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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