Download The Game between Family Firms’ Overseas Investment and the

The Game between Family Firms’ Overseas Investment and the
Beneficial Policies of Host Country
Zhang Dan1 zhang Mingyu2
School of Economics and Management
Beijing Jiaotong University, P.R.China, 100044
Abstract: When the family firms develops the certain stage, it must expand to the overseas inevitably,
and carries on the transnational investment directly. Family firms’ overseas investment has great
function to the growth of the economy of various countries. This paper mainly analyzes the game
relation between host country and whole family firms’ overseas investors, and sets up the game model
between the level of host country’s beneficial policies and the scale of FFOI. And analyze what are the
key factors that influence the level of host country’s beneficial policies and how to decide the level of
beneficial policies according to these key factors.
Keywords: FFOI, Game, Host country’s beneficial policies of foreign capital
1. Introduction
Family Firms’ Overseas Investment(FFOI) play an important role in the economy all over the
world. According to Kerlin. the most conservative estimate also accounts for 65% to 80% enterprises by
family all controlled or managed in the world. In the 500 strong enterprises of the world , about 40%
controlled or managed by the family. When the family firms develops the certain stage, it must expand
to the overseas inevitably, and carries on the transnational investment directly.
Foreign direct investment, refers to capital, technology and other factors of production maturity as
a carrier for the cross-border flow of foreign investors and the host country's trading activities.
Preferential policies attract foreign investment as the means is widely used in many countries . General,
the advantages of overseas investors to own the capital and technology, the host country has a
comparative advantage in exchange for the right to use elements of the market and of the host country
and certain interests of the host country is the process to acquire the necessary skills and capital, they
have acquired, they are winners. However, such activities with the specific operations was unusually
complicated, and in addition, the host country and overseas investors in the transaction, directly or
indirectly, the various conflicts of interest, the remaining transactions will not only decide the
distribution of the proceeds, but also has a direct or indirect impact of the transaction, and will
ultimately have an impact on trading procedures and efficiency. How to coordinate their conflicting
interests, to make a reasonable efficient trade balance, foreign direct investment become the core of the
problem naturally. In the host country, the crux of the problem lies in how to improve their competitive
position in the interests of the game, so as to achieve maximum interest.
This article takes the analysis by the gambling relations between host country and the overall
family firm's overseas investors as the key point. The host country foreign capital policy is described for
the host country gambling strategy here, the scale and the quality of family firm foreign investment is
described for the foreign gambling strategy. The foreign investment scale to the foreign merchant has a
most superior level, the host country preferential policy to the host country income and the cost
influence also is various, under the specific time and the specific condition, to some country has to be
able to cause various aspects the cost and profits achieves the overall most superior policy benefit level.
How to make the scale of family firm's foreign investment and host country preferential policy to be
equilibrium is this article core.
2. Set up the game model
2.1 The behavior description of foreign investors
We can divide the decision that is made by foreign investors in order to pursue maximized revenues
into two classes. One kind is decision of the investment scale, such as the decision of investing in or not,
519
how much do they invest in. We use QW to present this kind of decisions. Another kind of decision is
the quality of investment. We can sum up all the other decisions outside the scale decisions into the
second type of decision, and define this kind of decision as the quality of FFOI. In this case, family
firms’ overseas investors’ decisions can be simplified for the scale of investment and the quality of
investment. Because the quality of the foreign investment is a very abstract concept, so we only use the
scale of FFOI to analyze in this paper. Suppose the investment environment of the host country is H ,
the, the foreign investments beneficial policies of host country is B , and then the decision function of
scale of FFOI is:
Qw = a B + H
(1)
2.2 The behavior description of host country
Set Rd as the income that the host countries get by utilizing FFOI; set Qd as the optimum scale of
the demand of FFOI of host country, set Qd as the actual scale of demand of FFOI of host country. Set
k (k>0) as the lose coefficient of income of host country. Considering the level of as the beneficial
policies of host country, We use function to describe the maximized return of host country .As the
following function shows:
Rd = 2k1 Qd Qw − ( k1 Qw 2 + k2 B Qw )
(2)
The part of k2 B Qw has reflected the net losses of host country’s beneficial policies. The
higher the beneficial degree is, the more the foreign investors and the more the cost of host country to
absorb FFOI. We define 2 k1 Qd Q w as host country’s income from utilizing FFOI and define
( k 1 Q w 2 + k 2 B Q w ) as host country’s cost of utilizing FFOI.
We can get the largest revenue when the marginal cost equals to the marginal benefit of utilizing
FFOI.
：
suppose
∂Rd (Qw, B)
we can get
：
∂Qw
=0
(3)
B = 2k1 / k2 (Qd − Qw )
(4)
This is the reflection function of host country to FFOI. The basic meaning of this function is that:
given the scale of FFOI, the optimum beneficial policies of host country to maximizes his own
revenues is in inverse proportion to the actual scale of FFOI and in direct proportion to the size of the
capital shortfall, which can be called the capital demand of host country.
2.3 The analysis of game equilibrium
In this game relation, host country and foreign investors take action at the same time, and each
side always choose the action to maximize the revenue of his own. Under the condition of abundant
information, foreign investors and host country both know the rival’s reflection function accurately, so
the decision –making process of each side by choosing the tactic of one’s own optimum revenues in the
curve of the rival’s reflection function. Because the information of both sides is symmetrical, it must be
520
coincident of the two tactics selected by each side. When the two tactics are coincident at one point,
this point is the equilibrium of this game relation. Express with mathematics,
LB : B = 2 k1 / k 2 (Qd − Qw )
(5)
LW : Qw = a B + H
(6)
we can get
：
Bm = (2k1 Qd − 2k1 H ) /( k2 + 2a k1 )
(7)
Qm = (2a k1 Qd + k2 H ) /(k2 + 2a k1 )
(8)
( Bm , Qm ) is the equilibrium of the game between host country and foreign investors . This is one
of the Nash Equilibrium. Given the scale of FFOI, Qm , the optimum level of beneficial policies of host
country is Bm. Given the beneficial level of host country to the foreign capital Bm, then the optimum
scale of FFOI is Qm . The following picture shows the model:
QW
L3
L1
L2
E ( Bm , Qm )
LW
Qd
Qm
O
LB
Fig.1
B
The game equilibrium
In Fig.1, L1 - L3 are the equal revenue curves of host country with certain scale of actual
FFOI. E is the equilibrium point ( Bm , Qm ).
3.Analysis of the game model
3.1 The relation between the beneficial level of foreign capital policies and the shortfall of FFOI
With the other conditions definite, in order to get the maximized revenue, the optimum level of
the foreign capitals policies of host country should increase with the increase of the shortfall of the
capital, the degree of the increase depends on cost coefficient and host country’s income coefficient of
utilizing FFOI and the partiality degree of the foreign investors to the beneficial policies of host
country.
Suppose the scale of FFOI is fixed on Qm , namely suppose the scale of FFOI are at the optimum
level steadily, we can get the revenue function in different level of capital shortfalls and different
beneficial level of host country’s beneficial policies. In Fig.2 we can see that L1 - L3 are the equal
revenue curves of host country with definite demand scale of FFOI. From L3 to L1 ,
the revenue level
of host country rise constantly. It is prove that with the capital shortfalls of host country increasing,
host country’s potential revenue from FFOI will increase constantly. The reason is that: The larger the
capital shortfall of host country is, the more rare of the relative foreign capital demand of host country,
the more marginal output of unit foreign capital, and host country’s revenue of utilizing foreign capitals
521
can increase to some extent too.
L3
L2
L1
B2
E
B1
B3
Q1
Qd
Fig.2 The relation between the level of beneficial policies and the demand of FFOI
When the capital shortfall of host country is Q1 , its optimum level of policies is B1 . If host country
choose actual policies at B2 , namely the foreign capitals policies of host country is over beneficial in
scale to their demands of foreign capitals. The scale of FFOI will be greater than the real capital
demand of host country, thus it will go beyond the capital absorbability of the host country and can not
get the support from other essential factors of production, can't function effectively, the contribution of
FFOI to the economy of host country will be reduced thereupon and the reverse side effect will increase.
In addition, the revenue level of host country will also suffer corresponding losses because the
beneficial policies is too high .If the actual policies of the host country is selected at B3 , namely its
beneficial level of policies is lower than the required beneficial level compatible with actual capital
shortfall. The foreign capital scale that host country can absorb will be smaller than their capital
shortfall. Because there is still certain surplus capital shortfall, the revenue level of host country will be
still lower than correspondingly. From Fig.2 we can find that, at ( Q1 , B2 ) and ( Q1 , B3 ,), the revenue
level of host country is L2 , and at ( Q1 , B1 ) the revenue level is L1 , and it is higher than the former
two revenue levels. So under the condition that the shortfall of the domestic capital is Q1 , the rational
behavior of host country is to choose B1 as its beneficial level of policies.
So we get the following conclusion: As the capital shortfall is being reduced constantly, host
country should reduce the beneficial policies level of foreign capital progressively and vice versa.
3.2 The relation between the beneficial level of foreign capital policies and the investment
environment
With the other conditions definite, in order to get the maximized revenue of absorbing FFOI, the
optimum level of host country’s beneficial policies should be reduced with improvement of the
investment environment and should be raised with deterioration of the investment environment. The
revenue level of host country will obviously promoted with the improvement of investment
environment.
As Fig.3 shows, when the investment environment in host country is improved from H1 to
H 2 response line of foreign investor will move in parallel from LW 1 to LW 2 . Accordingly, the
optimum level of host country’s beneficial policies moves from B1 to B2 . The revenue level of host
country has been improved correspondingly too. If host country does not reduce the beneficial level of
decision properly with improvement of its investment environment and keep it at B1 , though scale of
FFOI will be greater and reach to QW 3 , B1 is not the optimum level of beneficial policies in the curve
of LW 2 , and the real revenue level of host country will be reduced.
522
QW
Lw 2
Lw1
QW 3
Qw 2
Qw1
B2
B1
B
Fig.3 The relation between the level of beneficial policies and the investment environment
4 Conclusion
This paper mainly analyzes the game relation between host country and whole family firms’
overseas investors, and sets up the game model between the level of host country’s beneficial policies
and the scale of FFOI. We prove that there is equilibrium of the game relation between them. For each
country, there is an optimum level of beneficial policies, which can make of both sides reach the
maximized revenue. Host country must decide the level of beneficial policies according to the actual
demand of FFOI and the investment environment instead of supplying as high level of beneficial
policies as the foreign investors want. Further research is needed to analyze how the foreign investors
change their investment behavior according to their own total amount of capital and investment
environment.
References
，
[1].Haugen, Modern Investment Theory NJ: Prentice-Hall, 1993, p. 12–14.
[2].Eric, D.Ramstetter, Direct Foreign Investment in Asia’s Developing Economics and Structural
Change in the Asia-Pacific Region.Westview Press, 1991
，
[3].Gunning,J.W., Rationing on an open economy, Fix price Equilibrium and two-gap models
European Economic Review, Vol.23, 1983, p. 76–102
[4]. Anderson, T.Multinational Investment in Developing Countries, a Study of Nationalization
and Taxation, Routledge, London, 1991, p. 57–66
523