Chapter 4. Analysis on Effects of Korea-China FTA
B. Model 1: Vertically-integrated companies are non-existent in the oligopoly market
For the basic model, the following worldviews can be assumed. There are three countries (Country 1, 2, and 3) and each country has oil refinery companies (Oil Refinery Company 1, 2, and 3) that produce petrochemical products monopolistically. Given that the FTA is a preferential trade agreement, both FTA partner countries (Country 1 and 2) and non-partner countries (Country 3) should exist. As mentioned above, monopolistic oil refinery companies supply petroleum products to domestic markets and export to other countries. Accordingly, each oil refinery company becomes involved in oligopolistic competition with the
26 According to Fraja & Delbono (1989), private companies strive to maximize profits, whereas public corporations aim at maximizing social welfare, a combination of profits (producers) and surplus (consumers).
markets in Countries 1 and 2.27 Also, the companies purchase crude oil from other regions’ crude oil producing companies based on the assumption that a petrochemical product (one unit) per crude oil (one unit) is produced.
Based on such assumptions, Model 1 can be illustrated as in Figure 4-1.
Assuming that the oil market determines the price depending on the supply and demand of oil, according to Cournot competition, then the game theory has to be conducted as follows: individual government’s decide tariffs on imports of petroleum products in the first stage. However, as analysis is limited to the imports and exports of petroleum products in the FTA, tariffs stemming from the import of crude oil are not present. In the second stage, crude oil producing companies set the supply volume of crude oil and its price is determined accordingly. In the third stage, oil refinery companies of each country determine the volume supplied to their countries and the volume exported overseas, and then determine the prices of petroleum products. Each company’s production volume and each government’s tariff levels—which belong to the sub-perfect Nash equilibrium—are derived through backward induction.
Figure 4-1. Overview of Model 1
원문 번역문
원유시장 Crude oil market 1국
2국 3국
Country 1 Country 2 Country 3
정유기업 Oil refinery companies 원유
석유제품
Crude oil
Petroleum products
27 The petroleum products market of Country 3 was assumed absent because even if Country 1 and Country 2 sign the free trade agreement, Country 3 without any changes in tariffs may lead to no particular changes in exports to Country 3. In practice, it may have no tangible impact on generating profits or improving the social welfare of Country’s 1 and 2.
To this end, it is necessary to derive the utility function of consumers. Based on the assumption that consumers from each country consume petroleum products produced at Oil Refinery Companies 1, 2, and 3, and that all petroleum products are equal, the reverse demand function derived from the consumers’ preference system in the process of utility maximization28 is as follows:
Here, the subscript means a country and the first letter in the subscript of (good) refers to a producing country. The second letter in the subscript refers to a consuming country. Also, refers to the market size of each country. Given that Country 1 and 2 is Korea and China, respectively, the market size of Country 1 is assumed as , whereas the market size of China is assumed as .
In the third stage, when the production volume of petroleum products is decided, based on the reverse demand function of each country and crude oil price, oil refinery companies determine the supply volume of petroleum products to each country. As crude oil corporations have to produce crude oil through procurement, they are regarded as downstream firms. Conversely, companies supplying crude oil are viewed as upstream firms.
First of all, the profit function that will be maximized by downstream firms is as follows:
Here, refers to the price of crude oil (intermediate good) and refers to tariff that is imposed by country .
If the first order condition is derived from the profit function, six response functions can be measured. If the response functions are solved as well, the production volume of the Nash equilibrium can be derived.
,
,
28 Singh and Vives (1984), Clarke and Collie (2003), and Haaland and Kind (2008) measure the reverse demand function based on the utility function—a form of quadratic utility.
Next, let’s take a look at the process of determining the production volume of crude oil (intermediate good).
Oil refinery companies in Country 1, 2, and 3 get crude oil (intermediate good) supplied from upstream Companies 4, 5, and 6. The total production volume of the end goods according to the sub-perfect Nash equilibrium is as follows:
Here, the total production volume of end goods ( ) relies on the price of intermediate good ( ). Based on this assumption, the reverse demand function in the intermediate goods market can be derived as follows (Salinger 1994, Lin & Saggi 2007):
If the total production volume of end goods is assumed to equal the total production volume of intermediate goods ( )29, can be set as a condition for equilibrium in the intermediate goods market.30
Next, based on the reverse demand function of the intermediate goods market, the issues involving the profit maximization of upstream firms can be set as follows.
In the process of maximizing profits, the production cost of an intermediate good company is defined as . is primarily decided by —the level of production capacity operated by upstream firms; thus, as the capacity becomes bigger, the product cost becomes smaller. Also, since the capacity of all upstream firms is assumed to be equal, the profit function of upstream firms is defined as below, determining the production volume of intermediate goods for the purpose of profit maximization.
, ,
To maximize profits, after identifying the first condition for each production volume, the sub-perfect Nash equilibrium should be derived to calculate the following equilibrium price for an intermediate good.
,
29 For the convenience of model analysis, the stocks of oil will be assumed non-existent.
30 According to Salinger (1994) or Saggi & Lin (2007), end goods firms are set as n and intermediate goods firms as m, making the equilibrium condition as .
The derived equilibrium price is dependent upon the levels of tariffs imposed on Korea and China, the size of production facilities owned by intermediate good companies ( ), and the size of the end goods market. If the end goods market grows larger, the demand for intermediate goods may increase, leading to an increase in the total production volume of intermediate goods and market prices. If the tariff levels of the two countries increase—resulting in the shrinkage of the end goods market—the demand for intermediate goods may decline.
In the end, the prices of intermediate goods and production volume may decrease simultaneously. On the other hand, as the size of the facilities of upstream companies increases, marginal costs may drop, making it possible to provide intermediate goods at a lower price. Therefore, the total transaction volume of intermediate goods may increase as the prices of intermediate goods decrease.
In terms of profits equilibrium, upstream firms increase profits when the size of the end goods market increases, which in turn means profits of firms producing intermediate goods may also increase. When the tariff levels of Korea and China are low, their profits may increase. Also, if the number of facilities producing intermediate goods increases, profits may also increase.
,
Next, let’s take a look at how optimal external tariffs are determined between Korea and China in the first stage. First, we will analyze how the two countries decide optimal external tariffs, in an uncooperative manner, for products exported by their end goods companies. Afterward, we will analyze circumstances in which FTAs are signed by Country 1 and 2. Under the FTA framework, the tariffs between Country 1 and 2 may vanish. As for the companies of Country 3—a non-trading country—optimal external tariffs will be set and analyzed.
1) Uncooperative Trade System
Two countries may set optimal external tariffs designed to maximize their domestic social welfare. The social welfare function will be categorized as consumer surplus, producer profit, and government income. Also, Country 1 (Country 2), as a means to maximize the social welfare function, may set optimal external tariffs for Country 2 (Country 1) and Country 3.
As for Country 1 and 2, both the first condition ( ,
) and the second condition ( ( )) to
maximize social welfare are satisfied, resulting in the following optimal external tariffs.31
,
If the market size of Country 2 is placed between and
, the optimal trade policy between the two countries turns into tariffs.32 If becomes larger than , it becomes optimal for Country 1 to provide a subsidy. If is smaller than , it becomes optimal for Country 2 to provide a subsidy as well.
If optimal external tariffs are put into consumer surplus, producer profit, and the government’s tariff income,
social welfare ( and ) can be derived from the sub-game perfect
Nash equilibrium, while deriving profits ( , , and ) that
oil refinery corporations can gain from the equilibrium. As a next step, by setting occasions when tariffs are eliminated through the signing of an FTA between Country 1 and 2, it is possible to derive the values from social welfare and individual factors within the sub-game Nash equilibrium. Additionally, by comparing with the results of uncooperative trade framework, we can analyze the effects of the FTA from Model 1.
2) Analysis on Effects of FTA
If tariffs are eliminated through the signing of an FTA between Country 1 and 2, the tariff levels of the two countries become 0. Conversely, Country 3 may be set as a non-trading country, leading Country 1 and 2 to impose optimum tariffs to non-trading countries. Accordingly, the process of maximizing social welfare in Country 1 and 2 may change as follows:
31 explains the optimal external tariffs that maximize social welfare.
32 It implies that is equivalent to .
And the optimal external tariffs derived based on such assumption are as follows:
,
The tariff levels that are imposed on non-trading partners after an FTA are shown as , , becoming even lower than before the signing of the FTA. A similar result is found in previous studies, including Bond (2008), Estevadeordal et al. (2008), and Missios et al. (2013). Accordingly, the production volume and price of intermediate goods produced by upstream firms are determined as follows:
,
Upstream firms set the price of intermediate goods ( ) while providing the degree of to downstream companies. The price is much higher than the one supplied by intermediate goods companies before the FTA. This is because the FTA causes the demand for end goods to increase while raising the demand for intermediate goods.
Next, by putting the derived equilibrium price of intermediate goods into the profit, consumer surplus, and government tariff income, while comparing the results derived from the uncooperative trade framework, the effects of FTA in Model 1 can be identified, as shown in Table 4-1.
Table 4-1. Comparisons Before and After an FTA Using Model 1
Before FTA After FTA
Incre ase or decrease
Before FTA After FTA
Incre ase or decrease
Country 1
Consume
r surplus +
Producer
profit +
Governm ent tariff
income
X Y -
Social welfare
=consumer surplus + producer surplus + tariff
income
=consumer surplus +
producer surplus + tariff income +
Country 2
Consume
r surplus +
Producer
profit -
Governm ent tariff
income
Z W -
Social welfare
=consumer surplus+
producer surplus+ tariff income
=consumer surplus+
producer surplus+tariff income
-
Upstrea m firms
Price of intermediate
goods
+
Note: refer to Appendix 1 for specific figures of X, Y, Z, W, and social welfare.
First, the consumer surplus of Country 1 and 2 may increase due to increases in trade and production along with lower prices through tariff elimination.
Second, Country 1’s company profit may increase, while that of Country 2 may show a downward trend.
When optimal external tariffs exist, companies in Country 1, as a result of tariff elimination in Country 2, may generate higher profits from Country 2’s larger market size. However, while companies in Country 2 previously enjoyed higher profits in their own country, and although profits may increase in Country 1, tariff eradication could cause a decline in profits in their own country.
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.