Discussion Paper No.272
A theoretical analysis on location andproduction of industrial park
Toshiharu Ishikawa
Faculty of Economics
Chuo University

January 2017

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, JapanA theoretical analysis on location and production composition of industrial park

Toshiharu Ishikawa

Faculty of economics Chuo university
Hachioji Tokyo, 192-0393 Japane-mail: ishiy@tamacc.chuo-u.ac.jp

Abstract
As firms’ production activity becomes large enough to cover the whole world, price and cost cuttingcompetition become harsher among the manufacturing firms. In order to deal with the costcompetition many manufacturing firms fragment the production process into small blocs, and they
move the small fragmented blocs to new location sites which provide the factories with favorable
production condition and reduce production costs. In searching new location site of a fragmented
production process, an industrial park is reevaluated as a location factor by the governments of thecountries as well as the manufacturing firms. Because industrial parks provide the factories withvarious sorts of external economies and they can attract the factories from foreign industrial
countries into a few specific sites in their territories. Present paper theoretically analyzes the locationand production composition of industrial park: First, the paper clarifies the mechanisms in which thedeveloper of the industrial park determines the location site of the industrial park by examining thefirms’ location selections. Second, this paper analyzes how external economies generated in theindustrial parks influence on the production composition in the park; the combination of the businesstypes of the factories, the numbers of the factories and their profits in the industrial park are derived.
Lastly, effects on factories’ profits of wage rate of workers is analyzed. It is shown in this analysis
that reduction of the wage rate which is generated by an improvement of the transportation condition
surrounding industrial park does not raise every factory’s profit because the production compositionof the park is changed due to the reduction of the wage rate.

JEL: R30

Keywords: Industrial park, External economies, Locational prospective area, Transfer price,
Production composition, Wage rate, Chaotic phenomenon1

A theoretical analysis on location and production composition of industrial park
Toshiharu Ishikawa

1 Introduction
The economic globalization gives rise to a harsher price competition among the manufacturing firms,
and it lead to a cost cutting competition in the manufacturing industry. In order to deal with theeconomic globalization many manufacturing firms fragment production process into small blocs.
The fragmented small production processes are scattered beyond the nations’ borders to the places
which bring lower production costs to the manufacturing firms. The places which attract the
fragmented processes from the foreign countries usually possess superior production condition
suitable to content of the productions. And the places are equipped with adequate infrastructure
enough for the firms to operate their factories smoothly. In this context, the industrial parks arehighly reevaluated by the manufacturers and the governments of many countries: Since an industrial
park is built in consideration of characteristics and quality of the factories attracted to the park, theindustrial park surely provides the factories with appropriate external economies in the park. Thus,
when the manufacturers determine factory’s location in region, they naturally consider an industrial
park as a location factor in searching location site of a new factory. While, the government planningto vitalize regional economy in a certain region by inducing factories often use an industrial park as
one of economic tools to accomplish the aim. Because the government can establish industrial park
which agglomerates the factories at a place and also induce them to a specific site in the region. In
addition, industrial park manages some sorts of the business functions through IT and ICT
technologies so that both manufacturers and the governments are able to speedily proceed the office
works. The fact that industrial park makes the firms’ management works smoother is one of the
production merits of industrial park.
This paper theoretically analyzes the following issues. First, the paper clarifies the concept of theprospective spatial area in which industrial park is likely to be established through the analysis offirm’s location selections, and then, by using the location prospective areas the combination ofbusiness types of the factories in an industrial park is derived. Second, the paper examines the effects
of external economies generated in industrial park on the numbers and profits of the factories
belonging to different business types. Lastly, effects on the production composition and factories’
profits of wage rate of workers is analyzed. The government of the country often plays a role of thedeveloper of the industrial park and it can influence the wage rates of workers by improving thetransportation infrastructure surrounding the industrial park. This analysis shows that reduction of
the wage rate which is generated by an improvement of the transportation condition does not raise
every factory’s profit because the production composition of the industrial park is changed due to the
reduction of the wage rate.
2

Present paper is organized as follows: section 2 explains the assumptions and framework of theanalysis and derives the firm’s profit function. Using the profit function, the concept of the locational
prospective area is elucidated by the chaotic phenomena. The location prospective area specifies
spatial range for a firm to search location site of a new factory: If a firm’s factory locates within thelocation prospective area, the firm can obtain almost highest profit irrelative to location site. And
then, expanding this analysis to cover two factories’ locations, the location site of the industrial park
and the combination of the business types of the factories which co-exist in the same industrial parkare derived. Section 3 shows how external economies in industrial park affect profits of the factories
in the park. Section 4 analyzes the effects on the production composition and the factories’ profits of
the reduction of wage rate of workers in the industrial park. Section 5 summarizes the results derived
in this analysis.

2

Derivation of location and composition of industrial park by location analysis of factories

2.1 Assumptions and framework of analysis
This subsection introduces assumptions and a framework of the analysis according to the traditional
location theory1.
A firm produces finished goods by using two production processes, the first and the second
process. The first process is conducted by the factory 1 which is in the home country. The factory 1
manufactures intermediate goods, mq. The second process is assigned to the factory 2 which locatesin the foreign country. The factory 2 composes final goods by using the intermediate goods.
The intermediate goods produced by the factory 1 are transported to the factory 2 by the transfer
price, mp. The factory 2 uses one unit of the intermediate goods to produce one unit of the final
goods. The factory 2 sells the finished goods to the market place in the foreign country. There is no
tariff in the movement of the intermediate goods from the factory 1 to the factory 2. The factory 2 isin the position of the monopoly in the market. The factory 2 can determines the supply quantity of
the final goods at the market in order to maximize the factory’s profit. On the other hand, the factory
1 decides the transfer price of the intermediate goods in order to maximize the firm’s profits. The
corporation tax rates of the home and the foreign country are represented by t and t*, respectively.

2.2 Derivation of the profit function of the factory 1
The profit of the factory 1, Y1, is given by equation (1),Y1 = (1- t)[ mp * mq – C(mq)－F1](1)where C (mq) is the cost function of the factory 1 and F1 is fixed cost. The cost function C (mq) is
1

The basic framework is constructed according to Weber (1909), Puu (1998), and Ishikawa (2016).
3

derived on the basis of the following assumptions. The factory 1 uses two different kinds ofmaterials m1, m2 to produce the intermediate goods. And the factory 1 needs lubricating oil m3 tooperate machines. The materials m1, m2 and the oil m3 are produced at points M1, M2 and M3 which
are identified by coordinates (x1, y1), (x2,y2), and (x3,y3), respectively. These materials aretransported to the factory 1 located at point L which is indicated by (x, y). Freight rates of thematerials m1, m2 are denoted by tm, and the rate of the oil m3 is given by te. The intermediate
goods are transported from the factory 1 to the factory 2 which locates at the market at point M4,（x4,y4). The freight rate of the intermediate goods is tg. Mill prices of these materials and oil are
assumed to be given for the simplicity, and these prices are denoted by p1, p2, and p3. Figure 1
illustrates the geographical relationships between the factory 1, the factory 2, the market and pointsof the three materials.
ｙForeign country

M4 (market, factory 2)■

d4
Home country◎ L ( x, y ) (factory 1)
0

d1

x

d2
▲

●

d3

M2 (m2)M1(m1)◆ M3(m3)

Figure 1 Location figure
The territory of the home country is shown by the square area and that of the foreign country is
rectangle area. The market is indicated by the black square mark at point M4. The border between thetwo countries is shown by the horizontal bold line in Figure 1.
The production function of the factory1 is supposed as equation (2),4mq= Am1αm2β(2)where A indicates the production efficiency of the factory 1, α and β are parameters and they aredefined as A>0, 0< (α+β) <1. And the distances between the material places, Mi (i=1, 2, 3) andthe factory1 are represented by d1, d2, d3, respectively:d1＝((x – x1 )2 + (y + y1)2)0.5

(3a)

2

(3b)

2 0.5

d2＝((x+x2 ) + (y +y2 ) )
2

2 0.5

d3＝(x + (y + y3) )(3c)

The distance between the factory1 and the factory 2 which locates at the market M4 is given by d4,
d4＝(x2 + (y–y4)2)0.5(3d)

The delivered prices Pi (i=1, 2, 3) of the two materials and the lubricating oil at the location site of
the factory 1 are shown by equations (4a, b, c), respectively:

P1= p1 + tmd1

(4a)P2= p2 + tmd2

(4b)

P3= p3 + ted3(4c)

And the price of the intermediate goods at location of the factory 2, DP, which is needed to calculate
the revenue of the factory 1, is represented by equation (5),DP = mp – tgd4

(5)Now, making use of the law of equi-marginal productivity, that is, the ratio between the
productivities of the two intermediate goods should be equal to the ratio between the delivered pricesof them, quantities of these materials are derived as equations (6a) and (6b): (For simplicity, α and β
are assumed α=β=0.4):
m1 ＝A-1.25 mq1.25( (p2+tmd2) /( p1+tmd1))0.5
m2 ＝A

-1.25

mq

1.25

0.5

( (p1+tmd1) /( p2+tmd2))

(6a)
(6b)

The quantity of the oil m3 is given by a linear function of amount of the final goods as equation (6c),5m3 ＝ mq

(6c)

From above equations, the cost function C (mq) is obtained as equation (7),C (mq) =2A-1.25mq1.25 (p1+ tm d1)0.5(p2+tm d2) 0.5 + mq (p3+ ted3) + F1

(7)

The profit function of the factory 1 can be rewritten as equation (8),Y1= (1-t) [mq ((mp-tgd4) - (p3+ ted3)) -2mq1.25 A-1.25(p1+tm d1)0.5(p2+tm d2) 0.5 – F1](8)

2.3 Profit functions of the factory 2 and the manufacturing firm
Let us derive the profit of the factory 2. The profit is derived under the following assumptions: The
market demand function is represented by equation (9),p= a - vQ(9)where p is the market price of the final goods, a is the maximum reservation price and v is aparameter. For simplicity a and v are assumed 600 and 1, respectively.

If the cost of composing

the intermediate goods to the finished goods is represented by C (Q) and the fixed cost of thefactory 2 is represented by F2, the profit of the factory 2, Y2, is represented by equation (10),Y2 = (1- t*)[pQ– mp *mq - C(Q)-F2](10)

Suppose that the composing cost C (Q) is given by equation (4-11),
C(Q) = b Q(g + Q)2/h(11)

where parameters b, g, h are assumed as1.5, 2, 200 for the simplicity of the calculation, respectively.
Since the factory 2 uses one unit of the intermediate goods to produce one final goods, the mq canbe replaced by Q. The profit function is rewritten by equation (12),Y2 = (1- t*)[(p – mp )Q – 1.5 Q(2+ Q)2/200 -F2]

(12)Since the market price of the final good, p, is a function of the quantity Q as shown by equation (9),the optimal quantity supplied at the market to maximize the profit of the factory 2 can be derived by6

using equation (12). The optimal supply quantity is given by equation (13),Q=0.22(- 206 + (582409 - 900mp )0.5

(13)

As the supply quantity Q is a function of the transfer price, the profit of the factory 2 is also
represented as a function of the transfer price as equation (14),Y2= (1-t*) [(600-(0.22(-206+(582409-900mp)0.5))-mp)(0.22(-206+(582409-900mp)0.5))-F2].

(14)

Summing up the profits of the factory 1 and 2, the firm’s profits, Y, can be obtained as equation (15).
The firm’s profits is a function of the transfer price, mp, and the location, (x, y), of the factory 1.
Y= (1- t)[(0.22( -206 + (582409 - 900mp)0.5))(mp - tgd4 ) - (p3+ ted3) ) –-2(0.22(- 206 + (582409-900mp)0.5))1.25 A-1.25(p1+tm d1)0.5(p2+tm d2) 0.5 ―F1]＋(1-t*) [(600-(0.22(-206+(582409-900mp)0.5))-mp)(0.22(-206+(582409-900mp)0.5))-F2].

(15)

2.3 Derivation of Location Prospective Area
2.3.1 Usefulness of chaotic phenomenon
Let us derive the optimal location (X, Y) of the factory1 and the transfer price by using
equation (15). To derive transfer price and the location of the factory 1, the gradient
dynamics is used (Puu, 1998, Ishikawa, 2016). This method is useful because if the solution
could not be specified, the area in which the solution is included is indicated by a chaotic
phenomenon.
The essence of the gradient dynamics is that first, an initial value set is given to xn, yn, and mpn in
the following equations (16a, b, c) as a temporal solution, and obtain the second tentative values of
xn+1, yn+1, and mpn+1 by calculations indicated by the three equations (16a, b, c). The same
calculation is iterated until a given tentative solution can be approximately judged as the solution: If
the values of (xn+1, yn+1, mpn+1) in equations (16a, b, c) become approximately the same as those of(xn, yn, mpn), the values can be admitted as the solution.
xn+1= xn +j*∂Y /∂x,(16a)yn+1= yn +j*∂Y /∂y,(16b)

mpn+1= mpn +j*∂Y /∂mp,

(16c)

7

where j is the width of a step and n shows the number of the calculation. And ∂Y/∂x, ∂Y/∂y, and∂Y/∂mp are given by the following equations (17a, b, c), where the production efficiency A isassumed as 1 and the corporation tax rates of the two countries are assumed as t=t*=0.82.
∂Y/∂x=0.18[-tgx (299.4-0.5mp)/d4+(299.4-0.5mp) (- tg(x/ d4) – te(x/ d3))- 1-1.25 (299.4-0.5mp)1.25

tm [ {(p2+tm d2)0.5/(p1+tmd1 ) 0.5} (x – x1)/d1 ++{(p1+tm d1)0.5/(p2+tmd2 ) 0.5 }(x + x2)/d2]=0(17a)∂Y/∂y=0.18[-tg(y-1)(299.4-0.5mp)/d4+(299.4-0.5mp) (-tg((y –y4)/d4)-te((y-y3)/ d3) - 1-1.25(299.4-0.5mp)1.25 tm [ {(p2+tm d2)0.5/(p1+tmd1 ) 0.5} (y +y1)/d1 ++{(p1+tm d1)0.5/(p2+tmd2 ) 0.5 }(y +y2)/d2] =0(17b)∂Y/∂mp=0.18[-(0.5*mp-299.4)] +0.22[299.4-2*0.5mp+0.5tg d4+ 0.5(p3 + ted3) ++2.5*1-1.25(p2+tm d2)0.5(p1+tmd1) 0.5(299.4-0.5mp)0.25 ]=0.

(17c)

Let us derive the optimal location of the factory 1 and the transfer price by assigning numericalvalues to parameters as follows: (x1=3, y1=-0.5), (x2= -30.5, y2=-0.5), (x3=0, y3= -1.5), (x4=0, y4=1),
p1=0.25, p2=2, p3=0.2, tm=0.11, te=0.01, tg=0.225, F1=5000,

F2=2500. The calculation results

derived from the gradient dynamics are shown by Figure 2. Figure 2 indicates that the optimaltransfer price is approximately 442 and the optimal location site is hidden by a chaotic phenomenon2.
Although the accurate location of the factory 1 is not identified by the appearance of the chaotic
phenomenon, the chaotic phenomenon provides very an important information that the optimal
location site is within the area where a chaotic phenomenon appears because phenomenon appears
surrounding the optimal solution. If firm locates the factory 1 within the chaotic area, the firm’s
profit is not varied so much3. When the firm locates the factory 1 at point M1, the profits is derived
as 3307. The firm can obtain the almost same profits when the factory1 locates within the area where
the chaotic phenomenon appears.
In this situation, if location of the factory 1 is fixed at point M1, profits of the factory 1 and firmand production amount can be derived; they are shown at the upper row in Table 1. And if the freightrate of the intermediate goods is higher as 0.85, as shown by Figure 2B, the location prospective area
appears around the market place. In this case the factory locates near the market place. And the2

The phenomena shown in Figure 2A and 2B are real chaos or chaotic phenomena which are
generated from the Cauchy convergence in the solution derivation process. The study to identify
these phenomena is not conducted in this paper because this problem does not make any obstacle tological development. This interest issue is going to be discussed elsewhere in near future.
3
See the analysis of Ishikawa (2016) and the subsection,3.1 in this paper. The difference of the
profits among the sites within LPA may be estimated less than 1 percent to the obtained profits.
8

location of the factory 1 is fixed next to the market place, profit and transfer price of the factory 1
and profits and production amount of firm are derived and they are indicated in the lower row inTable 1.

mp
442

p

0.2

441

440
0.4

y

439
2.6

x

0.6

2.8
3.0
3.2

Figure2A Location prospective area of factory in low freight rate

mp
p

y

x

Figure2B

Location prospective area of factory in high freight rate

Table1 Location, transfer price and profit of factory in different freight rates
freight rate

locationtransfer priceamountprofit of firm

profit of factory1

tg=0.225

around M1

442

49.19

3307

2968

tg=0.85

around M4

443

48.97

3278

2948

2.3.2 Interpretation of location prospective area
The chaotic phenomenon can be interpreted as follow: If a firm decides the location of the factory 1
and transfer price of the intermediate goods in the sphere of the chaotic phenomenon, the firm’s
9profits are almost same because the optimal solution is contained in this sphere. It can be, therefore,
considered that the spatial range of the phenomenon indicates a location prospective area, LPA for a
possible factory's location. By setting a LPA in large geographical space by using the chaotic
phenomenon the firm can determine the searching area into a small range; they can reducesignificantly the searching costs. Chaotic phenomenon may provide a firm with useful information in
the case a firm does not have adequate information about several countries and many regions in alarge space. Furthermore, the LPA provides a firm with various locational chances: when a firm
decides the factory’s location within the LPA, a firm can consider the factory’s location in a broader
perspective. A firm can incorporate education, culture, housing, safety, and welfare within the area
into its locational decision-making. Considering of the locational effects of these location factors, afirm can find out the location site of its factory, which would be the best site for the firm’s activity as
a whole.

2.4 Construction of industrial park
2.4.1 Necessity of industrial park
As shown in the above analysis, when the freight rate of the intermediate goods is relatively high,the factory 1 locates near the market place, while, if the freight rate is relatively low, the factory
locates near point M1. Thus, it is suggested that in the period that infrastructure of the transportation
is not adequate, industrial park tends to be constructed near market place; when the transportation
infrastructure is adequate and logistics system is developed, location of industrial park is not limited
to near the market place, but it is built at various sites departing from the market place. In thederivation of these results, agglomeration economies are not incorporated into the framework of theanalysis. If these economies would work in firm’s location decision-making, location of the factory 1
is surely influenced.
Suppose that when the factory 1 is moved to the market place, point M4, in the foreign country to
co-exist with the factory 2, scale economies are generated at the market place and decrease theproduction costs of the factories. Scale economies exercise its locational power for the factory 1 toshift to the market place. If the agglomeration of the two factories is realized at the market place inthe foreign country, the home country loses the tax revenue from the factory 1. In this context, theimportance to build industrial park is realized by the home country. It is said that the government of
the home country establishes an industrial park, which provides the factories with external
economies and useful business functions, in order to retain the factory 1 in the home country, or toregain the factory from the foreign country into its territory4.

4

Bredo (1960) analyzes industrial estates as a tool for industrialization. This analysis is instructive
to examining the role of the industrial parks for development of regional economy.
10

2.4.2 Combination of business types within an industrial park
According to the above analysis, location of industrial park is not confined to a specific site, but it isselected considering the LPAs of firms. And industrial park selects the factories which possesses theresemble characteristics in terms of the nature of the goods and production facilities. Hence, when adeveloper establishes an industrial park in a region, the developer is likely to induce factories ofwhich LPAs make overlapping area and establishes the park within the overlapping area. If thefactories’ LPAs, therefore, are not overlapped, these factories would not co-exist in the same
industrial park. Figure 3A and 3B describe these situations. Two chaotic phenomena in Figure 3A
are shown based on the analysis in the previous section. In this Figure 3A, the two factories’ LPAs
do not make an overlapping area, then, these two factories may not locate in the same industrial park.
While, Figure 3B shows that two chaotic phenomena for the two factories are overlapped near point
M1. The possibility would be high that these two factories are induced in the same industrial park
established near M1.

mp

ｘ ｘ

ｙ

ｘ

ｙ

Figure 3A Two LPAs departing each otherFigure 3B Overlapping of two LPAs

3 Relationships between external economies and production composition of industrial park
3.1 Business types combined in an industrial park
In order to examine the effects on industrial park of difference of the business types in an industrial
park, suppose three kinds of factories which belong to different business types, a, b and c.
Although they are in the same spatial and production situation shown in section 2, they are different
in terms of production of intermediate goods: the factory 1a which belongs to business type a isassumed that the production efficiency Aa is 1 and the freight rate of the intermediate goods tga is
0.225; factory 1b of business type b is that Ab=1 and tgb is 0.7728; the factory 1c of business type c isthat Ac=1.05 and tgc is 825.
11

On this assumption, let us derive the chaotic phenomena of the two factories,1a and1b. Figure 4
shows the two chaotic phenomena of the two factories. LPA of the factory 1a appears near point M1,and LPA of the factory1b.is long from point M1 to the market place, point M4. These two LPAs
makes an overlapping area near point M1. While, the chaotic phenomena of the two factories,1band1c. are shown in Figure 5. In this case, LPAs of the two factories, 1b and1c are overlapped near
the market place. It is said, therebefore, that the industrial park established near point M1 iscomposed by the factories,1a and1b, and the industrial park established near the market place iscomposed by the factories, 1b and 1c. Since the factory 1b has a long LPA, this factory has apossibility to locate either industrial parks.

mp

ｙ
x

Figure 4 Overlapping of LPAs of two factories near point M1ｙmpｘ
Figure 5

Overlapping of LPAs of two factories near the market place

If the factory 1b locates at point M1, the profit of the factory 1b is 2947.9, while, the factory 1b
locates at the market place, the profit is 2948.1. The difference of profits is only 0.2, which is12negligible. As the concept of LPA indicates, profits obtained at any sites within LPA are the samelevel.

3.2 Decrease of production costs of factories by enjoying external economies
It is needless to say that the number of factories in an industrial park is not limited to two. In thissubsection, introducing external economies generated in the park into the analysis, the number of thefactories in industrial park is analyzed. To this end, new six assumptions are added in the analysis.
(1) The business types of the factories are classified into the three types, a, b, and c; and based on
the result derived in the previous section, if industrial park is constructed near point M1, thecombination of business types is the combination of the type a and the type b: Whenindustrial park is established near the market place, the combination is the type b and the typec.
(2) The number of the factories, Ni (i=a, b, c), of each business type in the two industrial parks isdetermined by the developer of industrial park to maximize the profits of the individual firms.
(3) Individual factories employ workers, Li (i=a, b, c), to operate the factory as a whole. The
number of workers of a factory is determined by a factory to maximize its own profit.
(4) Industrial park provides two different kinds of external economies: One kind of external
economies, EEv, reduces the variable cost of the factories, and the extent to which theeconomies reduce the cost is a function of the total numbers of workers employed by in thepark. Equation (18) shows the function of EEv.

EEv = -h(18)

where TL is the number of the employees in the park, and h, j, and k are parameters. Wage rateof each business type is a function of the number of workers who are employed by eachbusiness type; wage rate of each business type is indicated by equation (19)wi＝g(NiLi)Ф

(19)

i=a,b,cwhere NiLi is the number of the workers employed by the factories of business type i (i=a, b,
and c),ｇand Ф are parameters.
(5) Another kind of external economies, EEF, reduces the fixed cost of the factories, and theextent to which this kind of external economies reduce the fixed cost is a function of the total
quantity,

TQ, produced in the park. Equation (20) shows the function of EEF,

13

EEF＝-α(T j )2 +β(T j )-(20)

j= M1, M4
TQM1=Na*mqa + Nb*mqb, TQM4= Nb*mqb +Nc*mqc
where α, β, andare parameters. When industrial park is constructed near point M1, TQ isshown by TQM1, and the park is constructed near the market place, TQ is given by TQM4. In
this section the fixed cost are supposed that the fixed cost contains not only the costs which
are directly related with goods production but the overhead costs of training of workers, guest
accommodation, catering and so on.
(6) Production amount and transfer price of each factory have been determined in the same way
used in the previous section. Therefore, minimizing the production costs of the factory iscompatible with maximizing profits of the firm.

3.3 Derivation of the number of the factories in industrial park
Using the analysis in the previous section, profit of individual factories is given by equation (21),Y1i=(1-t)[ mqi ((mpi-tgd4)- (p3+ ted3) ) –(2mqi1.25 (Ai)-1.25(p1+tm d1)0.5(p2+tm d2) 0.5 )/EEv- F1/EEF– g(NiLi)Ф ]
i=a,b,c(21)

Let us suppose that using the results in the previous section, production amount and transfer price ofthe factory 1a are that mqa＝49.19, mpa=442, and those of the factory1c are mqc＝49.09, mpc442.5:
And when factory 1b locates in industrial park established near point M1, production amount andtransfer price are ｍqb＝49.09, mpb=442.5; while, when the factory 1b locates in industrial park nearmarket place, they are that mqb＝48.97, mpb=443.Based on the supposition, let us analyze theproduction composition and profits of each industrial park.
Developer of industrial park decides the number of factories of each business type in order tomaximize profit of individual firms. The developer which establishes an industrial park near point
M1 determines the numbers of the factories, 1a and 1b. And each kind of the factory decides thenumber of workers to maximize its profit. Thus, the number of each factory and the number of theworkers of each factory in the industrial park near point M1 are derived by solving equation system(22i, i=a, b, c, d) with respect to Na, Nb, La, and Lb,∂Y1a /∂Na = 0(22a)∂Y1b /∂Nb = 0(22b)∂Y1a /∂La=0

(22c)
14

∂Y1b /∂Lb=0(22d)

In the same way, the numbers of factories, 1b and lc and the numbers of workers of the factories in
the industrial park near the market place are obtained.
Now, the parameters that determine the two kinds of external economies generated in theindustrial parks are the same and they are shown in Table 2. First, let us derive the number of eachfactory and the number of the workers of the factory in the industrial park which is established atpoint M1.
Table２ Parameters’ values that define external economies
h

j

k

0.01

4

20

α

β
0.0008

D
0.71

Ф

g
52.57

0.6

0.15

Solving equation system (22i, i=a, b, c, d) with respect to Na, Nb, La, and Lb gives the production
composition of the industrial park near point M1. The production composition and profits areindicated in Table 3A.

Table３A The production composition of the industrial park near point M1
number of factories

number of workers

production amount profit

factory1a

―

85.23

49.26

3872

factory1b―

121.37

49.09

3843

business type a

5.29

450.4

260.1

20449

business type b

3.74

454.3

183.6

14385

industrial park

9.02

904.7

443.7

34834

Second, the number of each factory and the number of the workers of the factory in the industrial
park which is established at the market place are obtained in the same way. The production
composition and profits are indicated in Table 3B. The comparison of production compositions in thetwo industrial parks which are shown in Table 3A and 3B indicates that even if the two industrial
parks have the same size and same quality, the production composition and profit generated in thetwo parks are different. Their differences are changed by the production characteristics of thefactories which co-exist in the industrial park.

Table 3B The production composition of the industrial park near market placenumber of factories

number of workers

production amountprofit15

factory1b―

119.52

48.97

3862

factory1c

―

95.2

49.09

3872

business type b

3.79

504.7

179.2

14653

business type c

5.30

452.9

264.6

20499

industrial park

9.05

957.7

443.8

35161

Especially, it is interesting to compare the profits of the factory 1b which are indifference in thefactory’s location between point M1 and the market place if the factory does not enter into industrial
park. The profits and production composition of the business type b are indicated by the bold figures
in Table 3A and Table 4B. Since the factories of the business type b are able to obtain the higher
profit in the industrial park near the market place than those of the park near point M1, the factories
of business type b locate in the park near the market place. The profit difference of the factory 1b isyielded by the difference of the production composition formed in each industrial park: As indicatedin the provirus subsection, when the factory1b does not join into industrial park and the factory
locates at point M1, the profit of the factory 1b is 2947.9, while, the factory 1b locates at the market
place, the profit is 2948.1. The difference of the profits is negligible of 0.2. If the factory 1b locatesin the industrial park at point M1, however, profit of the factory is increased by 895, while thefactory 1b locates in the park near the market, the profit is increased by 914. These profit increases
are generated by the factories’ entering into the industrial park. And the profit difference of 19 in
between the two industrial parks can be interpreted to be yielded by the differences of the production
compositions in the two industrial parks.

4. Effects on industrial park of the government intervention to transportation infrastructure
The government of the country often establishes the industrial parks to vitalize regional economy. In
order for the industrial park to contribute to the regional economy, the government can not only
design the production composition in the industrial park but also influence the wage rates of workers
in the park. The wage rate of the workers in the industrial park is influenced by the commuting areasurrounding the park which is determined by the transportation system. Thus, the government is able
to change the contents of the industrial park by the investment on the infrastructure surrounding theindustrial park greatly. This section focuses the influence of wage rate of the workers on theindustrial park and analyzes the effects of the reduction of the wage rate on the production
composition and factories’ profits.

4.1 Assumptions of the analysis
In order to analyze the relationships between the wage rate of the workers in industrial park, the16

production composition and profits of the factories of the industrial park, some assumptions of theprevious analysis are changed: Industrial park is limited to the area near point M1; the combinationof the business types in the industrial park is confined to the combination of a and b: Production
amount and transfer price of the factory 1a are assumed that ｍqa＝49.19, mpa=442; the production
efficiency, Ab, of the factory 1b is changed to be 0.5; while. production amount and transfer price ofthe factory 1b are changed as that mqb＝48.28 , mpb=445.8. And the efficiencies of the two external
economies and the wage rate of the workers in the industrial park are changed in this section. They
are indicated by the parameters’ values shown in Table 4.
Table 4 Parameters’ values that indicate external economies in industrial parkhj0.0135

α

k
1.443

8.57

β
0.00033

D
0.3842

Ф

g
27.67

0.6

0.4

4.2 Effects on industrial park of the government intervention to improve infrastructure
Using the same way that used in the previous sections, the production composition and factories’
profit in this situation are derived. They are shown by Table 5.

Table 5 Production construction and profits of the factories and the industrial park
number of

number offactories 1a factories 1b

8.38

3.47

workers ofworkers

profit offactories 1a factories 1b factory 1a

741.6

579.4

profit of

total profit offactory 1b in the park

3793.73818.545011.8

Now, if the government invests to improve the transportation infrastructure surrounding theindustrial park, the commuting area of the workers to the industrial park will be enlarged, as a result,the supply of the workers to the park is increased. Thus, the rise of the wage rate of the workers iscurbed, and the wage rate is expected to be lower. Based on this logic, assume that the parameterФislowered from 0.4 to 0.3 at the industrial park, while, the working levels of the two kinds of external
economies in the park are remained as those shown by Table 4 in order to derive the pure effects of
the wage rate of workers on the industrial park. Table 6 shows the production composition and the
profits of the factories and the industrial park after the government invests to transport infrastructure
surrounding the park to reduce the wage rate of the workers.

Table 6 Production construction and profits of the industrial park in better infrastructure
number of number ofworkers of workers of

profit ofprofit of

total profit offactories 1a factories1b

factories1a factories 1b factory 1a factory 1b the park

17

8.85

2.99

711.6

213.2

3830.53813.745277.1

The comparison of Table 5 and Table 6 shows the interesting facts that the number of the factories
and the total production amount in the industrial park are not varied by the reduction of the wage rateof the workers, while, the profits of the factories 1a are increased by 36.8 and also the profit of theindustrial park increases to 45277.1 which is higher than that earned by the industrial park by 265.3
before the government’s investment: The increases of these profits are anticipated: However, profits
of the factories 1b decrease by 4.8 after the wage rate decreases from 0.4 to 0.3, which is assumed tobe generated by the government’s investment to improve the transportation infrastructure
surrounding the park. It is interesting that the government’s investment to improve the infrastructure,
which aims to reduce the wage rate of the workers in the industrial park, does not make the profit ofevery factory in the industrial park higher.

5 Concluding remarks
In the period of the globalized economy, the production processes of the manufacturing firms are
fragmented into the small blocs, and they are scattered over the world. Corresponding to thefragmentation of the production, many governments try to induce these fragmented processes into
their territory to vitalize their regional economy. In this context, the industrial park is attractive toboth the manufacturing firms and the governments because industrial park provides the factories
with external economies and the necessary production functions and attract many factories to a few
specific places in regions. This paper analyzes the industrial parks according to the factory location
theory. The results derived from the above analysis are as follows. (i)The location site of industrial
park is not limited straight away to a specific point, but it is settled, after the process ofdetermination stages, at point within the overlapping area of the location prospective areas of thefactories. Using the location prospective area of the factories, the combination of the business typesof the factories in industrial park is anticipated. It would be said that the concept of the locational
prospective area of the factories are useful both for the manufacturing firms and the governments.
(ii) External economies generated in industrial park influence the combination of the business types,
production composition, and profits of the factories and industrial park. The performances of theindustrial parks are varied by the differences of the production characteristics of the factories which
co-exist in an industrial park. (iii) The government invests to improve the transportation
infrastructure in order to reduce wage rate of the workers in industrial park. The reduction of thewage rate of the workers does not always raise the profits of every factory due to the change of
production composition in the industrial park.

References18

Bredo, W., (1960) Industrial Estates, Tool for industrialization, The Free Press,
Glencoe, Illinois.
Ishikawa, T., (2016) Dynamic Location Phases of Economic Activity in the Globalized
World, Springer, Singapore.
Puu, T., (1998) “Gradient dynamics in Weberian location theory,” Beckmann et.al, Knowledge andNetworks in a dynamic economy, Springer.
Weber, A.,(1909)Über den Standort der Industrien,Tubingen, J.C.B. Mohr.

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