONSHIP BETWEEN
LAND VALUES AND FACTOR COSTS

by

Ghanbar Kooti

The purchase of farmland can be one of the most dif-
ficult investment decisions confronting farm operators.
Compared with other production inputs, land is purchased
infrequently and usually in a discrete size unit and involve
long term financial obligation. When a tract of land is
available for sale in the market, knowledge of how much a
farmer can afford to pay for that tract of land is very
important.

Land values are based on the incomes it can earn, now
and in the future, that is the present value of all future
benefits. In other words, land value today equals the
present value of the income expected from land plus the
present value of the price of land he receives when the
land is sold at the end of the planning period. Expectation »
about future incomes stream is estimated using the immediate
past incomes stream assuming that the best clue about the
future is the immediate past. Since land is a durable that

provides services to the production process for more than one

Ghanbar Kooti

period, the return to land input is determined as the value
of the portion of output attributed to land.

The purposes of this study were: First to review
the theory of partitioning output among inputs. Second to
compare and contrast land values under alternative acqui—
sition assumptions of land and machinery. Third, to study
the effects of increases in factor costs on land values.

A new theory of partitioning output among inputs is
introduced in this dissertation. This theory states that
the portion of output attributed to any input is the integral
of long run marginal value products along the firm's expan-
sion path. It is graphically and analytically illustrated
that the firm's expansion path and hence the share of output
attributed to land changes under alternative assumptions of
land and machinery acquisition. Next the effect of increas-
ing factor cost on the value of such inputs as land using
a Cobb-Douglas production function is illustrated.

The theory is implemented using linear programming (LP).
The LP model maximizes profits subject to resource constraints
in each time period for three consecutive periods: 1977,
1978, and 1979. The shadow prices, equal to long run mar-
ginal value products, were summed to determine‘the value of
output attributed to land.

The results indicatethat the value of the output attri-

buted to land, expected average income, and land values for

Ghanbar Kooti

the current period are greater under the assumption of

land ownership than those
that land is rented. The
land under the assumption
than that estimated under

machinery services. Land

estimated under the assumption
value of the output attributed to
of machinery ownership was greater
the assumption of custom hiring

value for machinery ownership was

greater than land value under the assumption of custom

hiring machinery services.

Lastly, the results indicated

that as costs of such factors as labor, fuel, and fertilizer

increase, the value of land would decrease.

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to
Dr. Lindon J. Robison, the Chairman of his Guidance Com-
mittee, for guidance, constructive criticisms and helpful
suggestions during the development of this research. Ap-
preciation is also extended to other members of the com—
mittee, Dr. Steve Harsh and Dr. Gerald Schwab who read
and made many helpful comments on the dissertation.

Special thanks are due to the author's parents,
Mr. and Mrs. Abid Kooti, for their encouragement and under-

standing throughout the author's graduate program.

Chapter
I I

II.

III.

IV.

V.

TABLE OF CONTENTS

INTRODUCTION. . . . . . . . . . . . .

Factors Effecting Land Values . . .
Determining Land Values . . . . .

Statement of the Problem. . . . . .
The Purpose of this Study . . . . .

Objectives. . . . . . . . . . .
Procedure . . . . . . . . . . . .
THEORETICAL FRAMEWORK FOR DURABLE ASSET

VALUATI ON C O C O O I O O O I O O O
A New Theorem . . . . . . . . . . .
The Medel O O O O I O 0 O O O O O 0
Chapter Summary . . . . . . . . . .

ILLUSTRATIONS OF THE THEORY OF PARTITION-
ING OUTPUTS TO FACTORS OF PRODUCTION.

Asset Divisibility in Acquisition

and Use . . . . . .-. .
Asset Indivisibility in Acquisition

and Divisibility in Use . . . . .
Output Attributed to Land with

Machinery Ownership . . . . .

The Effect of Increase in Factor Costs
on the Portion of Output Attributed
to Input Land . . . . . . . .

_ Chapter Summary . . . . . . . . .
IMPLEMENTATION OF THE THEORY. . .
LP As A Research Tool . . . . . .
Linear Programming Tableau Description
Sources of Data . . . . . . . . . .

Chapter Summary . . . . . . . . . .
MODEL RESULTS UNDER CONSTANT INPUT PRICES

Acquiring Land Services through
Renting . .

Portion of Output Attributed to Land

Average Expected Income . . . . . .

Land Value. . . . . . . . .

Page

00000th H

22

23
26

30

Chapter

VI. SE

VII. SU

APPENDIX . .

BIBLIOGRAPHY .

TABLE OF CONTENTS (Cont'd)
Page

Acquiring Land Input through Ownership 69
Acquiring Machinery Services through
Custom Hiring. . . . . . 78
Acguiring Machinery Services through
ombination of Ownership and

Custom Hiring. . . . . . . . . . . 82
Chapter Summary. . . . . . . . . . . 89
NSITIVITY ANALYSIS . . . . . . . . . 92
Analysis Procedure . . 92
Results of the Sensitivity Analysis. 94
Chapter Summary. . . . . . . . . . . 112
MMARY AND CONCLUSIONS. . . . . . . . 113
Areas for Future Research. . . . . . 120

o o o o o o o o o o o o o o I o o o 121

o a o o o c o 0 134

ii

Table
h.1

h.3

h.h

5.2

5-3

5.h

LIST OF TABLES

Linear Programming Model Activities
Considered in each Period. . . . .

Resource Constraints and Accounting
Equations. . . . . . . . . . . . .

An Example of Linear Programming
Tableau used in this Study: Complete
Ownership of Land and Custom Hiring
Machinery Services . . . . . . . .

An Example of Linear Programming
Tableau Used in this Study: Renting
Land and Machinery Ownership . .

Optimal Number of Acres, Operating
Incomes and Marginal Value Products
of Land for Different Levels of
Assumed Budgets. . . . . . . . . .

Estimated Portion of Output and
Annual Income to Land, Given that
Land Services are Acquired through
Renting. . . . . . . . . . . . . .

Marginal Value Products and Operating
Incomes for Different Levels of Acres
Under the Assumption of Land
Ownership. . . . . . . . . . . . .

Estimated Portion of Revenue Attributed

to Land and Annual Average Income to

iii

Page

“5

A6

“9

52

62

67

73

Table

5.5

5.6

5.7

5.8

5.9

6.1

LIST OF TABLES (Cont'd)

Land, Given that Land Services are
Acquired through Ownership. . .

Estimated Marginal Value Products and
Operating Income Under the Assumption
that Machinery Services are Acquired
through Custom Hiring . . . . . . .

Estimated Portion of Output and Annual
Average Income to Land, Given Complete
Custom Hiring Machinery Services. .

Estimated Marginal Value Product and
Operating Income Under Complete
Ownership of.Land and Combination of
Machinery Ownership and Custom
Hiring. . . . . . . . . . . . . . .

Estimated Portion of Revenue Attributed
to Land and Annual Income to Land
Under Combination of Ownership and
Custom Hiring Machinery Services. .

Estimated Expected Average Incomes and
Land Values Under Combination of
Machinery Ownership and Custom Hiring
Hiring. . . . . . . . . . . . . . .

Sensitivity of Marginal Value Products
and Potential Incomes to Change in
Diesel Fuel Cost. . . . . . . .

iv

Page

77

79

81

85

88

89

97

Table
6.2

6.3

6.h

6.5

6.6

6.7

LIST OF TABLES (Cont'd)

The Sensitivity of the Return to
Land to Change in Cost of Diesel
Fuel 0 O O C O O O I O O O O O O 0

Expected Average Incomes and Land
Values Associated with Changes in
Diesel Fuel Prices. . . . . . . .

The Sensitivity of Return to Land to
Change in Fertilizer Costs.

Expected Average Incomes and Land
Values Associated with Increase in
Fertilizer Costs . . . . . . . . .

The Sensitivity of Return to Land to
Changes in Wage Rate of Hired Labor

Expected Average Incomes and Land
Values Associated with Increase in
Wage Rate of Hired Labor. . . . . .

Page

102

103

106

107

110

111

Figure

LIST OF FIGURES
Page

Optimal Combinations of Inputs for
Different Levels of Outputs Assum—

ing x and y are Divisible in Purchase
and Use 0 O O O O O I O O O O I O O I 25

Isoquant and Ridge Lines and Expan-

sion Path of a Firm Under the

Assumption of Asset Indivisibility

in Acquisition and Divisibility in

Use. . . . . . . . . . . . . . . . . 29
Shifting the Expansion Path as Price

of Input x, Changes. . . . . . . . . 35

Different Budget Levels and the
Associated Expansion Path for 1977
PeriOd O O O O O O O O O O O O O O O 60

Graphical Representation of Marginal
Value Products Associated with Various
Level of Acres for 1977 Period . . . 66

Different Levels of Land Constraints
and Expansion Path for Land Owner—
ship for 1977 Period . . . . . . . . 72

Expansion Path Shifts Resulting from
Diesel Fuel Price Increase . . . . . 96

Changes in Marginal Value Products
of Land as Diesel Fuel Price Increase
for 1977 Period. . . . . . . . . . . 100
vi

CHAPTER I
INTRODUCTION

The purchase of farmland can be one of the most difficult
investment decisions confronting farm operators. Compared
with other production inputs, land is purchased infrequently
and usually in a discrete sized units and involves a long
term financial obligation. The decision to purchase a
parcel of farmland is crucial since only about three per—
cent of all the farmland in the U. S. is transferred from
one owner to another each year (Scott).

Land is different than man-made capital assets in that
there is a limit to the total supply and each parcel has a
locational monopoly. Therefore, when a parcel of land is
available for sale in the market, knowing, how much a farmer
can afford to pay that parcel of land is very important.

If his bid price is significantly below the asking price
then he might lose the opportunity to purchase. On the
other hand, if it is significantly above the asking price,
his purchase price might put him in a difficult financial
position leading to financial loss. Therefore, knowing how
much the farmland is worth is important for the farm oper—

ator.

F r E ' L Values:

The price that farmers are willing to pay is affected

,..=";f

by several factors. One basic factor is the current re-
turns, and expected increase in net returns due to expect—
ed increase in physical production over time due toim-
proved varieties and other technological improvements.
Scott indicated that the average yield increase in corn
production, has approximately doubled in the last 40 years.

People are willing to pay extra for land because of
expectations of further inflation. This, of course, depends
on how important inflafibnary forces in the economy seem to
be to the purchaser. Prices reflect this to the extent
that part of the expected future increase is captured now
by the seller, and the holding period required by the buyer
to realize this increase in value is lengthened.

Another factor is job security. A farmer buying land
assures himself of longer tenure than he could if he was
renting. Many people have pride of ownership or ego sat-
isfaction in being able to say they own farmland. This ego
satisfaction in owning farmland is certainly not confined
only to rural people (Scott).

In most cases, an expansion buyer with excess machinery
capacity can often afford to pay a higher than average price
for additional farmland. When technology creates a situation
in which a farm operation becomes land deficient in relation
to other inputs such as labor and machinery, the farmer needs

to increase the land input. Thus, it may be economically

feasible for him, if necessary, to pay a higher price for
land to increase the total land input of the farm and spread
his fixed costs over a larger land area, instead ofincreas-
ing only certain variable inputs, such as fertilizer and
pesticides (Kooti).

Availability and cost of credit also influence the
amount the farmer is willing to pay for a parcel of land.

As credit becomes easier to obtain, the number of potential
buyers for a tract of land increases, and so does the demand
for land. As a result, its price increases. The cost of
credit adds to the cost of land purchase; therefore, if he
pays less for the cost of credit, he may be willing to pay
more for the farmland (Kooti).

Government programs also influence the farmland prices.
Commodity price support programs insure farm owners a certain
minimum price for their crop (at least in the short run).
even if production increases. Therefore, it becomes profit—
able to increase production because by so doing, the net
income to land will increase. Acreage allotments, which
reStrict output in order to increase total revenue, may
increase land prices for those fortunate enough to have an
allotment. Expectations about the continuance of govern-
ment programs may affect land prices. With acreage allot-
ments it is essential that the owner be relatively certain

the program will be continued, if he is to pay the higher

 

prices for farmland with non-transferable allotments(Kooti).

DETERMINING LAND VALUES

The previous method of calculating the price of farm—
land, called the capitalization formulas, suggested that
land prices could be determined by dividing the average net
after-tax income per acre by the discount rate or return
from the next best alternative. For example, if after-tax
net return from land is $50 per acre and the rate of return
on the best alternative is 10 percent, dividing $50 by 0.10
would price the land at $500 an acre.

The formula, unfortunately, has become hopelessly
outdated, yet it continues in use for lack of accurate and
easy to apply alternatives. It is outdated because it
assumes constant income from land and that land will be
valued the same after some planning period as it was at the
beginning. Historical data has indicated that neither land
values nor net return to land have remained the same. During
the last ten years land values have increased at an average
rate of 9.5 percent while income to farmland has increased
at an average rate of 7 percent (Kooti). Therefore, if the
capitalization formula was to be used to estimate land values
using today's earnings, they would likely fall below current
land prices.

An alternative more realistic method to determine land

 

prices is to sum the discounted value of the after—tax
net income to land plus the discounted value of the after
tax capital gains.

Kooti analyzed several methods of determining land values
including the "Capital Budgeting Model" which determines the
land value given the expected net income to land, marginal
income tax rate, rate of pure time preference, planning
horizon, absolute risk aversion, and the variation of annual
income to land. He concluded that land value is very sensi-
tive to change in expected annual net income to land. An
increase in productivity of land increases the price of one
acre of land. Absolute risk aversion had a negative impact
on land values. An increase in the variation of income de—
creases the value of one acre of land. Any increase in risk
decreases the value of one acre of land. Finally, there
was an inverse relationship between the land value and the
rate of pure time preference.

Still another capital budgeting model included financial
terms and risk. This model was developed by Lee and Rask
and adapted by the author. This model determines the maximum
bid price of land given the expected annual net income to
land, marginal tax rate, tax rate applied to capital gain
income, interest rate on mortgage loan, opportunity cost of
capital, inflation rate, growth rate of income, planning

period, amortization period of the loan, absolute risk

aversion and the variation in income.

He concluded that the longer the amortization period
of the loan the greater the value of one acre of land. The
higher the interest rate on mortgage loan, the smaller the
value of one acre of land. The larger the down payment the
smaller the value of one acre of land.

The common feature of the capital budgeting models is
they assumed income for a lumpy asset was known and the
effect of factor costs already accounted for. AS-a result
the effectsof factor costs such as machinery, fuel, and

fertilizer an land values was not explicitly explained.

Statement of the Problem

The question of how to determine the price of land has
received considerable attention (Harris and Nehring, Lee
and Rask, and Kooti). But the question of how to identify

net return attributable to the capital asset has not received

much attention. Also the question of how factor costs
affect returns to land and hence land values has not received
much attention.

Net income to land is based on the farm receipts and
expenses. Cash farm receipts are based on the farm's prod-
uctive capacity--the crop mix, the typical prospective acre-
age yield per acre of various crops planted, and the prices

of agricultural products. Expenses should represent what

the typical farmer will spend in order to maintain and

run the business. Included are: seeds, fertilizer, chem-
ical, irrigation costs, harvesting expenses, fuel, machinery
expenses, hired labor, insurance, real estate taxes, and
depreciation. Increase in the price of energy related agri-
cultural inputs in particular and other inputs in general
without a comparable increase in output prices, decreases
the farm income and hence land value. When a farm operator
has excess machinery at hand, return to land can increase if
more land is available to him. Thus, land value to such.a
farm operator might be higher than a farm operator who has
no machinery at hand. Therefore, considering agricultural
factors are important in accurate estimation of return to
land and hence land value.

The analysis of output share attributed to each factor
of production such as land, machinery, labor, etc. usually
is found in the marginal productivity theory of factor
demand. According to this theory a factor share of output
is determined by multiplying the number of units employed
by its marginal value productivity. This is called the
Euler's theorem. However, Euler's theorem holds only if
all factors are assumed variable and homogeneous function
is assumed (Robison, 1980). Durables such as land and

machinery are usually acquired in a discrete sized unit,

the services they generate in each time period are divisible.

Therefore, a new approach of partitioning output among
inputs and therefore the return to each input needs to be

developed.
The Purpose of this Study

It is the intent of this study to find more accurate
ways of estimating the return to a durable in general and
farmland in particular. Once the return to the durable is
identified, we are then in a position to apply our capital
budgeting models. Robison's theorem of partitioning output
among inputs will be reviewed and applied. The application
in this study will be to measure returns to the durable
under two assumptions 1) asset is indivisible in purchase
but divisible in use, and 2) asset is divisible in purchase
and use.

Objectives
More specifically, the objectives of this study are:
1) To a new theory of durable asset valuation
in general and land valuation in particular.
2) To determine the portion of output attributed
to durable asset under the assumptions that:
a) Asset is indivisible in purchase but
divisible in use.
b) Asset is divisible in purchase and use.

3) Compare and contrast land values under:

a) Complete ownership of land.
b) Land rented.

Land values are determined using linear
programming technique and Michigan data for
the assumed activities.
A) To compare and contrast return to land and
hence land values under the assumptions of
a) Exess machinery ownership.
b) Custom hiring machinery services.
5) To study the effects of costs of factors of
production such as fuel, fertilizer, and

labor on the net income and hence on land value.

Procedure

The remainder of this dissertation is organized in
the following manner. Chapter II is an explanation of the
theory of durable evaluation and the developments of the
new theory of asset evaluation. Chapter III is a graphical
and mathematical illustration of the theory in which output
attributed to land is measured. Chapter IV implements the
theory using a linear programming technique. Chapter V
presents the results of the linear programming model under
constant input prices. Chapter VI presents the results of

the sensitivity analysis. Finally, conclusions of this study

are given in Chapter VII.

10

CHAPTER II

THEORETICAL FRAMEWORK FOR
DURABLE ASSET VALUATION

Durables are defined as factors of production that
supply services to the production process for more than
one period. While the durable is acquired in a discrete
sized unit, the services it generates in each time period
are variable. For example, tractors are available in finite
sizes, but once acquired the firm can use them up to some
maximum capacity determined by the size and reliability of
the tractor (Robison and Black).

If durables such as farmland and machinery are used in
the production process, the value of their services needs to
be determined. Note, that those durables are usually avail—
able in discrete sized units, but the services generated from
those durables are variable. Neverthless, the net returns
attributed to a durable is determined by measuring the portion
of output attributed to the services generated by the durable.

The analysis of the output share attributed to each
factor of production, usually is found in the marginal
productivity theory of factor demand. According to this
theory, a firm's demand for an input purchased in a purely
competitive market depends on its marginal value product--

the marginal physical products of the input multiplied by

11

the output price. The equality between marginal value
product and the factor price determines the units of input
employed. The units of input used multiplied by the input
price divided by the value of total output equalled the
input's share.

To illustrate, suppose x units of homogeneous labor
are employed at wage rate W. Also let total output Q mul-
tiplied by output price P equal the value of total output
which when divided into Wx equals the share of output re-
ceived by labor. If the share of each input used in the
production are summed, there is no assurance they would sum
to one hundred percent, leaving unanswered the question of
which factor gets the surplus or pays the deficit (Robison).

A special case, however, does exist under which, if
each input factor is paid its marginal value product, the
total product will be exactly exhausted. This, of course,
holds for homogeneous function of degree one as Euler's
theorem demonstrate.' Economically speaking, this implied
that pure economic profits are zero which describes the
long-run equilibrium under pure competition. Chiang ( 197A,
p. #07) makes the point that because linearly homogeneous
functions guarantee zero profit, it was at one time thought
only linearly homogeneous production functions would be
reasonable, which of course, is not the case.

Clark, Wicksteed and others proved that the long-run

12

competitive equilibrium, rewarding each input according to
its marginal product precisely exhausts the total product
if there are constant returns to scale which is, after all,
what was required for long-run equilibrium (Ferguson, 1972,
p. 410—413).

Suppose the firm produces with a variable input x for
labor and fixed capital C in the form of land. In the long
run, all factors are variable so that each receives their
marginal value product. But in the short run, the fixed
factor C cannot be varied, or at least we assume it cannot,
so that a marginal product cannot be derived for its services.
So the return to the fixed factor in the short run is deter—
mined using a residual approach.

According to rules of marginal analysis, the variable
input is employed until its marginal value product equals
its cost; then, if total profits exceed total variable costs,
the residual can be attributed to the fixed factor--a differ-
ence Marshal called "quasi rent". It is useful to note that
quasi rents are never negative because if profits are less
than total variable costs, the firm would not produce even
inthe short run. This residual approach is popular in the
farm management literature where it ascribes to agricultural
land and other capital inputs the difference between total
profits and variable costs. But why give all the residual

to the fixed factor—-why not some to the variable factor?

13

Robison argues that the short run residual approach
for allocating output among the inputs is not appropriate,
primarily because there is rarely an input that is fixed in
the production process. That is, even those capital assets
are purchased in discrete indivisible units, their services
are usually available in divisible units. To measure the
returns to durables which are indivisible but have divisible
services, a new theorem proved by Robison is now introduced.
The new theorem achieves for any function what Euler's

theorem did for linear homogeneous functions.

A New Theorem:

 

The new theorem, the output exhaustion theorem, states
that the value of any general process can be divided among
the inputs in such a way that the output is just exhausted
assuring the inputs each receiving the value of their long
run marginal value product.

According to this theorem if f(X.y) describes a cont-
inuous production process which depends on two inputs X.
and y, where x and y are related by the function y = 1(x)
for all X and y along the expansion path: then, the sum
of the integrals fX plus f.y equal f(x,y) for all x and y.
The proof of the theorem follows:

Since y = 1(X), f(X.y) and the derivative of f

with respect to X equals: df(x.l(x)) WhiCh equals

1h

fxdx + fyl(x)dx. But dy = l(x)dx and x = I1(y).
so that fyl(x)dx = fydy and df(x,l(x)) = fxdx +
fydy. By the fundamental law of calculus the
anti—derivative of fxdx + fyl(x)dx equals f.
Since fxdx + fyl(x)dx equals fxdx + fydy where

y = l(x), then the anti-derivative of fX plus

the anti—derivative of f must also equal f.

The theorem states that if in a two argument input/out—
put function, the relationship between the inputs is speci—
fied, then the sum of the integrated partials with respect
to the inputs equal the output. The results of this theorem
can be easily illustrated. Let output q equals f(x,y) where
f is the Cobb-Douglas function xayb. In addition let the

relationship between x and y be y = cx. The partial der—

ivatives of f with respect to x and y can be written as:

(11.1) fx = axa'lybdx
and
(11.2) r = bxayb'ldy.

y
Substituting cx for y in (11.1) and y/c for x in (II.2) and

integrating allows us to write the sum as:
_ _ + _
(11.3) f(x,y) = I acbxa+b 1dx + § bc aya b 1
+ +
= a cbxa b/(a+b) + bya b/ca(a+b)

Xayb.

15

Euler's theorem meanwhile, is written as:

(11.4) f(x,y) = xfx + yfy
= (a+b)xayb.

So that, the inputs only exhaust the output if a+b were
equal to one. Robison's more general theorem requires no
such restriction.

The theorem has been proven for three or more inputs.
For the three inputs: suppose a production process is a
continuous process defined over arguments x, y and 2. That
is let q equals f(x,y,z). Then, if the following binary

relationships exist: y = l(x), y = g(z) and z = h(x), then:

(II.5) f(X.y.Z) = IfX(X. l (X), h(x))dx +
X -1 1
If (y. l(y). é (y))dy +
yy

ffz(z. g(z), h1(z))dz
Z

Substituting l(x) for y and h(x) for z into f(x,y,z); then,
the derivative of f with respect to x after the substitution
equals:

(11.6) fx = fxdx + fyl(x)dx + th(x)dx

By the fundamental law of calculus, the sum of the anti-der-

ivatives of the partials equals the original function f.

That is:

(11,7) % fxdx + A fyl(x)dx + i fzh(x)dx = f

16

By the change in variable technique, the following equalities
hold:
(II.8) Ifx(x.l(X).h(x))l(x)dx

x

_ —1 —1

— If (1 (y).y.g (y))dy

y
and

(11.9) fo(x,l(x),h(x))h(x)dx

= ffz(h-1(z).g(z).z)dz.

Then, after making the required substitutions, it can be
written:

(11.10) If dx + If dy + ff dz
x x y y z z

Finally, if the results hold for both the case of two
and three inputs, by mathematical induction it holds for

functions of any number of inputs.

The Model

 

Now after having established a methodology for assign-
ing the output to the inputs, the next step is to establish
a proper relationship among the inputs. The relationship
among inputs depends on the marginal value product of the
inputs and their marginal costs. At a point in time, this
relationship depends only on those costs which vary with
use as opposed to costs which vary with time. Economists

prescribe that the relationship among the inputs should be

17

such that, the ratios of their marginal value products
divided by their prices be equal for all inputs at any

point in time. Thus, to determine the relationship among
inputs along the least cost combination curve, the physical
production function must be specified. The production
function specifies such that, at any time period the output
is a function of inputs such as labor, fertilizer, machinery
capital, land services and other factors at each time period,

assuming that all factors are divisible in use. That is:

(II.11) qt = f(x1t,...,x )

nt

where qt is the output at time period t and X1t""’x are

nt
the inputs at time period t. The firm determines the rela-
tionship among the inputs by maximizing the objective func-

tion as shown below at each time period.

1’1

(III12) Int =pq-t " .Elp-X- j: 1,000,110
J:

J Jt

where fit is profit at time period t, p is the price of
output q and pj is the price of the j—th input. By matching
added return to cost for each input, the optimal level of
that input will be determined. After solving, each input
expressed as a function of the input costs at each period

of time. To demonstrate, if output q valued at price p
produced from two inputs x and y which costs the producer

DX and Dy; then, the optimal relationship between x and y

18

would be such that:

(11.13) Pix/PX = pry/By.

This relatioship obviously results from maximizing

n = pf - pxx — pyy with respect to both x and y. Then,

from (11.13) an expression such as y equals h(x,px,py)

could be found. This expression is the relationship

between x and y along the expansion path for x and y.
The maximum units of input x may be given by a firm

budget:

M = pxx + pyy

from which x is determined to equal:

(M - pyy)/px
where M is the total amount of budget available for the
firm to spend on the two inputs x and y. Substituting
the function h(px,py,x) for y in (M - pyy)/px and solving
for x gives x as a function of the parameters pX, py and
M, that is:

x = l(px,py,M)-

Now that, the relationship between x and y and also
the maximum units of input x are determined, the portion
of output attributable to theinput x given a continuous
production function f(x,y) is examined. The portion of
output attributed to input x is the integral of the

long-run marginal value product—-pfx(x,y), where y equals

h(px,py,x), that is:

 

19

x = l(px,py.M)
(11.1h) R = Opfx(x,h(px,py,X))dx

OI‘

(II-15) R = pf(l(px.py.M). h(px.py.l(px.py.M)))

where R is the portion of output attributed to the input x.
Let us illustrate that with an example. Assume that the
production function f(x,y) is a Cobb-Douglas function x'8y'5
and a budget level of $1,000 with the input price x equal
to $5, while the input price of y equals $8, and output
price equals $10.
The firm determines the relationship between x and y

by maximizing the objective function n, at each time period.

- I8 '5
(II. 6) n — px y - pXX - Pyy

The marginal products of the input x, and input y can be

written as:

O 8
f =
y ' 5px y

The optimal relationship from (11.13) would be such that as:

(II-17) .8x"2y'5/pX = -SX'8y"5/py

This relationship obviously, results from maximizing (11.16)

20

with respect to input x, and input y. Then, from (11.17)

-1
y
expression simply is the relationship between x and y along

an expression such as y equals 0.625pxp x is found. This
the expansion path for x and y. This line shows that, there
is a positive relationship between x and y.

The maximum units of input x given a firm budget M of

$1,000 is determined from:

(11.18) M = pxx + pyy

Solving for x after substituting $1,000 for M gives:

(II.19) x = (1000 - pyy)/px.

-1

Substituting 0.625 poy

x for y, $8 for py, $5 for pX into
(11.19) gives:

x = 123.00
Then, the portion of output attributed to input x given
the continuous production function x'8y'5 is determined by
integrating the long-run marginal value product of the
-1

production function where y equals .625pxpy x. That is:

.5 _
R = f8(.625p p'lx) x '2dx
X y
where px equals $5, and py equals $8. Therefore, the

portion of output attributed to input x is:

123 123
R = [5x'3dx = 50x1'3
0 0
or R = $2,00A.00

21

Chapter Summary:

 

In this chapter the new theory of partitioning output
among inputs was introduced. According to this theory, the
durable asset share of the output is the integral sum of
the long-run marginal value product. The relationship among
inputs along the expansion path needs to be specified first
prior to the determination of the long-run marginal value
product and hence the portion of output attributed to the
durable asset. The relationship among inputs simply is

determined by equating the ratios of marginal value products

to their prices.

22

CHAPTER III

ILLUSTRATIONS OF THE THEORY OF PARTITIONING
OUTPUTS TO FACTORS 0F PRODUCTION

In Chapter 11, the general theory of partitioning
output among inputs was introduced. This chapter contains
graphical and mathematical explanations of that theory. The
first part of this chapter graphically illustrates the parti-
tions of output attributed to land under two different as—
sumptions about asset divisibility: 1) asset divisibility
in purchase and use, and 2) asset indivisibility in purchase
and divisibility in use. Asset divisibility in purchase
makes it possible for the farm operator to acquire this
resource in the quantity desired. Indivisibility in the
purchase of the asset limits the choice to acquiring the
asset in the amount available, even though the services
generated are divisible. For example, a farm operator may
have todecide to acquire 100 acres of land or none at all.
If he acquires the 100 acres then the use decision is di-
visible, allowing the farm to use any amount of land up
to 100 acres.

In the second section of this chapter, the portion of
output attributed to land under the assumption of machinery
ownership will be examined using a Cobb-Douglas production

function. That is, we allow the farm operator to own

23

machinery services T- The impact of this owned machinery
services Y on the portion of output attributed to the input
land is explored.

The third and last section of this chapter will examine
the change in the portion of output attributed to land as
the result of change in factor prices, again illustrated

using a Cobb—Douglas production function.

Asset Divisibility in Acquisition and in Use

 

Assume an asset divisible in purchase and use is used
in the production process of a firm. Under this assumption
the optimal combinations of inputs used by a firm is found
by equating the ratios of marginal value products to their
respective prices. Consider Figure 1. The curve Q1 and
Q2 are isoquants depicting various combinations of inputs,
e.g., labor represented by the variable x, and land input
represented by the variable y. The inputs x and y are
combined to produce outputsQ1 and.QZ, etc. Moreover, assume
that x and y are divisible in purchase and use. Lines B1B1
and B2B2 represent different budget lines, where the budget
line shows different combinations of inputs x and y which
have the same cost-—an isocost curve. Given the input prices,
the output corresponding to isoquantCH- can be produced at
least—cost at point A, where the isoquant is tangent to

isocost curve B1B1' At point A, the ratios of marginal

29

value products of each input to their respective prices

are equal, i.e. MVPX/ px equals MVPy/ py, where MVPX is the
marginal value product of input x, MVPy is the marginal value
product of input y, pX is the price of input x, and py is

the price of input y. When this condition is met, the farm
operator is in equilibrium.

Now, suppose the farm operator faces an increased
budget corresponding to budget line BZBZ. Since factor
prices remain constant, the slope of the budget line does
not change. Hence, it shifts from B1B1 to BZBZ. The new
equilibrium is found by shifting the isoquant curve until
it is tangent to BZBZ.

Connecting points A and K generates line OE, which is
the optimal combination of inputs with increasing resources
accompanied by constant input prices; meanwhile at each
resource level, the equilibrium point is defined by the
equality between the ratios of marginal products to the
ratios of input prices. Since the input price ratios have
remained constant, the equality forces the ratios of mar-
ginal products to remain constant. Therefore, OE is an
isocline, a locus of points along which the marginal rate
of technical substitution is constant. The expansion path
is the particular isocline along which output will expand

when factor prices remain constant. The expansion path

thus shows how factor proportions change when output or

Land in acres

Figure 1:

25

 

 

y
32
E
5'2 _________ K
B1 .
I
I
I Q2
y1 —————— A |
: I
' I
l
: I Q1
I I 'l "o
0 x1 B1 x2 B

x
2 Labor

Optimal Combinations of Inputs for Different
Levels of Outputs Assuming x and y are Divisible
in purchase and Use. OE is the expansion path

while lines B1B1 and BZBZ are budget 11nes(isoe

cost).

26

expansion changes, input prices remaining constant through—
out. The theory of partitioning output among inputs,

which was explained in Chapter 11, suggested that the
portion of output attributed to the respective input is
determined by integrating the long—run marginal value

products along the expansion path OE.

Next, we will examine whether the assumption of asset
indivisibility in acquisition would change the firm's expan-
sion path. If the firm's expansion path changes, so does

the portion of output attributed to y.

Asset Indivisibility in Acquisition and Divisibility in Use

 

Assume an asset used in the production process by the
firm is indivisible in purchase but divisible in use. Land
may be an example. It is generally acquired in discrete
size units but can be used in any amount up to the amount
acquired. This manner of acquiring may alter the expansion
path from the one derived under the assumption that the asset
is divisible in acquision. If this is the case, then the
portion of output attributed to the asset, determined by
integrating its long-run marginal value products along the
expansion path, will change.

Consider now the effects on the expansion path of acquir-
ing an asset in an indivisible quantity. For example, let

the firm acquire asset y in indivisible amount F but allow it

27

to utilize the services from F in any amount less than or
equal to F, which is the maximum capacity of the asset. Now
y represents the amount of services actually used, while F
equals the amount of services acquired. The firm's expansion
path under this assumption is now determined.

Consider Figure 2. The effects of limiting the use
of y to values less than or equal to F requires a vertical
constraint beginning from the horizontal axis at point F to
the budget line BB. The area OFDD is the feasible area,
i.e. all input combinations in OFDD are possible choices.
The curves OR and OR are the ridge lines. Along the ridge
line OR the marginal physical product of input x is zero,
while along the ridge line OR the marginal physical product
of input y is zero. The area between the ridge lines OR
and OR, the marginal products of x and y are positive. The
OCDH is both economically and physically feasible, because
the marginal products of input x and input y are positive
and because the resource requirements do not exceed re—
sources availability. Since the indivisible asset is already
vauired in amount F, increasing y incurs no additional
opportunity cost. As a result, input y is employed up to
the point where marginal value product equals marginal
cost, which is zero. Therefore, y is used in the production
process is described by the ridge line 00, along which the

marginal product of y is zero. However, when the use of

28

the asset services y reaches the maximum amount of services
available, F the firm will invest in other variable input x.
So the expansion path becomes OCD.

The portion of output attributed to input y, then is
found by integrating its marginal value products along the
expansion path, 0CD. In contrast, the value of the portion
of output attributed to y when y is divisible in acquisition
is the integral of the marginal value products of y along
0E. Since the expansion paths are different, the output
attributed to y along 0E and 0CD may also be different.

A special case is the Cobb-Douglas production function,
where the marginal value products are never negative. In
this case the expansion path becomes FD instead of OCD.

As a result the portion of output attributed to input y
is determined as a residual after subtracting all the var—

iable costs from the farm income.

 

29

 

 

 

. y
Land in acres
3 1':
Q
R
F C D
I I
l |
I I
I l
' l D
‘ I
' I
I
I ' ‘ ,
I
_ I B
O x x1 Labor, x

Figure 2: Isoquant and Ridge Lines and the Expansion
Path of a Firm Under the Assumption of Asset
Indivisibility in Acquisition and Divisibility
in Use.

30

Output Attributed to Land with Machinery Ownership

 

In the first part of this chapter we showed that the
firm's expansion path changes under the assumptions of:
1) asset divisibility in acquisition and use, and 2) asset
indivisibility in acquisition and divisibility in use. As
a result; we inferred that the portion of output attributed
to land may be different under the two assumptions. Now
another factor that may change the portion of output attri-
buted to the asset land is explained.

This factor is the availability and manner of acquisition
of inputs complimentary to y. Suppose for example, the
farm operator has machinery which can generates services
up to an amount y, in addition, assume the farm operator
can custom hire machinery services at the rate pX per unit
of x. Since the marginal cost of the owned machinery is small
or zero, as long as the services have positive marginal prod-
uct, Y amount of services will be used with the total ser—
vices equal the amount purchase plus the amount owned. If
x is the total amount of machinery services used in the
production process, then z is the amount of machinery ser-
vices purchased equal to x minus 7. Also, assume that the
firm is engaged in production process described by the
function f(x,y) that uses the machinery services x and the

divisible input land, y. Moreover, let f(x,y) be a

31

Cobb-Douglas production function of the form xayB.
The marginal products of each input are determined by
taking the partial derivative of f with respect to x and y.

These marginal products fx and fy can be written as:

(111.1) 1X = axa'lyB
and
(111.2) fy = sx“y9'1

Those marginal value products are needed to determine the
portion of output attributed to input land, since the portion
of output attributed to land is the integral of the long-run
marginal value products along the expansion path. However,
before the portion of output attributed to land can be de—
termined, the relationship among the inputs x and y need to
be specified. This relationship is derived by maximizing

the firm's profit. After multiplying f by the price of the
output p and subtracting the cost of the inputs, the profit

function n can be written as:

(III-3) n = pxayB - PX(X'Y) - p y

y
where pX and py are the cost of input x and input y.

Next, the profit function (111.3) is maximized, subject
to budget function M equals px(x-Y) plus pyy and with respect
to x and y gives the following relationship between x and

y. That is:

32

ay/Px = BX/P.y

or

(111.#) x = upyy /BPX

The amount of input y that can be used given a budget level

M is:

(111.5) y = (M - px(x-1))/py

where Y is the amount of machinery services owned by the farm
operator. Substituting apyy/BpX for x in (111.5) and solving
for y gives:

(111.6) 1 = :(M + pr)/py(a+a)

Equation (111.6) indicates that y is only a function of the
parameters. Then the portion of output attributed to input

y is determined by integrating the long-run marginal value

product along the expansion path. That is:

(III-7) paxayfl'ldy

:11
I!
O k.‘=<:|
E:
«3
I!
0 HR”

where R is the portion of output attributed to input y.
Substituting spyy/Bpx for x in (111.7) and integrating along
y gives:

0(_0(+B a
(111.8) R = Pfi(apy)y /(ppx)(a+B)
Equation (111.8) indicates that the portion of output attrib-

uted to y is a function of y, px, p and the parameters a

y
and 5. Now the effect of machinery services ownership on

33

the portion of output attributed to input y, can be illu-
strated.

The effect of machinery ownership on the value of the
portion of output attributed to input y is determined by
taking the partial derivative of R with respect to y. That
is:
aR/ay = (3R/9§)-(8.V/3Y)CY > 0
It is positive, since SR/éy from (111.8) is positive, and
;;§/;Y from (111.6) is also positive. Therefore, the

portion of output attributed to y increased as Y increased.

The Effect of Increase in Factor Costs on the Portion of

 

Output Attributed to Input Land

 

Thus far, in the analysis, the price of factors of
production have remained constant. In this section of the
chapter, we would like to illustrate the changes in the
portion of output attributed to y as the price of the factor
x changes.

As input prices increase, the farm operator must adjust
his cropping mix and his input combinations so that profit is
maximized. However, with increased input costs profit may
not reach the previous level, especially if crop prices
remain unchanged. If total profit is reduced then it follows
that output and revenue attributed to the input must also

change. Thus increasing costs of production may reduce income
attributed to agricultural inputs such as land.

Consider Figure 3. The curves Q1, and Q2 are isoquants,
and points A, and K, are profit maximizing combination of x

and y determined by input price PX and Py. B1B1 and B2 B2,

meanwhile are isocost lines associated with outputs Q1 and Q2.
Connecting the tangency points A, and K generates the expan—
sion path OD. Again the theory dictates that the portion of
output attributed to y is determined by integrating its long

run marginal value products along the expansion path OE.

35

xO “ w
I \. Q, 2

I Q
Q3 1

 

 

W o
0 131 Bl 2

Figure 3: Shifting the Expansion Path as Price of
Input x Changes.

36

Now assume that the price of input x increases while
the price of land's services remain unchanged. As a result

of increase in the price of input x,'MMabudget line B1B1 to
BlBl producing a new profit maximizing tangency point at C
with a reduced output of Q3. Assume that the factor price
ratio remains constant at the new level, and the farm oper-
ator wishes to expand output to level corresponding to the
isoquant Q4, the new equilibrium, D is found by shifting the
budget line until it is tangent to Q4. Since the new factor
price ratio remains constant, the slope of the budget line

does not change. The budget line shifts from B1B1 to BZBZ.

Connecting points C, and D generates a new expansion
path OE. It is possible that the integral of the long run
marginal value products along the expansion path OE is
different from the portion of output attributed to input y
determined by integrating the long run marginal value products
along the expansion path OE. That is, as price of input x
changes, the portion of output attributed to y may change.

Let us illustrate with an example. Assume the Cobb
Douglas described earlier, where the optimal amount of x is
determined by (111.h), and the optimal amount of y by (111.6)
where T is zero. The portion of output attributed to y is
determined by (111.8).

The effect of change in price of input x, px on the

portion of output attributed to input y is determined by

37

taking the partial derivative of R in (111.8) with respect

to px, while holding other inputs constant. That is:

(1+

u - B a-l a +1
(111.9) 312/an = -135 (aPy) y /(o + 5).. PX dPx<0

where y = BM/Py(u + {3).
Equation (111.9) is negative. That indicates, as price of
input x increases, the portion of output attributed to y

would decrease.

Chapter Summary

 

The first part of this chapter illustrated how different
ways of acquiring the asset affected the value of the
input--measured as the value of output attributed to the
input. The two ways of acquiring the asset are: 1) asset
is divisible in purchase and use, and 2) asset is indivisible
in purchase but divisible in use. It was illustrated that
firm's expansion path is different under the two assumptions.
Since the portion of output attributed to land is determined
by integrating the long-run marginal value products along
the their respective expansion paths, their values may be
different.

The second section of this chapter examined the portion
of output attributed to land under the assumption of machinery
ownership. This was accomplished by using a Cobb-Douglas

production function. It was concluded that as the farm

38

operator owns more machinery services, the value of the
portion of output attributed to land increased.

The third and last part of this chapter examined the
changes in the value of the portion of output attributed to
y as price of input x changed. It was concluded that
increase in the price of factor x would have an adverse

effect on the value of the share of input y.

39

CHAPTER IV

IMPLEMENTATION OF THE THEORY

In Chapter 11 a theory of partitioning outputs among
inputs was introduced. In Chapter III the theory was de-
scribed graphically and analytically using a Cobb-Douglas
production function. Now a method is derived to implement
the theory. For this purpose linear programming (LP) is
used. Linear programming is ideally suited to implement
the theory since this technique efficiently selectes the
strategy that maximize profit given various prices and
resource constraints for an individual farm. Moreover, the
solution of an LPlModel gives the shadow prices for different
resources such as farmland which are in fact the marginal
value products of land (Heady and Candler, P.85) given
optimal levels of other inputs. Positive shadow prices for
land means that a one unit increase in the amount of land
available would increase the potential income by the amount
of the shadow price. A set of shadow prices are derived
for farmland for different levels of land constraints and
for each time period. Summing the shadow prices at each
level of land (allowing other inputs to optimally adjust) is
equivalent to integrating the long-run marginal value product
along the expansion path as demonstrated in Chapter 11 and

Chapter III. The portion of output attributed to land is

#0

the sum of the shadow prices for each level of land used.

This approach to measure land values will now be discussed

in more detail.

LP As A Research Tool

 

Linear programming was chosen to implement the parti—
tioning theory because of its ability to maximize income
and , because of its potential to do sensitivity analysis,
allowing us to measure long run marginal value products
along the expansion path. There are two requirements for
using linear programming technique. The requirements are:

1) A linear objective function: LP maximize the
n

objective function.Z'ijj, where xj represents
3:1
the activity level and C. represents the net

J
revenues of—the activities.

2) Linear resource constraints such that:
n

2 ..x.$b., and x.>,0 for all '
jzlalJ J 1 J 3

where aij represents the technical input-output
coefficients for each activity and b.l represents
the availability of the resources. For example.
if one resource is a monetary budget used to
purchase other inputs, varying the amount avail—
able bk and resolving the LP optimal combinations
of inputs on different budget lines would be

determined.

#1

For binding constraints, linear programming obtains
shadow prices-—the amount of increase in the profit per
unit increase in the constraint given optimal levels of
other inputs. The shadow price is equivalent to the marginal
value product of the constrained input. 'By varying the level
of land services a set of shadow prices associated with dif-
ferent levels of land input constraint is derived. Because
we are dealing with linear programming, shadow prices remain
conStant between the points corresponding to successive levels
of the continuous solution. To demonstrate, let 1.1 represents
increments in the land input constraint. Moreover, assume
MVPlias the shadow price related to the i-th increment in
land input constraint. Then, according to the theory of
partitioning output among inputs: the share of land input

from output can be written as:

where R is the portion of revenue attributed to land, and
m is the total number of increments. The above procedure
is used to determine the value of the portion of output
attributed to land and hence the value for land under the
earlier divisibility and divisibility assumptions, namely:
1) Renting Land--under this assumption land is

acquired at any quantity desired, that is,

2)

3)

#2

land is divisible in acquisition and use. Under
this assumption land is rented at the market rate.
Labor is provided by the farm operator as avail-
able and additional labor is hired on an hourly
basis as needed. Operating capital services are
acquired by borrowing. The available capital is
set as a limiting factor. The operator owns his
machinery.

Complete Ownership of land--under this assumption
land is purchased in discrete size units but

it is divisible in use. It is assumed that the
farm operator owns the same number of acres as
under the assumption of rented land. All other
assumptions are the same as the case of rented
land.

Custom hiring machinery services-~under this
assumption, all machineryvservices are acquired
through custom hiring. It is assumed that the
farm operator owns the land, That is, land that's
indivisible in acquisition but divisible in use.
Labor is provided by the farm operator as avail-
able and additional labor is hired on an hourly
basis as needed. Operating capital services are

acquired by borrowing.

h)Machinery ownership--under this assumption the

43

machinery services are acquired through operator
ownership. All other assumptions are the same as
custom hiring assumptions.

After completing the above analysis, the change in the
portion of output attributed to land and land value as a
result of changes in factor prices will be examined. This
analysis will be accomplished by changing prices of factors
of production one at a time. It is assumed that land serv-
ices are acquired through operator ownership for this
analysis. Labor is provided by the operator as available
and additional labor is hired on an hourly basis as needed.
Operating capital services are acquired by borrowing. Final—
ly, machinery services are acquired through operator owner-
ship.

Linear Programming Tableau Description

The linear programming tableau for this study has 21
activities and 21 restrictions and accounting equations in
each of three periods. The activities and resource con—
straints and accounting equations are listed in Table 4.1
and Table 4.2, respectively. The activities are production
and sale of corn and soybean, hiring labor for different
months, fuel buying, fertilizer buying, corn and soybean

seeds buying, capital borrowing, custom hiring machinery

##

services, and land renting as indicated in Tableau #.3

and Tableau #.#. The resource constraints include maximum
amount of operator labor available, maximum operating capital,
land and machinery services. Now the activities and the
resources are discussed in more detail.

The income earning enterprises are the production and
sale of corn and soybean. The input-output for the assumed
level of production are given in Tableau #.3 and Tableau #.#.

The operator is considered as the major source of labor.
The total operator labor available is 3,000 hours per year.
The monthly operator labor available is given in Table A:1 of
the Appendix. It is assumed that family labor will be de—
pleted before other labor is hired. There is no restriction
on the amount of labor hired. Labor requirement per acre
for corn and soybean are presented in Table A:2 of the
Appendix and Table A:3 of the Appendix respectively.

Crop variable costs for corn and soybean production
are given in Table A:# of the Appendix. These values do
not include the cost of fertilizer, fuel, and seeds. The
costs of fertilizer, fuel and seeds are calculated by the
LP Nbdel. This is accomplished by including the costs of
fertilizer, fuel, and seeds in the objective function of the
linear programming model as shown in Tableau #.3 and Tableau
#.#. This will enable us to make sensitivity analysis for

such factors as labor, fertilizer, and fuel.

45

Table #.1 Linear Programming Model Activities Considered

In Each Period

 

 

 

Activity Activity Activity Description
Number Name
1 CRN Corn Production
2 SOY Soybean Production
3 SLCRN Corn Selling
# SLSOY Soybean Selling
5 HLRNM Labor Hiring for November — March
6 HLRAP Labor Hiring for April
7 HLRMY Labor Hiring for May
8 HLRJE Labor Hiring for June
9 HLRJY Labor Hiring for July
10 HLRAT Labor Hiring for August
11 HLRSR Labor Hiring for September
12 HLROR Labor Hiring for October
13 FUEL Diesel Fuel Buying
1# N Nitrogen Buying
15 PH Phosphorous Buying
16 POTS Potash Buying
17 CRNSD Corn Seed
18 SOYSD Soybean Seed
19 CAPBW Capital Borrowing
20 RENTLD Land Renting
21 MACH Machinery Activity in Dollars

 

#6

Table #.2 Resource Constraints And Accounting Equations

 

 

 

Row Row Row Description
Number Name
1 LANDT Total Land Utilized
2 RTLT Maximum Acreage Available for Rent
3 LRONM Maximum Operator Labor Available
in November - March
# LROAP Maximum Operator Labor Available
in April
5 LROMY Maximum Operator Labor Available
in May
6 LROJE Maximum Operator Labor Available
in June
7 LROJY Maximum Operator Labor Available
in July
8 LROAT Maximum Operator Labor Available
in August
9 LROSR Maximum Operator Labor Available
in September
10 LROOR Maximum Operator Labor Available
in October
11 SLTCRN Corn Transfer From Production to
Sale Activity
12 SLTSOY Soybean TransferFrom Production
to Sale Activity
13 TFUEL Total Fuel Utilized
1# TNITGN Total Nitrogen Utilized
15 TPH Total Phosphorous Utilized
16 TPOTS Total Potassium Utilized
17 TCRNSD Total Corn Seed Utilized
18 TSOYSD Total Soybean Seed Utilized
19 CAP Total Capital Borrowed
20 MACHS Maximum Machinery Services Owned
21 CAPM Maximum Available Capital

 

47

Diesel fuel for corn activity is 7.07 gallon per acre
and for soybean activity is 5.68 gallon per acre. Table
A25 of the Appendix presents fuel requirements for corn
and soybean production.

The amount of nitrogen applied to corn and soybeans
depends on the economic returns of application. Nitrogen
should be applied up to the point where marginal value cost
of the fertilizer equals marginal revenue of the increased
production. The optimal application rate of nitrogen for
corn is 120 pounds per acre and for soybeans is 10 pounds
per acre.

Application rate per acre for corn is 75 pounds of
phosphorus and 100 pounds of potash. A standard rate of
50 pounds of phosphorus and 25 pounds of potash is applied
to each acre for soybeans.

Corn is assumed to be planted at a rate of 13 pounds
per acre for each corn activity. Soybeans are planted at
50 pounds per acre.

Operating capital is assumed to be equalto the 'value
of machinery investment only. Table At6 of the Appendix
presents the maximum amount of operating capital that can be
borrowed at each period of time. The model is constructed
so as first to determine resource service requirements and

optimal organization based on the annual operating capital.

Total operating capital was chosen as the limiting factor

#8

because when borrowing the total amount borrowed at any one
period of time determines what can be purchased. In other
words, borrowed capital is in fact the farm firm budget
level at each time period. For example, the limiting budget
level for 1977 Period is $57,000 under renting land assump-
tion. This budget will be used to pay for: hired labor,
land rental charges, fertilizer costs, seed costs, and
other costs as presented in Tableau #.#. The limiting budget
level for 1977 Period under the assumption of land owner-
ship is $33,300 as indicated in Tableau #.3. This budget
will be used to pay for: hired labor, fertilizer cost, seed
costs, fuel cost, and crop variable costs as shown in Tableau
#.3.

Prices for the initial models (1 through #) are given
in Table A:7 of the Appendix. These prices are chosen which
should approximate prices for the various inputs and outputs
in 1977, 1978, and 1979 crop year. These prices include
the price of corn and soybeans, fertilizers, seeds, fuel,
labor, and capital. For example, the prices of the above
variables for 1977 Period are included in the profit row

of the tableaus as shown in Tables #.3 and #.#.

49

 

oo.H oo.H mmo< mmo<2 Hm

 

 

 

oom.mm W sm<o om
om.m om.m om.m om.mm om.o: ease as
oo.om ozpom amsome ms

oo.mfi azaom mmzmoa es

oo.mm oo.OOH mzsom meome es

oo.om oo.ms mzbom ems ms

oo.oH oo.omfi mzpom zoeHze H

mo.m so.s Zoqq<w amass H

oo.H oo.om- qmmmpm womBQm NH
oo.H oo.mm- smmmsm zmosgm as
sms.o ss.o osm moo: moomg Os

sms.o 0mm moon mmomq o

osw moo: esomq m

os:.o osm macs shoes s

mos.o ss.o omm mpom seems o

oo.fi- som.o oos.fi oem moot ssomq n
oo.fi- :m:.o m o.H com moor m<omq m

oo.e- m H.H ooH.H mpo: 220mg
oo.H oo.fi mmos oozes m
om.m- om.m- om.m- oo.o oo.m om.mm- om.os- a eHmomm H
Mamas memos szmqm womgm zmoqm sow zmo mmm Ass: sosH
.moofl>som

znmcflcoms wcflhflm Eopmso 0cm osmq mo mfinwsoQSO oPoHQEoo “hoopm
wane Ca comb smoanme wsflssmnwosm smocflm m mo mamsmxm C< m.: canoe

5O

 

 

mmos mmo<z Hm

smso om

ms. as. mos. om.m om.m om.m om.m om.m m ease as
mzpom mmwome ms

mzpom mmzmos es

ozaom some es

oo.H- ozpom ems ms
oo.fi- mzsom zoeHze AH
oo.HI zoqqso amass ms
ammmpm womagm NH

qmmmpm zmoeqm HA
oo.s- moor moomq OH

oo.s- msom mmomq o

00.“- meow e<omq m

oo.fi- zoom seems s

oo.H- moor meomq o

moor ssomq m

msom msomq s

maom szoma n

mmos oozes m

ms.- sfi.- mos.- om.m- om.m- om.m- om.m- om.m- a aHeomm H

mm 2 amps momqm mmmqm aemqm semgm wemqm pas: sopH

 

 

Aoosssesoov m.s oases

51

 

 

oo.HI mmo< mmo<s Hm
Ease om
oo.ss oo.fi- es. me. so. M ease as
oo.fi- azsom amsome ms
oo.fi- mzsom .omzmos es

oo.fi- QZbom meome SH
azsom mes ms
ozoom zoeHze A
zoqqse amass H
qmmmsm somanm NH
ammmsm zmoeqm as

mean moomq OH

moor mmoma m

msom e<omq m

moor shoes 5

mpom meomq o

meow Azomq m

moo: meomq s

mpom szomq m

mmos sozsq m

oo.::- mmo.- SH.I ms.- 00.- a eHmomm A

moss smaso amsom mmzmo meom Ass: soeH

 

 

Aoozcflpsoov m.: manna

52

 

 

mmos coax Hm
ooo.sm % Ease om

om.m om.m om.m oom.mm om.os ease as
ooo.om mzpom omsome ms
ooo.mfi azaom omzmoa us
ooo.mm ooo.oofi mzsom meome ms
ooo.om ooo.ms mzsom ewe ms

ooo.oa ooo.omH mzpom zueHza 2H
omo.m oso.s zoqq<u amass ms
oo.fi ooo.om- ammmsm womaqm NH

oonfi ooo.mm- qmmmpm zmQEQm as

ems.o oss.o osm mpom moomq OH

ems.o omm moom mmomq m

osm meow esomq m

om:.o oem moor seems a

mos.o oss.o 0mm moor meomq o

oo.HI omm.o cos.fi osm msom wacmg m
oo.H- sms.o m o.H com moor msomq m

oo.H- m H.H ooH.H mpom szomq
oo.H oo.fi mmo< anzsq m
om.m- om.m- om.m- oo.o oo.m om.mm- om.os- a sHmomm H
Mamas m<mqm szmqm womqm zmoqm sow zmo mam Ass: sopH

 

 

.mflnmnoszo whoswnomz can Gama waspsom_ “modem

maze SH comp smoanme wsflssmnwomm nmosflq m 90 oaaemxm :< 3.: manna

53

 

 

mmoe nose Am

smso om

ms.o sfi.o mos.o om.m om.m om.m om.m om.m M ease as
azpom amwome ms
mzpom omzmoa es

ozpom meome ofi

oo.HI mzpom mme ms
oo.H- ozsom zeeHza A
oo.fi- zoqqso amass H

ammmpm someqm NH

ammmsm zmoeqm HA

oo.fi- moon moomq os

oo.H- mpom mmomq o

oo.H- macs e<omq m

oo.H- macs seems s

oo.H- msom seems o

macs Azomq m

moon msomq A

mean szomq m

mmos oozes m

mH.- sfi.u mos.- om.m- om.n- om.m- om.m- om.m- a aHmomm H

mm 2 Amps memos mmmgm esmgm semqm memos sass sopH

 

 

Acossgsoov 3.: cache

5#

 

 

8. s mmos sssm Hm
oo.s asso em

00.“: ss. ms. so. % ssso ms

oo.s1 szsom amsoms ms

oo.s- szsos smzmos ss
oo.s- szsos msoss es

szsos mss ms

ozpos zesszs :s

sosq<e amass ms

ammmsm somssm ms

smmmpm zmossm so

soon mooms Os

macs mmoms m

msom ssoms m

msom seoms s

msom seems o

macs szoms m

. macs ssomq s

macs zzoms m

oo.s- mmos sszes m
oo.mm- mmo.- ss.- ms.- so.. a sssoms s

assZMm 3ms<o amsom smzmo msos Ass: sows

 

 

Aoosssssoovsiis oases

55

Sources of Data

 

Dry Corn Yield-—Corn yields are drawn from information

presented in Michigan Agricultural Statistics published by

 

the Michigan Department of Agriculture, July 1979. also
from unpublished Michigan agricultural data. The average
yield per acre are 85 bushels, 81 bushels, and 90 bushels for
1977. 1978, and 1979 Period respectively.

Soybean Yield--The information on soybean yields are

also drawn from information given in Michigan Agricultural

 

Statistics, July 1979. The average yield per acre are

 

30 bushels, 2# bushels, and 29 bushels for 1977, 1978, and
1979 periods, respectively.

Labor Requirements--This information is drawn from
the user mannual for telplan program 65:0 (F0), and Agri-
cultural Economics Report No. 350 both published by the
Department of Agricultural Economics, Michigan State Univer-
sity.

Variable Costs--Variable costs per acre for production
ofcorn and soybeans which include repairs and maintenance,
limestone, herbicide, utilities, harvest trucking, corn
drying and marketing and other expenses are drawn from
Agricultural Economics Report No. 31# and No. 350 published
by the Department of Agricultural Economics, Michigan State

University.

56

Diesel Fuel Requirements—~Diesel fuel requirements
for production of one acre of corn and soybeans are given
in Table A.5 of the Appendix. These datas are drawn from
James Allen Lehrman M. S. Thesis, M.S.U.

Fertilizer requirements—anitrogen, phosphorous, and
potassium for production of corn and soybeans are drawn
from Agricultural Economics Report No. 350 published by
the Department of Agricultural Economics, Michigan State
University.

In the next chapter the results of the analysis will

be presented.

Chapter Summary

 

In this chapter, implimentation of the theory of parti-
tioning output among inputs was discussed. A linear pro-
gramming technique(LP) was considered as one way of imple-
menting the theory. Activities, resource constraints and
accounting equations for the linear programming model was
set and discussed. Also example of the tableaus used in
the study were given. Finally, sources of data for such
inputs as crop yields, operating capital, operator labor,

diesel fuel, and fertilizer were discussed.

57

CHAPTER V
MODEL RESULTS UNDER CONSTANT INPUT PRICES

In Chapter IV we described the linear programming
model and the representative farm firm. This description
explained the farm firm's inputs, costs, and expected outputs.
In this chapter the model results are given under alternative
manners of acquisition and use of services from land and
machinery. The model results include shadow prices and
operating incomes for different levels of land services.
The shadow price for land is the additional revenue that can
be generated by increasing the availability of land services
one more unit. If one unit of land service can be purchased
for less than the shadow price, then the operating income
increases with an increase in land services. The series of
shadow prices for different levels of acres are summed to
determine the portion of output attributed to land. This
is equivalent to integrating the long run marginal value
products along the expansion path as the theory of parti-
tioning output among inputs indicated. Finally, we estimate
lifetime returns required for the estimation of land value
in the capital budgeting model based on three period LP
Models.

In the first part of this chapter, we compare land

values based on two alternative assumptions of land

58

acquisition, namely renting land, and land ownership. The
assumption of renting land is equivalent to the assumption
of asset divisibility in acquisition and use. While the
assumption of land ownership is equivalent to the assumption
of asset indivisibility in acquisition but divisibility in
use.

Simultaneously in this chapter, we compare land values
based on two alternative assumptions of machinery services
acquisitions, namely custom hiring and ownership. The
assumption of custom hiring is equivalent to the assumption
of asset divisibility in acquisition and use. While machin-
ery ownership is equivalent to the assumption that asset is

indivisible in acquisition but divisible in use.

Acquiring_Land Services through Renting

In this model we assume that land is divisible in
acquisition and use. That is, the farm operator acquires
land services by renting. In this model, machinery services
are acquired through ownership; that is, machinery services
are indivisible in acquisition but divisible in use. The
operator is the major source of labor with any additional
labor being hired as the operator's labor supply deleted.
Debt capital is the limiting factor. The borrowing limits
are $57,000, $71,000, and $78,000 for the periods 1977,

1978, and 1979 respectively. The limits on debt capital

59

limit the number of acres planted in each period. Then,

the budget availability constraint is set at different levels
to determine shadow prices associated with various levels of
land services. Since the budget is used to rent land and

to purchase other inputs in each time period, therefore,

by changing the budget constraint, the number of acres
planted also change. Figure #, graphically illustrates
different budget levels considered and the expansion path
for1977 period under the assumption of land rental arrange-
ment. Note, that this procedure is repeated for each of

the three periods: 1977, 1978, and 1979. The shadow prices
for each period are equivalent to the long run marginal value
products along the expansion path for that particular period.
Now the results are discussed in more detail.

Table 5.1 presents the shadow prices for land and the
associated profits under the assumption that land is acquired
by renting.

First the results for 1977 Period are discussed. The
maximum number of acres planted is 610 for this period. The
shadow price for the 610-th acre of land is $71.60. The
return for the entire farm over cash cost is $#8,005. The
shadow price is $76.90, when land services are 110 acres
associated with $10,000 budget level and remains constant
up to 219 acres associated with $20,000. When land services

are between 220 and 539 acres, the shadow price becomes $7u.

60

Other
Inputs I

 

 

, I. 1
Acres of land
Figure #: Different Budget levels and the Associated
EXpansion Path for 1977 period. The different

budget levels are those shown in table 5.1.

61

When land services are between 5#O and 610 acres, the
shadow price becomes $71.60. These shadow prices for dif—
ferent levels of land services associated with different
budget levels are equivalent to marginal value products
along the expansion path for 1977 period. These marginal
value products are summed to determine the“value of the land
share from the output for 1977 period.

The maximum number of acres is 730 for the period 1978.
The shadow price at the level of 730 acres, is $5#.50.
Marginal value products increased from $5#.50 at 730 level
to $62 at the level of 108 acres associated with budget level
of $10,000. It is obvious from Table 5.1 that marginal value
products of land for 1978 period are less than those esti-
mated for 1977 Period, because the costs of production are
relatively greater for the former period than the latter.

The maximum number of acres is 730 for the period 1979.
Shadow price at this level of land services associated with
$78,000 budget, is $67. Marginal value products increased
from $67 at 730 level to $78 at 98 acres associated with
$10,000 budget level. The return for the entire farm over
cash costs is $#6,501. Next the portion of output attri-
buted to land under the assumption land renting for the

periods 1977, 1978, and 1979 513 determined.

Table 5.1 Optimal Number of Acres, Operating Income and

Marginal Value Products (MVP) of Land for
Different Levels of Assumed Budgets for:

1) 1977 Period.

 

 

 

 

 

Budget Optimal MVP of Operating
Level, $ Number of Land, $ Income, $
Acres
10,000.00 110 76.90 8863.00
20,000.00 219 76.90 17727.00
30,000.00 328 7#.OO 26#O7.00
#0,000.00 #33 7#.00 3#560.00
50,000.00 539 7#.OO #2712.00
57,000.00 610 71.60 48005.00
2) 1978 Period.
Budget Optimal MVP of Operating
Level, $ Number of Land, $ Income, $
Acres
10,000.00 108 62.00 5757.00
20,000.00 215 62.00 1151#.OO
30,000.00 322 59.60 17139.00
#0,000.00 #26 59.60 22266.00
50,000.00 529 59.60 27382.00
60,000.00 629 5#.5O 31951.00
71,000.00 730 5#.50 39785.00

 

63

Table 5.1 (Continued).

3) 1979 Period.

 

 

Budget Optimal MVP of Operating
Level, $ Number of Land, $ Income, $
Acres
10,000.00 98 78.00 6800.00
20,000.00 196 78.00 13599.00
30,000.00 295 78.00 20399.00
#0,000.00 389 7#.80 26##9.00
50,000.00 #82 7#.80 32#53.00
60,000.00 576 73.00 38318.00
70,000.00 662 67.00 #30#0.00

78,000.00 730 67.00 #6501.00

 

 

6#

Portion of Output Attributed to Land

Thus far, the shadow prices have been determined for
different levels of land services associated with different
budget levels allowing other inputs to optimally adjust.

Now the value of the portion of output attributed to land
input is determined.

The theory of partitioning output among inputs suggests
that the portion of output attributed to land services is
determined by integrating the long run marginal value product
(LRMVP) for land. Shadow prices or marginal value products
are integrated along the expansion path over the range from
zero to the maximum number of acres planted given the avail-
able capital for the period considered. With linear pro-
gramming, the marginal value products may be conStant between
the different levels of land services. Therefore, the por-
tion of output attributed to land services is the sum of the
shadow price multiplied by the quantity of land services
over which the LRMVP is constant. For example, consider the
results of 1977 Period, the shadow prices are $76.90 between
0 and 219 acres, $7# between 220 and 539 acres and $71.60
between 5#O and 610 acres. Figure 5 depicts graphically the
same results for the 1977 period. As Figure 5, demonstrates
the portion of revenue attributed to land services, is the
sum of the multiplication of different increments of number

of acres by their respective marginal value products.

65

That is: RT = (219 x 76.90)+(320 x 7u)+(71 x 71.60)= $A5,605
where RT is the portion of revenue attributed to land is the
portion of output attributed to 610 acres of land services.1/
The net income to one acre of land is estimated by
dividing the value of the portion of output attributed to
land services by the maximum number of acres given the avail-
able capital for each period. For example, the return to
one acre of land is determined by dividing the portion of
revenue attributed to land input of $#5,605 by the maximum
number of acres of 610 for 1977 period. Therefore, the
average income to one acre of land is $7#.75 at 1977 Period.
That is, if the farm operator must decide to rent 610 acres
or nothing, he could afford to pay the $7#.75 per acre in,
1977. But if the land services were acquired individually --
one unit at a time, the farm operator could pay the marginal
value product for each acre. For example, the farm operator
in 1977 could afford to pay up to $76.90 to acquire the
services from the first 219 acres. For the next 320 acres he
could pay $7#.75 and for the next 71 acres he could pay
$71.60. This emphasizes the importance of the nature of the
acquisition. If divisible in acquisition-- the farm operator

pays the marginal value product, given in Table 5.2.

66

 

 

 

 

Shadow
Price,
76.90
I 7.... .
l 71.60
0 100 200 219 300 #00 500 539 610

Acres of land
Figure 5: Graphical Representation of Marginal Value
Products Associated with Various Levels of

Acres for 1977 Period.

67

Table 5.2 Estimated Portion of Output and Annual Income
to Land, Given that the Land Services are
Acquired through Renting, that is Land Services

are Divisible in Acquisition.

 

 

Period Optimal Total Portion Net Income
Number of of Output, $ to Land, $
Acres

1977 610 #5,605.00 7#.75

1978 730 #2,999.00 59.00

1979 730 5#,176.00 7#.00

 

 

 

 

 

68

Average Expected Income

In order to develop agricultural land prices, the net
income to land is capitalized. However, before any capital-
ization take place, the expected income has to be calculated.
A three year average is used under the assumption that the
best clue to the future is the immediate past. That is,
expectation about the future income streams to land under
this assumption are based on the average of the income
streams reported in Table 5.2, for the past three years.
The formula for the average net income is:
(V.2) R = (R(O)(1+g)3 + R(1)(1+g)2 + R(2)(1+g))/3
where R is the average expected income to land, R(1). R(1).
and R(2) are the annual net income to land for the period
1977 through 1979, and g is the growth rate in income. The

growth rate in income simply is determined as:

HMS

(V-3) g =
t

(((R(t) - R(t-1))/R(t—1))/h
1
In this case n equals 2, and g the average growth rate for
the annual incomes, when solved for, equals 6 percent. The
expected income calculated from (V.2) is $78. This expected

income is used to determine the agricultural land value,

based on a capital budgeting formula.

Land Value

A Capital Budgeting Formula under inflationary period

69

was derived in this author's master thesis. The value of
as asset under inflation is derived as current year's income

R, divided by the time preference rate r:
(V.#) V = R/r.

It was concluded in the master thesis that the simple formula
in (V.#) is more accurate in predicting land prices than

more complicated ones such as the Lee and Rask model that
included productivity and risk. So equation (V.#) is used
‘to estimate agricultural land value V given the expected
income to land R, and the rate of pure time preference r.
This author estimated an average time preference rate of 5.67
percent by dividing returns to land by actual land prices

for 1960-1977 periods(Kooti, P. 23). Hence, farmland price
for the current period (1980) simply is $78/0.0567 equals
$1,376. This is the land value estimated under the assump-
tion that land services are acquired through renting. This
land value will be compared to land value under the assump-

tion of land ownership, which it will be discussed next.

Acquiring Land Input through Ownership

In this model, we assume that land is indivisible in
acquisition but divisible in use. That is, the operator
acquired land services by ownership. In this model, machin-

ery services are acquired through ownership also. That is,

7O

machinery services are indivisible in acquisition but
divisible in use. The operator is the main supply of labor
with outside labor being hired when the labor requirements
exceed the capacity of the operator to supply them. Operating
capital is borrowed at the beginning of the production
period. Debt capital is the limiting factor. The limits of
debt capital are $33,300, $94,000, and $46,000 for the
periods of 1977, 1978, and 1979 respectively. By limiting
the debt capital, we limit the number of acres planted in
each period. Then, shadow prices are determined at various
levels of land constraints, allowing for other inputs to
optimally adjust. Since, in this case land is owned by the
operator, we change the land constraint instead of the
budget constraint. Because the farm operator already owns
the land, and if land is idle because of lack of available
capital its shadow price becomes zero. Therefore, we change
the land constraint such that all land will be used in the
production process. Figure 6 graphically illustrates those
constraints for 1977 Period. Since the prices remain
constant, the shadow prices for various levels of acres in
each period are equivalent to the marginal value products
along the expansion path OCD.

Table 5.3 presents the shadow prices for land and

theassociated profits given that land is owned by the farm

operator. The maximum number of acres planted, is 610 for

71

1977 period. With shadow price of $113.90. Operating
income of $73.81? is generated from the operation. Shadow
price is $123 at 100 acres level, and it remains constant
along the range of 100 to 300 acres. Shadow price becomes
$119.50 at #00 acres, and it remains constant along the range
of 301 to 500 acres. Shadow price changes from $113.90 at
600 acres, and it remains constant up to 610 acres.

The number of acres planted in 1978 is 730 acres
which is the same number of acres rented under the assump-
tion of renting land. The shadow price at 730 acres is
$80. The shadow price of land increased from $80 at 730
acres to $9# at 100 acres constraint.

The number of acres owned in 1979 period, is 730,
which is the same number of acres rented under the earlier
assumption that land was acquired through rental arrange-
ments. The shadow price at 730 acres is $99.60 which
increased from $99.60 at 730 acresin>$117.60 at 100 acres

constraint.

 

 

 

 

 

72

 

 

Other .
inputs E
l R
ll 1
III
I'*’
. D
I|I|I .
'. [ Q
III I
I II/
. I I l I 4/ -—$33,300 budget
l C level.
'I . I
l I
I II
I
.lIii - -
0 100 200 300 #00 500 610 Acres of land

Figure 6: Different levels of Land Constraints

and Expansion Path for Land Ownership, for 1977

period.

73

.woossom mums can mums nos meson so popes: Hmsspmo one mopmososs mane \M
.sopmsomo snow one an gonzo oossmmm ms monom so Henson mane

.oossom

mums nos sospassmmm wsspsos oswm Moos: oossssopoo meson so Hones: Hmsspmo \fl

 

 

oo.ommsm oo.om oo.oommo oo.om .............. \M oms
oo.msmms oo.mo oo.smsmo oo.om .............. oos
oo.ommoo oo.sos oo.mommm oo.sm oo.ssmms oo.mss \a oso
oo.omsmo oo.sos oo.mmomm oo.sm oo.msoms oo.mss ooo
oo.msssm oo.mss oo.mmmos oo.oo oo.mmwoo om.oss oom
oo.mmmos oo.mss oo.ommsm oo.oo oo.omoms om.ass oos
oo.mommm oo.sss oo.msmmm oo.so oo.ssoom oo.mms oom
oo.mmmmm oo.sss oo.osmms oo.so oo.ososm oo.mms oom
oo.aossa oo.ssa oo.moso oo.so oo.mmmms oo.hms oos
a .osooQH w w .oEoosH % a .oEoosH a

waspmsomo m>2 msspmsogo m>2 waspwsomo m>s moso¢

so nonesz

 

.ncossos osos-ssos

nos on: cs oapsms>sa Pop sospsmssvo< Cs mapsms>sosH ms ocmq

.ws Pans .stmsosso pang so Gospmssww< cap sous: moso¢ so mHo>oq
psosomssn nos mosoosH waspmsomo osm Am>2v mposoosm osam> stswnms m.m manna

7:.

Now the value of the portion of output attributed to
land given that the operator owns his land, is determined.
The value of the portion of output attributed to land under
the assumption that land is acquired by ownership, is deter—
mined as the sum of marginal value products for different
levels of land constraints over which the MVP is constant.
Table 5.# presents the portion of revenue attributed to land
services, the number of acres planted by the farm operator,
and the annual average income to one acre of land for 1977,
1978, and 1979 periods.

The expected average income is calculated in the same
procedure described earlier assuming the same growth rate
in income. The expected average income for the current
period is $120.

Farmland value under the assumption that land services
are acquired through ownership, is determined using (V.#),
where R is $120 and r is 0.0567. Therefore, the farmland
value is estimated as $2,116, given the assumption that land
services are acquired through ownership.

Comparing the results of Table 5.1 and Table 5.3
indicate that:

1) Shadow prices for land obtained under the assump-
tion that land services are acquired through ownership are
generally greater than those shadow prices obtained under

the assumption that all land services are acquired by renting,

75

because marginal cost of using additional units of land
under the assumption of land ownership is small or zero,
while under the assumption of rented land, it is the rental
charge.

2) Operating incomes associated with land ownership
are greater than those associated with rented land.

The results given in Table 5.2 and Table 5.# indicate
that the value of the portion of output attributed to land
serVices under the assumption of land ownership is greater
than those associated with rented land. Recall.from Chapter
111, that the firm's expansion path under the assumption of
asset divisibility in acquisition (land rental) is OE in
Figure 6. While the expansion path under the assumption
of asset indivisibility in acquisition (land ownership) is
OCD in Figure 6. As a result, the portion of output attri-
buted to land found by integrating the long run marginal
value products along the firm's expansion paths OE, and
0CD must be different.

The results given in Table 5.2 and Table 5.# indicate
that the annual average income for one acre of land is great-
er under the assumption of land ownership than that of rented
land. The average annual income is the value of the portion
of output attributed to land divided by the maximum number of
acres planted in each period. Since the value of the portion

of output attributed to land under the assumption of land

76

ownership is greater than that of rented land; and the
maximum number of acres planted is the same, hence annual
average income of one acre of land under land ownership is
greater than that of rented land.

Finally, land values associated with land ownership is
greater than that of rented land, since annual average
income for land ownership is greater than that of rented land
at each period. It is concluded that farmland is worth more

to farmers who own their land than those who rent their land.

I"

77

Table 5.# Estimated Portion of Revenue Attributed to Land

and Annual Average Income to Land, Given that

Land Services are Acquired through Ownership.

 

 

Period Maximum Total Portion Annual Income
Number of of Revenue, $ to Land, $
Acres

1977 610 73329.00 120.00

1978 730 65000.00 89.00

1979 730 81028.00 111.00

 

 

 

78

Acquiring Machinery Services through Custom Hiring

In this model, we assume that machinery services
instead of being divisible in use and indivisible in acqui-
sition (ownership). they are divisible in acquisition and
use--that is, the operator acquires machinery services by
custom hiring. The rates of custom hiring are $##, $53,
and $6# for 1977, 1978, and 1979 periods. In addition, we
assume the operator acquires land services through ownership.
The operator is the main labor supply with outside labor
being hired when the labor requirements exceed the capacity
of the operator to supply them. Debt capital is set as the
limiting factor. The limits of debt capital are $33,300,
$44,000, and $46,000 for 1977—1979 periods. Limiting the
debt capital limits the number of acres planted in each time
period. Then, shadow prices associated with various levels
of acres are determined for each time period. As mentioned
earlier, the shadow prices for various levels of acres are
equivalent to the marginal value products along the expansion
path.

Table 5.5 presents the shadow prices for land and
operating incomes associated with different levels of acres
for the periods 1977 through 1979. Maximum number of acres
planted are 3##, #01, and 37# for 1977, 1978, and 1979
periods, under the assumption that the operator acquires

machinery services by custom hiring.

79

Ho>os smmosp mums Co>sw newsman mosom so sopsss

so>os Powcsn mums so>sw oossmsm mosom so nomads

.ooo.::% so
Ho>os powUSQ mums Qo>sw nossmss mosom so popes: Hmsssmo one \fi
.ooo.w:w so

sssspso oas \M

.oom.mms so

seasons cos \a

 

 

 

 

I - oo.mmsss om.mm I I \n so:
- I oo.mssss om.mm - I oos
oo.onss oo.os oo.ssmmH om.mm - - \M sum
oo.oosos oo.os oo.momms om.mm oo.smmmm oo.ms \d ssm
oo.msass om.ss oo.smmos om.om oo.mmomm om.ms oom
oo.mssa om.ss oo.omms om.om oo.sosms om.ms oom
oo.smss om.ss oo.wmom om.om oo.omms om.ms cos
% .oeoocs w w .osoocs w a .meoozs % mosom
wssswsogo m>§ wsssmsoso m>s wsspmsogo m>2 so
season sass sconce mesa sosooc sass Losses
.uoossoo asaa-sssa nos wssssm
sosmso :msosnp.omsssoo¢ ohm moos>som ssosscoms Poss Cossgssmm< was
soon: osooss wcHsmsomo can .Am>2vsozoosm osam> Housman: cosmsssmm m.m ospwe

80

To determine the portion of output attributed to land
services, shadow prices or marginal value products are
integrated along the expansion path over the range zero to
the maximum number of acres. However, in linear programming
the marginal value products are constant between the points
corresponding to successive levels of land services supply
as discussed earlier. Therefore, the value of the portion
of output attributed to land is the sum of marginal value
products multiplied by the number of acres along the expan-
sion path over which the LPMVP is constant. Table 5.6
presents the value of the portion of output attributed to
land, the number of acres planted and the annual average
income to one acre of land for 1977-1979 Periods.

Comparing the results given in Table 5.# and Table 5.6
indicate that the portion of output attributed to land under
assumption that machinery services are acquired by ownership
is greater than that estimated under the assumption that
machinery services are acquired by custom hiring. The
maximum number of acres planted for the former is greater
than the maximum number of acres of the latter. Finally, the
annual average income for one acre of land under the assump—
tion that machinery services are acquired by ownership is more

than that of custom hiring.

81

Table 5.6 Estimated Portion of Output and Annual Average
Income to Land Given Complete Custom Hiring

Machinery Services.

 

 

Period Maximum Total Portion Annual
Number of of Revenue, $ Average
Acres Income to
Land. $/ac.
1977 3## 25950.00 75.#O
1978 #01 1#1#8.00 35.00
1979 374 17564.00 47.00

 

The average expected income using equation (V.2), is
$59.60 per acre given that the machinery services are acq—
uired by custom hiring. Farmland value estimated using
(V.#), is $1,051 given 5.67 percent rate of pure time
preference. This value is less than that estimated under
the assumption that all machinery services are acquired
through ownership. It was concluded that land is worth
more to farmers who own their machinery than those who

custom hire their machinery services.

 

82

Acquiring Machinery Services through Combination of
Ownership and Custom Hiring

In this model, we assume that machinery services are
partly divisible and partly indivisible in acquisition.
That is, the operator acquires machinery services through
ownership and custom hiring. The operator acquires land
services by ownership. It is assumed first that the owner
has enough machinery services to cover the first one hundred
acres. Any additional machinery services are custom hired
as needed at the rates of $##, $53, and $6# per acre for
1977, 1978, and 1979 periods respectively. Next we assume
the operator has enough machinery for the first two hundred
acres, and additional machinery services are custom hired as
needed at the rates given earlier. Lastly, we assume the
operator has enough machinery for the first three hundred
acres and additional machinery services are custom hired
as needed.

The operator is assumed to provide labor services for
operations of the farm up to 3,000 hours. Any additional
labor needed is hired as the operator's labor is exhausted.
As mentioned previously, operating capital is borrowed at
the beginning of the production periods.

The purpose of comparing land values under the above
assumptions is to Show that farmers are willing to pay

higher prices for land, if they have excess machinery

 

 

83

services on hand. That is, if the farmers have excess
machinery services that they own they will pay more for

one acre of land. This was illustrated by an example using
a Cobb-Douglas production function in Chapter 111. Now it
is empirically tested using linear programming technique as
described in Chapter IV. The results are followed.

Table 5.7a presents the marginal value products (shadow

prices), and associated operating income given that the
operator has enough machinery for the first one hundred
acres. Any additional machinery services are custom hired
as needed at the rates specified earlier in this section.
As mentioned earlier, shadow prices remain constant between
two successive levels of acres in linear programming. The
successive increments in number of acres multiplied by the
associated shadow prices are summed to determine the portion
of revenue attributed to land services in each of the three
periods: 1977, 1978, and 1979 one at a time. Then, the
annual average income to one acre of land is determined by
dividing the revenue share to land by the maximum number of
acres planted in each time period. The value of the portion
of output attributed to land, maximum number of acres _
planted and annual average income to land are presented in
Table 5.8a.

Table 5.7b and Table 5.7c present the shadow prices,

and the associated operating incomes given that the operator

8#

has enough machinery services to cover for the first two
hundred acres and three hundred acres. Any additional
machinery services are custom hired as needed. The value

of the portion of output attributed to land services, maximum
number of acres planted, and the annual average income to

one acre of land are presented in Table 5.8b, and 5.8c.

Comparing the results of Tables 5.8a, 5.8b, and 5.80
indicate that as number of machinery services owned by the
operator increase, maximum number of acres, portion of
revenue attributed to land, and annual average income to
land increase at each time period.

Table 5.9 presents the estimated expected average
incomes to one acre of land, and land values associated
with various levels of machinery services ownership. Expec-
ted average income to one acre of land is calculated using
the annual average income to land reported in Table 5.8,
and equation (V.2). Land values are determined by dividing
expected average income to one acre of land by the rate of

pure time preference of 5.67 percent.

85

.UOssom mums sos mosom so popes: Hmsssmo \H
.oOHMoQ mums nos wosom so songsc Hmsspmo \M
.oossom mmos sos wosom so hopes: Hasssmo \fl

 

 

 

 

 

 

- - oo.omssm om.mm - I \m was
oo.mssom oo.ms oo.sooom om.mm I - \M mm:
oo.mssmm oo.ms oo.ommos om.mm - - oos
oo.moosm oo.ms oo.momos om.mm oo.oosmm oo.ms \a mom
oo.msmam om.ss oo.sooos om.om oo.omssm om.ms oom
oo.mmsos om.ss oo.mmoms om.om oo.msmos om.ms oom
oo.sosas oo.sss oo.moss oo.ao oo.mmmms oo.mms oos

% .meooss % a .osooCs a a .oEooQH a mosom
wsssmsomo m>2 wsssmsomo m>2 wsssmsmgo m>z so
oossoa mums gossoa mums oossoa mums sopssz
.ooooos mm oops: sosmso ohm woosesom ssossnoms amsospsvom
.wosom commas: oso smsss was sos ssmssgoms oocmsssss sosmsoso Am
"msossgssmm< wsssossos ogs soon: wssssm sosmso osm
asgmsofiso zsossnomz so.sossmsspsoo osm osmg so msnmsoc30 osoHQeoo
Loos: osooss wsssmsomo osm .Am>zvsosoosm osam> Hmcswsms nosmssswm m.m canoe

 

 

.oosnom mums nos mopom so popes: amaspmo \fi
.oospoa mums hos wopom so Monesc amassmo \M
.oospom mums hos mopom so monesc Hasspmo \fl

86

 

 

 

 

 

-. . oo.m:nmm om.mm - - \n no:
oo.omomm oo.m: oo.mmomm om.mm - - \M mm:
oo.umsmm oo.m: oo.oomom om.mm oo.oHuH: om.fim \fl mm:
oo.mm:mm oo.m: oo.ooomm om.mm oo.fimmmm om.Hm co:
oo.mmmmm om.m: oo.mm:mm om.om oo.ommom oo.mu com
oo.mmmmm oo.mHH oo.ofimmfi oo.:m oo.m:o:m oo.mmfi com
oo.:omfifi 00.5HH oo.mo:m oo.:m oo.mmmmfi oo.mmfi oofi

% .oeooCH % w .mEooCH % % .mEooCH % mohom
mcsPMMomo m>2 wcsPMMon m>z szPMMoQo m>2 so
ooflomo ammo goooma ammo cooomoxssmfi “mpesz

 

.ooooo: mm oops: soswso ohm moos>sow humCHnome HMQospsoom .monom
omnocsn ozp thss ons hos moos>pom apocsnoms omnmsnpss hopmpogo AD
A.onov n.m mamas

 

.ooshom mums nos wohom so popes: Hasspmo \H
.oospoa mums nos mopow so popes: awassmo \M
.ooshmm mums hos mohom so songs: Hasspao \fl

87

 

 

 

 

 

- - oo.o:oom oo.mm - - \w mow
oo.mmm:: oo.m: oo.Hommm oo.mm . - \M own
oo.mmom: oo.m: oo.moo:m oo.mm - . oom
oo.mmom: oo.m: oo.mummm oo.mm oo.mmom: ow.fim \d.os:
oo.mm:mm oo.m: oo.m::Hm oo.mm oo.mmH:: om.Hm oo:
oo.mmmmm oo.mHH oo.mfimmm oo.:m oo.ommom oo.mmfi com
oo.mmmmm oo.nfifi oo.ofimmfi oo.:m oo.m:o:m oo.mNH oom
oo.moufifi oo.nHH oo.mo:m oo.:a oo.mmmmH oo.mmfi oofi

% .mEooCH a a .oeoocs % % .mEooCH w wohom
wcspmnomo m>2 waspmnmmo m>2 waspmpmmo a>2 so
uoflpmm ammo noopmg mmmfi oooomowsmmfi ompesz

 

.ooomoc mm oops:
eosmso ohm moos>pow shocsnome Hmaospsoom .wopom oopocsn
omszp pmgss was hos moos>pmw zhmsszome oonmszpss popwpwmo Ao
A.PcOov n.m magma

Table 5.8

88

 

Estimated Portion of Revenue Attributed to Land

and Annual Average Income to Land Under Combina-

tion of Ownership and Custom Hiring Machinery

Services.

a) Operator furnished machinery for the first

one hundred acres,

custom hired.

additional would be

 

 

 

 

 

 

 

 

Period Optimal Total Portion Annual
Number of of Revenue to Income to
Acres Land, $ Land, $
1977 88 34000.00 87.60
1978 48 21440.00 47.85
1979 425 - 26450.00 62.00
b) Operator furnished machinery for the first
two hundred acres, additional machinery would
be custom hired.
Period Optimal Total Portion Annual
Number of of Revenue to Income to
Acres Land, $ Land, $
1977 432 41878.00 97.00
1978 495 28729.00 58;00
1979 475 35570-00 75~00
c) Operator furnished machinery for the first
three hundred acres, additional machinery would
be custom hired.
Period Optimal Total Portion Annual
Number of of Revenue to Income to
Acres Land, $ Land, $
1977 476 49537.00 104.00
1978 542 35944.00 66.00
1979 526 44772.00 85.00

 

89

Table 5.9 Estimated Expected Average Incomes and Land

Values Under Combination of Machinery Ownership

and Custom Hiring.

 

 

Level of Owned Expected Land Values
Machinery Services Incomes, $ $

in Acres

000 59.60 1051.00
100 74.60 1316.00
200 86.70 1529.00
300 96.00 1693.00

 

The results presented in Table 5.9 indicate that as
the operator owns more machinery services, the expected
average income and hence land value would increase. This
results are consistent with the theory of partitioning output
among inputs introduced in Chapter II, and the illustrated
examples in Chapter III. In Chapter III, it was shown that
as the operator owns more machinery, the value of the portion

of output attributed to land input would increase.

Chapter Summary
This chapter contains the empirical results of the
theory of partitioning output among inputs using linear

programming techniques. First part of this chapter contains

90

model results under two alternative ways of acquiring land
services: 1) acquiring land services through renting, and
2) acquiring land services through ownership. The results
indicated that the portion of revenue attributed to land
services and hence land value were greater under the former
than the latter.

The last part of this chapter contains the model results
under two alternative ways of acquiring machinery services:
1) acquiring machinery services through custom hiring, and
2) acquiring machinery services through combination of
ownership and custom hiring. The results indicated that,
first the portion of revenue attributed to land services
and land value under combination of ownership and custom
hiring were greater than those estimated under custom hiring.
Second the portion of revenue attributed to land services
and land value increase as the operator has more machinery

at hand.

91

FOOTNOTE

1/ Euler's theorem demonstrates that the marginal value
product of any input is constant. Therefore, the output
attributed to that input is its marginal value product(MVP)
multiplied by the number of units employed. Let us assume
a production function f(x,y) of the form Cobb-Douglas xayb
Also assume the relationship between x and y is specified
as x equals ky. According to the Euler's theorem which
is based on production function of degree one, MVP of x
and MVP of y are both constant. For example, the marginal
value product of y is the partial derivative of f(x,y) with
respect to y. That is:
(1) fy = bxa‘yb-1
where fy is the marginal product of y. Substituting ky for
x in (1) gives:

a a+b-1

2 f=k
() yby

From (2) fy is constant only if constant returns to scale
exist, which that what the Euler's theory is based on, that
is (a+b) has to be equal to one. If there is increasing
returns to scale, a+b is greater than one, then the marginal
product is increasing. Finally, if a+b is less than one,
then marginal product of y is decreasing. Therefore,
determining the portion of output attributed to y as

the marginal product multiplied by the number of units used,

is correct only if constant returns to scale exist.

92

CHAPTER VI

SENSITIVITY ANALYSIS

As stated previously, the linear programming model is
developed to determine the income to land associated with
different levels of acres allowing for other inputs to
optimally adjust. Given a set of input and output prices
along with resource levels, the model generates shadow prices _
given the limited debt capital. The previous chapter present—
ed model results: under alternative assumptions of machinery
and land acquisition given that input prices remain constant.

Now the question becomes: how does income to land and
hence land value change as a result of input price changes?
By changing input prices in the model we can examine empir—
ically how input price changes affect land values. For the
purpose of this analysis we assume that the farm operator
owns his land and machinery.
Analysis Procedure

In this model, we assume that land services are indivis-
ible in acquisition and divisible in use -— that is, the
operator owns his farmland. Also it is assumed that machin-
ery services are provided by operator ownership. The result
of this model under the.assumption of constant input prices
were given in Chapter V, now the effect of input price
changes on land value is considered.

In this study several types of price variation were

93

considered. The sensitivity of the return to land and hence
agricultural land value to change in the level of prices for
diesel fuel, fertilizer, and hired labor are considered.

The sensitivity of return to land and land vlaue to
changes in the cost of diesel fuel while holding other input
prices constant is analized first. The following range of
price of diesel fuel in terms of $ per gallon for the periods
1977, 1978, and 1979 are assumed: I

1) Year 1977: 0.468 —0.94 — 1.87
2) Year 1978: 0.490 -O.98 — 1.96
3) Year 1979: 0.850 —1.70 — 3.40

The second part of the sensitivity analysis includes
The sensitivity of the portion of output attributed to land
services and land value to change in costs of fertilizer.

The following range of fertilizers costs in term of $ per
pound for the 1977-1979 period are considered:

I- The price range of Nitrogen:

1) Year 1977: 0.14 - 0.28 - 0.56

2) Year 1978: 0.14 — 0.28 — 0.56

3) Year 1979: 0.15 — 0.30 - 0.60

II — The price ranges of Phosphorus are the

following:

1) Year 1977= 0.18 — 0.36 - 0.72

2) Year 1978: 0.19 — 0.38 - 0.76

3

v

Year 1979: 0.19 — 0.38 - 0.76

94

III- The price ranges of Potassium are the
following:
1) Year 1977: 0.09 - 0.18 - 0.36
2) Year 1978: 0.09 - 0.18 - 0.36
3) Year 1979: 0.10 — 0.20 — 0.40
The last part of the sensitivity analysis includes
the sensitivity of the portion of output attributed to land
services and land value to change in wage rate of hired labor.
The following ranges of wage rate in terms of $ per hour are
considered:
1) Year 1977: 3.80 - 7.60 — 15.20
2) Year 1978: 4.10 - 8.20 - 16.40
3) Year 1979: 5.30 - 10.60 - 21.20
Next, the results of the sensitivity analysis are
discussed.
Results of Sensitivity Analysis
The first set of sensitivity analysis results deals
with the change in: long run marginal value products (shadow
prices), and hence agricultural land values when diesel fuel
prices increase. As mentioned in Chapter III, as the price
of an input increases the firm, wishing to maximize profits,
would change the combination of inputs and output levels.
Equating the ratio of marginal value products to their input
prices. Therefore, as diesel fuel price increases, the firm's

expansion path changes from OE to OE. This is illustrated

95

graphically in Figure 7. Since the value of the portion of
output attributed to land is determined by integrating the
long run marginal value products along the expansion path,
its value is different along OE than along OE. In Chapter
III, this result was illustrated using a Cobb-Douglas
production function, showing analytically how the value of
output attributed to land decrease as input price increases.
Now the effect of diesel fuel price increase on land
value is empirically tested using an LP Model. By changing
diesel fuel price in the objective function of the LP Model
a set of shadow prices are derived for each period and at
different levels of land constraints. Table 6.1 summarizes
the marginal value products associated with this sensitivity
analysis. The results given in Table 6.1 indicates that
marginal value product at each level of land constraint
decreases as diesel fuel price increases. Figure 8, shows
that marginal value product at each level of land constraint
decrease as diesel fuel price increases from $.94 to $1.87

per gallon in 1977.

 

96

 

 

 

8
Diesel
Fuel,
Gallons
E
I! Q
1\ 3
1'3 . \
2 \ B .
\\ E
\ //
//
n x’
/
B2
Q2
B2 B1
0 Acres of Land

Figure 7: Expansion Path Shifts Resulting from Diesel Fuel

Price Increase.

 

 

 

 

 

97

Table 6.1 Sensitivity of Marginal Value Products and

Potential Income to change in Diesel Fuel
Cost for different level of Acres for 1977
period.

 

Diesel Fuel Price Range $0.94-1.87

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 12034.00-11460.00 120.00-114.60
200 24067.00-22921.00 120.00-114.60
300 36101.00-34382.00 120.00-114.60
400 47765.00-45472.00 116.60-110.90
500 59428.00-56563.00 116.60-110.90
539 1/ 63935.00-60885.00 116.60-110.90
586 2/ 69366.00- — 116.60— —

 

1/ This represents the maximum number of acres
planted given a budget level of $33,300 and
price of diesel fuel of $1.87flper gallon.

2/ This represents the maximum number of acres
planted given a budget level of $33,300 and
price of diesel fuel of $CL94 per gallon.

 

Table 6.1 (Cont.)

98

1978 period

 

Diesel Fuel Price Range $0.98—1.96

 

 

Number of Operating Income MVP Range
Acres Range, $ $
100 9101.00- 8495.00 91.00-85.00
ZOO 18203.00—16990.00 91.00—85.00
300 27305.00-25485.00 91.00-85.00
4OO 36006.00-33579.00 87.00-81.00
500 44706.00—41673.00 87.00—81.00
600 53235.00-49594.00 81.00-75.00
656 1/ 57600.00—53711.00 77.00—75.00
7OO 61030.00- 77.00-

708 2/ 61657.00 77.00

 

1/ This is maximum number of

acres planted given

a budget level of $44,000 and price of diesel
fuel of $1.96 per gallon. \
g/ This represents the maximum number of acres
planted given a budget level of $44,000 and
price of diesel fuel of $0.98 per gallon.

 

Table 6.1 (Cont.)

99

1979 period.

 

Diesel Fuel Price Range $1.70—3.40

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 11233.00-10171.00 112.30—101.7O
200 22466.00-20341.00 112.30-101.7O
300 33697.00-30512.00 112.30-101.70
400 44409.00-40160.00 107.00— 96.00
500 55118.00—49807.00 107.00— 96.00
600 65603.00—59230.00 99.00— 88.50
611 1/ 66663.00-60260.00 99.00— 88.50
686 2/ 73893.00 99.00 -

 

1/ This represents the maximum number of acres
planted given a budget level of $46,000 and
price of diesel fuel of $3.40 per gallon.

;/ This represents the maximum number of acres
planted given a budget level of $46,000 and
price of diesel fuel of $1.70 per gallon.

$

Shadow
Prices

Figure 8:

 

100

120.00

 

1 _ 1_10.90

 

 

116.60

 

300 539 568
Acres of Land
Changes in Marginal Value Products of Land

as Diesel Fuel Price Increase for 1977 Period.

__ Related to diesel fuel price of $0.94 per

gallon.

-— Related to diesel fuel price of $1.87 per
gallon.

 

101

The value of the portion of output attributed to land
then is the sum of marginal value products at various levels
of acres. The results of Table 6.2 indicate that as diesel
fuel price increases the value of the portion of output
attributed to land would decrease. Also the average annual
incomesto one acre of land decrease as diesel fuel prices
increase, however, the decrease in annual income is not
significant. This is because the farm operator use of diesel
fuel per acre is relatively small compared to other inputs.
Table 6.3 summarizes expected average income which is the
average sum of annual income for 1977, 1978, and 1979 period.
Also Table 6.3 gives the land values associated with different

levels of diesel fuel prices.

102

Table 6.2 The Sensitivity of Return to Land to Change in
Cost of Diesel Fuel, Other Factors Remain Constant.
Assumption A: 100 Percent Increase in Price of

Diesel Fuel.

 

Period Diesel Fuel Total Portion .Optimal Income to
Price, $/gal. of Output, $ Number One Acre of
of Acres Land, $/ac.

 

1977 0.94 69,348.00 586 118.00
1978 0.98 61,116.00 708 86.00
1979 1.70 73,504.00 686 107.00

 

Assumption B: 200 Percent Increase in Price of

Diesel Fuel.

 

Period Diesel Fuel Total Portion Optimal Income to
Price, $/gal. of Output, $ Number One Acre of
of Acres Land, $/ac.

 

1977 1.87 60,885.00 539 112.95
1978 1.96 53,400.00 656 81.00
1979 3.70 59,533.50 611 97-00

 

103

Table 6.3 Expected Average Incomes, and Farmland Values

Associated with Changes in Diesel Fuel Price.

 

 

Percentage Expected Estimated Land
Increase in Averagelhcome, Value, $/ac.
Diesel Fuel Price $/ac.

000 % 120.00 2116.00

100 % 116.80 2060.00

200 % 109.00 1922.00

 

104

The results of Table 6.3 indicate that increase in
price of diesel fuel decrease the expected average income
for the current period, and the estimated land value. These
results are consistent with the theory of partitioning output
among inputs introduced in Chapter II. These results are
also consistent with the illustrated example in Chapter III.
In Chapter III, it was illustrated that as price of any input
increases the portion of output attributed to land input de-
creases. This is in fact what the empirical results are
showing. Therefore, it is concluded that as diesel fuel
cost increases the value of farmland decreases.

Next, the effect of increase in fertilizer costs on
land values are studied. This sensitivity analysis is
accomplished by increasing the costs of Nitrogen, Phosphorus
and Potassium simultaneously, while holding prices of other
inputs constant. Changing the fertilizer costs in the object-
ive function of the LP Model generate new series of shadow
prices. It is expected that shadow prices decrease as
fertilizer costs increase.

Table A:8 of the Appendix summarizes the model results
generated by increase in fertilizer costs for the 1977—1979
period. These results are shadow prices, and profits asso-
ciated with different levels of acres planted. Table 6.4
summarizes\the results generated by increase in fertilizer

costs for the 1977—1979 period. This Table presents the

105

portion of revenue attributed to land, maximum number of
acres planted, and annual average income associated with the
sensitivity analysis. Table 6.5 presents the estimated
expected average incomes and farmland values associated with
increase in fertilizer costs.

Examination of the results presented in Table A:8 indicate
that the shadow prices and profits associated with different
levels of acres decrease as fertilizer costs increase.

A few observations can be made from Table 6.4. The
portion of revenue attributed to agricultural land services
decreases as fertilizer costs increase. Annual average income
also decreases as fertilizer costs increase. Finally, maxi-
mum number of acres planted decreases as fertilizer costs
increase. These results are consistent with the theory of
partitioning output among inputs introduced in Chapter II,
and the graphical and mathematical illustrations of Chapter
III. The derivative of portion of output attributed to land
input is negative with respect to price of fertilizer. This
is shown in Chapter III, using a Cobb-Douglas production
function. The results in Chapter III indicated that the
portion of output attributed to land decreases as price of

any other input increases.

 

106

 

 

 

 

 

66.H5 66: 66.665.m6 66.6 65.6 66.6 656a
66.66 66: 66.666.mm 66.6 65.6 66.6 656a
66.66 666 66.666.66 66.6 55.6 66.6 556a
.om\a .6smq moho< so a .osmq op .QH\$ .pfi\w .nH\w
so opo< oso popssz 05Co>om so moses oophm oospm
op osooCH amaspmo Gospnom Hopoe ensmmMpom monogamonm Cowospsz oossom
.mpmoo amasssppos as ommosocs psoopom com um Coppmssmw¢
66.66 6H6 66.6H6.66 66.6 66.6 66.6 556s
66.65 6H6 66,666.56 6H.6 66.6 6m.6 656a
oo.moH oom oo.opo.dm ms.o 6m.o mm.o 55ms
.om\w .ocwq mopo< so a .oswq op .QH\$ .pfi\w .ps\$
so ono< oso nonssz osso>om so oosnm ooppm moses
op osoocs swappmo Sospnom Hopoa sopmmMpom msmonmmonm zomoppsz ooshom

 

.mpwoo sousssphos as cowouoss psoohom oos n< cospmesmm¢
.pCMpwcoo Cmeom moospm sopoms nonpo
.mpmoo sowsasppos cs owcmno op coma oe Gazpom so 6ps>spsmcom one 2.6 mamas

Table 6.5 Expected Average Incomes, and Farmland Values

Associated with Increase in Fertilizer Costs.

._.

-_.

 

Perentage Expected Average Estimated Land

Increase in Income, $/ac. Values, $/ac.

Fertilizer Costs

 

000 % 120.00 2116.00
100 % 106.00 1869.00
200 % 76.00 1340.00

 

108

The results of Table 5.11 indicate that increase in
fertilizer costs would decrease the expected average income
for the current period, and hence land value significantly,
because fertilizer use per acre is relatively greater than
diesel fuel use per acre. Land value is estimated as expected
average return divided by the pure time preference rate of
5.67 percent. These results are consistent with the theory
of partitioning output among inputs introduced in Chapter II.'
In Chapter III, it was indicated that the portion of output
attributed to land input decreases as price of any other input
increases.

The last part of sensitivity analysis shows the effect
of increase in wage rate of hired labor on land values.

This sensitivity analysis is accomplished by increasing the
wage rate of hired labor per hour in the objective function
of the LP Model. Note that, the prices of other inputs
remain constant throughout the sensitivity analysis. Chang—
ing the rate of hired labor generates new series of shadow
prices only if additional labor is needed over and above the
operator supply of labor.

Table A:9 of the Appendix summarizes the model results
for shadow prices, and profits associated with different
levels of acres and different wage rates of hired labor.

Table 6.6\presents the results of portion of output attri—

buted to land services, maximum number of acres planted,

109

and annual average income to one acre of land associated
with different levels of hired labor wage rates. Table 6.7
gives the estimated expected average incomes, and land values
associated with increase in wage rate of hired labor.

Examinations of the results presented in Table A:9 of
the Appendix indicate that the shadow prices and profits
associated with this sensitivity analysis decrease only
when additional labor is hired above the amount of labor
supplied by the operator.

A few observations can be made from Table 6.6. The
portion of revenue attributed to land decreases as wage
rate of hired labor increases. Annual average income also
decreases as cost of labor increases. Finally, maximum

number of acres planted decrease as labor cost increases.

 

 

110

 

 

 

 

 

 

66.66 666 66.655.66 66.66 6566
66.65 :66 66.666.66 66.66 6566
00.666 36m 00.66:.m6 om.m6 5566
.ofl\fi a .oc6q pso£\w
.oC6q so 666< 6:0 mono< so op osso>om so 6096A vossm
op osooss popssz H6sspmo mospsom H6pos so op6m 6663 oospom
.6on6H 6666: so op66 6663 :6 om6opos6 psoosom 006 “m Cospmesmm¢
66.566 666 66.656.65 66.66 6566
66.66 665 66.666.66 66.6 6566
66.666 666 66.666.65 66.5 5566
.o6\a a .oC6q ssog\a
.6966 so ono< oso mono< so op os:o>om so 6on6A ooppm
op osoocs nosesz H6sspmo Gospsom H6pos so op6m 6663 cosmos
.66366 6666: so op6p 6663 :6 66666096 pzoosom 006 “6 cospmssmm¢
.pC6meoo Cs6som moussm sopo6m sonpo .60966
oopsm so op6m 6663 as 66:6:0 op 626A op snapom so 6ps>spsmc6m one 6.6 66969

111

Table 6.7 Expected Average Incomes, and Farmland Values
Associated with Increase in Wage Rate of Hired

Labor, while Other Factor Costs Remain Constant.

 

Percentage Expected Average Estimated Land

Increase in Wage Income, $/ac. Values, $/ac.

Rate of Hired Labor,

 

$/hour
000 % 120.00 2116.00
100 % 116.70 2058.00

200 % 110.70 1953.00

 

 

 

112

The results of Table 6.7 indicate that increase in
wage rate of hired labor would decrease the expected average
income to one acre of land and hence land value.

The results of the sensitivity analysis have indicated
that the increase in input prices in fact, negatively affected
the farmland value. The results of the sensitivity analysis
are consistent with the theory of partitioning output among
inputs. The results are also consistent with the mathe-

matical illustrations of Chapter III.

Chapter Summary

This chapter contained the results of the change in the
value of portion of output attributed to land services and
land value as a result of change in diesel fuel costs,
fertilizer costs, and wage rate of hired labor. These results
indicated that as costs of factors of production increase,
land values would decrease. The larger the amount of input
used per acre the greater effect that input had on land

value.

113

CHAPTER VII

SUMMARY AND CONCLUSIONS

The purchase of farmland is one of the most difficult
investment decision confronting farm operators. Compared
with other production inputs, land is purchased infrequently
and usually in large size and involves long term financial
obligation. When a tract of land is available for sale in
the market, knowing, how much a farmer can afford to pay
for that tract of land is very important. Valuing land
is based on the income it can earn, now and in the future.
The land value today reflects the present value of all future
benefits. In the other words, land value today equals the
present value of the income expected from land plus the
present value of the price of land he receives when the land
is sold at the end of the planning period. Determining
future incomes to land, however, is difficult if not impos-
sible. Expectation about future income stream is estimated
using the immidiate past income stream assuming the best
clue about the future is the immediate past. Since land
is a durable that provides services to the production process
for more than one period, the return to land input is deter-
mined as the portion of output attributed to it.

The purposes of this study were: first to review the

theory of partitioning output among inputs. Second, to

 

114

determine agricultural land values under the assumptions of
1) acquiring land services through ownership, 2) acquiring
land services through renting, 3) acquiring machinery serv-
ices through custom hiring, 4) acquiring machinery services
through combination ownership and custom hiring. Lastly,
to study the change in land value resulted from change in
costs of factors of production.

Chapter II contained the theoretical framework for
durable asset valuation. In this chapter the theory of
partitioning output among such inputs as land and machinery
was introduced.

The analysis of the output attributed to each factor
of production, usually is found in the marginal productivity
theory of factor demand. According to this theory, the
share of each input is estimated by multiplying the units
of input employed by the input price divided by the value of
total output. However, the theory of marginal value produc-
tivity that stated each input paid its marginal value producd,
holds only for homogeneous function of degree one as Euler's
theorem demonstrated. Economically speaking, this implies
that pure economic profits are zero which describes the
long run equilibrium under pure competition.

Robison developed a new theorem on how to value the
asset. This theorem stated that the value of any general

process can be divided among inputs in such a way that the

 

 

115

output is just exhausted which each input receiving the

value of its long run marginal value product. This new
theorem stated that the relationship between inputs is
specified, then the sum of the integrated partial derivatives
of output to each input will equal the output of the firm.
The proof of this theory was stated in Chapter II.

The relationship among inputs depends on the marginal
value product of the inputs and their marginal value costs.
Economists prescribe that the relationship among inputs
should be such that, the ratios of their marginal value
products-to their prices be equal for all inputs. Thus, to
determine the relationship among inputs along the least cost
combination curve, a physical production function must be
specified. Therefore, the relationship among inputs is
determined by maximizing the objective function of the firm.

When, a relationship among inputs and the marginal
value product of land along the expansion path is derived,
integrating the long run derived demand for land input sums
the values of output for each level of the input land and
at the optimal levels of other inputs. That is the sum of
the integrals of the long-run derived demand curves for all
inputs just exhaust the output. The advantage is that no
restriction about the production function is imposed. While
the Euler's theorem is implied only to homogeneous production

\

of degree one.

 

 

116

Chapter III contains graphical and mathematical
illustrations of the theory of determining the portion of
output attributed to asset land. The first part of this
chapter graphically illustrated the portion of output attri-
buted to land asset under the assumptions of: 1) land
is divisible in purchase and use, and 2) land is indivisible
in purchase and divisible in use. Asset divisibility made
it possible for the farm operator to acquire land in any
quantity, and the farm can acquire any desired level of
services. Asset indivisibility on the other hand, is avail-
able only in discrete size: while the services generated
are divisible. It was illustrated that firm's expansion
path under the assumption of asset divisibility is different
from that under asset indivisibility. The second part of
Chapter III indicated that the portion of output attributed
to land input is greater under the assumption of machinery
ownership than under custom hiring. This was illustrated
using a Cobb-Douglas production function. The last part of
this chapter examined the change in the portion of output
attributed to land input as the result of change in factor
prices, using a Cobb-Douglas production function. It was
concluded that as price of factors of production increase,
the portion of output attributed to land decreases. The
theory was implemented using a linear programming technique.

The operating charadsristicscfi? a representative farm were

 

 

 

117

incoporated into the model. These characteristics included
such factors as land availability, potential crop outputs,
labor availability and prices. The LP Model maximizes
profits, subject to resource constraints at each time period
for the three consequetive periods of 1977, 1978, and 1979.
The marginal value products (shadow prices) of land for diff-
erent levels of acres associated with different budget levels
under the assumption that the operator acquired land services
by renting was examined first. Then, the marginal value
products were integrated along the expansion path to deter-
mine the portion of output attributed to land input given
the assumption that land services were acquired by renting.
The return to one acre of land then is the total portion
of output attributed to land divided by the maximum number
of acres. The expected average income to land was estimat—
ed as the average sum of the average incomes for 1977, 1978,
and 1979 periods. This expected average income was used
to estimate the agricultural land value for the current
period using a simple capital budgeting formula. The esti—
mated value of land under this assumption was 1,376 dollars.
The assumption that the operator acquired land services
by ownership resulted in increasing marginal value products
,(shadow prices) of land associated with different levels of
acres and optimal levels of other inputs. Under the same

assumption the portion of output attributed to land services

 

118

increased. The annual average income to land and expected
average income were greater given that land services were
acquired by ownership than estimated under the assumption
that land services were acquired through renting. Under
land ownership, the estimated value of land was $2,116
compared with $1,376 under land rental arrangement.

Chapter V also contains the analysis of variation in
output attributed to land and hence its value due to dif-
ferent manner of acquiring machinery services. It was
assumed that machinery services were acquired by custom
hiring first, and second under combination of ownership and
custom hiring. Under the assumption of custom hiring, the
expected average income and hence land value were less than
those determined under the assumption that machinery services
were acquired through combination of ownership and custom
hiring.

The results of this analysis indicated that as the
operator own more machinery services than custom hire, the
expected average income and hence land value would increase.
This was consistent with the theory that indicated as oper-
ator has more machinery at hand, the portion of output
attributed to land input would increase.

The sensitivity analysis wasthe subject of Chapter VI.
The sensitivity analysis was used to study the effect of

increasing costs of such factors as: labor, fertilizer, and

 

119

diesel fuel. This type of analysis was accomplished by
changing prices and resource level at each time period in
the model. The sensitivity analysis resulted in obtaining
new series of marginal value products (shadow prices) of
land associated with different levels of acres and optimal
levels of other inputs.

The results of the sensitivity analysis indicated the
following: 1) An increase in wage rate of hired labor has
considerable negative effect on the value of output attri-
buted to land services, maximum number of acres planted,
and land value. 2) Increase in the costs of diesel fuel
decreased the amount of revenue attributed to land services,
maximum number of acres, and land value. 3) Increasing the
costs of fertilizer would decrease the value of the output
attributed to land services, maximum number of acres, and
land value.

In summary it was concluded that:

1) Land is worth more to farmers who own their
land than those who rent their land in the
farm operation.

2) Land is worth more to farmers who have excess
machinery at hand than those who custom hire
their machinery services.

3) Land value is affected negatively by increase

in costs of such factors as labor, diesel fuel,

120

and fertilizer.

Areas for Future Research

While the research in this dessertation contributes
in its oWn right to part of the development of the theory
of asset valuation, it is also provided the basis for con-
tinued development of the theory of investment.

The major areas for future research would involve
relaxing the assumption of perfect knowledge. The optimality
conditions and the value of agricultural land would be
affected by the relaxation of this assumption.

Another area of new research is to build a simultaneous
model of supply and demand for durable asset to determine
its value at the equilibrium point. Development of simul-

taneous model for a risky asset is another area of future

research.

APPENDIX

 

121

Table A.1 Available Operator Labor By Time Period 1/ g/

 

 

Time Period Available Operator
(hours)
November - March 1,160
April 260
May 270
June 250
July 270
August 270
September 250
October 270
3,000

 

1/ Kenneth Neal Wegenhoft, "An Economic Comparison of
Major Farming Systems on Southern Michigan Cash-Grain
Farms", Unpublished M.S. Thesis, M.S.U., 1970.

2/ Assumed that operator works 60 hours per week for 50
weeks per year with two weeks vacation in the
November-March time period.

 

 

122

.6566

..D.m.S .omm .oz psomom mossosoom H665pasopnw<

 

N

.6.6.2 .66666 66 6666666

:6Hmsoe Hos H6oc62 6.6662: .Q666m .m Gonmopm 6:6 ppoz .m asnponm6

 

 

 

666.6 666.6 665.6 666.6 666.6 66.6 666666
665.6 655.6 665.6 666.6 666.6 66.6 6666666
nnnnnnnnnnnnnnnnnnnnnnnnn nun: sonsopmom
uuuuuuuuuuuuuuuuuuuuuuuuu nun: pwsws¢
lllllllllllllllllllllllll :11: mafia
665.6 655.6 665.6 666.6 666.6 66.6 6666
665.6 665.6 666.6 666.6 666.6 66.6 662
666.6 666.6 666.6 666.6 666.6 66.6 66666
666.6 666.6 566.6 666.6 666.6 66.6 66662-66666>6z
6660< 66606 6660< 6oso¢ 66666 666poe

6666 666 666 666 66 so 6 666666 6666

.zsou hos

66ssmsopcm so 6666 6m opo< 66m pcososssuom sop6q oop6Esp6m N.¢ 6696s

 

 

.6566 ..D.m.E .066 .oz p6om6m 666Eo6oom 6665p65666w¢m

.6.6.2 .66666666 2666666
6669669 6os 66:66: 6.6669= .26663 .m 66:66pm 666 ppoz .m 66666666

 

123

666.6 666.6 666.6 666.6 666.: 66.6 666666
666.6 666.6 666.6 666.6 656.6 66.6 6666666
666.6 666.6 666.6 666.6 656.6 66.6 666666666
nnnnnnnnnnnnnnnnnnnnnnnnn nun: pmsws<
666.6 666.6 666.6 666.6 665.6 66.6 6666
666.6 666.6 666.6 566.6 666.6 66.6 6666
656.6 666.6 666.6 666.6 666.6 66.6 66:
666.6 666.6 666.6 666.6 656.6 66.6 66666

uuuuuuuuuuuuuuuuuuuuuuuuu nun: :666S:66ns6>oz

 

666o< 6666< 666o< 66666 666o< 666poe
6666 666 666 666 66 66 6 666666 6866

 

666696om
6os 6666666psm so 6666 mm 6666 66m p665666366m 66966 66p6s6p6m 6.6 66669

 

124

.6566 .6666666 .6666666 6566 666666666
xoop66>66 666 6Qo6o 66669662 6666>6m .066 .oz p6om6m 666so6oom 6665p65666w¢ \fi

.666666666 666

pssooo6 op 6opo6s 6.6 69 6p66 5566 66666666638 69 66p6s6p66 66666696666666 \M
.5566 .66w69o62 6powosm 6666666p6m :66 .oz p6om6m 666Eo6o6m 6665p65666w< \A

 

 

 

 

 

66.66 66.66 66.66 66.66 66.66 66.6: 6666\6 .66666
6666666> 66666
66.6 66.6 66.6 66.6 66.6 66.6 66666666 66666
---- ---- ---- 66.66 66.66 66.66 66666666: 6:6
666660 66oo
65.: 65.: 66.: 66.66 66.66 66.66 66666666 666>66m
66.6 66.6 66.6 66.6 66.6 66.6 666666666
66.66 66.66 66.66 66.66 66.66 66.66 666666666
66.6 66.6 66.6 66.6 66.6 66.6 666666666
66.6 65.6 66.6 66.6 66.6 66.6 66666666662
666 666s6m

\n 6566 \M 6566 \6 5566 \m_6566 \M 6566 \6 5566
62666666 Z666 66666

 

 

6:6696om 6:6 :6oo so 6o6posoo6m 6os

6666 666 6p6oo 6696666> :.¢ 66966

 

 

125

Table A.5 Diesel Fuel Requirements for Production of Corn

and Soybeans.

 

 

 

Operations Corn ‘ Soybeans
(gallon/acre) (gallon/acre)
Discking Stalks 0.56 0.56
Plowing 1.62 1.62
Harrowing 0.38 0.38
Amonia Application 1.15 1.15
Cultivation 0.92 _--_
Harvesting 0.69 0.69
Hauling 1.97 1.16
Others 0.28 0.12
7.07 5.68

 

Source: James Allen Lehrmann, "Direct Economic Effects of
Increased Energy Prices on Optimal Corn and Soybeans
Production on Cash Grain Farms in Southeastern

Michigan", Unpublished M.S. Thesis, M.S.U., 1976.

 

 

126

Table A.6 Estimated Operating Capital 1/

 

 

Time Period Average Land Rental Machinery Annual
Size of Rate Investment Operating
Farms Capital
1977 g/ 990 39.00 . 57,033.00 57,000.00
1978 g/ 960 37.00 71,419.00 71,000.00
1979 3/ 600 99.00 78,000.00 78,000.00

 

1/ Operating capital is determined as equal to the machinery
investment.

g/ A ricultura Economics Re ort N0. 0, "Business
Analysis Summary for Cash Grain Farms, 1978, Table 1.

3/ Data for 1979 was estimated from 1978 data using
inflation rate of 10 percent and the size of farm

increased by 8 percent.

 

 

127

Table A.7 Estimated Price Received and Paid by Farmers

 

 

 

1977 1978 1979

Crops:

Corn ($/bushe1) 2.00 2.05 2.10
Soybean ($/busbe1) 6.00 6.95 6.25
Fertilizers:

Nitrogen ($/1b.) 0.14 0.14 0.15
Phosphorous ($/lb.) 0.18 0.19 0.19
Potassium ($/lb.) 0.09 0.09 0.10
Seeds:

Corn ($/1b.) 0.75 0.80 0.88
Soybean ($/lb.) 0.17 0.18 0.17
Diesel Fuel ($/gal.): 0.468 0.99 0.85
Labor ($/bour) 1/ 3.80 4.10 5.30
Cash Rental of Land

$/aore 39.00 37.20 40.00
Capital, % 8.50 9.00 10.00

 

l/ The wage rates reported are the normal rates multiplied
by a factor of 1.33. The factor allows for labor used
during repairs, trips between fields, social security,
and workmen's compensation costs. The normal wage rates
of labor were $2.85, $3, and $4 for 1977, 1978, and
1979 periods, respectively.

128

Table A.8 Sensitivity of Marginal Value Products of land

and Potential Incomes Associated with different
levels of acres to change in Fertilizer Costs
for 1977 period.

 

Nitrogen Price Range $0.28-0.56
Phosphorus Price Range $0.36—0.72
Potassium Price Range $0.18-0.36

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 10952.00- 8207.00 109.50-82.00
200 21909.00—16914.00 109.50-82.00
300 32856.00—24995.00 109.50—82.00
366 ;/ 39890.00-29828.00 105.80-80.00
400 43938.00- - 105.80 -
500 1/ 59239.00 - 105.80 -

 

l/ The maximum number of acres planted given
the price of nitrogen of $0.28, price of
phosphorus of $0.36, and price of potassium
of $0.18 per pound.

g/ The maximum number of acres planted given
the price of nitrogen of $0.56, price of
phosphorus of $0.72, and price of potassium
of $0.36 per pound.

Table A.8

129

(Cont.) 1978 period.

 

Nitrogen Price Range $0.28-0.56
Phosphorus Price Range $0.38-O.76
Potassium Price Range $0.18-0.36

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 7972.00— 5105.00 79.70-51.00
200 15943.00-10210.00 79.70-51.00
300 23915.00-15315.00 79.70-51.00
#00 31486.00-20020.00 75.70-47.00
456 g/ 35725.00—22664.00 75.70—97.00
500 39056.00 — 75.70 -
600 96455.00 - 69.60 —
618 1/ 47709.00 — 69.60 -

 

l/ The maximum number of acres planted given
the price of nitrogen of $0.28, price of
phosphorus of $0.38, and price of potassium
of $0.18 per pound.

g/ The maximum number of acres planted given
the price of nitrogen of $0.56, price of
phosphorus of $0.76, and price of potassium
of $0.36 per pound.

130

Table A.8 (Cont.) 1979 period.

 

Nitrogen Price Range $0.30—O.6O
Phosphorus Price Range $0.38-O.76
Potassium Price Range $0.20-0.90

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 10279.00- 7310.00 102.80-73.00
200 20558.00-14617.00 102.80-73.00
300 30837.00-21927.00 102.80-73.00
400 40593.00-28713.00 97.50-67.80
960 g/ 46446.00-32789.00 97.50-67.80
500 50348.00 — 97.50

600 59879.00 — 89.60

618 1/ 61569.00 - 89.60

 

1/ This represents the maximum number of acres
planted given a budget level of $46,000 and
price of nitrogen of $0.30, price of phosphorus
of $0.38, and price ofpotassium of $0.20 per

pound.

g/ This represents the maximum number of acres
planted given a budget level of $96,000 and
price of nitrogen of $0.60, price of phosphorus
of $0.76, and price of potassium of $0.40 per

pound.

 

131

Table A.E? Sensitivity of Marginal Value Products of Land
and Potential Incomes Associated with different
Level of Number of Acres to change in Costs of
Hired Labor for 1977 period.

 

Wage Rate of Hired Labor Range, $/hr. 7.60-15.20

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 12325.00-12325.00 123.00-123.00
200 24699.00-29699.00 123.00-123.00
300 36979.00-36974.00 123.00—123.00
#00 48559.00-47820.00 115.80-108.00
500 60143.00-58662.00 115.80-108.00
564 ;/ 67553.00—65505.00 115.80-108.00
593 1/ 70910.00 — 115.80 —

 

, 1/ This represents the maximum number of acres
planted given a budget level of $33,300 and
wage rate of hired labor of $7.60 per hour.

g/ This represents the maximum number of acres
planted given a budget level of $33,300 and
wage rate of hired labor of $15.20 per hour.

 

 

132

Table A.9 (Cont.) 1978 period.

 

Wage Rate of Hired Labor Range, $/hr. 8.20-16.40

 

 

Number of Operating Income- MVP Range
Acres Range, $ $

100 9405.00- 9405.00 94.00-94.00
200 18810.00-18810.00 99.00-94.00
300 28215.00-28215.00 99.00-94.00
400 36819.00-36019.00 86.00-78.00
500 45921.00-43817.00 86.00-78.00
600 53679.00-50928.00 73.80-53.60
659 g/ 57348.00-53350.00 73.80-53.60
700 1/ 60473.00 — 66.00 —

 

1/ This represents the maximum number of acres
planted given a budget level of $44,000 and
wage rate of hired labor of $8.20 per hour.

g/ This represents the maximum number of acres
planted given a budget level of $44,000 and
wage rate of hired labor of $16.40 per hour.

133_

Table A.9 (Cont.) 1979 period.

 

Wage Rate of Hired Labor Range, 10.60-21.20

 

 

Number of Operating Income MVP Range
Acres Range, $ $

100 11764.00-11764.00 117.60-117.60
200 23528.00-23528.00 117.60-117.60
300 35292.00-35292.00 117.60-117.60
900 46011.00-44966.00 107.00- 96.70
500 56727.00-59639.00 107.00- 96.70
600 66995.00-63406.00 91.00- 64.90
641 2/ 70458.00-65713.00 91.00- 69.90
690 1/ 74597.00 - 91.00 -

 

1/ This represents the maximum number of acres
planted given a budget level of $46,000 and
wage rate of hired labor of $10.60 per hour.

g/ This represents the maximum number of acres
planted given a budget level of $46,000 and
wage rate of hired labor of $21.20 per hour.

 

134

BIBLIOGRAPHY

Chiang, Aipha C. Fundamental Methods of Mathematical
Economics, 2nd Ed. New York: McGraw—Hall
Book Company, 1974.

Ferguson, C. E. Microeconomic Theory, 3rd Ed. Homewood,
Illinois: Richard D. Irwin Inc. 1972.

 

Harris, Daune, G. and R. F. nehring, Impact of Farm Size
on the Bidding Potential for Agricultural Land,
American Journal of Agricultural Economics,
May 1976.

Heady, Earl O. and Wilfred Candler, Linear Programming
Methods, the Iowa State University Press, Ames,
Iowa 1973, P85.

Kelsey, M. P. and Archie Johnson, Agricultural Economics
Report No. 357 Business Analysis Summary for
Cash Grain Farms) 1978 table 1.

Kooti, Ghanbar Capital Budgeting Formulas for Determining
Land Values with Programs for Hand-Held Calcul-
ators, Unpublished M. S. Thesis, Michigan State
University, 1980.

Lee, W. F. and Norman Rask, Inflation and Crop Profitability:
How Much can Farmers Pay for Land? American
Journal of Agricultural Economics Dec. 1976.

Lehrman, J. A. , J. R. Black and L. J. Conner, Direct
Economic Effects of Increased Energy Prices on
Corn and Soybean Production on Cash-Grain Farms in
Southeastern Michigan, Agricultural Economic
Repprt No. 310, Michigan State University,
September 1976.

135.

Lehrman, James Allen, Direct Economic Effects of Increased
Energy Prices on Optimal Corn and Soybean Produc-
tion on Cash Grain Farms in Souteastern Michigan,
Unpublished M. S. Thesis, Michigan State University
1976.

Michigan Department of Agriculture, Michigan Agricultural
Statistics, July 1979.

Nott, Sherril B. and Stephen B. Harsh, User‘s Mannual
65:0 (F0), Michigan State University.

Nott, Sherril B., Archie Johnson, Gerald D. Schwab, W. Conard
Search and Myron P. Kelsey, Agricultural Economic
Report No. 314, Enterprise Budgets Michigan, 1977.

Nott, Sherril B., Archie Johnson, Gerald D. Schwab, W. Conard
Search and Myron P. Kelsey, Agricultural Economic
Rgport N0. 350, Revised Michigan Crops and
Livestock Estimated 1979 Budgets, January 1979.

R0bis0n,J. Lindon, A New Development in the Marginal
Productivity Theory of Factor Demand, paper
presented at Michigan State University, 1980

Robison, J. Lindon and J. Roy Black Combining Lumpy and

Divisible Assets Under Uncertainty, memo presented
at Michigan State University 1980

Rossmiller, George E. Farm Real Estate Value Patterns in
the U. S. 1930-1962, Unpublished Ph. D. Thesis,
Michigan State University, 1965.

Scott, John T. Jr. Land Returns and Land Values Effected by
Grain Prices and Government Supports , Illinois
Agricultural Economics Staff Paper,Department
of Agricultural Economics, University of Illinois
N0. 78 E-50, may 1978.

9.

136

U. S. D. A. Farm Real Estate Market Development, Economics,
Statistics and Cooperative Service, table 40, July
1980.

Wegenhoft, Kenneth Neal, An Economic Comparison of Major
Farming Systems on Southern Michigan Cash-Grain
Farms, Unpublished M. S. Thesis, Michigan State
University, 1970.

 

 

 

      

IIIIIIIII

”‘Wfiifiyflxfilfl’w 11111111191111“H

o3