Chapter 4. Analysis on Effects of Korea-China FTA
C. Model 2: Vertically-integrated firms in the integrated oligopoly market
Third, if tariff income that Country 1 and 2 have earned through optimal external tariffs disappear due to the elimination of trade barriers, a decline in tariff income through signing an FTA is expected. In conclusion, when compared before and after the FTA, Country 1’s tariff income decreases, whereas both consumer and producer surplus increase, resulting in the improved social welfare thanks to the FTA. Conversely, Country 2 shows a rise in consumer surplus, but a decline in producer surplus and tariff income, leading to a decrease in social welfare as a whole.
It is crucial to note that a variable that generates differentiation in social welfare between Korea and China due to the FTA is the market size of Country 2. In other words, if different variables that exist between the two countries are viewed as equal, the asymmetry of market size may play a decisive role in the FTA between Korea and China.
In Model 2, oil refinery companies in Country 1 and 3 may choose a production volume with a focus on profit maximization, whereas companies in Country 2 may opt for a production volume that maximizes social welfare.
On the other hand, companies in Country 2 will be set as vertically-integrated through the integration of downstream and upstream companies, based on the assumption that end goods are produced after acquiring intermediate goods autonomously. Also, the order of the game is similar to Model 1. However, the profit function of vertically-integrated companies in Country 2 will be transformed as follows:
Here, is the price of intermediate goods that vertically-integrated companies in Country 2 procure from upstream companies. As the level of facilities that are manufacturing intermediate goods is assumed to be smaller than the of other upstream companies, turns out to be larger than 1 all the time. Therefore, implies the inefficiency of the production of intermediate goods in Country 2. In addition, vertically-integrated companies in Country 2 are assumed to determine the production volume with the aim of maximizing social
welfare ( ).
Accordingly, after measuring the first condition of each company’s objective function,33 six optimum response functions are calculated for respective production volumes. Then, the Nash equilibrium will be as follows:
,
The derived equilibrium production volume34 shows a significant difference between Country 1 and 2. In the Country 1 market, it shows the production volume of Cournot—a typical trend observed in an oligopoly market.
33 Companies in Country 1 or 3 become the auto-profit functions and companies in Country 2 may become the social welfare function of its own country.
34 When and satisfy and respectively, an adequate volume
of production can be maintained. Unlike a model that determines the optimal external tariffs uncooperatively, if the tariffs between Country 1 and 2 are eliminated through an FTA, if , changes into , maintaining the same condition after the signing of the FTA. The likelihood of Company 3
switching from to may become lower. Therefore, after the signing of an
FTA, companies in Country 3 cannot but be completely excluded from the Country 2 market.
Conversely, in the Country 2 market, it becomes similar to the production volume of a wholly competitive market due to the decisions made on production volume for the purpose of maximizing social welfare of oil refinery companies. In this regard, the exports from oil refinery companies in Country 1 to Country 2 are made when the size of facilities of intermediate goods owned by firms in Country 2 ( ) is small (when the production cost is high; when is larger).35
If the process of meeting the equilibrium conditions in the intermediate goods market is examined, vertically- integrated firms in Country 2 may acquire intermediate goods by themselves while companies in Country 1 are supplied with intermediate goods from upstream companies. Then, considering these conditions
( and ), the following demand of intermediate goods firms can be
induced.36
The total volume of the end goods market ( ) relies on the prices of intermediate goods ( ) set by companies in Country 3. If the prices of intermediate goods are on the rise, the total production volume of end goods declines. Therefore, in consideration of the relationship between the production volume of end goods and the price of intermediate goods, the reverse demand function of the intermediate goods market can be derived as follows (Salinger 1994, Lin & Saggi 2007):
In order to satisfy 이 , the value of should be larger. Namely, if the size of facilities for intermediate goods in Country 2 is relatively small or inefficient, can be met. After calculating the equilibrium production volume of intermediate goods supplied by intermediate goods companies, the equation value is input into . The equilibrium price of intermediate goods can then be derived as follows:37
,
35 If the prices of intermediate goods in Country 3 are derived based on the local production volume and export volume of Company 1, the value becomes higher than . Consequently, the exports from companies in Country 1 to 2 do not exist.
36 For more convenient analysis, the production condition of companies in Country 1 and 3 is assumed as follows:
. If compared after inserting the optimal external tariffs, the two values become equivalent.
37 In the case of a monopoly, where only one upstream company exists in the intermediate goods market, the prices of intermediate goods may increase, whereas the production volumes of intermediate goods may decline. Consequently, the end goods market may shrink.
Also, if the above equation’s value is input into the profit function of upstream firms, the following equation will be shown.
Using Model 2, we will examine how optimal external tariffs are determined between Korea and China under the uncooperative trade framework. We will also analyze the effects of the FTA by comparing a case in which tariffs are eliminated under the FTA framework.
1) Uncooperative Trade Structure
The functions for when the two countries aim to maximize social welfare are as follows:
,
Similar to Model 1, if the first and second conditions are met to maximize social welfare, based on the condition that all the production volume of oil refinery corporations is in the positive, the equilibrium tariffs of both Korea and China can be calculated as follows:38
Assuming that the size of the upstream facilities of vertically-integrated companies in Country 2 are relatively smaller than that in other countries,39 the optimal external tariffs of the two countries are as follows:
38 shows that the second condition to maximize social
welfare is satisfied.
39 Assuming that the threshold of ( ) exists, if is smaller than the threshold—in other words, if the size of the upstream facilities of vertically-integrated companies in Country 2 is above the threshold, the exports from oil refinery companies in Country 1 to Country 2 may end. If is larger than the threshold—in other
. Also, the prices of intermediate goods produced by intermediate goods manufacturers are . The producer profits of oil refinery corporations in Country 1 and the profits and social welfare levels of vertically-integrated companies in Country 2 are and
, respectively.
2) Analysis on Effects of an FTA
In Model 2, tariffs on a non-trading country (Country 3) where tariffs are eliminated while maximizing the social welfare functions of the countries concerned through the signing of FTA between country 1 and 2 are set.
As exports from oil refinery firms in Country 3 to Country 2 are eliminated, optimal external tariffs imposed on Country 3, which are derived Cy country 1 are as follows:
If the derived optimal external tariffs are inserted into the production volume and price of the Nash equilibrium in relation to intermediate goods, the production volume and price of intermediate goods, decided by intermediate goods companies, is as follows:
,
Also, the production volume of oil refinery corporations and vertically-integrated companies is as follows:
words, if the size of the upstream facilities of vertically-integrated companies in Country 2 is below the threshold, the exports from oil refinery companies in Country 1 to Country 2 exist.
, ,
,
Changes in consumer surplus, producer profit, government tariff income, and social welfare of the two countries before and after an FTA are illustrated in Table 4-2.
Table 4-2. Comparisons Before and After an FTA Using Model 2
Before FTA After FTA
Incre ase or decrease
Countr y 1
Consume
r surplus +
Producer profit
-(m↓) +(m↑
) Governm
ent tariff income
X Y -
Social
welfare = consumer surplus+ producer profit+ tariff income
= consumer surplus+ producer profit+ tariff income
-(m↓) +(m↑
)
Countr y 2
Consume
r surplus +
Producer profit
+(m↓
) -(m↑)
Governm ent tariff
Z 0 -
Before FTA After FTA
Incre ase or decrease income
Social
welfare = consumer surplus+ producer profit+ tariff income
=consumer surplus + producer surplus
+(m↓
) -(m↑)
Upstre am firms
Price of intermediate
goods
-
Note: refer to Appendix 2 for specific figures of X, Y, Z, W, and social welfare.
The derived results are as follows: first, like Model 1, consumer surplus may increase in both Korea and China with an FTA primarily due to an increase in supply and a drop in price.
Second, with regard to consumer surplus, if the production cost of intermediate goods manufactured at companies in Country 2 is assumed to be equivalent to that of non-trading upstream companies, then when is low (or high), it appears to be negative (or positive) in Country 1 and positive (or negative) in Country 2.
Third, tariff income may decline in both Korea and China, but with regard to social welfare, when is low (or high), it appears to decrease (or increase) in Country 1 and increase (or decrease) in Country 2.
Therefore, in comparing Model 2 with Model 1, companies in Country 2 that strive to maximize social welfare turn out to be state-owned oil corporations as well as vertically-integrated companies. However, due to inefficiency in the production of intermediate goods, the benefits of social welfare as a result of signing an FTA may vary. From Country 1’s perspective, if the production inefficiency of companies in Country 2 worsens, the signing of an FTA between Korea and China may still be beneficial to social welfare, but if companies in Country 2 secure efficiency in production, market dominance can be expanded dramatically on the basis of vertically-integrated structure and characteristics of state-owned oil companies, resulting in a drastic drop in the producer surplus of Country 1 and a decline in its social welfare.