Development of the analytical model for farm management to decrease red soil
runoff in Ishigaki Island
Ryoma HIRAOKA, Miya SAWADA, Seigo NASU，Yasushi MABUCHI
Department Infrastracture Systems Engineering, Kochi University of Technology

1. Introduction
1.1 Preventing red soil runoff mainly with companion cropping at sugarcane fields in Ishigaki Island
Ishigaki Island with about 223km 2 in area and a population of approximately 43,000 is located at
the west end of Japan. Its residents make a living predominantly from agriculture and tourism. On
Ishigaki Island, red soil runoff induced by sugarcane growing has become a serious problem, so it isnecessary to develop a solution to the problem as soon as possible. So far, they have adopted hardmeasures, such as gradient modification of firm lands, green belt, underdrain, grit chambers, andinfiltration ponds, as well as soft measures, for example covering the section of sugarcane withvegetation. These methods, however, have been difficult to be carried out because of their high costs,
and it is not easy to convince the farmers. Because of this, it is necessary to offer alternatives which
are practical for the farmers. Recently, as a soft measure, furrow planting in sugarcane fields has
attracted attention due to the additional revenue from sales of the vegetables such as pumpkincultivated at furrows of sugarcane fields. It is well-known that the ridge surface of sugarcane fields iseroded by rainwater, then red soil drains through furrows from sugarcane fields into roads. Therefore,
covering this ridge surface as completely with vegetation as possible is anticipated to protect it fromraindrop erosion leading to the red soil runoff mentioned above. On the other hand, carrying out thesesoft measures in an effective manner requires cooperation from farmers and must be feasible in termsof farm management. To meet these conditions, it is essential to investigate the revenue andexpenditure associated with companion cropping of vegetables and then to adopt an appropriate sizeof companion cropping so that a farmer can have a surplus.
1.2 Objectives
The ultimate purpose of this study is toestablishtheanalysis
model
for
an
environmental management at watershed whichcaneconomicallyassesslong-term
farmmanagement and also prevent red soil runoff. To
accomplish this purpose, first of all, the model
for a farmer’s technical capability andwillingness to cooperate is developed. Then, theanalytical model for farm management isprovided to figure out the real extent of theircooperation related to the analysis of farmmanagement by farmers. Finally, this model isused for estimating the scale number of farms
able to have a surplus from companion croppingof pumpkin from equal analysis.

Figure 1 shows the entire picture of theanalytical
model
for
an
environmental
management at watershed in Ishigaki Island. The
red soil runoff that has been a growing problem
on Ishigaki Island is supposed to be improved bydeveloping this model, which is appreciated withthe reduction rate of red soil runoff. The
reduction rate is calculated by two functions: theachievement of public projects and the

Public projectProtectionof Red SoilrunoffSubvention

Intercrop
pumpkin

TargetsugarcaneMarket of
pumpkinin Okinawa

Farmer’s
cooperation
Awareness
analysis

2. The analysis model for an environmental
management at watershed in Ishigaki Island

BusinessanalysisMarket ofTechnical
analysisMarkets inother prefecture

Fig.1 Overview of the analysis model for
management of a regio nal environment in
Ishigaki Island

2.1 Overview of the analysis model for anenvironmental management at watershed1

Scenario for intercropping

proportion of introducing companion cropping
into sugarcane fields. As for the achievement ofpublic projects, we do not discuss it here since itshould be addressed by the autonomous
community. Therefore, we will talk about the
proportion of introducing companion cropping
into sugarcane fields. Before a farmer introduces
the companion cropping into the sugarcane fields,
three points should be mainly considered:
whether it is appropriate for the farmmanagement (business analysis), whether theowner will introduce it into his or her fields(attitude survey), and whether the owner hasenough skills of companion cropping (technicalissue). These three points affects the possibility
for introduction of companion cropping whereby
the proportion of companion cropping intosugarcane fields is worked out. For the businessanalysis, the market situation of sugarcane andvegetable is surveyed. Since the income of a
farmer is affected by the market situation, thefarmer would make a decision about the
introduction of the companion cropping based on
it. Taking into account the factors mentioned
above, increasing the rate of the companion
cropping would require the stability of the farmmanagement and the raise of a market price ofre levant vegetables by stimulating the demand
for them with new businesses.

Farmer’s
awareness
Intercropping area

Total cost curve
Fixed Cost

Variable Cost

Depreciation
Repair cost
Maintenance cost
Various rents costetc.

Land improvement costMaterial cost
Seedling costFertilizer cost
etc.

Farmer’s
technique

Total revenue curve
Revenue

Markets ofVegetable

Income per farm
Crop production
×Market priceAnalysis of management

Fig. 2 Examination procedure of the analysis model foran environmental management at watershed
attitude, the technical capability, and the demand
curve. The feasibility of the companion cropping
at a sugarcane field is estimated in te rms of them anagement by studying the balance.

3 . The development of the analysis model fora
farmmanagement
introducing
thec omp anion cropping of pumpkin
Existing case
Sugarcane(planted in summer)
Cost pre unit area
： Ａ yen
Revenue pre unit area ： Ｂ yen
Companion cropping
Scenario②
Sugarcane(planted in summer)+ pumpkin： Ａ + Ａ’ yen
Cost pre unit area
Revenue pre unit area ： Ｂ + B’yen

2.2 The procedure to assess the analysis model
for an environmental management at watershed
Figure 2 shows the procedure to assess theanalysis model for an environmental management
at watershed. First of all, the vegetable to beinterplanted at furrows of sugarcane fields(currently sugarcane is planted just in summer
season) and its farming method are considered.
Then, the farmer’s attitude and technicalcapability for the companion cropping arequantified by a questionnaire survey. In addition,
the demand curve for the related vegetables isplotted based on the information about thew holesale trade in vegetable market. Considering
the area for the companion cropping, the balance
between total revenue and expenditure in
introducing the companion cropping is obtainedby combining the information from the f armer’sFig. 3 Scenario for examination(sugarcane, summer + companion
cropping of pumpkin)
The resources for management include ①
financial resources, ② human resources, ③physicalresources,etc.
The
effective
combination of these resources is evaluated as anenvironmental effect. The impact of thecompanion cropping of pumpkin on environment
conservation is yielded by the combination of theintroduction of the companion cropping of
pumpkin (financial resource), the labor required
for the companion cropping of pumpkin (humanresources), and effects of environmental
integrity resulting from prevention of red soil

2

⑤ Demand function③
Technical coefficientrunoff. Therefore, the companion cropping of
pumpkin to reduce red soil runoff would bereasonable from the s tandpoint of management.
In t his study, we address the case of introducing
the companion cropping of pumpkin into thefurrows of a sugarcane field (sugarcane iscultivated only in summer) (see Fig.3).
In this case, since planting pumpkin at the
furrows of a sugarcane field does not interferewith the cultivation of sugarcane, the income
from pumpkin (B’ yen) would be added simply tothe income from sugarcane (B yen). Because ofthis, in the case of the companion cropping ofsugarcane (summer planting) + pumpkin, them ana gement analysis for only the area of
pumpkin would be sufficient for making adecision on the introduction of the companion
cropping.

intercropping
houses

Total
area

③

Total
production

Equilibrium
point(STOP)

Market price

Initial market price (START)Technical coefficient①
Farmer’sscale

Growing area

Production

Benefit②
Benefit - Cost

Cost

Benefit – Cost > 0

Benefit – Cost < 0④
Execution rateof intercropping

Awarenesscoefficient

CancelFig. 4 Examination procedure of the analysis offarm management through companion cropping(pumpkin)
if the estimated inc ome is hig her than theestimated cost, the parameter of the farmer’s
attitude depending on the profit is calculated.
Then, the factual proportion of introducing
companion cropping is investigated, and thefactual production according to the size of farmand the factual market price corresponding to it
is recalculated. Repeating this procedure finallyleads to the condition that the estimated market
price gives close agreement with the factual one.
This condition would provide the predictedvalues reason able for farmer management: thepredicted area for companion cropping, thepredicted number of farmers, and the predicted
production.

3.1 The procedure to assess the analysis model
for a farm management introducing thecompanion cropping of pumpkin
Figure 4 shows the procedure to assess theanalysis model for a farm management
introducing the companion cropping of pumpkin.
To begin with, the number of farmers according
to the size of farm is obtained from “Statistic of
Ishigaki”, a statistical data about Ishigaki city,
to set the parameter of the farmer’s attitude
according to the size of farm and estimate thearea for companion cropping. The price of
pumpkin in the Tokyo market is determined, thenthe proportion of introducing companion
cropping according to the size of farm is
calculated based on the price. The area forcompanion cropping and the technical coefficientare established. They are used for estimation of
all pumpkin production, and then the market
value corresponding to the pumpkin production
is presumed. As the next step, the production
cost and the revenue per farm according to thesize of farm are estimated from the cost function(fixed and variable costs), and the technicalcoefficient and the estimated market price,
respectively. In each size of farm, the estimatedincome is compared with the estimated cost;companion cropping is not introduced if theestimated income is less than the estimated cost;

3.2 The estimation of the cost function, theparameter of a farmer’s attitude, and thetechnical coefficient
In order to estimate the cost function, theparameter of a farmer’s attitude, and thetechnical
coefficient,interviews
andaquestionnaire survey were really conducted on
Mr. Masaharu Iridakanishi, Ishigakijima farmerof farming corporation with limited liability;
pumpkin gr owers in Ishigaki island; andsu garcane growers in Ishigaki island. T hese
values were calculated based on the resu lts ofth e surveys.
(1) The calculation of the cost function
The cost function represents the expenditure
to introduce the companion cropping of3

y=6254.5x+50100 ・・・Eq. (2)y: total cost per area under crops (yen), x: area
under cro ps (a)pumpkin. In this study, the items such as theworking hours, equipment and so on wereasked according to each step to grow pumpkin.
The fixed cost includes land improvement,water, amortization of farm equipment,
maintenance and fuel for a car, repair costs,
and public dues. On the other hand, thevariable cost consists of seedling, fertilizer,
agrichemical, spreading material, workforce,and shipment box. These costs were estimatedfrom each category. The interview about thecompanion cropping of pumpkin was given to
five farmers. The items us ed in the interview
are as follows:a) Work items for cultivation from land
improvement to harvestb) Working hours for each work itemc) Farm equipment used for c ultivationd) The cost for land improvement (including
the cost for water facility to improve land)e) The cost for amortizationf) The cost for repairment and maintenanceg) Rental h) The cost for energy and poweri ) The price of seedling per 10aj) The price of fertilizer per 10ak) The price of agrichemical per 10a(2) The estimation of the parameter of a farmer’s
attitude
The items used in the interviews to estimate
the parameter of a farmer’s attitude ar e as
fol lows. The equation to represent the relation
bet ween the proportion of the introducti on andthe profit was established from the results:a) Do you introduce the companion croppingof pumpkin into your sugarcane field?
b) How much profit motivates you tothecompanion
croppingofintr oduce
pum pkin?
c) Does the f act that the companion croppingof pumpkin can contribute to protecting
coral reef from red soil runoff change yourattitude?

Cost（yen）

y = 6254.5x + 34167 Pumpkin（fixed/variable costs)
R2 = 0.9678
70000061125060000059416050000040000030000020000059888

100000Figure 5 shows the fixed and variable costs,
which were obtained from the interviews, basedon the area under crops of pumpkin. To take into
account a certain difference between the farmers,
15,933yen was obtained as the average of their
fixed cost (the cost for amortization, the cost fo r
re pairment and maintenance, and rental). As forthe variable cost, the data was linearly
approximated, and equation 1 was established.

166054
15933

Fixed costs
Variable costsLine(variable costs)

0
0

20

40

60
80
100
Planted acreage（ａ）

120

Fig. 5 The fixed and variable cost based on
the area under crops of pumpkin.
Total costy = 6254.5x + 50100
2
R = 0.9678

1200000

Cost （yen）

1000000

y =6254.5x+34167 ・・・Eq.(1)y: Variable cost per area under crops (yen), x:
Area under crops (a)8000006000004000002000000
0Figure 6 shows total cost (the fixed +variable costs) per area under crops of
pumpkin. T he cost curve of the companion
cropping of pumpkin was expressed with linear
relation to the area under crops as shown inequation 2.

20

40

60
80
100
Growing area（ａ）

120

140

160

Fig. 6 Total cost per area under crops of pumpkin

Figure 7 shows the results from the attitu desurvey. The largest population, 44% of thepeople answered that they would introduce the4Figu re 9 shows the results of the attitude
survey. In the case of the prof it of more than 1
milli on and less than 2 million yen, theproportion of introducing the companio nc r opping is 44%; more than 2 million and lessthan 3 million yen, 56%; more than 3 million andless than 4 million yen, 59%; more than 4
million and less than 5 million yen, 63%; andmore than 5 million yen, 69%. The data wasapproximated with multinominal, and theequation 3 was established (in this study, tertiary
expression was used becau se of low co llection
r a te of questionnaire).

How much earn income is necessary for catch cropping.
14

16
14
12
10
Persons 8
6
4
2
0

10
4

b le
via
un

en

0

0～
50

50

0
0～

0～
30

40

0～
20

2

1

40

0

0～
10

30

20

0

1

million yen

Fig.7 The results from the attitude survey
com panion cropping with the profit of from 1 to
2 million yen. On the other hand, ten peopleanswered that they would never introduce it
regardless of the profit because they think “itwould make their work harder” or “it woul d not
be practical because of the difference ofagrichemical between pumpkin and sugarcan e.”
Figure 8 shows the distribution of househo ld
membership by age. According to figure 8, ab out
59% of the total of 3346 people were 50 years ofag e or older. Because of this, some gave thereason “they do not have any successor” or “theydo not have enough workforce” to introdu ce
co mpanion cropping.

y＝2E - 8x 3 - 2E - 0.5x 2 + 0.0057x + 0.0069
Eq.(3)
y: population (ratio), x: pro fit(3) The estimation of the technical coefficient
The production of pumpkin depends largely
on farming methods adopted, farming equipm ent
owned , and so forth. According to the result of
the te chnology survey asking five farmers theirharv est of pumpkin per 10a, two farmers
an swered 0.75t, one said 0.8t, one provided 1t,
and one gave 1.5t (but it is not exact because
1.5 t is just an assumption).
In this st udy, it is assumed that the harvest
per unit area ranges 0.6t/10a to 1.4t/10a.
Th erefore, the harvest per unit area is presumed
as shown in table 1.

The number of household membership at different age
542
600
500
395 383391
358
400
291 298262
persons 300
204
180
200
129 135 121 157
100
0

～
15 14
～
20 1 9～25 2 4～30 2 9～35 3 4～40 3 9～45 4 4～50 4 9～55 5 4～60 5 9～65 6 4～70 6 9～74
75～

Table.1 The estimation of the technicalcoefficient per unit area
Amount of productper area（ｔon/10 ａre）

The number of
person(rate)

0.6

0.1

0.8

0.2

1.0

0.4

Attitude analysis

1.2

0.2

Polynomial(Attitude analysis)

1.4

0.1

age

Fig. 8 Number of household members by age

Number of people(rate)

Attitude analysis・ ・ ・

y = 2E-08x 3 - 2E-05x 2 +0.0057x + 0.0069
R 2 = 0.996

0.8
0.6
0.4
0.2
0
0

200

400

600

3.3 The estimation of revenue function
In order to get total revenue curve, themarket situation of pumpkin in Okinawa
prefecture was investigated, and the relation

ProfitFig. 9 Results of attitude analysis

5between the production of pumpkin and themarket price was analyzed.
70000000
Total revenue（yen）

Price（yen/ｔ）

80000000
400000350000300000250000200000150000100000
50000
0
0

200

400

451

600

800

60000000
50000000
30000000
20000000
10000000
0

1000

0

Quantity of pumpkin (ton)Fig. 10 Relation between market demand andy = 419776e −0.0022 x

2000 4000 6000 8000 10000 12000
Planted acreage（a)Fig.11 Total revenue curve per area for growing

supply of pumpkin p roduced in Okinawa

In 2004, Okinawa produced pumpkins of
2100t. Among them, pumpkins of 275t (13%)
were consumed in Okinawa, and 1522t (72%)
were exported to the other prefectures, meaningthat the amount of exported pumpkins was
relatively large r. On the other hand, in 2004,
Okinawa centr al wholesale market imported
pum pkins of 1192t including 397t (33%) fromother areas in Japan and 520t (50%) fromoverseas, meaning that the amount of pumpkins
got from overseas has been larger.
According to the relation between the amountof received pumpkins produced in Okinawa andthe price per unit amount, as the amount of
imp orted pumpkins increases, the price per unit
amount decreases, and the relation is not linear(see fig. 10). The data was approximatedexponentially, and the equation 1 wasestablished.

0.6t
1.0t
1.4t

40000000

pumpkin base d o n th e t e ch n ic a l c oe f fi c ient

3.4 The number of farmers according to the areafor farm management
Table 2 shows the number of farmers in
Ishigaki city according to the area for farmmanagement (2004). The majority are 0.5ha ～1.0ha and 2.0ha ～ 3.0ha which are 232 and 224
farmers, respectively. The number of farmers
possessing less than 1ha is 329 farmers, which isabout 26% of the total, and the number of big
farmers with more than 10ha is 34 farmers, 3%.
Table 2City of Ishigaki

Number of farmers according to the areafor farm management
Area size
0.3 0.5 1.0 1.5 2.0 3.0 5.0 10. 20. 30. 50.0
～
100.0
Total
～ ～ ～ ～ ～ ～ ～ 0～ 0～ 0～ ～0.3
ha～
0.5 1.0 1.5 2.0 3.0 5.0 10. 20. 30. 50. 100.000001,284 17 80 232 175 143 224 213 164 27
60
30

4. The analysis for a farm management
introducing the companion cropping of
pumpkin・・・ (1)

As mentioned above, t he cost function, thetec hnical coefficient, the parameter of a farmer’s
attitude, and the market function were estimated.
Then, the area for comp anion cropping of
pumpkin and the number of farmers introducing
it, which are reasonable for farm management,
were calculated.
Table 3 shows the area for companion
cropping of pumpkin and the number of farmers
introducing it, which are reasonable for farmmanagement, according to the size of farm.
As the table shows, the number of farmers
introducing companion cropping is 155 farmers,
the area for companion cropping is 236.80ha,

where y: the price per unit amount of imported
pumpkin (yen/kg) and x: the amount of imported
pu mpkin (t). In figure 9, the agreement between
demand and supply offers the production of
pumpkins of 433t. Figure 9 also indicates thatthe production more than this agreement leads toreduction of social redundancy.
The demand curve of pumpkin produced in
Okinawa was used to get a total revenue curve
according to the area for growing pumpkin .
F igure 11 shows the total revenue curve per areafor growing pumpkin based on the technicalcoefficient.

6

Table 3 The area for companion cropping of pumpkin and the number of farmers introducing it,
which are reasonable for farm management
Cultivated acreage per farm(a)
57
101
169

3

10

17

30

39

349

573

911

1585

2249

Number of farmers introducing
companion cropping (farm)

0

0

6

10

11

28

40

48

9

1

0

2

0

Total area for companion cropping (ha)Pumpkin production (t)Profit (10 thousand yen)

0
0
0

0
0
0

1.359
11.46965.0983.238
31.485209.0505.310
48.014337.457

16.929174.291
1283.000

38.704388.6142917.880

85.469866.9596673.123

35.766317.098
2436.826

15.29756.223420.082033.734
0 337.338
0 2540.534

000 To estimate the cost function of pumpkin
more precisely
To define the relation between the sizeof farm and the variable cost
To investigate the laborsaving induced
by farm expansion
 To assess the market situation of
pumpkin more accurately
To research the sales of pumpkin toboth the inside and the outside of thisprefecture
To improve the precision of thedemand curve

and the total production of pumpkin is 2231.49t.
In this case, the market price in Tokyo wholesalemarket is 138 yen/kg.
It is significant to investigate whether the
farmers of Ishigaki Island in real life will act as
unsteadily as they do in our assumption. Even if
they act steadily, t he proportion of introducing
companion cropping based on the total area ofsugarcane fields is 236.8ha÷667.6ha=35％. Since
this proportion is too low, it is im portant to findsome kind of solution such as official support
and auxiliary business.
Through the fieldwork in this study , werecognized several problems on introduction ofcompanion cropp ing of pumpkin; they need toconvert to organic cultivation because of thedifference of agrichemical bet ween sugarcane
and pumpkin; there are not so many farmers
having the knowled ge about the companion
cropping of pumpkin; and so on. Therefore, they
may not introduce it even thou gh they make aprofit with it. As for local environmental
management, it is significant to consider the
local
managem ent
systemwherebythemanagement model of this study is accepted
actually.

5. Future topic
The analysis model for an environmental
management at watershed discussed in this study
has not been practical because of limited
information and many assumptions. Therefore, itis necessary to consider the following items andtry really to apply them to actual places. This
will
help
our
analysis
model
for
an
environmental management at watershed gain
higher credibility.
 To develop the best method to prevent redsoil runoff in another case taking into
account
management
 To quantify a farmer’s level of skill andattitude for companion cropping byconducting questionnaire survey
7