Journal of Applied Input-Output Analysis, Vol. 4, 1997

Input-Output Marketing Analysis Table:

Consumer Behavior Analysis Based on Closed Systems1

By

Yoshio Yuge*

Abstract
The current analysis model calculates the transition probability matrix based on the

results of market research of consumer behavior. This analysis is introduced to solve theproblem of estimating consumer behavior and to forecast the consumer behavior among three
trade areas. Furthermore, consideration based on the results of market research is given tothis theoretical model. The significant features of the analysis model are the transition
probability matrix among trade areas based on a sample of inflow-outflow investigation for
consumer behavior, and the attraction index of trade area introduced from the transition
probability matrix.

1. Introduction
We propose the analysis theory based on market research to forecast consumer hehavior
among regions. Consumer behavior is dependent on the attraction of retail supply aswell as the real distance between the physically separated demand and supply. It has
been argued by several authors that consumer behavior can be related to physicalposition between consumer demand and retail supply (Reily, 1929; Converse. 1949;
Kotlar, 1971). Also, a network model for consumer behavior has been studied from ananalogy of classical transport in resistor networks (White and Ellis, 1971). Muchsignificant study has been conducted in this field. Among many other advances, Huff
has conducted many practical experiments on consumer behavior and developed adetailed analysis theory (Huff, 1962).

Manuscript received February 14, 1996.

* Sakushin Gakuin University, Japan.
1 This research is part of a paper published in Sakushin Business Review (in Japanese, March 1994).
The author wishes to express his gratitude to Prof U. Hori, who encouraged him to study the social
sciences. He also is greatly indebted to Honorary Profs. K. Yanaihara, A. Tokiwa, and I. Ozaki of Keio
University for their many discussions and helpful suggestions, as well as Prof. K. Oyachi of Aoyama
Gakuin University and Profs. H. Sakuramoto and M. Shimizu of Keio University for their helpful
conversations and interest. Finally, he is very happy to express his gratitude to Honorary Prof. W.
Leontief, who give him his helpful comments and kind suggestions.

2

Journal of Applied Input-Output Analysis, Vol. 4, 1997

There is, however, no analysis theory for consumer behavior based on market

research. In this paper, we propose a probability analysis model that uses information
obtained from market research. The conventional studies that have used only physicalfactors could not realistically forecast dizzily changing consumer behavior. We must

carefully inspect and analyze the structure of consumer behavior, and must reflect the
information obtained through market research in the consumer behavior model. This

analysis does not depict the relationship between consumers and retail stores, but it does
analyze the relationship between a region with stores and its competing regions.
In Section 2 we describe the method of constructing the fundamental model whichanalyzes consumer behavior of trade areas in a city. Next we present in theory theforecast of consumer behavior when the number of stores within a trade area haschanged. In Section 3, we propose a numerical example to analyze consumer behavior

among three trade areas. Furthermore, we forecast consumer behavior among three
trade areas when the number of stores has increased. Next we comment on consumer

behavior among three trade areas when a large-scale retail store has made inroads into

the neighborhood adjacent to the trade areas. In Section 4, we show that the analysis
theory can predict consumer behavior among four regions in the Utsunomiya industrial
zone.

This study is suggested from the fundamental concept of the Input-Output Table(Leontief, 1986; Miller and Blair, 1985) for consumer behavior between regions,

including stores. We feel that the present analysis is very promising for the study of
consumer behavior.

2. Input-Output Marketing Analysis Table
2.1. Construction of Fundamental Model
In order to construct the model, the following assumptions must be introduced as
elements of the consumer input-output analysis table.
(1) There is a one-to-one corresponding relationship between each consumer andeach trade area. That is, one consumer belongs to each trade area.

(2) The number of inflow and outflow consumers from a trade area is proportional
to the number of consumers in that trade area.
(3) The sum total of each trade area's number of individual inflow and outflow
consumers is equal to the number of consumers occurring in those trade areas at

the same time. In other words, there are no interactions between the consumer
behavior of each trade area.

When the city's economic consumption sphere is constructed of trade areas tx . . .
tn, we consider the inflow and outflow of consumers among these trade areas. If there isa number x v of consumers shopping from trade area tt to trade area tj, from thelinearity assumption, the proportion coefficient av is obtained:Input-Output Marketing Analysis Table

3

where C, indicates consumers belonging to trade area t,. The proportion coefficienta,j shows the rate of consumers shopping from trade area /, to trade area tj ■ For thiskind of transition probability av, an arrangement of all trade areas tj 's transition

coefficient for all the trade area t, is called a transition probability matrix:

a

a.

2]

;

transition probability matrix

(2)

nn J

Each column of this transition matrix A indicates the probability of each trade area's
inflow of consumers. The numerical value indicates the degree of ability to attract
consumers from trade area tj to trade area t,. The balance equation of consumers is
expressed as,\22\

X2n = ^ 2

(3)

or, when using the coefficient of transition probability,"ll ' ^1 +"12 ' ^-1 ""a21 -C2•" a\n ' ^1 ~ ^1

C2 =C2is given. The number of customers Y, shopping in trade area t, is,

(4)

4

Journal of Applied Input-Output Analysis, Vol. 4, 1997

xl2+x22+-(5)

When this is expressed via the transition probability coefficient, it becomes,

an-Cx+a2X
n-Cx+a2X -C2(6)-CH =Yn

When this equation (6) is expressed by using the transition matrix A and the consumer
matrix C, the following equation (7) is attained:

fv \

Y =

a

='A-C=cc(7)

where / indicates the transposed matrix. By using the transition matrix in this way, we
can forecast the number of consumers shopping from trade area t, to trade area t, ■Also, the consumer behavior among trade areas can be calculated by the following
equation:Input-Output Marketing Analysis Table

5

Table 1: Input-Output Marketing Analysis Table
Outflow

Trade areas

Inflow

Trade areas

ti

tn

X\\

X\2

X\n

h

X2\

Xll

Xln

tn

Xn\

Xnl

Xnn

xu

Xp

xu

X2\

X12

xn

\Xn\

Xn2

'C,

0

0

C,

x =

Cx

Cn

Yn

Number of inflow consumers/

Number of outflow consumers

t\

v°

0^

= Cf-A

»11

a\2

Q2\

«22

CJ Ki a»a2] • C2

a22 • C2«nl * Cnan2 ■ Cn

a

nn J

(8)

Matrix X, which contains the element x,, represents the input-output marketing
analysis table as shown in Table 1. It is possible to forecast consumer behavior among
trade areas or the number of customers accumulated within each trade area.
Furthermore, when the number of consumers in each trade area changes, we canforecast consumer behavior among trade areas and the number of customers shoppingin each trade area.

2.2. Forecast of Consumer Behavior among Trade Areas
When the number of retail stores within a trade area has changed, the ability to attract

consumers into its trade area and the number of consumers shopping in its trade area
increase. In the case of information related to the transition matrix being available, if

the attraction index of a trade area, that is, the ability to attract consumers to a trade6

Journal of Applied Input-Output Analysis, Vol. 4, 1997

area, is tentatively examined, the transition probability matrix can be created using
direct and indirect information.

Presently, if the attraction index of a trade area is defined as the sum total of thetransition probability of consumers shopping from trade areas tj to trade area t,, theattraction index F(fj) is shown as follows:

A

='A-

(9)

when
7=1

If the attraction index F is changed to i7', it becomes,

FV'j) -

n ;

when

(10)

The new transition matrix A can be found upon using the following recurrent equation
with modification diagonal matrices R and S := 0,1,2, •A(o), 7?(0), S(0):initial value

when

fx
i=\

/:
1=1

(11)

Input-Output Marketing Analysis Table

The most recently calculated transition matrix A

7and the consumer matrix C

forecast the number of customers shopping in each trade area by using the following
equation:aY' =='A'-C=
, Y'

\n
r

a

a

In

c.

(12)

ni

where / indicates the transposed matrix. The most recently calculated new transition
matrix A' finds the input-output marketing analysis table as shown in Table 2, which
forecasts consumer behavior by the following equation:

V12

X2\

X2

= Cf-A'

v«2

C,

0

0

C,

o

a'u-Cxa[2-CxKa'ml.Cma[2.Cn

...

*

"u

an

?2,

<2

a

a'

a'

fll-C.

\

\n
t

In

(13)

8

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Table 2: Input-Output Marketing Analysis Table

Outflow

Trade areas

Inflow

Trade areas

t\

h

t\

x'u

X'n

h

x'n

x'n

tn

X'n\

X'nl

Tx

Y'l

Number of inflow consumers

■

'

■

■

Cl
Cl

v'

Cn

Y'n

trade area h

^

c,

X'\n
X'ln

X nn

trade area t\^

Number of outflow consumers

tn

^

\

60units

trade area

\

/

C,

\

V

45units/

5 5 units

Figure 1: Structure of Three Trade Areas

3. Numerical Example for Three Trade Areas
3.1. Consumer Behavior among Three Trade Areas
We explain how consumer behavior is forecasted by using the numerical example of thesimplest case of three trade areas. There are three trade areas, that is, trade areas tx,

t2, and ^3, as shown in Figure 1. The number of consumers belonging to these tradeareas is 60 units, 55 units, and 45 units, respectively. However, one unit can have up to
10,000 people or number of households.

According to the market survey for a definite period of time, the number ofInput-Output Marketing Analysis Table

9

Table 3: Consumer Inflow-Outflow Table in Market Survey
Outflowt\t\hTrade areas

Number of outflow consumers

Trade areas

Inflow

h

h

tn

ew

en

£13

Ex

(105)

(45)

(30)

(180)

ei\

en

£23

Ei

(45)

(75)

(45)

(165)

£31

eyi

£33

£3

(45)

(30)

(60)

(135)

consumers shopping from trade area t\ to trade area t\ was 105. The numbers ofconsumers shopping from trade area /i to trade area t2 and from trade area t\ totrade area ti were 45 and 30, respectively. At the same time, we can also find thenumber of consumers shopping from trade area t2 and trade area /3, as shown in

Table 3. The coefficient of transition probability ay

is each element 6fj of theconsumer inflow-outflow table shown in Table 3 divided by the number of outflow
consumers E} as follows:

a

a21

n

a22

E-,

E->

« 32

0.25000.1667^0.27270.45450.27270.33330.22220.4444

E-,
'33

1*3

A0.5833v(14)

From the transition matrix A and the consumer matrix C, we can find the number ofcustomers shopping in trade areas t,, t2 and /3, as found in the following equation:t /='A-C=

«11

«12

«2.

°22

(cx\
50

(15)

V45y

where t indicates the transposed matrix. For that reason, it is forecasted that the

number of Qustomers shopping in trade area t\ is 65 units, in trade area t2 is 50 units

10

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Table 4: Consumer Input-Output Marketing Analysis Tablet\

Trade areas

ti

h

t\

h

h

X\\

X\l

X13

d

(10)

(60)

(35)

(15)

X21

Xll

X23

Ci

(15)

(25)

(15)

(55)

X33

C3

(10)

(20)

(45)

X31

(15)
Number of inflow consumers

and in trade area

Number of outflow consumers

Trade areas

Outflow
Inflow

Y\

Yi

73

(65)

(50)

(45)

ti is 45 units. The following equation (16) can be used toforecast these consumer behaviors among the three trade areas.

X

xu

X,3

x21

x22

*23

,*31

x32

*33 J

(c

0

0N

0

C2

0

,o

0

= Cr-A

•

^11

«12

«13"

a21

a22

«23

^31

«32

«33,

=

15

15

10'

25

15

Il5 10 20,(16)

Matrix X, which has the elements xij9 arrives to the input-output marketing analysis
table as shown in Table 4. In this way the transition matrix, which introduces the ability

to attract consumers to a trade area, can be used to calculate these consumer behaviors
between trade areas.

3.2. Consumer Behavior with Re-equipment of Shopping Center
When the shopping center within trade area ti has re-equipped, or the number of storeswithin trade area t3 has changed, we are able to forecast the changes in consumer
behavior among the three trade areas. The attraction matrix of ability to attract
consumers is based on the definition in equation (9):

I1]

UJ

='A- 1'1.1894N=

0.9268^0.8838(17)

Input-Output Marketing Analysis Table

11

trade area

trade area t\

10

Figure 2: Consumer Input-Output Diagram

where Fifi indicates a relative attraction index of each trade area. When the shopping
center within trade area /3 has been re-equipped, and the attraction index of trade area

ti is changed from 0.8838 to 1.2, a new attraction index F'if) is calculated as follows:'l.0117N

F'ifj):(18)

0.7883v 1-2 ,The new transition matrix A' can be sought by using the following recurrent equation:'"(*)>-d(h+2) ~ R(h+\) ' -^(A+l)(" = *-*,l,2,'")(19)

In this way, the transition matrix A' can be obtained by modification matrices R and

S.

A'.

/0.5243

0.22710.2486N

0.23020.38780.3820v0.2573

0.17340.5694y(20)

12

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Table 5: Consumer Input-Output Marketing Analysis Table
Outflow
Inflowt\hTrade areasft

Number of inflow consumers

Number of outflow consumers

Trade areas

t\

h

h

x'u

X\l

x'n

G

(31)

(14)

(15)

(60)

X'll

xhi

X'23

(13)

(21)

(21)

X'l\

X'32

X'33

C3

(ID

(8)

(26)

(45)

T\

Y'i

y3

(55)

(43)

(52)

(55)

trade area

trade area t\

Figure 3: Consumer Input-Output Diagram

In accordance with the most recently calculated transition matrix A, the input-output
marketing analysis table, which forecasts consumer behavior, can be found as follows:

*\2

■*21

x'

C

31

14

15'

4 = C'.A' = 13
11
4

21

21

8

26

(21)

Input-Output Marketing Analysis Table

13

trade area t\

trade area t\

trade area U

trade area U
trade area

trade area t2
trade area t2

Figure 4: Configuration of Present and Future Trade Areas

Tables 4 and 5 and Figures 2 and 3 show that because the attraction index of tradearea t3 had increased, the consumers in trade area t3 had not shopped in trade areast\ and t2 but only within trade area t3. On the other hand, the number of consumers
from outside regions shopping in trade area t3 increased. The decrease of consumers intrade areas U and t2 is an extremely interesting phenomenon. We can forecast
consumer behavior among trade areas by using this technique.

3.3. Influence of Inroads of a Large-scale Retail StoreIn this section, we presuppose that a large-scale retail store is scheduled to makeinroads into the neighborhood adjacent to trade areas t\ and t3. Because thecharacteristics and primary marketing factors of a large-scale retail store are equivalent
to those of a trade area, the large-scale retail store forms a new trade area. Even if theinformation relating to the inroads of a retail store is scarce, we can obtain the transition
matrix which forecasts the changes in consumer behavior among three trade areas and afourth trade area from existing consumer behavior within the three trade areas.

Suppose that a large-scale retail store has made inroads into the neighborhood

adjacent to trade areas U and t3 and now forms new trade area t4 as shown in Figure
4. For the sake of this exercise, the number of consumers belonging to trade area t4

consist of 20 units which have transferred from trade area U and 15 units which havetransferred from trade area t3. There is a great variety in the technique of how
consumers move, but they are not discussed in this paper.

In the previous section, the transition matrix A of the present three trade areas has

14

Journal of Applied Input-Output Analysis, Vol. 4, 1997

been already found. We estimate the initial value of the transition matrix of the four

trade areas in accordance with the foundation of the new trade area t4. Furthermore,

the attraction index of the previous three trade t\9 t2 and t3 is as per below. Namely,^'/A/2 ='A-(22)

0.92680.8838Here, because the only information related to the trade area t4 is the relative
attraction index, the initial transition probability of trade area t4 is the average of thatof trade areas ti9 t2 and /3. However, if the relative information is available, theweighting average is preferred.

'13

7 23

4 24

*32

733

4 34

f42

743

*44 J

*22

a

31

^33

*32

+ a 314 32'220.58330.25000.16670.2083^0.27270.45450.27270.27270.33330.22220.44440.27780.30300.23610.21970.4941(23)

Supposing the large-scale retail store makes inroads and trade area ti is formed, andthe attraction index /„' of its trade area is 1.2, the attraction index F'ifj) is calculated
as follows:Input-Output Marketing Analysis Table

15'1.1101^
0.8650fi

when

0.8249

(24)

=4
7=1

, 1-2 ,The new transition matrix A' is obtained from the initial transition matrix Ao, the

new attraction index ^'(/'), and the recurrent equation (11).

A' =0.45540.19750.13310.21400.19900.33570.20350.26190.24180.16320.32980.2652v0.21390.16870.15860.4589y(25)

Newly calculated transition matrix A' introduces the consumer input-output marketing
analysis table and examines the influence of the existing three trade areas in which thelarge-scale retail store has made inroads.

*12

V13

V23

X'.

= Cf.A' =

18

8

5

9'

11

19

11

14

32

V33

34

7

5

10

8

V42

V43

KAA J

7

6

6

16

(26)

The consumer input-output marketing analysis table shown in Table 6 can be used

to forecast changes of consumer behavior occurring within each trade area. When alarge-scale retail store has made inroads into the neighborhood adjacent to trade areast\ and /3, the consumer behavior among each trade area can be forecasted by using
this table. Next we will show how diagrams use the consumer behavior before and after

inroads into the trade area. Consumer behavior before and after inroads of a large-scaleretail store are shown in the following diagram. Although trade area t2 is positioned

relatively far from trade area t*, many consumers are still shopping in trade area t4.

Similarly, consumers shopping from trade areas U and t3 to trade area t2 prior to
inroads of the large-scale retail store have decreased significantly, and consumers

shopping in trade area t* have increased. We cannot conclude that the influence of
inroads of the large-scale retail store is weak just because it is far away. This influence

16

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Table 6: Consumer Input-Output Marketing Analysis Table

t\

h

ft

U

x'n

Inflowt\

Trade areas

Number of outflow consumers

Trade areas

Outflow

tl

h

n

x'n

X'l3

X'l4

d

(18)

(8)

(5)

(9)

(40)

X'll

x'n

X'23

X'24

C2

(11)

(19)

(ID

(14)

(55)

X'31

X'il

X'33

X'34

a

(7)

(5)

(10)

(8)

(30)

X'aI

x'n

X'43

X'44

C4

(7)

(6)

(6)

(16)

(35)

Y\

Ti

Ti

Y'*

(43)

(38)

(26)

(38)

Number of inflow consumers

18 / c,3 5units

trade area /i V 40units/ trade area

trade area

trade area

V 55units

/*v
\
19

*s

J

v_V,0

Figure 5: Consumer Inflow-Outflow Diagramof the large-scale retail store first spreads to the most adjacent trade area and thenspreads to the next most adjacent trade area. In this way, we can understand the process
by which this influence extends to one trade area after another.
When the large-scale retail store makes inroads into the neighborhood adjacent totrade areas U and ti, in the same way as other trade areas new trade area tA is
formed according to retail characteristics and marketing factors of that large-scale retailInput-Output Marketing Analysis Table

d\: Utsunomiya

dr. Kaminokawa

d2: Kanuma

dg: Ninomiya

dy. Awanodg: Kamikawachid^\ Mibu

d\Q. Kawachi

d5: Mooka

du'-^ziie

d$. Ishibashi

d\2\ Takanezawa

17dn\ Haga

Figure 6: Utsunomiya Industrial Zone

Table 7: Consumer Inflow-Outflow Table in Market Survey
Outflow
Inflow

Utsunomiya industrial zone

t\

ti

h

Total number of ballots

Number of households

U

Utsunomiyat\53,06653,066

5,522

Kanumah

4,601

13,051

83

17,735

1,944

Mooka

h

2,397

151

13,88916,4371,760

14,570

1,524

Kawachi

7,559

753

6,25

store. From results of this analysis we understand that the ability to attract consumers
from other trade areas is extremely large. In this case of large-scale retail store inroads,

this technique can be extended to quantitatively forecast the influence of changes in
consumer behavior within each trade area.

4. Empirical Test for Input-Output Marketing Analysis
When the shopping center has re-equipped, or the number of stores has changed, we
demonstrate how consumer behavior within the Utsunomiya industrial zone in 1991 isforecasted from consumer behavior in 1988. The 13 administrative districts in the
Utsunomiya industrial zone are shown in Figure 6.
In Table 7 we present the inflow and outflow table based on the market survey for1988 that has been aggregated into four regions (Tochigi prefectural office, 1988a).

18

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Their regions are Utsunomiya (Utsunomiya), Kanuma (Kanuma, Awano, and Mibu),
Mooka (Mooka, Ishibashi, Kaminokawa, and Ninomiya), and Kawachi (Kamikawachi,
Kawachi, Uziie, Takanezawa, and Haga).
The most right-hand column is the number of households drawn as a random sample

from residents, and the next most right-hand column is the total number of ballots usedwithin this zone. They have 10 ballots and can give their ballots to some regions inwhich they shop.

The transition probability matrix A

is obtained from the row element of theconsumer inflow-outflow table shown in Table 7 divided by the number of ballots.

1. 0000

000

0. 2594

0. 7359

0.004700. 1458

0. 0092

0.845000.518800.05170.4295(27)

Matrix A, which has the elements of transition probability, arrives to the input-output
marketing analysis table as shown in Table 8. In this way, the transition matrix can beused to calculate these consumer behaviors within the industrial zone with four regions.
In the same way, market research has been also assembled for 1991 as shown in
Table 9 (Tochigi prefectural office, 1991a).
When the shopping center has re-equipped, or the number of stores has changed, weare able to forecast the changes in consumer behavior within the Utsunomiya industrial

zone with four regions. The attraction matrix f(f) °f ability to attract consumers isbased on the definition in equation (9):(A)

'l.9240N

A
A

0.7451UJ

0.9014(28).0.4295,

In Table 10 we present the floor space of retail stores for 1988 and 1991 that has been

aggregated to four regions (Tochigi prefectural office, 1988b, 1991b).
Now we introduce an assumption of the gravity model, such as Huff's model, that a
region's ability to attract consumers is in proportion to total floor space of retail storesexisting in the region. When the number of stores has been increased as shown in Table

10, the new attraction index F(f) is calculated from the rate of increase as follows:Input-Output Marketing Analysis Table

19

Table 8: Consumer Input-Output Marketing Analysis Table for 1988

Outflow

Utsunomiya industrial zone

Inflowt\tl

ft

Number of householdstA

Utsunemiyat\

130,997

Kanumatl

8,963

25,428163

34,554

Mooka

ft

4,423

279

25,63530,337

KawachitA

12,984
157,347

Number of consumers

130,997

25,707

1,294

10,74927,092

10,74925,027

Table 9: Consumer Input-Output Marketing Analysis Table for 1991
Outflow

Utsunomiya industrial zone

Inflowt\

Number of householdstl

ft

Utsunomiyat\143,570

884

295

tA

144,749

Kanumatl

6,094

31,222

213

37,529

Mooka

ft

4,618

559

29,42618

34,621

KawachitA

12,36315

1,009

14,94028,327

Number of consumers

166,645

321,680

30,943

14,958

Table 10: Floor Space of Retail Stores
Floor space (nf)
1988

1991

Rate of increase

Utsunomiyat\434,807535,9271.2326

Kanumatl

122,634

143,3121.1686Mookaft

109,652

124,928

1.1393

KawachitA69,21773,6341.0638'/>*/2.0072^
0.7369si

0.8692(29)

0.3867

The new transition matrix A
recurrent equation (11), namely,

can be sought from equations (27), (29), and the20

Journal of Applied Input-Output Analysis, Vol. 4, 1997

Table 11: Consumer Input-Output Marketing Analysis Table
Number of households

Utsunomiya industrial zone

OutflowhhInflow

144,749

Utsunomiyat\144,749

Kanumah10,10927,269151

37,529356

28,341

34,621

Mooka

h

5,924

Kawachin16,053

Number of consumers

176,835

27,625

1,320

10,95429,812

10,954

r 1.00000000.26940.72660.004000.17110.01030.818600.566700.0466

0.386728,327(30)

In accordance with the most recently calculated transition matrix A , the input-output
marketing analysis table, which forecasts consumer behavior, can be found in Table 11.

The results shown in Tables 9 and 11 are sufficient to show the excellent agreementof the empirical data with the numerical data calculated by the present model. Thus,
present consumer behavior as well as the floor space of retail stores and the distance
between regions are of considerable importance in determining future consumer
behavior between regions.

5. Conclusions
We have proposed the probability analysis model, the input-output marketing analysis
table, as a means of analyzing consumer behavior. We have also considered in theory
the fundamental way of thinking behind the closed-system analysis and the three
examples of the region with three trade areas, and have applied this analytical model topredict consumer behavior in the Utsunomiya industrial zone.

Previous analyses have merely forecasted consumer behavior among trade areas
considering only physical distance. The present analysis calculates the transition
probability matrix based on results of market research, and formulates the input-output
marketing analysis table from that matrix. Defining the relative attraction index of a
trade area, and depending on the relationship among trade areas, we were able toforecast the consumer input and output behavior between each trade area.
Finally, the present analysis theory based upon the input-output marketing analysis
table can be widely applied to predicting other economic transport phenomena, such as
the transport of goods and the transmission of information among regions. The

theoretical analysis based on the open system and the numerical example for consumer

Input-Output Marketing Analysis Table

21

behavior among a city, including three trade areas and its competing two cities, shall bepresented in a next paper.

References[1]

Converse, Paul D. (1949), "New Laws of Retail Gravitation", Journal ofMarketing, Vol.
14, pp. 379-84, October.

[2] Huff, David L. (1962), Determination ofIntra-Urban Retail Trade Areas, Publication ofReal Estate Research Program, Graduate School of Business Administration, Division of
Research.

[3] Kotlar, Philip (1971), Marketing Decision Making: A Model Building Approach, New

York: Holt, Rinehart and Winston.

[4] Leontief, Wassily (1986), Input-Output Economics, Oxford University Press, New York.
[5] Miller, R. E. and Blair, P. D. (1985), Input-Output Analysis: Foundations and Extensions,

New Jersey, Prentice-Hall, Inc., Englewood Cliffs.

[6] Reily, Wiiliam J. (1929), "Method for the Study of Retail Relationships", University ofTexas Bulletin, November, No. 2944.

[7]

White, L. A. and Ellis, J. B. (1971), "A System Construct for Evaluating Retail Market
Locations", Journal ofMarketing Research, Vol. 8, pp. 43-6, February.

[8] Tochigi Prefectural Office (1988a, 1991a), Research Report of Consumer Behavior in
Tochigi Prefecture (in Japanese).

[9]

Tochigi Prefectural
Japanese).

Office(1988b,

1991b),

Commerce

inTochigi Prefecture(in