Chapter 3 International Joint Venture in an Integrated Market with Different
3.3 Both Countries adopt Commodity Tax
In this section, both the two countries adopt the commodity tax at the same time.
So the profit function of the firms in the case of joint venture in country1 will be
J
The two firms maximize their profits by the first order conditions and get the optimal output levels The governments of the two country maximize social welfare and get the optimal tax rate
The optimal share ratio derived by the first order condition is
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Then we do the same calculation with the case of joint venture in country2 and get
2
3.3.2 Comparison between the Locations of the Joint Venture
We compare the results of the basic settings, the differences in profits of the foreign firm and the differences in social welfares are
)
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We then have the following proposition.
Proposition 3.5
The profit of the foreign firm will be higher when the joint venture takes place in country1, but the social welfare of one country will be lower when the joint venture takes place in that country.
3.3.3 Comparative Statics Analysis
From the results of the basic settings, there are kinds of ways to discuss with respect to the exogenous parameters like country size, marginal cost, and technology absorption ability. For the country size “”, the results of the case of joint venture in country1 will be
And the results of the case of joint venture in country2 will be ) 0
) 0 2 (3 ) 4(1
) c a ( ) 4 (5 ) c a ( ) 2 t (3
2 2
1 J
2
2
,
where cJ c2 k2(c2 cF)
We then have the following proposition.
Proposition 3.6
In the situation of one foreign firm entering one host market having a monopolistic incumbent, we find that no matter what country the foreign firm chooses to set up the joint venture, the commodity tax rate of country 1 will be lower but the commodity tax rate of country 2 will be higher when the market size of country 1 gets larger.
For the marginal cost of the foreign firm “c ” , the results of the case of joint venture F in country1 will be
4 0 4
k c
t 1
F
1
, 0
4 4
k c
t 1
F
2
,
And the results of the case of joint venture in country2 will be 4 0
4 k c
t 2
F
1
, 0
4 4
k c
t 2
F
2
,
For the marginal cost of the host country firm “c ” , the results of the case of joint 1 venture in country1 will be
4 0 4
1 k c
t 1
1
1
, 0
4 4
) k (1 c
t 1
1
2
,
And the results of the case of joint venture in country2 will be ) 0
2 )(3 4(1
8 14 5 c
t 2
1
1
, 0
) 2 )(3 4(1
2 5 4 c
t 2
1
2
,
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For the marginal cost of the host country firm “c ”, the results of the case of joint 2 venture in country1 will be
) 0 3 5 4(2
4 5 2 c
t
2 2
2
1
, 0
) 3 5 4(2
) 5 )(4 (2 c
t
2 2
2
,
And the results of the case of joint venture in country2 will be 4 0
4 1 k c
t 2
2
1
, 0
4 4
) k (1 c
t 2
2
2
,
We then have the following proposition.
Proposition 3.7
In the situation of one foreign firm entering one host market having a monopolistic incumbent, we find the following facts.
I. The commodity tax rate of both countries become lower when the marginal cost of the foreign firm or the marginal cost of the host country firm gets larger, no matter which country the joint venture is set in.
II. The commodity tax rate of both countries become higher when the marginal cost of the firm in the opposite country gets larger, no matter which country the joint venture is set in.
For the technology absorption ability “k ” , the results of the case of joint venture in 1 country1 will be
4 0 4
c c k
t 1 F
1
1
, 0
4 4
) c (c k
t 1 F
1
2
,
And the results of the case of joint venture in country2 will be 4 0
4 c c k
t 2 F
2
1
, 0
4 4
) c (c k
t 2 F
2
2
,
We then have the following proposition.
Proposition 3.8
In the situation of one foreign firm entering one host market having a monopolistic incumbent, we find that the commodity tax rate will be higher when the technology absorption ability of the host country of the joint venture improves.
3.4 Summary
Under the circumstances that two countries are different in size and only the host country of the joint venture can adopt the commodity tax, the foreign firm will choose country1 to set up the joint venture, and the social welfare of one country will be higher when the joint venture takes place in that country. When the market size of country1 gets larger, the commodity tax rate of the host country of the joint venture gets higher while the foreign firm chooses country2 to cooperate but gets lower while the foreign firm chooses country1. The commodity tax rate will be higher when the technology absorption ability of the host country of the joint venture improves.
Under the circumstances that two countries were different in size and both the two countries can adopt the commodity tax, the profit of the foreign firm will be higher when the joint venture takes place in country1, but the social welfare of one country will be lower when the joint venture takes place in that country. No matter what country the foreign firm chooses to set up the joint venture, the commodity tax rate of country1 will be lower but the commodity tax rate of country2 will be higher when the market size of country1 gets larger. The commodity tax rate will be higher when the technology absorption ability of the host country of the joint venture improves.
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Chapter 4 Firm Migration in an Integrated Market