Model 3: Vertically-integrated corporations in the oligopoly market

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.

Figure 4-3. Overview of Model 3

Accordingly, the production volume of the Nash equilibrium that satisfies the conditions for profit maximization of oil refinery corporations in Country 1 and 3 in addition to vertically-integrated corporations in Country 2 is as follows:

,

,

Whereas vertically-integrated companies in Country 2 acquire intermediate goods by themselves, companies in Country 1 and 3 are supplied intermediate goods from upstream Company 4 and 6. Given that one unit of an intermediate good is assumed to produce one unit of an end good, the total demand in the intermediate goods market is represented as follows:

Here, declines depending on the intermediate good price ( ), which is determined in the intermediate goods market. Therefore, the reverse demand function in the intermediate goods market can be represented as follows (Salinger 1994, Lin & Saggi 2007):

The equilibrium condition involving demand and the total production volume ( ) of intermediate goods in the intermediate goods market will be . Consequently, the profit function of upstream companies,

similar to Model 2, is as follows:

, ,

If the Nash equilibrium is derived by solving the profit maximization of upstream corporations, the total production volume and price of intermediate goods can be derived as follows:

The equilibrium price relies on the tariff levels imposed by the two countries ( and ), the size of production facilities owned by intermediate good companies ( and ), and the size of the end goods market. As the market size increases, the demand for intermediate goods increases, leading to a rise in both the total production volume of intermediate goods and market price. As the tariff level of Country 1 becomes higher, companies in Country 1 will be safeguarded, which may raise the demand for companies supplying intermediate goods. This could eventually increase the price and production volume of intermediate goods simultaneously. If the tariff level of Company 3 goes up, the production of its end goods may shrink, resulting in a decline in the demand for intermediate goods. In this way, the equilibrium price of intermediate goods and equilibrium supply volume could diminish. By contrast, if the tariff level of Country 2 increases, the production of companies in Country 1 may slow down; thus, the demand for intermediate goods by companies in Country 3 could decline.

This may lead to a drop in both the price and production volume of intermediate goods. If the level of intermediate goods facilities of companies in Country 1 ( ) increase, the supply of intermediate goods could rise.

This may in turn lead to a decline in intermediate goods prices and production volume. If the size of intermediate goods facilities of companies in Country 2 relatively declines (when increases), the price and supply volume of intermediate goods could rise. In other words, if the size of intermediate goods facilities of companies in Country 2 shrinks, the production of end goods in Country 2 could decline. Meanwhile, the production of end goods in Country 1 may increase. As a result, the demand of companies in Country 1 for intermediate goods from companies in Country 3 may increase, leading to an increase in both the price and supply volume of intermediate goods.

1) Uncooperative Trade System

The two countries may set the optimal external tariffs to maximize their social welfare. As the first and second conditions of optimal external tariffs are met, the tariffs in the Nash equilibrium engaging the two countries are as follows:⁴⁰

40 With , the second condition to maximize social welfare is

satisfied.

Under an uncooperative trade system, the optimal trade policy of Country 1, depending on the size of , can take the form of either tariff or subsidy. However, the optimal trade policy of Country 2, when the assumption represented in Model 2 is maintained, appears to be the implementation of tariffs.⁴¹ Meanwhile, for a tariff trade policy applied by Country 1 to corporations in Country 2, the value of should be smaller than

, but larger than . Under this condition,

Country 1 can impose optimal external tariffs on Company 2 and 3.

2) Analysis on Effects after FTA

In Model 3, with the signing of an FTA between Country 1 and 2, the tariffs between the two countries can be eliminated while the tariffs on non-trading Country 3 can be set to maximize the social welfare functions of Country 1 and 2.

Namely, tariffs imposed by Country 1 on corporations in Country 2 as well as by Country 2 on corporations in Country 1 may disappear due to an FTA. These two countries may impose tariffs on products manufactured by Country 3, a non-trading country. Based on this circumstance, the following optimal external tariffs can be calculated.

,

As the production of intermediate goods by Country 2 is deemed inefficient—that is, when is higher—

41 Under the condition ( ), is absolutely met.

Country 1 and 2 may raise tariff levels imposed on Company 3. Even if Country 2’s domestic firms are regarded as inefficient, the degree of attraction for Company 3 to make inroads into Country 2’s market is likely to increase, and companies in Country 3 may try to export more to Country 2 despite increased tariffs. Therefore, with higher tariffs, Country 2 may possibly achieve better social welfare through tariff income and profits generated by its domestic companies. But as increases, and Country 2 increases tariffs further, companies in Country 3 may have easier access to the Country 1 market, leading to increased exports. At the same time, by increasing tariffs, Country 1 may achieve improved social welfare. In this regard, when the size of intermediate goods facilities of Country 2 is small, Country 2 and 1 could increase the level of optimal external tariffs for Company 3.

On the other hand, the optimal external tariffs involving non-trading countries for Country 1 and 2 were confirmed to be low ( , ) after an FTA. If the tariffs imposed on Company 3 by Country 2 increase, the terms of trade are generated. Also, as the exports from companies in Country 3 to Country 2 show an upward trend, Country 2 may increase its tariff level on companies in Country 3.

,

Upstream companies set the prices of intermediate goods ( ) through the supply of to downstream companies. Such prices ( ) are higher than the ones supplied by intermediate goods companies before the signing of an FTA. After an FTA is in place, the two above effects disappear due to tariff elimination. With accelerated expansion of companies in Country 1 into Country 2’s larger market, the increasing demand for intermediate goods by companies in Country 1 may lead to a rise in the prices and production of intermediate goods. As a result, the profits of upstream firms in Country 3 may increase. Next, the prices of intermediate goods set by upstream firms, if input into the production volumes of end goods companies, would be as follows:

,

,

Along with tariff elimination by Country 1, an increase in the prices of intermediate goods produced by companies in Country 1 may lower marginal revenues and increase marginal costs in determining the equilibrium production volume of its companies, leading to a decline in production volume ( ). The tariff elimination policy of Country 2 may lower its marginal revenues of companies, resulting in a drop in production volume ( ) supplied to its domestic market. Meanwhile, the export volume ( ) of companies in Country 1 to Country 2 would increase significantly. This is because, with an FTA, the decline in marginal costs (an increase in marginal incomes) of Country 2 due to tariff elimination is higher than an increase in marginal costs from rising intermediate goods prices. Also, because of a decline in the marginal costs of Country 1 due to tariff elimination, the export volume ( ) from Country 2 to Country 1 may increase. In the following study, assuming that the size of intermediate goods facilities run by vertically-integrated companies in Country 2 is

equivalent to that of the intermediate good facilities owned by upstream companies in Country 3, the export volume ( ) of companies in Country 2 to Country 1 will be set to be higher than 0. In other words, if the size of intermediate goods facilities in Country 2 is viewed as small and fairly inefficient, companies in Country 2 may have no access to Country 1’s market.

To match this situation, the following condition ( ) should be satisfied.

Considering that consumer surplus, producer surplus, tariff income, and social welfare will change after the signing of an FTA, we will analyze the relations among all parameters within the scope of the above situation.

Alternatively, during the above process, Company 1 and Company 2 could be said to have reduced the supply volume for their own countries, while increasing the supply volume for their counterparts after the signing of the FTA. In this case, if the increase in export volume turns out to be larger than the decline in these companies’

domestic supply volume, the profits of the companies may increase, but they would decrease in the opposite case. The changes in relation to consumer surplus, producer surplus, government tariff income, and social welfare as a result of the FTA framework can be seen in Table 4-3.

Table 4-3 shows that both consumer surplus and total social welfare increased for Country 1 and 2 in most of the parameters section. Due to an increase in exports from Country 1 to 2 and from Country 2 to 1, prices dropped in each market, bringing more surplus for the consumers of the two countries. Due to tariff elimination, the producer profit of Company 1 may increase, but the producer profit of Company 2 will change depending on . If increases, the producer profit of Company 2, in conjunction with tariff elimination, may diminish, but if decreases, the producer profit may show an upward trend. If increases more than a certain value, the extent of decrease in producer profit may be larger than that of an increase in consumer surplus as a result of tariff elimination in Country 2, resulting in a decline in social welfare as a whole. Conversely, if decreases, a drop in the producer profit and government tariff income of Country 2 may outpace a rise in consumer surplus, leading to a general decline in social welfare.

Table 4-3. Comparisons Before and after FTA Using Model 3

Before FTA After FTA

Incre ase or decrease

Countr y 1

Consume

r surplus +

Producer

profit +

Governm ent tariff

income

X Y -

Social welfare

=consumer surplus+producer surplus+tariff

income A

= consumer surplus+producer surplus+tariff

income B

+

Note: refer to Appendix 3 for specific values of X, Y, Z, W, and social welfare.