This paper investigates the impact of economic development on international trade and sources of gains from trade based on a theoretical model that considers consumers’ preference diversity for quality and economies of scale in production. We confirm that both the volume of trade and the share of intra-industry trade increase with increases in the level of economic development in the region. We also find that the intra-industry trade share increases as the technology levels of the two countries become similar. Additionally, we find that both countries can gain from trade and that those gains come from three sources: internal economies of scale, more consumption, and more variety of goods.
It has been generally accepted that trade is concentrated among the industrialized countries, and trade among industrialized countries is principally vertical intra-industry trade (IIT). For example, Bergoeing and Kohoe [
In explaining these characteristics of trade, most studies have emphasized economies of scale, product differentiation, and imperfect competition as the determinants of intra-industry trade. For example, seminal papers by Krugman [
In the opposite direction, Falvey and Kierzkowski [
The contribution of this paper is as follows. First, we considered determinants of the international trade with the assumption that products are vertically differentiated. It is worthwhile to note that Krugman [
This paper is organized as follows. Section 2 describes the basic model, and Section 3 derives the determinants of trade volume and vertical IIT share using a theoretical model. Section 4 examines the sources of gains from trade. Section 5 presents empirical implications of our findings. The final section contains our conclusions.
We consider a 2 × 2 × 2 model: two countries, two firms, and two varieties of goods. Suppose that there is a world in which only two countries exist. One of them we will call Home, and the other we will refer to as Foreign. Both countries are assumed to be at the same level of economic development, and their per-capita incomes are assumed to be identical. We also assume that their technology levels differ from industry to industry. For example, Home enjoys higher-level technology in some industries, but Foreign has higher-level technology in other industries. As the two countries trade with one another, Home exports higher-quality goods in some industries, but also exports lower-quality goods in other industries. Even though there may be many different industries in a country, we hereinafter focus on the trade of goods in a single industry wherein goods are identical, but can be differentiated by quality. We utilize the term “qualitydifferentiated good” to reference this industry.
Each country has one firm that produces one type of the quality-differentiated good1. Without any loss of generality, we assume that the foreign firm produces high-quality goods and that the home firm produces low-quality goods in the considered industry; this implies that the technology level of the foreign firm is higher than that of the home firm in that industry2. In Grossman and Helpman’s [
In producing the goods, two firms have cost functions as follows:
In the cost function (1), we utilize H and L to designate the high and low quality firms, respectively. Thus, the total cost,
The populations of consumers in Home and Foreign are the same and are normalized to 1. In each country, consumers are distributed uniformly between 0 and b according to the preference for quality
This function is an indirect utility function of consumer i, identified by the parameter
We denote the corresponding quality level and price level of high-quality and low-quality goods by
Some consumers do not wish to buy any goods at the prevailing prices. We denote by JL a consumer who is indifferent with regard to the purchase of a low-quality product or refraining from buying. In Equation (2), this type of marginal consumer is defined as
All consumers satisfying the condition Ji > JLH will purchase high-quality goods, all consumers having JL < Ji < JLH will purchase low-quality goods, and all consumers having Ji < JL will purchase no goods5.
Let us model a game as follows: There is not any trade barrier between Home and Foreign, and the two firms sell their goods to both countries. Thus, the competition is purely Bertrand in price. We also assume that no price discrimination is possible because the goods can move freely without any transportation costs between the two countries.
Now, we go back to the two-country world. If countries are in trade, each country exchanges its products with the other country6. Home buys high-quality products from Foreign, and Foreign buys low-quality products from Home. Put differently, home consumers with a higher preference for quality will consume high-quality goods imported from Foreign, whereas foreign consumers with a lower preference for quality will buy low-quality goods from Home.
Trade between the two countries can be explained by
The optimal price of the two firms can be obtained by using the Nash Equilibrium. Based on
Using (1), (5) and (6), we can derive the profit functions of low-quality and high-quality firms, as follows:
The first part comes from the revenue of low-quality (or high-quality) firm; the second part is the total cost of low-quality (high-quality) firm.
From (7), the best response of the low-quality firm
Similarly, from (8), the best response of the high-quality firm
The Nash Equilibrium is derived by solving (9) and (10) with
Lemma 1: Low-quality firm will not offer any goods if the consumer’s preference diversity for quality is low
Proof: A low-quality firm will not produce low-quality goods if the optimal price is lower than the marginal variable cost, which is
Lemma 1 implies that low-quality firms will exit the market if the quality preference diversity of consumers is insufficient. In this case, high-quality firms will monopolize the market. In other words, the trade flow of the considered goods is only from Foreign to Home. Preference diversity b, is a measure of differences in the taste for quality among consumers. As conceptualized by Gabszewics and Thisse [
We allow
A region is considered to have a high economic development level if it has high income and a high technology level. For this reason, we utilize bQ as a proxy for regional economic development. It is also worth noting that
Proposition 1: Vertical intra-industry trade is unlikely to be observed in a region at very low economic development
If
Now, replacing optimal prices in (11) and (12) into (13) and (14), and then substituting
Proposition 2: When both trading countries are at a higher level of economic development, the volume of trade between them will be higher.
Proof: From (15) and (16), we can conclude directly that X and M both increase in b and Q.
Now, note that the imports (M) shown in (16) always exceed the exports (X) shown in (15). Thus, the Grubel-Lloyd index used to compute the IIT index can be written as follows, and is related to the ratio of exports to imports,
We can see that IIT increases directly with R. That is, IIT behaves as R does.
Proposition 3: The regional development exerts a positive impact on vertical IIT share. However, when the region achieves a certain level of economic development, vertical IIT share tends to no longer be affected by the development level.
Proof: Based on the signs of
For the purpose of visually presenting propositions 1 and 3, we draw
Proposition 4: The IIT index increases as the technology levels between countries become similar.
Proof: We only prove
In this section, we try to identify why countries become better off when they are in trade with each other. We prove that countries in trade are better off for the following three reasons: goods are produced more efficiently, more goods are consumed, and a greater variety of goods are available. All of these findings are derived from analyses of the welfare of both countries before trade and after trade.
If the two countries are not currently trading with each other, the high-quality firm will be a monopolist in Foreign and the low-quality firm will be a monopolist in Home.
For the purposes of our analyses, the following are the optimal prices, the consumers with the lowest preference for quality who can buy goods, and the welfare in both Home and Foreign. The detailed mathematical calculations are presented in the appendix section.
1) The optimal prices established by the high-quality and low-quality firms are
(In Foreign, set by high-quality firm)
(In Home, set by low-quality firm)
2) The marginal consumer with the lowest preference for quality can buy the good:
3) Welfare when countries are closed:
Note that the superscript NF or NH indicates the “notrade” case in Foreign or in Home.
If Home and Foreign are currently trading, each country exchanges its products with the other country. Home consumers with a high preference for quality buy highquality products from Foreign, and foreign consumers with low preference for quality buy low-quality products from Home. From section III, we have the following:
1) From (11) and (12), the optimal prices established by high-quality low-quality firms are
(High-quality good)
(Low-quality good)
Note that these prices are the same in both countries.
2) Substituting (11) and (12) into (3) and (4), the marginal consumers with the lowest preference for quality can buy the high-quality good and the low-quality good as follows:
(For high-quality goods in both countries)
(For low-quality goods in both countries)
3) Welfares when countries are in trade (see appendix for detailed mathematic calculations).
Note that the TF or TH superscript indicates the “trade” case in Foreign or in Home.