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ABSTRACT

FARM ORGANIZATION AND THE FEASIBILITY
OF AGRICULTURAL MECHANIZATION IN THE RICE REGION OF
TAICHUNG AREA, TAIWAN

By
Ming-Wu Wu

Problem - Farming in Taiwan is highly intensified,
and it often gives rise to severe peak labor requirements,
chiefly in March, July and November. Labor supplies in these
months are most likely to be limiting factors in the choice
of certain cr0p patterns. The number of draft animals is
decreasing, due to the shortage of feed to maintain a draft
animal. At least 60% of the farmers in Taiwan have neither
draft animals nor power tillers but are compelled either to
\NOFk without them or to hire them from their neighbors. The
dependence on one's neighbor for farm power is likely to
create serious problems in that the selected crops frequently
cannot be planted on time. The time available between cr0ps
is critical in that the following crop needs to be planted
just as soon as possible, so adequate power is essential.

Purpose - The purposes of the study were to measure

-.
I‘D.

n'!

Ming-Wu Wu

the economic efficiency and resource productivity of current
farm organization. They were, firstly, to measure the

marginal value productivity of resources used, and, secondly,

to study the feasibility of farm mechanization (use of power
tillers). More specifically, the study may indicate, (l) the
return to be expected when different quantities and combina-
tions of resources are used under the current cropping patterns,
and (2) the way farm resources should be allocated to produce
optimum profit or a higher profit.

Method - The Cobb-Douglas form of production function
was derived from a cross section sample containing 40 farms
in the Rice Region of Taichung Area relating to the production
year of I967.

Analysis of data involved measurements of reliability
of the production function, and the regression coefficients
of the production function. The marginal value productivity
of the inputs were estimated and compared to the corresponding
marginal factor costs.

Cost and working capacity of a power tiller, economic
advantages of mechanization, possible farm reorganization for
higher profits and Optimum conditions were discussed.

Findinqs - The marginal value productivities of each
input were higher than the corresponding factor cost. Among
the five input categories, the marginal value productivity

of machine use was about 56 times higher than its marginal

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Ming-Wu Wu

factor cost, and h.ll, l.hl, l.35 and l.3l times higher on
bullock labor, human labor, working capital and cropland,
respectively.

In other words, the per dollar additional input used
in machine may earn NT $56 gross return, which was by far the
highest of all input categories. This means, of any change
to be made in input combination for higher profits, increased
use of machine (power tillers) should be regarded as the first
consideration.

It may be possible to increase the machine use by 40
times. In this case, the total cost is increased by NT $l,696,
while cropland, human labor, bullock labor and working capital
remain at the usual level, and will result in an increase in
the estimated gross farm income from NT $76,908 (the current
organization) to NT $86,289, or NT $9.38] total increase, or
NT $7,685 net increase. The ratio of each marginal value
productivity of input to the respective marginal factor cost,
except for the input of bullock labor, which has been const-
rained by the feed supply, are almost equal to a constant
value l.5. So, increasing the machine use by #0 times may
be highly considered.

Conclusion - There is little chance for expansion of
farmland in Taiwan, consequently, higher output per hectare
will be needed to meet with the continual increase in

population. With power tillers speeding up the land prepara-

Ming-Wu Wu

tion work, the farmers can time their crop planting and harvest-
ing to their best advantage, and in most cases, realize added
crop production that was previously unattainable, due to delay
in planting, caused by the shortage of animal or human labor
for land preparation. Thus, farm incomes may be increased
through a higher multiple cropping index, made possible by
having more adequate power. In other words, increased use of
power tillers not only may replace the bullock labor but also
may provide more power for more highly intensified farming
operation.

Use of power tillers will be one step forward toward
the long range goal of more intensive utilization of farmland
to produce more food.

An average farm in Taiwan (about 1 hectare) is not
big enough to keep the power tiller working up to the minimum
economic annual working hours (#90 hours). Therefore, it is
not sound economics to persuade every farmer to purchase a
power tiller. Rather it is feasible that one power tiller
be purchased cooperatively by several nearby farmers. Five
to 10 farmers having a total farm area of 7 to 8 hectares

could make efficient use of a power tiller.

FARM ORGANIZATION AND THE FEASIBILITY
OF AGRICULTURAL MECHANIZATION IN THE RICE REGION OF
TAICHUNG AREA, TAIWAN

By

Ming-Wu Wu

A THESIS

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

MASTER OF SCIENCE

Department of Agricultural Economics

I970

a fmer
a:;~'ec I a

‘I“ f
5.23 rim:

ACKNOWLEDGMENTS

The author gratefully acknowledges the assistance of
a number of persons in the development of this study. Sincerely
appreciation is expressed to Dr. Dale E. Hathaway, Head of the
Department of Agricultural Economics, for the financial assis-
tance via a graduate assistantship.

The author is immeasurably indebted to his major
professor, Dr. Karl T. Wright, for generously of his patient
guidance, constant advice and tireless assistance in the
development and completion of this thesis.

The author also wishes to express his special appre-
ciation to Dr. David L. Armstrong for his guidance and helpful
suggestions in the formation and preparation of the thesis;
and to Dr. Glynn McBride and Dr. Mason Miller for their valued
counsel and support.

Sincerely appreciation is extended to Dr. Merle L.
Esmay, Professor of Agricultural Engineering Department for
his constant encouragement and valuable help during the course
of this study as well as in the preparation of this manuscript.

Thanks are due to Miss Laura Robinson, Miss Judy Pfaff
and Mr. Daniel Tsai of Michigan State University Computer
Center for untiring assistance with the computer work. Thanks
are also due to the Sacretaries, Miss Kathleen Rodgers and

Miss Mary James for typing the preliminary manuscript with

reed ar

speed and accuracy.
Finally, the most loving appreciation is expressed
to the author's wife, Chin Shang, for her patience, under-

standing and constant encouragement at all times.

IIKHO'IIL
LIST OF
LtSl 0F

Sweater

I.

III.

TABLE OF CONTENTS

ACKNOWLEDGMENTS
LIST OF TABLES
LIST OF FIRURES

Chapter
I. INTRODUCTION .

General Situation of the Study Area
Intensity of Cropping . .
Current Problems .
Decline in Average Farm Size and Increased
Demand for Food
Peak Labor Season in Crop Production
Shortage of Farm Power - Insufficient
Draft Animals
Objectives of the Study .
About the Area and Data Selected

II. THE THEORETICAL FRAMEWORK

The Conceptual Problem .

The Model to be Used

Marginal Productivity .

Specification and Measurement of. the
Variables .

III. ESTIMATION OF PRODUCTION FUNCTION BY THE USE OF
COBB- DOUGLAS TYPE .

Production Function Estimation

Statistics from Production Function
Estimated

Marginal Productivities of Inputs

IV. FEASIBILITY OF FARM MECHANIZATION AND POSSIBLE
FARM REORGANIZATION . .

34
34

35
#2

SO

VI.
ESL IOI
IliEND

Page

Feasibility Suggested by the Production

Function . . . . . . . . . . 50

Optimum Conditions . . . . . . . . 54

Possible Farm Reorganization . . . . . . 57

V. AGRICULTURAL MECHANIZATION . . . . . . . 67

The Needs of Agricultural Mechanization . . 67

Cost and Working Capacity of a Power Tiller . 73

Economic Advantages of Mechanization . . . 76

Some Difficulties to be Recognized . . . . 82

Process of Agricultural Mechanization . . . 84

VI. CONCLUSION . . . . . . . . . . . . 9O
BIBLIOGRAPHY . . . . . . . . . . . . . . 97
APPENDICES . . . . . . . . . . . . . . . IOI

Table

I0.

ll.

l2.

l3.

LIST OF TABLES

Page
Multiple Cropping Index of the 40 Sample Farms,
Rice region of Taichung Area . . . . 4
Total Population, Cultivated Land and Farm Families,
Taiwan . . . . . . . . . . . . . . . 9
Average Area Per Head of Draft Animals: l962-l967,
Taiwan . . . . . . . . . . . . . . I3
Regression Coefficients and Related Statistics for
Crop Production in the Rice Region of Taichung Area 35
Coefficient of Partial Correlation of the Inpurs,
4O Farms, The Rice Region of Taichung Area . . . 38
Beta Coefficients of the Variables for the 40 Farms,

The Rice Region of Taichung Area . . . . . . 40

Geometric Mean, Marginal Productivity and Average
Productivity of Inputs Used in Production, The

Rice Region of Taichung Area . . . . . . . 43
Comparison Between Marginal Value Productivities and
the Respective Marginal Factor Costs, The Rice Region
of Taichung Area . . . . . . . . . . . SI
The Coefficients of Multiple Inter Correlation of
Inputs, The Rice Region of Taichung Area . . . 52
Simple Correlation Between Machine Use and each of

the Other Variables, The Rice Region of Taichung

Area . . . . . . . . . . . . . . . 54
Estimate Marginal and Gross Value Product of the
,Current Farm Organization, The Rice Region of

Taichung Area . . . . .. . . . . . . . 58
Estimated Marginal and Gross Value Productivity with

Machine Use Increased by 40 Times . . . . . . 58

Estimated Marginal and Gross Farm Receipts with the
Level of Increase Machine Use by 30 Times and
Working Capital by l.S Times . . . . . . . 60

The

The
GUI

The
Tai

The
Yie

Table
T4.

IS.

I6.

l7.

I8.

l9.

Page
The Change of Gross Farm Receipts By Adding
NT ST, 200 to the Inputs Separately, The Rice
Region of Taichung Area . . . . . . 62

The Ratio of Marginal Productivities of Inputs and

Its Respective Marginal Factor Costs by Adding NT

$l, 200 to the Inputs Separately, The Rice Region

of Taichung Area . . . . . . 63

Optimum Input Magnitudes for a Given Outlay of
Funds, and the Estmated Marginal Value Productivities,
The Rice Region of Taichung Area . . . . . . 64

The Human Labor Distribution per Hectare for Rice
Cultivation, Taiwan . . . . . . . . . . 69

The Number of Draft Animals and Power Tillers in
Taiwan: T960 - I967 . . . . . . . . . . 7T

The Relation of the Depth of soil plowed and the
Yield of Rice, Taichung Area . . . . . . . 77

vii

ihhe

U1

. MajOI

TaIcI

LabOI
Farms

Tota'

. Marg

ConS'

TrenI
Tilh

Aver
Use

The
YieT

LIST OF FIGURES
Figure Page

I. Major Cropping Patterns of the Rice Region of
Taichung Area, Taiwan . . . . . . . . . 7

2. Labor Distribution During a Year, 40 Sample
Farms, The Rice Region of Taichung Area . . . I0

Total Product of Labor, Holding Others Constant . 20

4. Marginal Value Product of Labor, Holding Others
Constant . . . . . . . . . . . . . 20

5. Trends and Projections of Bullocks and Power
Tillers in Taiwan . . . . . . . . . . 72

6. Average Total Cost Curve Per Hour of Power Tiller
Use . . . . . . . . . . . . . . . 75

7. The Relation of the Depth of Soil PIowed and the
Yield of Rice, Taichung Area . . . . . . . 78

viii

CHAPTER I
INTRODUCTION
General Situation of the Study Area

The rice region of Taichung area is located in the
central part of Taiwan, which is considered the best farming
area. The average annual temperature is about 72° F. The
temperature in the coldest month, January, averages 58° F
compared with 90° F in the warmest month, July. The average
yearly percipitation is around 75 inches. Summer rainfall
makes up 70 per cent or more of the whole year's rainfall.
The index of humidity is about 85 per cent.1 Winter is a
dry season with lots of sunshine, hence the climate is
favorable for crop growth tweles months of the year. These
climatic characteristics of the area make possible intensive
cultivation of the farm land.

Rice is usually the cr0p of first choice of farmers
in their use of paddy land. It is planted primarily for the
purpose of home consumption, payment in kind of rent, taxation
and in exchange for fertilizers. This region is often called
the granary of Taiwan and produces rice of high quality and

yield. In addition to rice, this area produces important

 

ILee, Shison C.,“An Economic Analysis of Land Use in
Taichung Hsien and City,” Provincial Chung Hsing University,

I960.
l

quantities of vegetables, beans and tobacco.

Farming in this area is characterized by small sized
family farms because land is a scarce factor. The average
size of farms is 0.99 hectares.2 With an average family of
7.02 persons per farm to be supported, intensive cultivation
is required when the farm is less than one hectare.

The functions of production and living are combined
into one unit, the farm family. The main purpose of farming,
in general, is to provide employment opportunity for the
farm family throughout the year in order to earn a living for
the family. Therefore, the motivational forces behind the
farm production unit are consumption-inspired as well as
profit-inspired. Maximization of satisfaction of the family
is generally considered as the goal for farming, and the goal
of satisfaction will not deviate very much from the goal of
profit or return maximization.

Since land is more limited than the supply of capital
and labor on a majority of farms in the area, the goal of
farmers’ planning for choice and combination of cropping
systems on a farm is generally directed to obtaining the
highest return per unit of land. This may explain why farm
land in the area is intensively cultivated.

Family labor constituted 88.ll% of total human labor

 

2One hectare = 2.47Il acres.

a.

.4

 

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IV"

used in farm production, according to a I967 study, while

the remaining ll.89% was hired labor.3 The supply of family
labor is usually constant throughout the year in the majority
of farm families. The hiring of labor involves cash outlay.
So farmers, after considering the competitive and supplementary
relationships among crops, tend to choose a cropping system
or a combination of cropping systems which will provide an
opportunity for the full use of their family labor throughout
the year and will require the least hired labor to fill the
gap between total labor requirement and the available family
labor supply at any given period during the year.

Agriculture in the area is relatively unmechanized,
with human labor being of special importance on the majority
of farms. All kinds of farm work are carried out by the
hands of farmers with the assistance of simple implements
and animal labor.

Besides human labor, animal labor is the major source
of power for cultivating the land. The draft animals in
Taiwan are first the water buffalo and, second in importance,
the yellow cow. The water buffalo is a strong animal, slow
in movement, likes to wade in water, and is satisfied with
coarse fodder. The yellow cow is less powerful but more

quick moving.

 

3Report of Farm Record-keeping Families in Taiwan:
l96 , Department ongrTculture and Forestry, TaTWaanrovincial
Government, I968, p. I96.

The Intensity of Croppinq

The multiple cropping index, which is measured by
the ratio of gross crOpped area in a year to total cultivated
area, is on the average 304% in the region. It is the highest
on the smallest size group farms and decreases with the inc-
rease in farm size (Table I). The cropping index is higher
on the smaller farms because the farmers with small farms
have to use their limited land more intensively to support

their families.

TABLE I

MULTIPLE CROPPING INDEX OF THE 40 SAMPLE FARMS,
RICE REGION OF TAICHUNG AREA

 

 

 

Farm Size Number Multiple
(ha) of Farms Cropping Index

Less than 0.5 5 464

0.5 - 0.99 l2 34l.6

l.O - I.49 8 260

l.5 - l.99 6 243.3

2.0 and over 9 246.6
Average/Total 40 304

 

In the area irrigation water is available, usually

5

two crips of rice are grown per year, which are supplemented
with winter crops such as Sweet potatoes, vegetables, wheat,
etc. They select different crops which will make full use
of their limited land.

The farm operation is also highly diversified. The
diversification of farming is to save cash outlay as much as
possible, by providing for the sufficient primary needs of
the family and to have as much Opportunity as possible to
make use of family labor all the year. Accordingly, in
determining what crops should be selected and how to organize
a well-balanced farming program, farmers usually take into
consideration the requirements of the different enterprises
so there will be a minimum conflict for available resources.
Attention also has to be given to the utilization of by-
products, In this sense, most farmers generally keep three
or four hogs, and some poultry either for home consumption
or sale. Also a diversifiedfarming program may reduce the
risk faced by the farmers. (In this study, hog and poultry
enterprises are excluded because the data are not available
and the difficulties in estimating the amount of labor being
used.)

The cropping patterns, as shown in Figure l, are
fairly complicated ones. To introduce second crops, it is
not only the input-output relation that is important but
also the timing -- proper time to plant and harvest paddy

rice, the first cr0p should be harvested as early as possible

 

and a new crop planted as soon as the old one is harvested,
or if intercropping is feasible, even before it is harvested.
The time required for threshing and husking also matters.

It must be shortened.

Let us take the Type I cropping pattern, for an
example (Figure l). The first rice crop can be transplanted
at the earliest in the middle of February and may be harvested
in the middle of June; or transplanted at the latest date,
at the end of March and may be harvested in the middle of
July. The second rice crop can be interpreted in the same
manner. But the winter crop, sweet potatoes in this case,
is planted in early October, before the second rice crop is
harvested, and harvested in early March of the next year.
Thus, intercropping of second rice crop and sweet potatoes
occur for about two weeks during the middle of October.
Certainly, it needs special skills for this kind of farm
operation.

If, in case, sweet potatoes are considered to be not
profitable, or the labor required for such crop is not avai-
lable, farmers may choose other crops which requires less
labor, or shorter period of growing or one that might yield

higher profits.

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Current Problems

Decline in Average Farm Size and Increased
Demand for Food

The rapid growth of population and limited arable
land available cast a gloomy shadow over the future prospects
of Taiwan's agriculture. Expansion of cultivable land is now
almost at a standstill (Table 2, Column 2), while population
is growing continuously at an annual rate of 2.3 per cent,LI
thereby exerting an increasingly heavy pressure on available
food supply. Agriculture, therefore, is faced with the
serious problem of how to get the limited land area under
cultivation to produce more in order to cope with the food
requirement of a fast growing population.

In other words, the limitation on possible expansion
of cultivated land area and the continuous growth of pOpulation
have presented two serious problems. One involves the steady
decline in the average size of farms (Table 2, Column 6), due
to the increase of agricure population and farm families,
while the other is related to an increasing demand for food
supplies. Both the decline in average farm size and the
increase demand for food indicate a strong need for more inten-
sive use of available farm land unless it is imported. But

most foods produced in Taiwan are much cheaper than that of

imported ones.

 

#Taiwan Statistical Data Book:l968, Council for Inter-

national Economic Cooperation and Development, Executive Yuan,
Rep. of China, I968

U J3<I~.

mom. .mc_;u mo .aom .cm:> o>wosooxM .ucman_o>mo 6cm co_umeoaooo o_Eocoom

 

 

 

—mco_umc..®uc_ ...Om :UCDOU .wmm— uv_OOm Mama —mo_um_wmpm Cm3_m._. "OULJOm
mm.o :....km omm.mmm mmm.m omo.m. mom.
30.. .m..mom mo:.~om mam.m .m~.m. Rom.
mo.. mo~.:mm ksm.omw oom.m mam.~. mom.
mo.. Nem.ksm mom.mmm mm..m m~0.~. mom.
$0.. .Nm.:mw mm~.~mm mam.m .mN.N. sea.
00.. omm.:Nm mom.~.m ..m.m :mm... mom.
mo.. ..m.mom mmw...m .mm.m N.m... Nam.
mo.. mmm.oom mmk..km .m:.m m:.... .om.
.... «mmfimm 3%QO mumd Nmnd. com.

.2. an”. exam. may”? .emmwwmmm: ..cmwmwmmwu. ......
Loo mmL< wo Lon53z .muOF .mL:p_:o_Lm< .mboh

 

z<3.<. .mm_._z<. 2m<L Lo
mastz oz< oz<. omh<>_husu .zo_.<.:¢oa .«Ao.

N m4m<H

gTIes ris
spring, S
selected ,

:Ie year

1.)" y ”‘

. 1;..—
L)

LVx-fl

 

 

 

 

 

lO

Peak Labor Season in Crop Production

Since farming is so highly intensified that it often
gives rise to severe peak labor requirements, chiefly in the
spring, Summer and Fall, no matter how crop patterns may be
selected, family labor may be distributed evenly throUghout

the year (Figure 2).

FIGURE’2

LABOR DISTRIBUTION DURING A YEAR: 40 SAMPLE FARMS, THE
RICE REGION OF TAICHUNG AREA

 

 

6O
Hired labor

SC]
U')
>
(O
O
.240)
L
o
3:

30 Family labor

0 . . , . . - .
Jan Mar May July Sept Nov

Month

In general, it is believed that in terms of total

labor supply, labor is not a limiting factor on crop choice

II

in the majority of farm situation. However, when labor supply
is divided into months, labor may become a limiting factor in
the choice of a crop with a heavy demand in a given month.
Under the farm situations in the area, labor supplies during
the busy seasons of farming, i.e. March, July, and November,
are most likely to be limiting factors in the choice of

certain crop patterns.
Shortages of Farm Power - Insufficient Draft Animals

Animal power is usually deficient in both number and
quality. They consume food in competition with humans. They
cannot supply the power needed to rapidly till a soil when
timing of this operation is critical.5

_The number of farm families in Taiwan in I968 was
977,ll4 (Table 2, Column 5), and the total number of draft
animals was 337,000 (Table 3, Column 2). Assuning the total
number of draft animals are in working condition (actually
many of them are not in a good working condition), then an
average of only 0.33 head (one third) of a draft animal was
available for each family. The total number of power tillers

was about 20,000.6

 

SClyma, Wayne, ”Engineering, Economic, and Educational
Factors to Consider in Changing From Animal to Tractor Power
in Developing Countries,” Papers in the I968 ASAE Annual Meeting,
No. 68-507, I968.

6Estimated based on Taiwan Agricultural Yearbook,
Provincial Department of Agriculture and Forestry, Taiwan, I967,

p. 329.

l2

The point which is that at least 60% of the farmers
in Taiwan have neither draft animals nor power tillers but
are compelled either to work without them or to hire them
from their neighbors. The dependence on one's heighbor
for farm power is likely to create serious problems. As a
result, each of the selected crops often cannot be planted
timely and hence it is hard to carry out intensive farming
effectively.

The time available between crops for intensive
cultivation is often very short. The time interval between
the harvesting of one crop and the planting of a new one
must be reduced as much as possible. This is completely
different from the traditional custom in that in the past
farmers have passively accepted the natural, annual cycle.
of seasons, letting the fields lie fallow in winter, or
plow the field after the crop is harvested and expose the
soil to the air for a couple of weeks before the new crop
is planted. Because the tight farming schedule as it is
today, some operations require more power than a bullock
can supply.

Furthermore, we may note the growing problem of
shortage of draft animals by comparing the area per head of

draft animals of a year with the previous years.

The average area per head of draft animal is increas-

ing and the situation is becoming less and less favorable.

 

l3

The area per draft animal was 2.l5 hectares in I962, increasing
to 2.65 hectares in I967, or an increase 0.5 hectares during
the five year period. The increasing rate was 0.l hectare per
head per year (Table 3).

Animals must have rest. They cannot work incessantly,

even for relatively short periods of time, as can a tractor.

TABLE 3
AVERAGE AREA PER HEAD OF DRAFT ANIMALS: I962 - I967, TAIWAN

 

 

 

Year Draffiegggmals CU]ti(:;?d Area Aregfpgrafiead
Animal (ha)

I962 405,026 87I,858 2.l5

I963 389,448 872,208 2.24

I964 379,073 882,239 2.32

I965 370,3I6 889,563 2.24

I966 360,294 896,347 2.48

I967 33I,878 902,406 2.65

Source: Derived from Taiwan Statistic Data Book: I968,

 

Council for International Economic Cooperation and Development,

Executive Yuan, Rep. of China, I968.

In the above table, only cultivated land was taken
into consideration, not multiple cropping, which is in fact
larger, and was growing rapidly, due chiefly to the improve-
ment of irrigation systems and land consolidation, so that

the situation is actually worse than the figures suggest.

 

.,A

.IU

AIIU

I4! ‘

A:

.4

Q
.-

l4

Timeliness factor is one of the major considerations
in modern farming operations. Higher yield and intensive
cropping patterns can be attained only when a crop is planted
in a given time period. Soil is prepared only when it is an
ideal condition and moisture content. Farmers should get
the job done on time before the soil becomes too dry or the
season too late for seeding.

There is another problem involved in draft animals
that should not be overlooked. That is the scarcity of feed
Supply. Generally speaking, for keeping draft animals, feeds
and labor are required. And that, such costs have little or
no bearing upon the frequency of use of draft animals. Feeds
for draft animals in Taiwan consist of the following:

(I) By-products of rice and other crops, such as rice

straw, bean, etc.

(2) Forage crops grown in farmland, such as barley, etc.

(3) Feeds collected by family labor, such as wild green

grass, etc.

(4) Commercial feeds.

Roughage should constitute 80% of the total quantity of the
feeds. Wild grasses, rice straw, sugarcane tops, sweet
potatoes, etc. are the major ones. Today, sweet potatoes
and their leaves are used by farmers mostly as hog feed.
Rice straw is used for making compost for growing mushrooms,
and therefore can not be used entirely as cattle feed. In

the very well developed rural area, there is very little land

l5

that can be spared to produce roughage for draft animals.
It is much harder to maintain a draft animal than in earlier
times.

There may be various alternatives to overcome such
difficulties, but one of the most important means that has
been carried out effictively in Japan and other developed
countries is to provide farmers with the various equipment
or machinery required for successful carrying out of such

intensive farming operations.

Objectives of the Study

Based on the above described problems, this study
will be dealing with the economic efficiency of resource
use in farm production in a specific area. It is intended
to measure the economic efficiency and resource productivity
of current farm organization and operation. The central
objectives of this study are firstly to measure the marginal
value productivity of resources used, especially labor and
power in crop production and to predict the effect of different
quantities of resources used on the value of the products
produced; and secondly to study the feasibility of farm
mechanization in the area. From the standpoint of the
individual farmer the study may indicate (l) the return or
income to be expected when different quantities and combi-
nations of resources are used under the current cropping

pattern, and (2) the answer to the question as to how farm

OCT

P\v
....

.\d

‘1!

l6

resources should be allocated to produce optimum profit or
a higher profit within the limitation of the methods of

production being used.

About the Area and Data Selected

 

The rice region of Taichung area was chosen as a case
study for several reasons: (I) this region is located in the
central part of the island and the land, as well as physical,
climatic and other features are representative of Taiwan and
are homogeneous which is suitable for intensive cultivation,
(2) this region constitutes a representative rice farming
region and is an important agricultural region of Taiwan,
known as the rice bowl of Taiwan;7 (3) the crop pattern and
its production are also homogeneous with very little varia-
tion from year to year; and (4) the farmers have a strong
desire to improve their farm organization.

The data were collected by survey by the author with
the help of the extension agents of the local farmers asso-
ciations in I967. The primary purpose of the survey was for
a study on the crop rotation systems in the area.

The sampling procedure adopted was a random sampling
from a given group. A random sample of 40 farms was taken

from the l,l00 farms who were involved in the Farm Extension

 

7Lee, Shison C., op. cit.

'JF
...

RES

I7

Discussion Groups of the Farmers' Association.8 The sample
size was approximately 3.63% of the whole groups in the
region.

The distribution of farms by size of the sample farms
in the region may be seen in Table l. The average farm size
was 0.99 hectares, while the average of all farms in Taiwan

was l.02 hectares.

In view of various criteria these data seemed fairly

 

likely to meet the requirements for further study in this
analysis. Therefore, this study was based mainly on the

sample farms relating to a single production year of I967.

 

8Volunteer organization of adult farmers for the
purposes of improving agricultural techniques and social life.
These farmers may be considered to be above average level in
regard to their agricultural techniques.

CHAPTER II
THE THEORETICAL FRAMEWORK
The Conceptual Problem

Land is the most scarce production factor in Taiwan,
and we shall assume that the input of land is fixed. Other
inputs are treated as variable inputs. Let us take labor as
an example here. The important question is how to improve-
the productivity of the labor force without reducing the
total product. There are many theoretical alternatives in
coping with this problem. The important ones are, (l) to
improve the production potential of the land, (2) to improve
the equipment or machinery being used by the laborer, and
(3) to improve the techniques of the laborer.

Raising the productivity of the land may take a
variety of forms such as land consolidation, improvement of
irrigation system, seed variety improvement, and application
of farm machinery or any other measure that would shift the
production function upward. The effect of this improvement
is illustrated in Figures 3 and 4 where land is fixed and
the labor is variable. Assume labor will be adjusted to the

point where, for the optimum combination, marginal value

l8

 

N'fid
,0

‘0ij

I‘uIIU

HIU
p\¢

. 1'?

:70

II

l9

productivity equals marginal factor cost.

In Figure 3, improved land consolidation practices
or the use of farm machinery in Taiwan may shift the land
production function upward from TP] to TP2. The marginal
productivity curves corresponding to the two production
functions are shown in Figure 4. The marginal productivity
also shifts from MRI to MR2. Marginal factor cost of labor
is equal to the wage rate and assumed to be constant. With
the improvement in land quality or the use of farm machinery,
the intersection of marginal factor cost and marginal produc-
tivity has shifted to the right from Point A to Point B. The
aggregate effect is to increase total output by adjusting the
quantity of labor that can be profitably combined with the
land. In other words, land can now absorb more labor without
reducing the labor productivity.

If, in other cases, the quantity of labor being used
in the production is too great as a result, the marginal
productivity is smaller than wage rate, the production as
far as the labor input is concerned, may be over employed.
Under this circumstance, the withdrawal of a certain amount
of labor will not cause reduction in total product, but on
the contrary, it will allow the total product return to the
higher level along the same production curve. To what extent
the surplus labor should be withdrawn will depend on the
reduction of the total product. Assuming other factors

remain unchanged, the amount of labor should be added if the

 

‘8

20

marginal value productivity of labor is greater than the
wage rate, and vice versa.

The problem involved is to decide the proportional
make up of the package of resources that will be required to

make the jump from Point A on TP] to Point B ofi TP2.

Figure 3 TOTAL PRODUCT OF LABOR, HOLDING OTHERS CONSTANT

 

 

 

 

 

A B
-AFNJPZ
A
Output I\\\\
\\TPI
0 Labor

Figure 4 MARGINAL VALUE PRODUCT OF LABOR, HOLDING OTHERS

 

 

 

 

 

CONSTANT
I I
Output
4:“ \.
//;/ ‘.\‘~Eg MC
A \\ \\ .4
0 \ M R

 

of

q
I-

IE

_\u
.

2l

It is not enough to simply suggest that farmers should
use certain amounts of resources. It may also be necessary
to improve other situations, such as, land tenure situation
to create the proper incentive, or to improve the marketing
system which may provide further encoruagement. The kind of
measures that will be discussed in this study are mainly
related to the machine or power use.

9

Machine use not only can increase the productivity
of land and human labor, but also can substitute for labor,
capital, etc. If the output of a crop is given, the crop can
be produced by different combination of labor and machine use
assuming other factors remain unchanged. The optimum combi-
nation of labor and machine use for instance, is the point

where the iso-product curve is tangent to the price line of

the two inputs.

The Model to be Used

A general approach to the problem is to derive produc-
tion functions from which to measure the regression coefficients
of production and the marginal productivity of the input factors.
The Cobb-Douglas form of production function is chosen for this
analysis because of its possibility of goodness of fit to the

data, and also because of the usefulness of interpretation of

 

9Machine use in this study is meant particularly the
use of power tillers.

22

the obtained regression coefficients.

The coefficients of the production function are
estimated from a cross section sample containing 40 farms.
The Cobb-Douglas type production function is applied to the
logarithms of the variables. The data are concerned with
the short-run of a single production year. The variables
being studied can not be considered as a function of time.
The gross farm receipts (Y) is used as the dependent variable
of the various input factors, or the independent variable,
(Xi)-

By the nature of the Cobb-Douglas functions, if
output is to be nonzero, at least some quantity of each
input must be used. This does not hold true in real world
situation, for instance, we might get some product without
applying any fertilizer. Because of the multiplicative
basis of aggregation approaches of the production function,
if any one or more independent variables is zero, the total
product or dependent variable will be zero. The difficulty
arises in the conversion of the data to a logarithmic form,
the logarithm of zero equals minus infinity. But the Cobb-
Douglas functions have greatest use in the diagnostic anaysis,
reflecting marginal resource productivities at mean levels
of inputs.

The general production function may be written as:

Y = f (X1, X2, . . . . . Xn)

Which expressed the output as a function of the various

 

 

23

input factors. In Cobb-Douglas type, the mathematical

notation is:

bI b2

Y=aX1X2 xbn

l'l

Where a and b's are the parameters of the function. .b's are
the regression coefficients with respect to each of the inputs, [ma
they are the elacticities of production for the production

function or regression equations in the form presented above.

 

The elasticity of production simply shows the average percentage Qj
change in the product for each increase of one per cent in
input of respective resources and can be expressed in the

formula below:

In the Cobb-Douglas production function, the sum of
the regression coefficient of the independent variableszzbi,
is an indication of the returns to scale.:z bi = I implies
constant returns to scale, i.e., a one per cent increase in
all inputs results in a one per cent increase in total output
and constant productivity prevails as all resources are inc-
reased in constant proportions. By the same token zzbiI< l
indicates decreasing returns to scale and z:b;:>l, increasing
returns to scale. However, such estimates of returns to
scale may be biased unless all input factors are included in
the production function.

There will be no bias in the estimates of returns to

24

scale if the excluded variables vary on the average in same
proportion with proportional variations in all the included
variables. But the returns to scale will be underestimated
if the proportional changes in the included inputs are asso-
ciated with less than pr0portional changes in the excluded
variable in the sample and vice versa.‘0
The Cobb-Douglas production function, for computa-

tional convenience is usually estimated by use of a logarithmic

transformation, such as

Log Y z a + b] log X] + . . . . . + bn log Xn + U
Where the Q's become the regression coefficients of the inputs.
U is the residuals.
The reasons why the logarithm form is used in addition
to the computational convenience are:
(l) The relationships between the variables are believed
to be multiplicative rather than additive.
(2) The relations among variables are believed to be
more stable in percentage than in absolute thems, and
(3) The unexplained residuals are believed to be more
uniform over the range of the independent variables
when expressed in percentage rather than in absolute
terms.

From the production function derived, we can easily determine

 

10Griliches, Z., ”Specification Bias in Estimates of
Production Function,” Journal of Farm Economics, Vol. 39, p.l2.

25

if production is located in stages I, II, or III. The
rational stage of production, stage II, for a particular

input is characterized by a, the function 5 constant having

a positive sign, and by b, the power of the particular input
being a positive fraction. However, no maximum can be reached

by this kind of production function.

Marginal Productivity

The marginal productivities of each input in the
process of production can be defined as the change in the
total physical product caused by a small change of the
particular input, while the other inputs are held unchanged
at a mean level. The marginal productivity estimates may
be computed by taking the first partial derivatives with
respect to each of the input factors included in the production
function.

Let all the variables be set at their respective

geometric mean levels, then the production function is:

Log 7 = a + b log 7} + b

I log Y2 + . . + bn log 7n

2

The marginal productivity of Xi, holding all variables

at their respective geometric mean level, is estimated with:

IV = (antilog a ) kaI

-Q

d
d

d(antilog a) 7kbl

 

>4

i d7i

 

 

26

 

= bi (antilog a ) iji - I
bi (antilog a) 7;bl
7i
biY
=_§__

This derivative gives the slope, at a particular point of the
production curve.

The efficiency of resource use, then, can be measured
by comparing the marginal productivities of factors with
their prevailing market prices or opportunity costs. If the
marginal productivities are higher than opportunity costs of
the factors, this indicates the scope for raising output
profitably through the increased use of the resource input
concerned, whereas those less than market costs indicate the
unprofitable nature of resource use.

But there is some limitations of using the marginal
productivity as a tool for the guidance of farmers. First
of all, it is not easy for a farmer to readily vary such
inputs as land and durable machinery which are more or less
fixed for him. This may leave relatively little freedom for
the farmer to optimize profit by equating marginal product
with marginal cost. Secondly, since the marginal productivities
are derived from regression coefficients, which may be biased

due to exclusion of certain variables from the function, the

27

estimated marginal products would also be biased in the

same direction as the regression coefficients.

Specification and Measurement of Variables

 

A farm is not merely a piece of land. People cannot F“
Operate the land as a farm unless they have buildings, live- I-mfl

stock, machinery, and other things to go with it. Land is

 

I
the thing into which inputs are put. Labor is the input of ' :..J
man's efforts. Capital is wealth used in the production of j
new wealth and in one form or another is necessary in order
for the farm to be a productive unit. In the basic sense
all these inputs are essential to constitute a farm unit.

There are many kinds of inputs in agricultural
production. Some are visible and measurable, while Others
are invisible and it is difficult to measure their quantity
as well as their influence on production.

The unmeasurable or excluded variables are usually
regarded as constant. However, the measurement problem
exists so long as the excluded variable is uncorrelated with
any Of the other inputs being included, and its omission will
not bias the estimates of the coefficients. Still the assump-
tion of zero correlation between the excluded inputs and any
of the other inputs is not likely to hold in the real world.
The result will be a tendency to overestimate one or more of

the coefficients of the included variables.]l

 

 

I'Heady, Earl 0., and John L. Dillon Agricultural
Production Functions, Ames, Iowa, I966, p. I

28

In classifying or aggregating the variables, two
rules should be used in order to minimize the bias. First,
resources with perfect complements in the production process
should be aggregated as a single input, such as fuels and
maintenance costs being used more or less in fixed prOportions.
To include each of the complementary categories
would lead to multicollinearity because of the perfect corre-

l2

lation between levels of the complementary input. Secondly,

 

perfect substitutes should also be aggregated into a single
input category.

Ideally, the input and output variables to be used
in deriving the production functions should be measured in
physical units of a homogeneous nature. But there is no
common physical unit for measuring the heterogeneous capital
goods and services. They must be aggregated to some extent
and measured in value terms for computational purposes.

Some resources can be distinguished as productive
and non-productive. Only productive resources which contri-
bute directly to production were included, and such as assits
not directly related to farming were excluded. Problems
arise in regard to the fact that farm production and family
living are not mutually exclusive nor separable from each

other. The farm house, for instance, is both a means of

 

12Johnston, J., Econometric Methods, McGraw-Hill
Book CO., New York. I960, pp. 20l-7.

29

farm production and family living. Some farmers may have
much better housing than others. These factors were excluded
in this study.

However, one can make certain plausible assumptions
regarding the behavior of these inputs vis-a-vis other
included inputs and then interpret the results in the light -
I3

of such assumptins.

The variables included in this study are: (l) gross

 

farm receipts, which is the dependent variable; and (2) land,
(3) human labor, (4) machine use, (5) bullock labor and (6)
working capital, which are independent variables. Management
and fixed capital inputs are not included. In fact, most
studies on farm production functions have not been able to
include the management input, owing to the difficulty of
measurement, which is essentially a qualitative rather than
quantitive character.“+ As for the exclusion of fixed capital
in the production analysis, this is due to the difficulty of
measuring its value.

The procedure followed for standardizing and aggrega-

ting the variables is explained below:

 

I3Griliches, Z., Op.cit. pp. 8-20.
I"'Heady, Earl 0., and John L. Dillon, op. cit. p.224.

30

(I) Gross farm receipts: Gross farm receipts is
the independent variable and consists of the value of different
crOp outputs during the year. Data on prices of individual
products, and also of different qualities of the same product,
were the basis for converting these quantities into the
values for the gross farm receipts. In other words, the output
was the aggregation of the value of different crop products
produced during a given time period, because most farms produce
either more than one type of product or several qualities of
the same kind of product. Since the products were aggregated
on a value basis, nothing can be said in regard to the input-
output relations in the individual crops.

The price of farm products may change from time to
time, and the output value in different years might not
represent adequately the physical output in different periods.

There are generally two conceptions of agricultural
product: gross product and net product. Their relation
culd be represented by the following equation:

Net product = gross product - (depreciation of capital
+ expenses of intermediate goods)
Net product is an added value produced in a given period and
is equivalent to the value of agricultural production after
depreciation of capital and expenses of intermediate goods
used in the production are deducted from the gross product.

If depreciation of capital and expenses of intermediate

 

3l

goods in the production process are different in different
periods, the percentage of net product in gross product will
accordingly change over time. Because there are many difficulties
in accurate measurement of expenses Of intermediate goods used

in production, as mentioned before, it is reasonable that f
gross farm receipts should be used in this study as an indi-
cator of agricultural output.

(2) Land: Two kinds of measurement may be used to

 

represent land as a factor of production. One is land value
based on market price and the other is the physical quantity
of land. In this study, physical quantity in terms of cropland
in hectares is used as the measurement of land as one of the
independent variables, bucause the valuation work is difficult.

(3) Human Labor: To measure the input of human
labor in subsistence agriculture is a difficult problem,
espicially in our area where surplus labor exists. In this
study, the input of human labor is measured by man-days
actually worked on the farm. A man-day is defined as one
adult male, from the age of TB to 60, working ten hours a
day on a farm at direct crOp production work. Days worked
by female adults and young boys are converted to man-days by
multiplying by 0.8 and 0.5, respectively.

By doing the above valuation problems can be partially
avoided. There seems little problems in measuring hired labor
by work days, since the farmers never hire labor unless the
work is ablolutely necessary. This is not true in the case

Of family labor, expecially during slack seasons when there'

32

are few off-farm employment Opportunities.

(4) Machine use and bullock labor: Machine use
and bullock labor have been considered to be the important
sources of agricultural power. Bullock labor included the
drivers of the animal was measured by days worked during
the year. Machine use was measured by working hours of
power tillers including the operator of the maChine.

There were two ways prevailing in the area in hiring

farm machine use and bullock labor, as far as the ways of

 

payment was concerned. One is payment by hours of work and
the other was by the area worked. In order to standardize I
the measurement, the latter one was estimated and converted
into hours of work based on the area covered. In general,
ll hours are needed to plow one hectare of paddy field by

a power tiller and 3.5 days by a bullock labor.

(5) Working capital: Working capital is a collec-
tion of physical items different from each other in many
respects, and was viewed as the value of all components.
Thus, aggregation of the single values is a necessary step.
Aggregation is made according to the degree of correlation
between items. Theoretically, as discussed previously,
items highly correlated to each other should be aggregated
into a single category and within a category all items are
highly correlated to each other or highly substitutable.
However, this is less possible in the case of the data

Obtained of non-experimental origin.

33

In this analysis, the independent variable of working
capital includes seeds, fertilizers, irrigation charges,
insects, pests and disease control, and miscellaneous farm
expenses. They were converted into value forms by multiplying
by the respective prevailing prices. F“
The outlays of human labor, machine use and bullock

labor were not included in this input category, because these

items are used as independent variables in the production

function.

 

CHAPTER III

ESTIMATION OF PRODUCTION FUNCTION BY THE

 

 

r;
USE OF COBB-DOUGLAS TYPE
Production Function Estimation
The derived results for the production function .

based on the sample of 40 farms involved in this study are
as shown in Table 4. The numerical values of the original
Observations were grouped under the prOper variables, and
are shown in Appendix Table I.

The constant, a and the regression coefficients bi

may be fitted into the production function, i.e.,

Y = 290.59 X].2136 X2.4614 X3.0312 XA.I276 X5.2523

or in logarithm form as:

Log Y = 2.4624 + .2l36 log X] + .46l4 log X2 + .03l2 log X3
+ .I276 log X4 + .2523 log X5

Variables used in the model are defined in the
following way:
(I) Y is the value of crop production, measured in New Taiwan
dollars, and includes all crops produced in the year such
as products sold, stored or used as an input for producing

other crops or consumed by the farm family.

34

(2)
(3)

(4)

(5)

(6)

35

XI is the input of cultivated land measured in hectares.

X2 is the input of human labor used on crops and is

measured in days. It includes hired labor plus the labor
by the operator and family members.

X3 is the input of machine use, measured in hours of
work, mainly in preparation of soil, and transporting

the farm products.

X4 is the input of bullock labor, measured in days of

 

work, performed either by water buffalos or yellow cows,
in preparation of soil or transporting the products.

X5 is the input of working capital used on crops and is
measured in dollars. It does not include fixed capital
and wages paid for human labor, bullock labor and custom
rates for machine use. It represents the variable capital
input; such as the expenses for seeds, fertilizers, irri-
gation charges, insects, pests and disease control and
other miscellaneous outlays for crops during the period

of production.

The parameters are estimated at the geometric mean

level of each variable. But there were some zero observations

in the inputs of machine use and animal labor in the original

data. In calculating the respective geometric mean value,

these zero observations were arbitrary set at 0.l unit for

the machine use and l unit for the human labor, or no geome-

tric mean could be calculated due to the multiplicative

nature of the mean.

35

TABLE 4

REGRESSION COEFFICIENTS AND RELATED STATISTICS FOR CROP
PRODUCTION IN THE RICE REGION OF TAICHUNG AREA

 

 

Variables Regression Standard Error

Coeffécgents of Coefficients
Constant 2.4624a 0.3885
CrOpland, x] 0.2136b 0.1026
Human Labor, X2 0.46l4a 0.l204
Machine Use, x3 0.0312C 0.026]
Bullock Labor, X4 0.1276d 0.0678
Working Capital, X5 0.2523d 0.l283

 

Sum of regression coefficients, l.086l

Multiple correlation coefficient, R = 0.9365

Coefficient of multiple determination, R2 = 0.877l

 

a, significant at probability level of l%
b, significant at probability leVel of 5%
c, significant at probability level Of 24%
d, significant at probability level of IO%

Statistics from Production Function Estimates

The regression coefficient of cropland is significant
at a probability level of 5%, human labor is significant at
l%, machine use is significant at 24%, bullock labor and

working capital are significant at l0% level. The logic of

36

production suggests no basis for dropping any one of these
variables from production function.

The multiple correlation coefficient is 0.9365,
implying that the correlation between the dependent variable
and the combined independent variables is quite high. The
coefficient of multiple determination, usually expressed by
the symbol R2, measures the portion of the variation in the
dependent variable associated with or explained by all the
independent variables. The R2 estimated in the sample farms
is 87%, which indicates that the variation explained in
output by all the five independent factors combined together
is 87% on the sample farms.

The remaining l3% of the unexplained variation in
the dependent variable may be caused by the variables excluded
in the estimates, such as management, soil fertility, weather
and so on. Sampling and.measurement errors may also cause
the unexplained variation in the output.

In order to test the nature of production function,
we make the hypothesis that there is a linear homogeneous
production function or that the sum of the regression
coefficients is equal to I. This is to say that there are
constant returns to scale.

The sum total of therregression coefficients,z:b;
from the production function derived was l.08, which may
be considered as constant return to scale, because when all

factor inputs are increased by I% from the respective mean

 

37

levels, the gross farm receipt increased l.08%, slightly
higher than the change of input.

The regression coefficients of "the production
function indicate the percent change in output which would,
on the average, be associated with one percent increase in
the input factor concerned while other factors are held
constant.

For example, the regression coefficient of the

 

logarithm of cropland hectares, X], on the logarithm of
output, Y, for the 40 farms in the study area is 0.2l
which indicates that, on the average, an increase in cropland
input, X], by one percent, holding other factors constant,
is associated with an increase of output of 0.2l%. If the
standard error of X], i_0.l, is taken into consideration,
one percent increase cropland, holding other factors constant,
is associated with an increase of 0.ll to 0.3l% of output.
Similarly, one percent increase in human labor,
holding other factors constant is accompanied by a 0.34 to
0.58% increase in gross output. The responses from each
of machine use, bullock labor and working capital can be
interpreted by the same way that each of them may increase
0.05 to 0.57%; 0.06 to 0.l9%; 0.l2 to 0.38%, respectively,
by increased use of l% in each of the inputs.
In addition to the above mentioned overall measures,
it is desirable to measure the importance Of each of the

individual variables taken separately. There are, in

38

general, two different types of such measures. One is measured
by coefficients of partial correlation. The other is measured
by beta coefficients. Both measurements may serve the same
purpose.

(a) Measurement of the coefficients of partial

correlation:

Coefficients of partial correlation are useful in
measuring the correlation between the dependent variable and
each of the independent variables. The coefficients indicate
what the correlation would be between the gross farm receipts
and the input while holding other independent variables
constant at their respective mean levels. Each of the
coefficients of partial correlation is usually converted to
squared forms and for comparative convenience, they may be
expressed by the percentages of the coefficient of multiple

determination (R2) as shown in Table 5.

TABLE 5

COEFFICIENTS OF PARTIAL CORRELATION OF THE INPUTS,
4O FARMS, THE RICE REGION OF TAICHUNG AREA

 

 

Inputs r r2 Egrcig;%of
X] 0.3364 0.ll32 l4.99
X2 0.5492 0.3025 40.05
X3 0.2003 0.040l 5.3T
X4 0.3070 0.0942 l2.47
X5 0.3l96 0.l07l 9.32

Total 87.00

 

 

39

Human labor was the most important variation
explanation, which had about 40% of the variation observed
in the gross farm receipts of the sample farms. The variations
in gross farm receipts accounted for by other variables are
approximately; land, l5%; bullock labor, l2%; working capital, .
9%; and machine use 5%. There was l3% explained by unknOWn l—}“
|

factors.

 

(b) Measurement of beta coefficients: I."

It might be interesting to examine which independent .1
variable has the most influence on the variation of the
output. The beta coefficients will be used for this test.
The regression coefficients of the variables, converted into
the unit of their respective standard deviations, are called
beta coefficients. This is to compare the net regression
coefficients between each independent variable and dependent
variable by the units of its own individual standard devia-

tions. The general formula is

Si
Bl = bl—
SY
Where, Bi = Beta coefficient of Xi
b; = Regression coefficient of X;
S; = Standard deviation of independent variable X;
Sy = Standard deviation of dependent variable Y
The calculation is shown in Appendix Table II, and the result

was shown in Table 6.

40

Converting the beta values into the percentage of
the coefficient of multiple determination (R2), we may see
results similar to those obtained from the partial correlation
coefficients, as discussed in preceding section. About 35%
of the variation in the dependent variable can be explained
by the variation in X2, the input of human labor. This is
followed by working capital and cropland, with 20% and l6%,
respectively. Bullock labor and machine use contributed
much less toward the explanation of variation in gross farm

receipts.

TABLE 6

BETA COEFFICIENTS OF THE VARIABLES FOR THE 40
FARMS, THE RICE REGION OF TAICHUNG AREA

 

 

Beta Values Percentage of
R2 (=87%)
B] (Cropland) 0.2068 I5.93
B2 (Human Labor ) 0.4543 35.0l
B3 (Mechine Use) 0.0902 6.95
B4 (Bullock Labor) 0.ll89 9.l6
B5 (Working Capital) 0.2585 l9.92
Total 87.00

 

Both types of measurements, coefficients of partial
correlation and beta coefficients, showed that human labor

was the most important factor, followed by working capital

4l

and cropland. Machine use and bullock labor seemed less
important but they could not be neglected in the production
process because they help the other resources, such as land,
labor and capital to be more productive. They cannot be
shunted abruptly out of the farming.

Lastly, it is necessary to measure the simple
correlation coefficients between each pair of variables as
shown in Appendix Table III, indicate that gross farm outpot
is more closely correlated with human labor and working
capital, than with cropland, machine use and bullock labor.

Between independent variables, the correlation
coefficient between human labor and working capital was 0.85,
which is more closely correlated than any other pairs of the
independent variables.

In an analysis of Cobb-Douglas type of production
function, the independent variables should be categorized
such that the correlation coefficients between each pair of
independent variables should be small. This means the cate-
gories of inputs should be neither perfect substitutes nor
perfect complements. In reality, it is true that greater
labor use in production will accompany more working capital
uSe. Thus, human labor and working capital posses a near-
linear relationship.

The high simple correlation coefficients may result

in an error in the regression coefficient. The regression

LIZ

coefficients of human labor and working capital may by
interchangeably affected. One cuuld be higher while the
other be lower. In order to make possible a comparison of
the absolute output response per unit of factor inputs, it
is necessary to compare the marginal value productivity of

each factor input.

Marginal Productivities of Input

The marginal productivity refers to the amount added
to total value of product by adding one more unit of the
particular factor input, holding all other inputs at the
geometric mean levels. In this case, the one unit addition
refers to addition beyond the geometric mean level of inputs.

The marginal productivity, computed from the production
function, are given in value terms. They are dollar returns
per unit of input. The marginal value productivities were
calculated by the method shown in Appendix Table IV, and the
results together with the geometric mean and the average
productivities are presented in Table 7.

The average productivities are computed from the
actual product dividing by mean quantity of each resource.
The average productivity includes the product returns of
all inputs, and not simply the product retrun attributable
to the single resource. Average returns are always greater
than their marginal returns when marginal returns are

diminishing as in the case of all the individual figures

43

shown in the table.

This indicates that the production in

respect to each of the inputs were in stage II.

TABLE 7

GEOMETRIC MEAN, MARGINAL PRODUCTIVITY AND AVERAGE

PRODUCTIVITY OF

INPUTS USED IN PRODUCTION, THE

RICE REGION OF TAICHUNG AREA

 

Item Geometric

Marginal Average

 

Means Productivities Productivities
(NT $) (NT $)
Gross Farm Receipts, 76,92l.67
(NT $) '

Cropland,(ha) 0.99 l6,59l.60 77,698.66
Human Labor,(days) 4l6.52 85.22' l84.66
Machine Use,(Hrs) l.06 2,254.05 72,567.6l
Bullock Labor,(days) l9.87 494.0l 3,873.78
Working Capital,(NT $) l4,427.67 l.35 5.33

 

On the other hand, from the production function,

the constant a, has a positive sign while all of the

regression coefficients are also positive.

This also in-

dicates that each of the inputs being used in the production

were located in stage II, the rational stage.

Production stage II

is characterized by decreasing

average and marginal physical productivity of the input,

and the marginal physical productivity is positive and

LILI

always smaller than the average productivity. The total
physical product increases but at a diminishing rate. This
is an efficient stage of production.

The marginal value productivity of cropland was
NT $l6,59l.60 per hectare, which implies that an increase of
one hectare in crOpland would be accompanied by an increase
of NT $l6,59l.60 in gross farm receipts holding other input
items constant at their respective mean levels. Comparing
this estimated marginal value productivity of cropland with
its marginal factor cost, shows whether or not it is worth-
while to expand the cropland in production. A marginal
value productivity lower than the corresponding marginal
factor cost means that the particular input was over employed.
In other words, the additional cost of the input unit
exceeded the value of the additional output produced. This
is an inefficient use of the factor, since its amount may
be reduced without decreasing profit. This means an increased
profit may result by reducing the amount over employed. 0n
the contrary, a marginal value productivity larger than the
corresponding marginal factor cost indicates that the
particular input was under employed, and its use should be
increased to obtain a greater profit.

The marginal factor cost of land is the average
annual rent per hectare, which is, according to the prevailing

official rent rate, the value of 37.5% of the annual major

45

products. In the area under study the major product was
rice. Two crops of paddy rice were grown annually. The
average yield of paddy rice per crop was 3,289 kilograms!5
A 37.5% of the annual product (two crops) gave 2,476.5
kilograms. The price of paddy rice in'the area was NT
$5.08 per kilogram,16 during the study period. The total
marginal factor cost of land was, therefore, NT $l2,580.42
per year. This amount may be regarded as the opportunity
cost of the land per hectare. The marginal value productivity
of land was greater than the marginal factor cost. Thus, an
increase of cropland to some extent in the production,
holding other factors constant, would likely result in a
higher gross farm receipt.

The marginal value productivity of human labor was
NT $85.22 per work day, implying that a change of one work
day, holding other factors constant, would be associated
with a NT $85.22 change in the same direction in gross farm
receipts. The human labor in this study included both hired
and family labor. The female labor was converted into man
labor. Wages paid to the hired man labor plus the food
expenses provided was, on the average, NT $60.00. The

marginal value productivity of human labor was greater than

the marginal factor cost of labor or the wage rate. It is

 

I5Taiwan Agricultural Yearbood, 99, cit. p. 6l

16Ibid.

46

evident that an over intensive application of human labor
in the area was not the situation. However, the higher
marginal value productivity of human labor in relation to
the wage rate may lead to the conclusion that an increase
in the farm work days will bring forth an increase in net
farm income.

The marginal value productivity of machine use
was NT $2,254.05 per hour of work, which was extremely
high as compared with the custom rate of machine paid.

The custom rate or the marginal factor cost of power tiller,
on the average, was NT $40.00 per hour. This suggests that
machine use was very productive in the sense that potential
returns were especially higher than the marginal cost. This
was not a surprising finding because the machine use on the
small farms was extremely under employed. In order to
increase farm receipts, to apply more machine use may be
strongly recommended.

It has been long argued and generally considered that
mechanization was absolutely infeasible in Taiwan, which is
characterized by small farms. Of course farm machinery may
substitute for labor. But, which is more important that
machinery may also be a substitute for certain biological
forms of capital. For example, machine cultivation which
may plow deeper and increase yields is a substitute for

fertilizer, a biological form of capital.‘7

 

I7Heady, Earl 0.,et. al. Roots of the F rm Probl m,
Iowa University Press, Ames, Iowa, I965, p. I2I.

47

The marginal value productivity of bullock labor,

NT $494.0l per work day, as compared to the wage rate, NT
$l20.00, was larger than the marginal factor cost.

Inithis case, bullock labor was also under employed.
therefore, increase use of bullock labor may be associated
with a higher gross farm receipt. But the number of bullocks
available for farming is decreasing year by year due to the
shortage of feed supply.

The marginal value productivity of working capital
invested was NT $l.35 per NT dollar which was 35% higher
than the marginal factor cost, because the marginal factor
cost for a unit of this input category was one NT dollar
since one dollar of the marginal product is the recover of
the original investment and the marginal productivity is
computed in gross terms.

The value of working capital was an aggregation of
different farm expenses which was utilized for production in
fifferent periods throughout the year. It was a flow variable
representing the accumulated amount of investment.

The original funds required in tth category were
actually one-half or one-third the amount of the annual
average because the investment might turn over two or three
times during the year, especially in the area where multiple
cropping patterns were prevalent. The income of the first
crOp may be used as a source of funds to finance investment

needs of the second. The aggregation of the farm expenses

48

from different periods of time made the annual working
capital larger than the real funds required.

The multiple cropping index of the sample farms was
304% (Table l) which implies that three crOps were grown
on the same land during the year. In this sense we may
consider that the working capital was originally about one
third of the aggregated farm expenses truning over three times
during the year. This result showed that a single crop
production period, on the average, was about four months.
Assuming that the average interest rate was l.2% per month,
then the interest charge on the single cropping period, was
4.8%. After deducting this 4.8% interest cost from the
percentage of marginal value productivity of working capital
exceeding the marginal cost, 35%, the balance was 30.2% per
production period, or 90.6% per annum (30.2 x 3 = 90.6).

Every dollar of investment made in working capital
generates, on the average, 30 cents net return per crOp or
90 cents per annum. Such high marginal value productivity
of working capital implies that there is substantial under
investment in this input category, which is not reflected
by the marginal value productivity derived from the
production function.

All of these five independent variables, namely,
cropland, human labor, machine use, bullock labor and working

capital were under employed in the sense that all of the

49

marginal value productivities are greater than the respective

marginal factor cost. We may conclude that there was quite

high potentiality for the farmers to strive for even higher

farm receipts by adding more of the above mentioned resources

in the production.

CHAPTER IV
FEASIBILITY OF AGRICULTURAL MECHANIZATION
The Feasibility Suggested by the Production Function

Assuming that all prices of the variables are constant,
the Optimum profit is reached only when all marginal value
productivities of input factors equal their respective factor

prices. Thus the equilibrium condition requires:

 

fl=m=... =MVPX5']
PXI sz Px5

The economic meaning of this equilibrium condition
is, assuming there is no constraint in each of the resource,
that the variable resources should be allocated in such a
way that the MVP from each resource should equal the cost of
the last unit of each resource.

If there is a resource constraint, the optimum profit
under this condition is that the ratio of MVP and its respec-
tive prices equal a constant value greater than I.

As shown in Table 8, all marginal value productivities
are higher than the corresponding factor costs. The value
of the additional output produced exceeded the additional
cost of the last input unit. Among the five input categories,
the marginal value productivity of machine use was about 56

times higher than its marginal cost. This means that the

50

5l

farming operations in the area was highly under mechanized.
The per dollar additional input used in machine use may
earn NT $56.36 gross return. According to the current

farm organization, increase use of machine should be taken

TABLE 8

COMPARISON BETWEEN MARGINAL VALUE PRODUCTIVITIES AND THE
RESPECTIVE MARGINAL FACTOR COSTS, THE RICE REGION OF
TAICHUNG AREA*

 

 

Input Xi MVPX; P(MFEX?) Xi S%%§%
X] (ha) 0.99 l6,59l.60 l2,580.42 l.3l
X2 (dys) 4l6.52 85.22 60.00 l.4l
X3 (hrs) l.o6 2,254.05 40.00 56.36
X4 (dys) l9.87 494.0l l20.00 4.ll
X5 (NT $) l4,427.67 l.35 l.00 l.35

 

*Estimated from the Cobb-Douglas production function.

as the first priority rather than the other resources.
However, the marginal productivity estimate for an input
may not be valid beyond the range Of the original data.

The possible errors may involve in the estimates
of marginal value productivities and regression coefficients.
In order to find the feasibility of farm mechanization, we
need to examine again carefully the relationship between
machine use and other independent variables from the

production function derived. In other words, it is necessary

52

to see the reliability of the marginal value productivity
of machine use.

An examination of the coefficients of multiple inter-
correlation and simple correlation coefficients among the
independent variables may indicate possible biases in the
regression coefficients. Firstly, the required condition
is the coefficients of multiple intercorrelation between
a specific independent variable and the rest of the

independent variables appear to be low (Table 9).

TABLE 9

THE COEFFICIENTS OF MULTIPLE INTERCORRELATION
OF INPUTS, THE RICE REGION OF TAICHUNG AREA*

 

Coefficients of Multiple
Intercorrelation

 

R] 2345 0.3364
R2.]3h5 0.5492
R3.]245 0.2003
R4.1235 O~3070
RS.1234 0.3196

 

*Derived from the production function.

The coefficient of multiple intercorrelation of
machine use was as low as R3.l245 = 0.2003. This indicated

no important correlation among machine use and the rest of

53

the independent variables.

Secondly, a higher correlation coefficient between
independent variables may result in a biased estimate of the
regression coefficient, and hence may also cause some errors
in the respective regression estimates. The effects of these
possible errors will undoubtedly be carried into the marginal
productivity estimates derived from the production function.

Relatively speaking, X2, human labor is highly
intercorrelated with X5, working capital (r25 = 0.85, see
Appendix Table III). Some biases are possible in.the regre-
ssion coefficient as well as the marginal value productivity
of X2 and X5 estimated. The marginal value productivity of
X2 may be underestimated while the marginal value productivity
of X5 are overestimated, or the reverse may hold true. Thus,
the multicollinearity problem exists among the inputs of
human labor and working capital. However, the coefficient
between these two inputs does not seem too high to be used
in this study.

The coefficients of simple correlation between
machine use and each of other independent variables, as
shown in Table l0, ranged from -0.0650 to 0.5557. This
also indicates no important relation with other independent
variables.

Therefore, we may conclude that the marginal value
productivity of machine use as well as the regression

coefficient were fairly reliable.

54

TABLE I0

SIMPLE CORRELATION BETWEEN MACHINE USE AND EACH OF
THE OTHER VARIABLES, THE RICE REGION OF TAICHUNG AREA*

 

Coefficients of Simple
Correlation

 

r3] 0.5557
r32 0.5l89
r34 -0.0650
r35 0.50l5

 

*Estimated from the prOduction function.

The reliability of the marginal value productivity
and the regression coefficient, plus the fact that the highest
ratio of MVPX3 to MFCX3, indicate a high feasibility of farm
mechanization in‘the area.

Therefore, a reorganization in the input combination
toward higher profits by means of adding more machine use in

the production process is essential.

Optimum Conditions

The marginal value productivities of each input factor
estimated from the production function can be reasonably consi-
dered as an approximation of the actual marginal value
productivities in the farm operation in the area of study.

As analyzed previously, the optimum condition of

55

farm operation in the sample farms was not yet achieved.

The ratio of marginal value productivities to the respective
marginal factor costs among the five input categories

varies from l.3l to 56.36. This means that there was a

wide range in the return per additional dollar input among
the five input factors. The return per additional dollar
input on land was NT $I.3l, and $56.36 on machine use

(Table 7).

The optimum condition of reorganization farm produc-
tion is to approach the condition that the return per addi-
tional dollar input in each input category is equal to
$I.00 in the competitive economy. However, if there is an
input constraint, the optimum condition will be that the
return per additional dollar input is greater than $l.00.
The higher degree of constraints, the greater is this
value.

The marginal value productivities suggest that a
reorganization in the input combination is necessary in
order for farmers to operate in a more profitable manner.
Theoretically, it is possible to shift some inputs that
have a lower marginal value productivity to those that have
higher marginal value productivity. More specifically, the
equating of the ratio of marginal value productivities to
their corresponding marginal factor costs is the key to

reorganizing the farm for optimum profit.

56

Among the fove input categories, an increase in the
use of machine should be regarded as the first consideration,
because the potential return per additional dollar added to
the machine use was NT $56.36, which was the highest of all
input categories.

The second consideration as suggested by the marginal
value productivity was the increase use of bullock labor.

The potential return per additional dollar added to this
input category was NT $4.Il. But the number of draft animal
available was constrained by the shortage of feed supply as
discussed in Chapter I. Therefore, to consider increase use
of bullock labor will be out of question.

Third consideration should be given to the possibility
of increasing the human labor, or working capital, or cropland.
The marginal productivities of each input was around l.35 times
higher than its respective marginal factor costs. But the
total land available for cultivation was limited unless
some farmers leave the farm. Increased use of human labor
in farm production may also be limited due to rapid indus-
trial growth and the absorption of labor by industrial
sector. The average annual growth rate of industrial produc-
tion during l96l to I968 was I6.0%, and agricultural produc-
tion, 5.9% (Appendix Table V). Farmers usually supply a
large amount of labor for industry and the transfer of labor

from farm to factory constitutes one of the most significant

 

57

‘8 Increased

aspects of the process of industralization.
use of working capital seems to be feasible, because there
are different kinds of loans available through Farmers'

Associations, the Cooperative Banks, the Land Banks, etc.

Possible Farm Reorganization

Estimation of the gross farm receipts at the
respective mean levels of the inputs suggest by the
production function may indicate the possibilities of
reorganizing the farms for higher profit operation.

The production function derived previously was

.2I36 X2.4614 X3.0312 .I276 X5.2523

Y = 290.59 xI x“

Substituting all X; in the equation, the gross farm
receipts estimated from the present farm organization gives
NT $76,908.l7 (Table II).

As we have found previously, the first consideration
in reorganizing the farm should be given to increasing the
use of machine. Since the ratio of marginal value productivity
and marginal factor cost of this input category was the
highest of all (l:56), it may be possible to increase the

machine use by 40 times (Table l2). In this case the total

 

l8Chang, Pei-Kang, Agricultural and Industrialization,
Howard University Press, I949, p. l27.

58

TABLE II

ESTIMATED MARGINAL AND GROSS VALUE PRODUCT OF THE
CURRENT FARM ORGANIZATION, THE RICE REGION OF TAICHUNG AREA

 

 

Input Geometric __ ._ MVP
Factor Mean Log Xi b; bi(logXi) MVP ———'
(Xi) (XL) MFC
X] 0.99 -.0044 .2l36 -.0009 l6,59l.60 l.3l
X2 4l6.52 2.6l95 .46l4 l.2087 88.22 l.4l
X3 l.06 .0253 .03l2 .0008 2,254.05 56.36
X4 l9.87 l.2928 .l276 .l657 494.0l 4.ll
X5 l4,427.67 4.l592 .2523 l.0494 l.35 l.35

 

 

Log constant a = 2.4624
Log Y =zbi log(Xi) + a = 4.8860
Y = 76,908.I7

 

TABLE I2

ESTIMATED MARGINAL AND GROSS VALUE PRODUCTIVITY
WITH MACHINE USE INCREASED BY 40 TIMES

 

 

(Xi) (7}) Log X} b; b;(log 7;) MVP MV£_

MFC
x] 0.99 -.0044 .2136 - 0009 18,451.20 1.47
x2 416.52 2.6196 .4614 1.2087 94.37 1.59
X3 42.40 I.627H .03l2 .0508 63.50 I.58
x4 19.87 1.2987 .1276 .1657 549.18 4.61
X5 I4,427.67 4.I592 .2523 l.0494 I.50 I.5I

 

Log constant a. 2.4624
Log Y = 4,9360

Y = 86,289.26

 

59

cost is added by NT $l,696.00 while land, human labor,
bullock labor and working capital remain at the usual level,
will result an increase in the estimated gross farm income
from NT $76,908.l7 (Table II) to NT $86,289.22, or NT
$9,38l.09 total increase. Subtract the added cost from the
increased gross income, and the net income is increased by
NT $7,685.09.

The ratio of each MVP to the respective MFC, except
for the input of bullock labor which has been constrained
by the feed supply, are almost equal to a constant value l.5.
So, by adding the machine use by 40 times more to the current
farm Operation may be highly considered.

Probably, it would be preferable to recommend that
farmers increase the machine use by 30 times and working capi-
tal by l.5 times simultaneously. Thus, the machine use will
increased by 3l.8 hours per year and working capital, NT
$2l,64l.5l, while using the usual quantities of the other
inputs. The effect of the change of these input combinations
is shown in Table I3.

Increasing the use of machine by 30 times and
working capital by l.5 times, the total cost added is NT
$8,443.43 (machine use, NT $l,229.60; working capital, NT
$7,2l3.83), which will result in an increase in the estimated
gross farm income of NT $l7,82l.60. Thus, the net income

is increased by NT $9,387.l7. Obvioulsy, the ratios of each

60

TABLE I3

ESTIMATED MARGINAL AND GROSS FARM RECEIPTS WITH THE LEVEL OF
INCREASING MACHINE USE BY 30 TIMES AND WORKING CAPITAL BY l.5

 

 

TIMES
Input Quantity Log Xi b; bi(logX;) MVP ‘MVE
(Xi) MFC
X] 0.99 -.0044 .2l36 -.0009 20,438.66 l.62
X2 4l6.52 2.6l96 .46l4 l.2087 l04.94 l.75
X3 3I.80 l.5024 .03l2 .0469 92.94 2.32
X4 l9.87 l.2987 .I276 .l657 608.33 5.06
X5 2I,64I.50 4.3353 .2523 l.0938 I.l0 I.IO

 

Log constant §_= 2.4624
Log Y = 4.9765
Y = 94,729.77

 

MVP to the respective MFC are larger than I. It is still
possible to increase the use of some inputs level for higher
profit.

However, one point should be kept in mind that
the errors may increase rapidly as marginal productivity
estimates are made further away from the geometric mean

l9

levels. _ In other words, if the input level used is far

from their mean levels, the estimated marginal value

 

19Heady, Earl 0., and John L. Dillon, Op. cit.
p. 231.

6l

productivity may be biased or useless due to the nature of
the Cobb-Douglas model.

It might be interesting to test the feasibility
of resource combination from a different point of view.
Assume a farmer has additional NT $l,200 available for pro-
duction. The question is how he should use this capital for
production. The first consideration, as we have analyzed,
should be the increase use of machine. But, to what extent
can the gross farm receipts be increased. What difference
would there be, if this capital was added to other inputs.

To solve this problem, it is necessary to convert
the available capital into physical unit of each inputs,
except for the input of working capital. Then, add the
tentative unit to the respective input separately and see
the results. The computation method is shown in Appendix
Table VI. The results are presented in Tables l4 and IS.

From Table I4, we may note that the most profitable
way to use the additional available resource is to add to
the machine use. The farm receipts may increase by NT
$8,459.99 and is the highest of all. Its increased gross
farm receipts is approximately eight times higher than the
added cost.

The second consideration is to add to the input
of bullock labor, its return was about three times higher

than the added cost, but this input is constrained by the

62

TABL

E l4

THE CHANGE OF GROSS FARM RECEIPTS BY ADDING NT $l,200 TO
THE INPUTS SEPARATELY, THE RICE REGION OF TAICHUNG AREA

 

 

Changed Adde Total Unit Gross farm Gross Farm
Inputa Unit Used Receipts Receipts
(NT $) Increased
(NT 3)
X1/2345 .0954 1.08 78,350 1,443.83
X2/1345 20.0000 436.52 78,620 I,68I.8I
X3/1245 30.0000 3I.06 85,420 8,459.99
X4/1235 I0.0000 29.87 80,850 4,I04.40
X5/1234 I,200.0000 I5,627.67 78,5I0 I,462.93

 

possible feed supply.

aOnly one input was changed at a time, the rest of the
inputs were held constant at their respective mean

levels.
b

NT $l,200 divided by respective marginal factor costs.

CGross Farm Receipts Increased = Gross Farm Receipts
- Original Gross Farm Receipts (NT $76,908.00).

The other three alternative uses, namely

adding to working capital, human labor and cropland, showed

that the returns are much less than that of adding to machine

use.

As for the ratio of

of inputs to their respective

adding NT $l,200 to one input

to the macnine use has higher

marginal value productivities

marginal value productivities

marginal factor costs, by

at a time, we find that adding

profit because the ratios of

to marginal factor cost of

63

each input are rather uniform and closer to l than other

alternatives (Table l5, column 4).

TABLE -I5

THE RATIO OF MARGINAL VALUE PRODUCTIVITIES OF INPUT AND
ITS RESPECTIVE MARGINAL FACTOR COSTS BY ADDING NT $l,200

 

 

 

 

SEPARATILY TO THE INPUT, THE RICE REGION OF TAICHUNG AREA E“
Changed Inputa

X.

l

X1/2345 X271345 X3/1245 X4/1235 X5/1234

xI 1.23 1.34 1.46 1.38 1.31 .3
4x2 1.45 1.38 1.57 1.49 1.44
x3 57.65 57.82 2.21 59.61 32.74
x4 4.19 4.20 4.56 2.83 4.19
x5 1.37 1.37 1.49 1.42 1.27

 

aOnly one input was changed at a time, the rest were
held constant at their respective mean levels.

A more theoretical approach to allocating the available
resources under a given total outlay for an optimum profit
is to compute the quantity of each input used based on the
production function and cost function.

The production function derived is:

Y = 290.59 x] 2'36 X2.4614 x .0312 X#1276 x .2523

3 5

The cost function for a given outlay, while holding

all other excluded inputs constant, can be expressed as:

64

C = l2,508.42 XI + 60 X2 + 40 X3 + I20 X4 + X5

Where, C'is the given outlay. Under current organization,

the total given outlay is NT $54,345.28.

 

Thus,
L = 290.50 Xl.2l36 X2.46l4 X3.03l2 X4'1276 X5.2523 E

+LX4543345.28 - 12,580.42 x] - 60 x2 - 40 x3

- l20 X4 - X5)
To maximize the profits, all of the partial derivatives with
respect to each of the unknowns (X1, X2, X3, X4, X5 and >x) 9'
have to be equated to zero. The computational method is
shown in Appendix Table VII. The results are presented in
Table I6.

TABLE I6

OPTIMUM INPUT MAGNITUDES FOR A GIVEN OUTLAY OF FUNDS,
AND THE ESTIMATED MARGINAL VALUE PRODUCTIVITIES,
THE RICE REGION OF TAICHUNG AREA

 

 

 

. MVPX.
Xi MagnItude MVPXi MFCXi )\= fiff;f
xI (ha) 0.85 16,382.81 12,580.42 1.3
X2(Dys) 384.80 78.13 60.00 1.3
X3(Hrs) 39.02 52.09 40 00 1.3
X4(Dy5) 53.21 156.27 120.00 1.3
X5(NT $) 12,638.44 1.30 1.00 1.3

C = NT $54,345.28

Y = NT $77,487.24

 

65

Under optimum conditions the current farm organization
of the area under study suggested is to use 0.85 hectares of
cropland; 384.80 work days of human labor; 39.02 hours of
machine use (power tiller); 53.2l work days of bullock labor
and NT $l2,638.44 working capital. The total gross farm
receipts under those conditions are NT $77,487.24.

Comparing the suggested farm organization with the
original one (see Table II), we may note that the biggest
change in the resource allocation is the amoUnt of machine
use; which is suggested to be increased from l.06 hours per
farm to 39.02 hours.

The gross farm receipts are increased from NT $76,908.l7
to NT $77,487.24. A net increase of NT $579.07 is obtained
by reallocation of the inputs.

From the above analysis, we have found that, for
optimum profit, the power tiller should be used approximately
40 hours per farm per annum (Table I6) on crop production,
or approximately 40 hours per hectare per annum, since the
average size of farm was 0.99 hectares.

We assume based on general estimate that in addition
to crop production, the power tiller will have an equal amount
of use on other than crop production, such as for livestock
production, transporting farm products to the market, potato
slicing, feed cutting,.etc.

The economic working capacity of a power tiller is

66

about 800 hours per year (will be discussed in Chapter V).
Thus each power tiller would cultivate approximately l0

hectares of land under the condition of reallocating the

inputs for optimum profit.

 

CHAPTER V

AGRICULTURAL MECHANIZATION

The Needs of Agricultural Mechanization

The man-land ratio in Taiwan is among the highest in

 

the world (Appendix Table VIII), and it is getting higher.
Increased food production must come from new and more efficient
methods to production. Since it is clear that increased
machine use is essential and feasible for any substantial
increases in production, it is now appropriate to discuss

the promotion of mechanization.

Mechanization in this study implies mainly the appli-
cation of power tillers on the small-sized paddy farms. The
power tiller can pull any kind of farm implement just like
the larger tractors; only these implements are smaller in
size as well as in working capacity. The engine can be used
for different kinds of farm work, for instance, pumping
.water, spraying, pulling trailers and so on. The power tiller
may also serve as a small power plant to do other work on the
farm. Another point which is more important is that by

changing to different kinds of wheels, the tiller can be used

in muddy fields, upland fields, and on roads.

67

68

The power tiller for paddy fields was first developed
and widely adopted in Japan, because Japanese consider paddy
rice as their major crop. After World War II, many machinery
manufacturers in Japan, originally ingaged in war supplies
and weapons, were converted into factories for the manufac—
ture of macnines for peaceful use.

Generally speaking, the use of modernized, improved
power machines is now very limited in Taiwan. Most of the
farm operations are done by hand, by the use Of animal labor
and with simple tools. Some of the operations are done
exclusively by hand, particularly the transplanting of rice
seedlings and the harvesting of rice. Notwithstanding that,
these are primary and important operations in peak labor
seasons. In the spring, summer, and fall peak labor seasons,
farmers are rushed with such seasonal operations as harvesting
the first crop by reaping, threshing, husking, winnowing,
sorting, then preparing for the second by plowing, sowing,
and transplanting.

Since rice is the most important crop grown and the
one where the power tiller is likely to be used thernost in
(Taiwan, it is necessary to know how much labor is needed for
rice cultivation. With a brief look at Table I7, we may see
that about l00 man days of labor are used in production of
one hectare of rice. The distribution of labor is approximately
23% for plowing; 25% for weeding; 24% for harvesting and the

remaining 28% is used in fertilizing, disease control, cleaning

 

69

the rice and in transporting straw.

TABLE I7

THE HUMAN LABOR DISTRIBUTION PER HECTARE FOR
RICE CULTIVATION, TAIWAN

 

First Rice Second Rice

Items Crop Crop

 

lst dry plowing
2nd dry plowing
Basic fertilizer
Land preparation
Transtlanting
(including removal of seedling)
lst fertilizer
lst weeding
2nd fertilizer
2nd weeding
lst disease control
3rd weeding
3rd fertilizer
Removing barn yard grass
2nd disease control
Harvesting
Cleaning, winnowing, storage
Transporting straw
Total I

OP-PW-I?
mooowwrwrwowmw mwrxom
—'-P'-IT| -F'

N

N
ooooonowrwowmw mo:- 4?

mW-P'w—‘dedm—‘md

\O

O

 

Source: Summarized from Chang, Chen-Chang,”Agri—
cultural Engineering Analysis of Rice Farming Methods in
Taiwan,” National Taiwan University, Taiwan, I963, pp.32-3.

Labor used for water irrigation or drainage was not
included in the above table, because it should he done
frequently during the whole period of production. The

amount of labor required for irrigation is fifficult to

70

estimate. In drought deasons labor requirement for irriga-
tion will be much higher. All of the human labor required,
except for removing barn yard grass from the paddy field,
may be replaced or reduced by machine use. It is hard to
estimate the extent to which the human labor can be reduced.
But, it is likely, in the beginning stage that most plowing
and transporting work may be mechanized; in the second
stage, harvesting work; and in the third stage, weeding,
fertilizing and disease control, etc.

However, it might be worthwhile to predict the
years required to mechanize Taiwan's agriculture. Fnom
Table I8, we may see that the total number of power tillers
in I967 was I5,523 units. The number of power tillers is
increasing year by year. The total number of bullocks in
I967 was 33I,878 head, which is decreasing year by year.
The rate of change during l960-l967 of power tillers was,
on the average, an increase of l,754 units per year, while
bullocks were decreasing l2,l77 head per year. The ratio
:7.

This means every seven bullocks decreased was replaced by

of change between power tillers and bullocks was I

one power tiller.

Projecting the rate of change in the above period
20 years in the future, the total number of power tillers
in use by I987 would be 50,000 units(Figure 5). The total
number of bullocks at that time will be l20,000 head.(This

projection is rather weak because of the shortage of data).

 

7l

TABLE I8

THE NUMBER OF BULLOCKS AND POWER TILLERS
IN TAIWAN: I960 - I967

 

Year

Bullocks (head)a

 

Power Tillers (units)b

 

 

 

 

Number Change Number Change
I960 4l7,l22 3,242
l96l 4l4,208 -2,9l4 4,4l4 +l,l99
I962 405,026 -9,l82 6,l45 +l,704
I963 389,448 -l5,578 7,756 +l,6ll
I964 379,073 -l0,375 9,367 +I,6II
I965 370,36l -8,757 II,379 +2,0l2
I966 360,294 -I0,022 l3,438 +2,059
I967 33I,878 -28,4l6 l5,523 +2,085
Raézrofeghange 7" -l2,l77 +l,754
Ratio of Change 7 l

 

Source:algiwan Agricultural Yearbook: I967, PDAF,

Taiwan.

bEsmay, Merle L., ”The Introduction of Two-
wheeled Tractors in Japan and Taiwan,‘I p. 4,
which was sourced from JCRR, Taipei, T967.

72

Bullocks (l,000's)

Lmo>

 

 

 

 

0mm. km mmm. 0mm. mkm. cam. mom. oom.
o o
oo. ,,,, o.
//// \\
oom 77,, \\ ON
oom ... 7,,,, om
ooa ... axoo..am. . oa
,. mLo___P Lozom
oom \\ om
z<z_<4 z. mmmoo_4 mmzoa oz< mxoooosm Lo mzo_.omaoma az< mazmmp

m mane—m

(5.000‘1) $491111 JeMOd

73

Costs and Working Capacity of Power Tiller

It is fifficult to accurately compare the cost of use
of bullocks and that of power tillers, because it is not easy
to calculate the cost of keeping a bullock on the farm and
the daily cost of use of bullocks for field work.. At the
beginning stage, the method of using the power tiller was to
do only the same work as the bullock and therefore only part
of the capacity was utilized. This gave the power tillers no
opportunity to work with their maximum efficiendy. Further-
more, the operatiors of these power tillers had little training
and their skill and ability in utilization of the power tiller
was not uniform and was poor. Under such conditions, the
depreciation and maintenance costs of the power tiller may be
higher.

However, we may calculate the theoretical cost of the
power tiller by the number of hours of service it may render
the farmer per year. In general, within the capacity of the
power tiller, the more working hours in a year, the Tower is
the cost per working hour. This can be illustrated in the

following formula:

F
C a -—E- + VC
X .
Where, C = total cost per hour of use

FC = annual fixed costs

X = working hours per year

74

VC = variable cost per hour

The fixed cost includes the following items:

a.

Depreciation of power tiller: the purchase price of
power tiller is NT $45,000 (including all attachments
and a trailer) and its service life is generally figured
as seven years. Assuming no salvage value, its depre- F5:
ciation will be NT $6,430 per year (simple straight line
method).

Interest of investment: the prevailing interest rate

 

is ID per cent per annum. The interest on envestment I:
will be NT $2,250 per year (45,000 x % x 0.l).

Tax, insurance, storage cost, etc.: approximately l.5%

of the purchase price, or NT $675 per year.

Repair, lubrication, and regular maintenance: assuming

4% of the purchase price, or NT $l,800 per year.

The variable costs include the following items:

a.

Thus, the average total cost curve is:

Fuel: the power tiller with 7.5 HP (an average type)
consumes an average of about 0.6 gallon of gasoline
per hour, or NT $ll.4 per hour (NT $l9.00 per gallon).
Operator's wages: NT $8.75 per hour (NT $70 per day).
Lubricant, grease, and miscellaneous: approximately

NT $0.50 per hour.
20

C =(9I26/X) + 20.65

 

20
C _45,000 x (14.28% + 0.5% + 1.5% + 4%)

X

 

+ (ll.40 + 0.50 + 8.75)

75

The average total cost curve per hour is illustrated

in Figure 6.
FIGURE 6
AVERAGE TOTAL COST CURVE PER HOUR OF POWER TILLER USE

\j

'= c = 9126/x + 20.65
\\ Custom rate

50 : \
\.
40 l‘\\\\\\\\

30 I

Cost per Hour (NT $)

 

I I . ‘ ‘

O 200 400 600 800 I000

Hours of Work per Year

The power tiller is being used about 500 hours a year
according to a I963 study?] The total cost per hour is NT
$38.90 on this basis, which is quite close to the prevailing
custom rate (NT $40.00). Roughly speaking, the economic
range of using a power tiller as indicated in the diagram, is

around 800 to 900 hours per year, while the total cost per

 

2IChang, Chen-Chang, ” Agricultural Engineering Analysis

of Rice Farming methods in Taiwan,‘I National Taiwan University,
Taiwan, I963.

Jan: “1 I

 

76

hour may reduced to around NT $32.

One hectare of crop production under the current type
of operation, needs approximately 90 hours of power tiller
use per year.22 In order to be able to cover the total cost,
a power tiller should be used at least 490 hours per year
(read off from Figure 6) or about 5.5 hectares. For more
economic operation, a power tiller may be used about 800
hours or enough to handle 8 to 9 hectares per year.

A small farm in Taiwan (about I hectare ) is not big
enough to keep the power tiller working up to the minimum
economic annual working hours, thus investment made in a
power tiller becomes uneconomical unless custom work for
other farmers is available.

Therefore, it is not sound economics to persuade every
farmer to purchase a power tiller. Rather it is feasible that

one power tiller be purchased cooperatively by several farmers.

Economic Advantages of Agricultural Mechanization

As discussed previously, the increased production must
come from an efficient and intensive use of land in farm
production. Therefore, in the first place, the soil prepared
7 for a crOp should be plowed well and turned over completely,
thus both the upper and lower parts of soil can be used

efficiently by succeeding crOps. Green manure, compost and

 

22Derived from Chang, Chen-Chang, 92,‘gi£., i.e. two
crops of rice per year = 64 hours, (lst dry plowing, ll hours
per crOp; 2nd dry plowing, ll hours per crop; pulverizin ,
eveling and misc., l0 hours per crop) winter crop = 26 flours.

 

 

77

other basic fertilizers also should be turned down into the
soil.

A study made by Taichung District Agricultural Improve-
ment Station showed that the yield of rice increased with an
increase in the depth the soil was plowed (Table I9 and Figure
7). r7

TABLE 19 I

THE RELATION OF THE DEPTH OF SOIL PLOWED AND THE I
YIELD OF RICE, TAICHUNG AREA

 

 

Depth of Soil Rice Harvested per Ha. I“

 

PIowed (cm) of paddy field (kg)* “
l0.5 4,025
l3.5 5,257
l6.5 5,669
I9.5 5,848

 

* l kilogram = 2.2 pounds

Source: Taichung Agricultural Imprivement Station, I966.

According to Chang,23 the average depth of cultivation
by.draft animal was l2 centimeters, while the depth plowed
by power tiller in the same field was l5.8 centimeters, or
3.8 centimeters deeper than thet of draft animals. The inc-

rease in yield of rice was 880 kilograms(read off from Figure

7).

24

The rate of increase was about l8.6%. Stout also points

 

23Chang, Chen-Chang,ygp.cit.

2l+Stout, B. A.,“Equipment for Rice Procuction,” FAO,
Rome, I966, p. 47.

78

FIGURE 7

THE RELATION OF THE DEPTH OF SOIL PLOWED AND
THE YIELD OF RICE, TAICHUNG AREA

 

 

6,000
A //
UT
3
o '/
E 5,200 1 /
L /
8 //
8 4,800 ,
'C 4.720
u.
0
-0 4,400 I
E
>—
4,000 1‘
T 4- . . - . . .
0 10 12 14 16 18 20

Depth of Soil PIowed (cm)

Source: Same as Table l0.

out that depths greater than 20 centimeters can result in
decreaded yield. This is probably due to the fact that the
organic matter becomes buried too deeply for the root systems
to reach the plant nutrients.

Making a conservative estimate, each power tiller would
cultivate eight hectares per season. Fifty thousand tillers

would cultivate 400,000 hectares of land per season ( the total

 

79

cultivated land in Taiwan was 899,926 hectares, see Table 2).
The output increase in rice production would be 352,000 metric
tons,25 (400,000 x 880). The total increase for the two crops
per year from the 400,000 hectares of land cultivated by power
tillers would be over 704,000 metric tons. Even if the increase
is cut down to l0%, we still have 328,900 metric tons in increas-
ed rice output. This additional 328,900 metric tons of rice
from no extra land will have undeniable effect on improvement
of the food supply. If this Quantity of rice is exported to
foreign countries it.would earn foreign exchange amounting to
34.5 million US dollars (assuming that 70% 0f the paddy rice
will become polished rice and sold at US $l50 per metric ton).

0n the other hand, let us calculate the amount of foreign
exchange to be spent for purchase of 50,000 power tillers. At
present, assuming we have to buy the whole machine from Japan,
each power tiller costs us about $500.26

Taking into consideration home production of 2,000
tillers a year, it is estimated that we would have to import
20,000 whole units from Japan. Later we only have to pruchase
the engines and some of the parts from abroad, at a cost of
US $300 per unit. We assume that l5,000 such tillers will

‘ be sold in the rural area at this stage. In a still later

 

25

26The whole sale price of a power tiller in Japan was

$335, (Shin-norin Sha Co. Ltd., Farm Machinery Yearbook,-
70, p. l09), the shipment fee, tax, etc. was estimated US
65 per tiller.

l metric ton = l000 kilograms

US
l9
$1

 

80

period, most of the parts may be manufactured in Taiwan,
except for the engines and some inportant materials each
power tiller will then cost us only about US $l00. The
50,000 tillers will cost Taiwan a total of US $l6 million,
which is 46.3 percent of the increased value of rice derived
from the use of the power tiller in one year.

Setting the serviceable life of a tiller at 7 years,
the total increased value of rice in that period would be
24l.5 million US dollars (34.5 x 7). If one hectare of rice
required 64 hours of machine use (see footnote 23), and the
operating cost is NT $36 per hour, or US $0.90 (assuning the
tillers reach certain economic use), the total cost would
be US $57.60 per hectare annually. The total cost for 400,000
hectares will be 23 million US dollars. For the estimated
seven years of machine life, the total operating costs for
the 50,000 tillers would be US $l4l million. The total net
increased value of rice during the seven year period is:

Total increased value of rice US $24l.5 million
Total operating costs US $l4l.0 million
Total net value increased US $l00.5 million

Dividing the total net value increased of US $l00.5
million, by seven years we would have 14.28 million US dollars
net profit per year. We can well see the actual profit of

using power tillers.

These calculations do not include the value created

 

8l

by using the power tiller for possible increased intensity
of land utilization, from crOps other than rice, and other
farm work, which is hard to estimate but should not be
neglected. Furthermore, Taiwan has now two power tiller
manufacturing factories, producing 2,000 tillers per year.
Thus the increased use of power tillers may help in the
develOpment of rural industries.

Secondly, to increase farm incomes from a given

acreage of land, a farmer should, in general, increase land

 

utilization in terms of the multiple cropping index. In so
doing, all harvesting, plowing, and transplanting are limited
to within a very short time period, thus the supply of labor
or power must be sufficient to meet the demend in that period.
Tsui27 indicated the time required per hectare for preparing
rice paddy was 3.5 days at 8 hours per day for a tiller and
10.5 days at 10 hours per day with bullock labor.28 This
means that the second crOp can be planted 7 days earlier.
Judging from all criteria, mechanization of agriculture
would be beneficial in all respects. The important ones may
be summarized as follows:
(I) Increase crop yields per unit of land, to meet

the growing demand of foods.

(2) Increase farm intensification, or multiple cr0pping

 

27Tsui, Young-Chi, ”A report on Economic Analysis of
Farm Mechanization”, JCRR, I962.

Land preparation is defined as consisting of the
operations of plowing, breaking, pulverizing and leveling.

 

82

index. The use of power tillers may permit an
additional crop by more rapid harvesting the
first crop or land preparation for the succeeding
crops.

(3) Reduce the amount of land devoted to the produc-
tion of feed and forage for bullocks.

(4) Break the bottle neck of seasonal peak labor
requirements, such as harvesting the first crop I

and planting the succeeding crops in March, July II

 

and November.
(5) Help in the development of the farm machinery
manufacturing industry as well as overall economic

development.

Some Difficulties to be Recognized

There are several problems which should be solved
before any program of trying to mechanize the farm operation
is undertaken. The most important problem is the farm
people who are largely composed of small, independent,
tradition - bound farmers. The characteristics of being
small and indepent have beCome increasingly universal since
the completion of the land reform program in I953.29 By

small, it is meant that the farm owned and Operated by a

 

29Yang, Martin M.C., ”Social Factors in the Joint
Cultivation of Rice”, National Taiwan University, Taiwan,
I968, p. 4.

83

family and the farming Operation on it are all small in size,
as mentioned in Chapter I. The use of power tillers, if
limited to use on one farm, would be very much limited.

In Taiwan, farm Operation practices are affected by
the shape and size of fields, which in turn are partly inf-
luenced by the land inheritance system and partly by the fmi
nature Of farm practices. The influence is particularly

important in areas where pOpulation growth outstrips available

 

farm land. Even after the enforcement Of land reform program, I!
the law still gives equal right Of land inheritance among
several heirs. The situation has caused farm holdings tO
become even smaller, as an average, and particularly when
there are several heirs.

In rice cultivation, for example, paddy fields must
be irrigated and the irrigation water must be adjusted as
rice plants grow. For this, the size Of each plot Of paddy
field should not be tOO large. If the size of a plot of
paddy field is tOO large, it will be impossible to maintain
the desired water level above the surface Of the ground
after the paddling. Thus the water depth would become
different in different parts Of the same paddy feild, with
the mud being exposed in some parts Of the field. Thus
weeds will spring up.

Therefore, even when several plots Of arable
land are consolidated into one plot, it must be partitioned

into smaller plots by border ridges.

84

On the other hand, it is usual that a farmer's paddy
fields are widely scattered and the shape of each plot is
frequently not regular. If the holdings are widely scattered
and each plot is not regular in shape, labor efficiency may
not be increased much, even if the Operation is done with a
power tiller. It is also very troublesome to convey the le
power tiller from place to place.

Operating practices are affected by the above factors.

 

For this reason, in order to introduce power tillers, projects .j
for water use improvements, consolidation of fragmented I
holdings, and the rearrangement Of local roads and farm

roads have been planned and carried out in many parts Of the

island in the past few years. Some of the above projects are

serving as a basis for the more intensive use Of farmland.

However, to encourage the use of power tillers, we cannot

avoid exerting great efforts to make attitudinal changes

on the part Of farmers toward faster adoption.

Processes of Agricultural Mechanization

TO develop agricultural mechanization, the government
must make provision for spending a great deal Of capital to
encourage, organize and set it to work, especially in an area
characterized by small holdings like Taiwan. A cooperative
venture, as being successfully done in Japan, might apply to

Taiwan. However, local conditions, and farmer's attitude,

85

for instance, may dictate the method of implementing the
mechanization project.

The ways of adopting the power tillers may differ
according to the farmer's purchasing power and size Of his
farm. In general, there are three ways: (I) Individual
ownership and use on his own farm. (2) Partner ownership and
joint use, and (3) Individual ownership, and, when possible,
doing custom work for other farmers. Each of the three ways
has its merits and shortcomings which we shall compare and
discuss briefly in the following:

(I) Individual ownership and for use in his own farm:

a. Merits: The owner will constantly and strenuously
study the ways to utilize the power tiller on his farm. This
will greatly extend the working scope of the power tiller in
his farm. 0n the other hand, he will be attentive to the proper
maintenance and repair of the power tiller.

b. Shortcomings: When the owner's farm is not big
enough to heep the power tiller working up to the minimum
economic annual working hours, i.e. 800 to 900 hours per year,
investment made on the power tiller will be uneconomical.

(2) Partner ownership and joint use:

a. Merits: Farmers who do not have sufficient money
to buy a power tiller individually may pool their funds and
all enjoy the use of power tiller. In this case, the working
capacity Of the power tiller will be fully utilized.

.b. Shortcomings: Every owner has equal right in use

 

86

of the power tiller. During busy seasons it becomes fifficult
to make the power tiller available to all the owners satisfac-
torily. None of the owners will pay attention to the prOper
repair and maintenance of the power tiller.

(3) Individual ownership and doing custom work for
others:

a. Merits: Work schedule will be well arranged by
owneraccording to priority, and the working capacity Of the
power tiller is fully utilized.

b. Shortcomings: Individual ownership may delay the
adoption of power tillers. The custom rate may change in
different seasons.

Based on above comparison and analysis, we think that
if an individual can afford to buy a power tiller, it is best
for him to buy one for his own use. If the area of his farm
is limited and cannot utilize the power tiller fully, he can
do custom work for neighbors. If the individual does not
have or cannot raise the money to buy a power tiller, he can
pool his funds with his nearby neighbors for purchase of a
power tiller. But the number of parters in this case should
not be many. As we have mentioned before, the power tillers
can be effectively used over 7 to 8 hectares of land. There-
fore if 5 to l0 persons have a total farm area of 7 to 8
hectares, the power tiller may be very efficiently used in
the small group cooperatively.

In view of the shortcomings of joint use, an ingenious

 

87

working plan covering all fields of member farmers is required
to be laid down in advance. If the tiller is Operated by
member farmer himself, sufficient knowledge and skill for
Operating the power tiller are the primary requirements.
Which type of ownership and use to be adopted may depend on
the local situations.

Bunkel3O points out that prviding for adequate
educational facilities, including qualified instructors, is
an important prerequisite for mechanized agriculture. In
this regard, the Farmers' Associations would seem to be
able to carry out this phase of mechanization projects. In
every towndhip and village in Taiwan there is set up a
voluntarily organized and democratically run farmers' asso-
ciation. These organizations serve local farmers in matters
of credit, wholesale purchasing, cooperative marketing,
warehousing, and agricultural extension and education. The
associations are managed by officers elected by their members.
In the last decade, the associations have been actively
engaged in agricultural extension and education work, under
the assistance of the Joint Commission on Rural Reconstruction
(known as JCRR) and the Provincial Department of Agricultural
and Forestry with promising results.

Farmers' Associations may provide a sound foundation
for agricultural mechanization, such as proViding credit for
purchase of the machines, training the farmers to Operate

power tillers, establishing machine shops, and helping to

 

3OGunkel, Wesley W., ”Implementation and Over Mechani-

zation in Developin Countries,” ASAE Annual Meetin , a er
NO. 68-508,]968. g g p p

 

88

organize the farm machinery cooperative teams, etc. In Taiwan,
there is no other organization which is so closely related to
all farmers.

Power tillers, to be used effectively, must fit into
the agricultural conditions. We must be careful in selecting
the right type Of power tillers, such as (l) Tractive type: In]
may pull various farm implements, i.e. plows, harrow, culti- I

vators and trailers. This type of power tiller is suitable

 

for dry fields, (2) Rotary type: rather bulky and heavy, Ji‘
difficult for traveling on the narrow footpaths, and (3) _-
Screw type: equipped with track laying ground driving
devices. This type is suitable on the deep mud paddy field.
The use of small power tillers is likely the key to
the solution Of the problem Of overall agricultural mechani-
zation. We should allow sufficient time for farmers to
learn how to use power tillers to replace present cultivation
tools, even if we want to extend the use Of power tillers as
rapidly as possible. Besides, an adequately trained supply
Of extension workers to give the necessary guidance and
supervision to farmers is also needed.
In starting intensified promotion Of power tillers,
we ought to advocate concentrated efforts in selected
localities where we can consentrate available efforts in
training farmers how to operate the power tillers. When
success is attained in these experimental localities, the

work can be gradually extended to other areas.

89

To summarize, to successfully implement the agricultural

mechanization program, the following steps have to be taken:

 

(l) Demonstrate power tillers Of suitable type in
selected areas. The essential thing is to show the farmers

the results of and advantages of using power tillers and to

téll them how to use power tillers the year around to do IT!
different kinds of work in their own farms. IN]
(2) Design new farm implements attachable to the i
power tillers and adaptable to the conditions Of the 5:“
u

 

localities.

(3) Train technical workers to assure adequate number
of extension and repair personnel.

(4) Train the farmers how to operate and maintain
the power tillers.

(5) Provide long thrm loans at reasonable interest
rate to help the farmers purchase the power tillers.

(6) Guide and assist farmers in organizing joint use
teams and set up the working plans for the groups.

(7) Provide competent servicemen and adequate repair
facility at places convenient to farmers.

The above comprise the necessary processes for the
agricultural mechanization. They are all indispensable and
supplementary to each other. Shortage of either one of them
will affect the sound development of the whole program. No

single element should be ignored.

CHAPTER VI

CONCLUSION

The production function derived from the sample farms
was fairly reliable as indicated by the relatively small
standard error of estimate (the standard error is 0.13),
highly significat levels of each independent variable, and
specified by other statistics. The production indicated by
the positive sign of constant value as well as positive
regression coefficients of each independent variable showed
that each of the quantities of inputs being used were located
in Stage II, the rational stage. But the ratio of the marginal
value prodictivity estimates to their respective marginal
factor costs, clearly indicated that the resources were not
properly allocated to obtain Optimum profit.

The sum Of regression coefficient was l.08, which
implies that the production was near constant return to scale.
Among the five inputs used, human labor had the most influence
(40%) on the variation in the output, followed by working
capital (about 20%) and land (l6%), others have less influence.

The marginal value productivities of all inputs were

higher than their respective marginal factor costs. This means

90

 

9l

that increased use of each input will result in higher farm
profits.
The possibility of increasing the use of power tillers
should be considered first among the other possibilities,
because the ratio of the marginal value productivity Of
machine use to its marginal factor cost, 56:l, was by far iii
the largest of any inputs. In other words, any change to I"

be made in input combination for higher profits, increased

 

use of power tillers should be given first consideration. j
The second possible consideration of input combi- *'

nation for higher profit. as suggested by the production

function, was the increased use of bullock labor. But in

view of the real situation, the total number of bullocks

has been decreasing year by year, due to the shortage of

feed supply. Increased use of bullock labor will be out Of

the question. Increased use of power tillers not only may

replace the bullock labor but also may provide more power

for more highly intensified farming operation.
By adding an additional given amount of input (in

value terms) to each input separately, we also see that the

highest profit could only be attained by adding to machine

use. Reallocation Of the present input combination for

Optimum profit also indicated that the biggest change could

be made by increased power tiller use from l.06 hours per

year to 40 hours per year. These facts showed that mechani-

zation in terms of use of power tiller is highly feasible

93

 

and desirable.

In earlier years, it was conceived that labor force
was an abundant agricultural resource in Taiwan, and that
there was a considerable amount of excess labor or under-
employed labor in the agricultural sector. Actually instead
of an excess labor supply, even on an annual basis, there
has been a shortage of labor in the last two or three years.31
Agricultural mechanization would partially solve the problems

of labor shortage.

 

In the long run, with the increase in pOpulation,
there will be growing need for more food production, but:
there is little chance for expansion of farmland. Conse-
quently, higher output per hectare will be needed. Use of
farm machinery will be one step forward toward the long
range goal of more intensive utilization of farmland to get
more food. With power tillers speeding up the land prepara-
tion work, the farmers can time their crop planting and
harvesting to their best advantage, and, in most cases,
realize production potential of crops that was previously
unattainable, due to delay in planting caused by the shortage
of animal or man power for land preparation. Thus, in a
sense, farm incomes may be increased with a high multiple

3i

Wu, T. C., ”On the Research Diminution of Winter
CrOp Acreage in Taiwan,‘I JCRR, Taiwan I969.

94

cropping index, made possible by having more adequate power.

Esmay32 points out ”If a country is to prosper over
a long period of time, its resources of manpower must be
utilized carefully. From a physical standpoint, man can
develop only about one tenth Of a horse power. From a power
standpoint he is overpaid. Man was created as a thinking
creature and this potential must be developed. Even in
view of this, engineers realize that in manpower-surplus
and land-deficient countries, mechanization must justfy by
either reducing costs or increasing yield per hectare.”
Thus, to increase the yield of crOps, mechanization is
extremely essential, even if the farms are small in size.
Further, it is important to relieve farm labor from over-
wOrk by the use Of machinery. The labor saved by the use
of mechanical power may be used in other types of work on
the farm or part-time work, or the reduction of time needed
would make possible participation in cultural and social
activities. This is important in modern life.

The extension job of promoting power tillers is
difficult. The farmers of Taiwan are accustomed to bullocks
and they know how to treat and drive them. As power tillers
are totally new to them, they would hardly know sound selection

and operation. Improvement in farm mechanization requires

 

32Esmay, Merle L., ”Rice Mechanization,” Sixth Semi-
Annual Report of Michigan State University Advisory Group to
the Rep. of China and AID, I963, P. 50.

 

95

adoption of changes which should be accepted by individual
farmers as well as groups of farmers.

Taiwan's agricultural mechanization as indicated by
the introduction of power tillers is starting a pattern
similar to Japan's with a time lag of about twelve years.33
In view of the success there, mechanization in Taiwan should
be promoted strongly. Local demonstrations showing the
results of using power tillers compared with bullocks should
be put on to convinence farmers of the economic advantages
Of power tillers. The types of power tillers to use must
be such that they can fit into the agricultural situations
of the localities. Farmers should have sufficient knowledge
of how to operate power tillers. In other words, research
and education are prerequisites to large scale extension of
agricultural mechanization in Taiwan.

Power tillers may be jointly owned and used among
small groups of nearby farmers. But the overall working
plans have to be arranged in advance. This kind of organi-
zation should be supervised by farmers' associations. This
will ensure profitable utilization of the investment.

Therefore, in achieving the objective of agricultural
mechanization, social service organizations, the government,

the farmers associations and farmers themselves have their

 

33Esmay, Merle L, ”The Introduction of Two-wheeled
Tractors in Japan and Taiwan,’I Mimiograph, Agr. Eng. Dept.,
MSU, I967, p. .,

 

96

important roles to play to help Taiwan to achieve the

desired success.

 

BIBLIOGRAPHY

 

98

Castle, Emery N., and Manning H. Becker, Farm Business
Management, the Macmillan Company I969.

 

Chang, Cheng-chang, ”An Agricultural Engineering Analysis of
Rice Farming Methods, in Taiwan, I'National Taiwan University,
Taiwan, I963.

Chang, Pei-kang, Agricultural and Industrialization, Harvard
University Press, Cambridge, Massachusetts, I949.

Clyma, Wayne, ”Engineering Economic, and Educational Facts
to Consider in Changing from Animal to Tractor Power in

Dezgloping Countries,” ASAE Annual Meeting, paper No. 68-507,
l9 .

Esmay, Merle L., ”Rice Mechanization,” Sixth Semi-Annual
Report 2f MSU Advisory Group to the Republic of China and
AID, l9 3.

Esmay, Merle L., I'The Introduction Of Two-wheeled Tractors
in Japan and Taiwan,” (MimeOgraph), Dept.of Agricultural
Engineering, MSU, I967.

Farm Machinerinearbook, Shin-Norinsha Co. Ltd., Tokyo, Japan,
970.

 

Griliches, Z., ”Specification Bias in Estimates of Production
Function,” Journal of Farm Economics, Vol. 39, I957.

 

Gunckel Wesley W., ”Implementation and Over Mechanization in
Dezgloping Countries,” ASAE Annual Meeting, paper No. 68-508,
9 .

Heady, Earl 0., Glenn L. Johnson, and Lowell S. Hardin, Resource
Productivity, Returns to Scale, and Farm Size, Ames, Iowa, I956.

Heady, Earl O. and John L. Dillion, Agricultural Production
Functions, Ames, Iowa, I966.

 

Heady, Earl 0., £3, gl,, Roots of the Farm Problems, Ames,
Iowa, I965.

Johnston, J., Econometric Methods, MeCraw-Hill Book CO., Inc.
Kogakusha Company, Ltdi, Tokyo,fil963.

Kuwahara, Masanobu, (ed.) et. al., Economic Approaches to
Japanese Agriculture, Fuji—PUbTTshing CO., Ltd. Tokyo, Japan
969.

 

99

Lee, Shison C., llAn Economic Study of Land Use in Taichung
Hsien and City,” Chung Hsing University, Taiwan, I962.

Lee, T. H., ”Impact of Land Reform on the Farm Economy
Structure,” (MimeOgraph), JCRR, Taiwan, I968.

”Major crops Grown in Taichung Area,‘I Extension Bulletin,
Taichung District Agricultural Improvement Station, I967.

Mukumoto, lsutomu, I'Changes'and Mechanization in Agriculture
in Japan,” Farm Machinery Industrial Research CO. Japan, I969.

Production Yearbook, FAO,Rome, I967.

Soejono, Irlan, ”Resource Allocation on Small Farms in Bogor,
Indonesia,” Kentuckey State University, I964.

Stout, B. A., ”Equipment for Rice Production,” FAO, Rome, I966.

Taiwan Agricultural Statistics: l90l - I965, JCRR, Economic
Digest Series No. l8, Taiwan, I966.

Taiwan Statistical Data Book, Council for International Eco.
Coop. and Development, Executive Yuan, Rep. Of China, I969.

Taiwan Agricultual Yearbook, Provincial Department of Agr.
andForestry, Taiwan,_l967.,

Tsui, Yong-chi, ”A Summary Re ort on Economic Analysis of
Farm Mechanization in Taiwan,‘ JCRR, Taiwan, I962.

Wright, Karl T., ”Taiwan's Post War Agricultural DeveIOpment,”
Department of Agricultural Economics, MSU, I965.

Wu, T. C. ”On the Recent Diminution of Winter Crop Acreage
in Taiwan,” (MimeOgraph), JCRR, Taiwan, I969.

Yang, Martin M. C. ”Social Factors in the Joint Cultivation
of Rice,” National Taiwan University, Taiwan, I968.

 

 

APPENDICES

APPENDIX TABLE |

DATA USED FOR REGRESSION ANALYSIS FROM
THE SAMPLE FARMS IN THE RICE REGION OF
TAICHUNG AREA, TAIWAN

 

 

Gross Human Machine Bullock Working
Farm Croplang Labor Use Laborb Capital
Receipts (ha) (Dys) (Hrs)a (Dys) (NT $)
(NT $)

138,000 2.3 1,403 0.0 35.0 32,820
15,977 0.1 67 0.0 12.0 2,632
32,775 0.4 230 0.0 23.0 5,755
40,325 0.5 138 0.0 25.0 5,950
67,248 1.3 342 0.0 31.0 13,728
34,500 0.6 204 6.0 17.0 5,174
25,400 0.8 215 4.5 8.5 9,776
32.550 0.6 147 0.0 9.0 6,117
45,720 1.0 264 0.0 12.0 7,360
35,400 0.8 164 3.0 19.0 5,168
31.890 0.5 186 0.0 32.0 6,390

112,400 1.1 375 0.0 44.0 8,750

342,220 3.2 2,802 52.0 51.0 62.807
81,725 0.8 227 9.5 10.0 9,500
41,100 0.6 190 0.0 18.0 11.390

114, 920 1.0 800 8.5 24.5 24,750

117,160 2.5 1,115 20.0 13.0 43,984

164,420 1.7 545 19.2 19.2 15.253

108. 251 0.9 589 0.0 50.0 28,368

108,260 1.5 534 4.5 17.0 30,469
51,335 1.0 236 0.0 12.0 15,007
80,200 1.5 629 0.0 11.0 20.140

181,675 2.5 750 0.0 27.5 39,765
53,400 1.0 266 4.0 18.0 10,030
38,450 0.4 299 0.0 23.0 5,423

141,360 2.2 806 9.5 45.5 30,695

267,600 0.8 1 120 14.5 69.0 29,200

216.500 2.5 580 3.5 59.5 29.725
53,030 1.8 287 4.0 15.0 10.648

9,950 0.1 177 0.0 9.0 4,170

47,250 0.5 250 0.0 21.0 9,680

144,900 0.7 630 1.0 54.5 55,958
90,000 1.8 400 4.5 16.5 14.400

414,450 2.7 2,237 114.6 0.0 83.880

262,300 2.8 728 26.0 59.0 41,860
51,525 1.5 242 8.0 12.0 7,585

124,365 2.3 ,025 12.0 15.5 19,630

156,945 1.3 1,061 20.5 34.5 26,710
85,040 0.4 814 0.0 8.0 5,185
75,250 1.0 321 0.0 26.0 20,494

 

 

APPENDIX TABLE I (continued)

 

234,235,766 51.0 23,395 349.30 1,006.7 816,326
Ma 105,894.5 1.28 584.88 8.73 25.17 20,408.15

Mg 76,921.67 0.99 416.52 1.06 19.87 14,427.67

 

aZerO values were converted to 0.1 for cu1CU1ating the Mg'
bZero values were converted to 1.0 for culculating the Mg'

Ma = arithmetic mean, M9 = geometric mean.

, APPENDIX TABLE II 7‘
CALCULATION OF BETA COEFFICIENTS

 

 

General formula = B. = b--.§l
I I 5y

.34924

B] = (.2136) = .2068 = 17.99%
.36068
.35510

82 = (.4614) --—-——-= .4543 = 39.52%
.36068
.04338

B3 = (.0312) _——————'= .0902 = 7.85%
.36068
.33631

B# = (.1276) ——————— = .1189 = 10.34%
.36068
.36962

B5 = (.2523) = .2585 = 22.49%
.36068

>:Bi = 1.1287 = 87%

Unknown =_13%

Total = 100%

102

 

APPENDIX TABLE III

CORRELATION COEFFICIENTS BETWEEN VARIABLES

 

 

Y 1.0000

XI .7948 1.0000

x2 .8861 .7056 1.0000

x3 .5628 .5557 .5189 1.0000

x,+ .2734 .1561 .1532 -.0650 1.0000

x5 .8776 .7688 .8540 .5015 .2257 1.0000
Y x1 x2 x3 x4 x5

APPENDIX IV

CALCULATION OF MARGINAL VALUE PRODUCTIVITIES

MVPX]
MvPX2
MVPX3

MVPXA

 

 

 

 

Y’
General formula = MVPX. = b.":"
' ' x.
I
76,921
(.2136) = 16,591.60
0.99
76,921
( 4614) ——————_ = 85.22
416.52
76,921
(.0312) = 2,254 05
1.06
76,921
(.1276) = 494.01
19.87
76,921
(.2523) = 1.35
14,427.67

MVPX5

103

 

APPENDIX V

ANNUAL GROWTH RATE OF AGRICULTURAL AND INDUSTRIAL
PRODUCTION, TAIWAN

 

 

 

Year 33583311333I%1 P?§33§EI§I 1%)
1961 8.5 15.2
1962 2.1 11.2
1963 -0.5 9.2
1964 12.7 19.2
1965 7.4 18.9
1966 5.2 16.0
1967 5.9 16.8
1968 6.1 21.4

1961 - 68 Average 5.9 16.0

 

Source: Taiwan Statistical Data Book, Council for
h1ternationa1 Economic Cooperation and Development,Executive
‘Yuan, Taiwan, 1968.

104

APPENDIX TABLE VI

VI-A ESTIMATED MARGINAL AND GROSS FARM RECEIPTS WITH

THE LEVEL OF INCREASING CROPLAND BY NT $1,200

(.0954 ha.) WHILE HOLDING OTHER INPUTS CONSTANT

 

 

 

. , MVP

Input QuantIty Log X: bi bi(log Xi) MVP MFC

X] 1.08 .0335 .2136 .OO7I~ 15.495.06 1.23

X2 416.52 2.6196 .4614 1.2087 86.79 1.44

X3 1.06 .0253 .0312 .0008 2,306.22 , 57.65

X4 19.87 1.2982 .1276 .1657 503.16 4.19

X5 14,427.67 4.1592 .2523 1.0494 1.37 1.37

§.= 2.4624

Log Y = bi (IOg Xi) + g_ = 4,8941

Y = 789352-00

 

105

 

LEE,

APPENDIX TABLE VI (continued)

ESTIMATED MARGINAL AND GROSS FARM RECEIPTS WITH
THE LEVEL OF INCREASING HUMAN LABOR BY NT $1,200
(20 Dys) WHILE HOLDING OTHER INPUTS CONSTANT

 

 

X5

 

 

Input Quantity Log Xi bi bi(log Xi) MVP %¥%_
X] 0.99 -.0044 .2136 -.0009 16,956.38 1.34
X2 436.52 2.6400 .4614 1.2183 83.07 1.38
X3 1.06 .0253 .0312 .0008 2,313.21 57.82
X4 19.87 1.2982 .1276 .1657 504.68 4.20

14,427.67 4.1592 .2523 1.0494 1.37 1.37
§_= 2.4624
Log Y = 4.8954
Y = 78,589.98
VJ;£_ ESTIMATED MARGINAL AND GROSS FARM RECEIPTS WITH

THE LEVEL OF INCREASING MACHINE USE BY NT $1,200
(30 Hrs) WHILE HOLDING OTHER INPUTS CONSTANT

 

 

 

Input Quantity Log X. b. b.(log X-) MVP MVP.

' ' ' ' MFC
X] 0.99 -.0044 .2136 -.0009 18,418.83 1.46
X2 416.52 2.6196 .4614 1.2087 94.57 1.57
X3 30.06 .0253 .0312 .0461 88.61 2.21
X4 19.87 1.2982 .1276 .1657 548.21 4.57
X5 14,427.67 4.1592 .2523 1.0494 1.49 1.49
§_= 2.4624

Log Y = 4.9313

Y = 85,368.16

lO6

 

APPENDIX TABLE VI (contunued)

VI-D ESTIMATED MARGINAL AND GROSS FARM RECEIPTS WITH THE
LEVEL OF INCREASING BULLOCK LABOR BY NT $1,200
(10 Dys) WHILE HOLDING OTHER INPUTS CONSTANT

 

 

 

 

Input Quantity Log Xi bi bi(log Xi) MVP g¥%_
X1 0.99 -.0044 .2136 -.0009 17,479.07 1.38
X2 416.52 2.6196 .4614 1.2087 89.74 1.49
X3 30.06 .0253 .0312 .0008 2,384.52 59.61
X4 19.87 1.4753 .1276 .1882 346.14 2.88
X5 14,427.67 4.1592 .2523 1.0494 1.42 1.42

a.= 2.4624

Log Y = 4.9086
Y = 81,012.57

 

VI E ESTIMATED MARGINAL AND GROSS FARM RECEIPTS
WITH THE LEVEL OF INCREASING WORKING CAPITAL BY
NT $1,200 WHILE HOLDING OTHER INPUTS CONSTANT

 

 

 

Input Quantity Log Xi bi bi(log Xi) MVP %¥%
X, 0.99 -.0044 .2136 -.0009 16,390.71 1.31
X2 416.52 2.6196 .4614 1.2087 86.93 1.44
X3 1.06 .0253 .0312 .0008 2,309.71 32.74
X4 19.87 1.4653 .1276 .1657 503.92 4.19
X5 15,625.16 4.1938 .2523 1.0581 1.27 1.27
a_= 2.4624

Log Y = 4.8949
Y = 78,471.01

 

107

 

 

APPENDIX TABLE v11

THE COMPUTATION TO SOLVE FOR THE OPTIMUM INPUT
COMBINATION AT A BIVEN OUTLAY OF FUNDS

Costs at the Means of the Original Input Combination:

 

 

Input Geometric MFC Cost
Mean
X1 0.99 12,580.42 12,454.62
X2 416.52 60.00 24,991.20
X3 1.06 40.00 42.40
X4 19.87 120.00 2,384.40
XS 14,427.67 1.00 14,427.67

 

Total Costa = 54,345.28

 

*aCosts of the inputs included in the production
function.

The production function and cost function are:

Y = 290.59 Xl°2136 X .h614 X .0312 X#.1276 X502523 . o (I)

2 3
54,345.28 = 12,580.42 x] + 60 x2 + 40 x3 + 120 x,

+ X5 . . . . . . . . . . . . . . . (2)
Thus
3 _ .2136 .4614 .0312 .1276 .2523
L — 290.59 x1 x2 x3 x4 x5
+4(54,345.28 - 12,580.42 x] - 60 xz - 40 x3

- 120 X4 - X5)

)Nis a Lagrange Multiplier which is unknown value.

108

 

109

The necessary condition to maximize Y is all of the partial
derivatives with respect to each of the unknowns have to be
equated to zero. For computational convenience, we shall

use general notations such as
L = (antIIOg a)X]b' X2b2 X3b3 XL,“I X5b5 +)\(C - X] P]

' X2 P2 ' X3 P3 ' X“ Pu ' X5 P5)

Where X X . X5, and)\are unknowns. The partial

'l, 2’
derivatives are:

 

 

 

 

 

 

dL . b-1 b b
37} = (antllog a) b] X] 1 X2 2 . . X5 5 -)~P] = O
. -] b b b _
(antIlog g) b] X] X] 1 X2 2 . 'XS 5 -X.P] - 0
, b b b lit—.LX
(antIlog a) X] 1 X2 2 . X5 5 - b]
Y=L:L_x'_....................(3)
b'1
S f dL dL dL h
ame or e—-” -—-, . . . ——- t us we get
dX2 dX3 dXS,
b] 7 b2 7 b3 7 b, 7 b5
0.,, 1118329 53.33 5.139 :51;
p b
Therefore, X2 =-“l——Z'X], X3 = P1 b3 X]:
P b
2 1 P3 b]
P b P b
X4 = 1 2 X], X = 1 5 X],

P4 b1 7 P5 b1

 

lIO

Substituting X2, X3, X4, and X5 in the partial

derivative of Y with respect to,x:

 

 

dL _ _ _ _ _
'3: — C-PI X1 - P2 X2 P3 X3 P4 X4 P5 X5 _ 0: the“
P b P b P b P b
1 1 1 1
= PI X1 (2 b1)
b1

Then, X1 =_£_b_1_
P](2 bi)

Th f X 54,345.28 (.2136)
e e ore, = =
r I 12,580.42 (1.08) 0°85°

By the samernethod we get:
384.80

39.03

58.93

- 12,609.11

 

X X
W N
11 11

U1
1

Substituting the values of Xi to (1)

.2136 .4614 .0312 1276

Y = 290.5 (.87) (384.80) (39.03) (58.93).

(12,609)'2523

4.8897
77,487.24

Log Y
Y

Substituting the value of XI and Y to (3)

 

_ 77,487.24 (.2136)

3~ = 1 022
12,580.42 (0.85) '3

Fit to the condition of optimum profit

 

111

 

 

 

 

 

 

 

 

MVPX] MVPX2 MVPX3 MVPXu MVPX5
:1". = = = = /\
P1 P2 P3 P4 P5
Thus, MVP MVP MVP MVP MVP
x X X
X' = —-52- = 3 = “ - = —-——§= 1.3022
12,580.42 60 40 120 1

So, the MVP estimated are:

MVPX] 16,382.82 MVPx2 = 78.13 MVPx3 = 52.09

MVPXA = 156.27, and MVPx5 = 1.3

 

APPENDIX TABLE VIII

POPULATION PER HECTARE OF ARABLE LAND IN
DIFFERENT COUNTRIES

 

Population per Hectare

Countries of Arable Land

 

Japan 1
Taiwan 1
U. K.

West Germany

Philippine

Italy

India

France

U.S.A.

U. S. S. R.

Canada

mod-IT—MI-‘NOWUJU'I

Od-‘NUUUO-I-‘NN-F'O‘

 

Source: FAO Production Yearbook 1967

'71
I
III