1

The Theory of Intra-Industry Trade: A review Carlos Cortinhas 1 Abstract Several empirical studies in the 60's and 70's proved that a large portion of international trade is Intra-Industry trade (IIT). This phenomenon cannot be explained by the traditional trade theory. Since then, a vast number of both theoretical and empirical studies have been produced in attempts to explain it. This paper presents a review of the existing theory on IIT, dividing it into the major existing fields: (1) Differentiation by quality approach, (2) Love-of-variety approach, (3) Product specification approach and (4) 'Reciprocal dumping' approach. Finally, some conclusions concerning the merits of the various approaches are presented. Keywords: Intra-Industry Trade; International Trade. JEL Classifications: F49, F14. Introduction In the traditional Hecksher-Ohlin-Samuelson (H.O.S.) theory, each industry is assumed to produce a single homogeneous product, with each country exporting the products in which it has a comparative advantage in its production (based in relative factor endowment abundance) and importing those goods in which it has comparative disadvantage. In this framework only inter-industry trade can occur. However, empirical studies in the 60's and 70's (see for example Verdoon (1960), Balassa (1966) and Grubel and Lloyd (1975)), showed that a considerable proportion of world trade can be defined as intra-industry trade (IIT) - where a country simultaneously imports and exports (differentiated) products which are close substitutes within the same industry 2 . The inability of the traditional H-O-S theory to explain IIT, stimulated a large number of new theoretical models that tried to explain this new phenomenon. The purpose of this paper is to present a concise theory survey of the most important and accepted theories in IIT, trying to give a representative sample that covers all the important currents of thought. Since the phenomenon of IIT can be associated with a variety of product differentiation types, the analysis of the theory of intra-industry trade will be separated accordingly. Finally, the main conclusions of the present study are presented.

2. A theory survey on intra-industry trade As we have seen from the introduction, the apparent incompatibility of the traditional theory with the concept of IIT has stimulated new theoretical models. Most of these new models where based on imperfect competition, economies of scale and horizontal product differentiation.

1 e-mail: [email protected]. A version of this paper was published in Revista de Ciências Empresariais nº2/2003, Universidade Lusíada de Vila Nova de Famalicão, (ISSN: 1645-4529). 2 This phenomenon is also commonly known as 'two-way trade' and 'trade overlap'.

1

2

However, not all models completely dismissed the basic premises on which the H-O-S theory was based. Falvey (1981) and Falvey and Kierzkowski (1987) developed models based on perfect competition and constant returns to scale where IIT appears as a natural consequence of (vertical) product differentiation (different qualities) in a multi-product industry. I will start by examining the neo-H-O-S models in section 2.1. Next, in sections 2.2 and 2.3 the models based on horizontal product differentiation are examined (love-of-variety approach and product specification approach, respectively). Finally, models where IIT occurs without product differentiation are presented in section 2.4.

2.1 Vertical differentiation models: Differentiation by quality approach Falvey (1981) is a partial equilibrium model based on a 2 country (home and foreign) and 2 factors of production (capital, K and labour, L). As in the H-O-S framework, each country has different initial endowments of the factors of production which will result in different factor prices in the two countries. However, the model differs from the H-O-S model in two essential respects. First, although there are 2 factors of production, capital is assumed to be industry-specific. Capital is thus assumed to be immobile between sectors but completely mobile within a given industry. Secondly, each industry will produce (vertically) differentiated goods, i.e., with different K/L ratios or different qualities. In a way which is consistent with the H-O-S theory, this model predicts the direction of trade where each country will export the qualities in which it has comparative advantage (products that use the relative abundant factor more intensively). The model Then, following Falvey (1981) we consider a single industry which uses labour at a given wage rate (w) and sector-specific capital (K) at a given rental rate (R) to produce a "continuum of qualities" or of different qualities (α) of the (vertically) differentiated product. In Falvey (1981) the demand side of the economy is not formally developed. Demand for differentiated goods is assumed to be a function of a quality's relative price and of consumer income (assumed constant in the model) 3 . Each quality α is the K/L ratio used in its production. Then, higher quality products are more capital-intensive than lower quality products. Each unit of quality α will require one unit of labour and α units of capital. The different goods are produced in the two countries using the same constant returns to scale technology. The costs of producing one unit of α can be represented as;

π(α) = w + αR π*(α) = w* + αR* where w = given wage rate 3However,

in Falvey and Kierzkowski (1987) general equilibrium model, the demand side is fully developed and it is assumed that consumer's choice is income constrained and that consumers will always prefer a higher quality to a lower quality product. As income increases, consumers will switch from low quality to higher quality products. 2

3

R = rental on quality-specific capital * = foreign country It is further assumed that w*R which implies that the home country has a comparative advantage in producing high quality goods. Because α is assumed continuous on the range [ α < α < α ] it is clear that there will be some central point (α1) (which Falvey (1981) defines as "marginal utility") such that π(α 1) = π*(α1), or;

α1 =

w − w* R*−R

(1)

and for all other qualities; ⎛ w − w*⎞ ⎟⎟(α1 − α ) α 1 ⎠ ⎝

π (α ) − π * (α ) = ⎜⎜

(2)

It is immediately evident from (2) that (w-w*)/α1 is always positive and thus; π(α)>π*(α) when α1<α π(α)>π*(α) when α1>α

and

In other words, the home country will have a comparative advantage in the goods whose qualities are above the "marginal quality" or in the range [ α 1 < α < α ] and the foreign country will produce those goods whose qualities are below α1 or in the range [ α < α < α 1 ] . This can be easily seen in the following graphic 4 ;

π(α) π∗(α)

π∗(α)= w*+ α R* π(α)= w + α R

α

α

α1 foreign country

home country

Figure 2.1

4This

figure is an adaptation from Falvey and Kierzkowski (1987), p.149. 3

4

Figure 1 In conclusion, this model predicts the pattern of trade, in a way that is consistent with the traditional H-O-S theory, with each country exporting the qualities in which it has a comparative advantage, i.e., with the Home country exporting those qualities above the marginal quality and the Foreign country exporting those qualities below the marginal quality. Furthermore, this model predicts that when in presence of tariffs, some qualities will be produced by both countries, with no trade occurring in those qualities. In this model, there is no gain from trade via economies of scale or via increase in product varieties. The benefits arise mainly from the usual reasons of comparative advantage: with free trade, consumers are able to buy the quality they want at cheaper prices. In this sense, the Falvey (1981) model (as well as the Falvey and Kierzkowski (1987)) is a natural extension of the H-O-S framework, taking into account product differentiation without completely dismissing the basic premises of the H-O-S theory: constant economies of scale and perfect competition. Extensions of the basic model Shaked and Sutton (1984) incorporated vertical IIT in an imperfect competition context. They assume that the quality of product depends not on its price but on R&D, which is reflected in fixed costs 5 . Like in Falvey (1981) and Falvey and Kierzkowski (1987) consumers who have higher income will demand higher quality goods. The equilibrium is obtained in a three-stage game where decisions related to entry, quality of the product and price, are taken. With the opening to trade, average costs decrease due to economies of scale in the most competitive firms and R&D profitability increases. Thus, in the new equilibrium, for a given price the quality of all varieties will have increased, which together with the fact that the remaining firms will be located in different markets, vertical IIT will occur. Furthermore, if the average variable costs increase moderately with quality improvement, the model predicts the emergence of a ‘natural’ oligopoly.

2.2 Horizontal differentiation models: Love-of-variety approach

The demand for variety idea was first introduced by Dixit and Stiglitz (1977) in the context of a closed economy on the lines of the Chamberlinian model of imperfect competition. Since then, a number of authors have adapted this concept to the open economy in the presence of product differentiation (examples are Krugman (1979, 1980) and Dixit and Norman (1980)). The main features of this approach can be illustrated by reference to Krugman (1979). In this model, each country has only one industry which produces a range of differentiated goods under increasing economies of scale. The closed economy equilibrium will be first analysed. On the demand side, it is assumed that all consumers share the same utility function (which immediately implies similar tastes among all consumers), into which all goods enter symmetrically: U =

n

∑ v ( c ), i

v ' > 0 and v ' ' < 0

(3)

i =1

5

From this fact it can be said that this model is more suited to high technology sectors. 4

5

where ci is the individual's consumption of variety i. It can be showed that (3) has the property that, the level of utility increases with the number of varieties 6 . This characteristic of the utility function is why this approach has become to be known as the "love-of-variety" approach, since the more varieties available to the consumers, on a given income level, the better off they will be. This utility function is the single most important aspect of this model of intra-industry trade, since as we are going to see, it will be the consumers demand for variety that will determine all trade between similar countries. Assuming that the number of varieties, n is very large, so that the cross-price elasticity is zero, the elasticity of demand facing an individual producer is given by 7 : v ' ( ci ) v ' ' ( ci ). ci where it is assumed that ∂εi/∂ci<0.

εi = −

(4)

Krugman (1980) introduces the special case where v(ci)=ciθ. In this case, as n tends to infinite, the elasticity of demand is constant and equal to 8 :

εi =

1 1− θ

which implies that a consumer is indifferent between any two varieties and also that there is no significant interaction between any two firms. Dixit and Norman (1980), using a model incorporating two sectors (differentiated goods and homogeneous goods) reached the same constant elasticity of substitution using a different utility function. The utility function developed in their model, is defined as: α

⎛ n ⎞β U = ⎜ ∑ ciβ ⎟ c10−α ⎝ i =1 ⎠

with 0 < α < 1, 0 < β < 1

where c0 = consumption of the homogeneous good. In this case also, the elasticity between any two differentiated products, when n tends to infinite, is constant and equal to 1/(1-β) The fact that the elasticity of substitution between differentiated goods in this two models is constant, has led some authors to cast doubt on their usefulness, since the degree of substitutability between differentiated goods is the same whether the choice available to consumers is only two or whether they can choose among hundreds of varieties. Recently, Goto (1986), using the same utility function as Dixit and Norman (1980), try to solve this problem by assuming that β is an increasing function of n, that is: β=β(n), with 0<β<1 and β'>0 Therefore, the elasticity of substitution between any two differentiated goods is positive and takes the form: 6

See section A.1 of the appendix A for proof. See section A.2 of appendix A. 8 See section A.3 of appendix A. 7

5

6

εi =

1 ⎛ 1⎞ 1 − β ⎜1 − ⎟ ⎝ n⎠

In other words, in Goto (1986) model, differentiated goods become closer substitutes as the variety of goods increase and the assumption that n tends to infinite is not required. Turning to the supply side, Krugman (1979) assumes that there is only one factor of production (Labour) and that the cost function, which is common to all firms is given by: li = α + β xi

(5)

with α and β representing fixed and marginal costs, respectively, with xi representing output and li representing labour used in the production. This cost function implies that there are increasing returns to scale and that the number of varieties which can be produced is limited. With increasing economies of scale, only one firm will produce each variety and therefore, there will be as many producers as the number of varieties supplied to the market. (If two firms produced the same good, one firm could always drive the other out of the market by increasing its production and therefore reducing its unit costs (while increasing it for the other firm)).It is assumed that the economy's labour force equals the number of individuals, L, so that the output per firm xi will be equal to Lci. The profit condition for each firm is given by:

Πi = pixi - (α+βxi)w

(6)

and each firm will try to maximize its profits by equating its marginal revenue (MRi) to its marginal costs (MCi), that is 9 : ⎛ 1⎞ MRi = pi ⎜⎜1 − ⎟⎟ = MCi = wβ ⎝ εi ⎠

which can be rewritten as: pi ⎛ ε i ⎞ ⎟β (7) =⎜ w ⎜⎝ ε i − 1 ⎟⎠ On the other hand, it is assumed that the number of firms is sufficiently large to drive profits to zero (along the lines of Chamberlinian monopolistic competition). From equation (6): pixi = (α+βxi)w which can be rewritten as:

9

The derivation of these equations is presented in section A.4 of appendix A. 6

7

pi α =β+ w Lc i

(8)

Equations (7) and (8) jointly determine ci and pi/w. Because of the symmetry of the model, all varieties produced will sell at the same price and will be produced at the same quantities, so that, if an equilibrium exists, it will be an unique solution. Also because of the symmetry of the model, output per firm will be the same for all firms, i.e., xi=lci, and therefore the number of varieties in the economy, will be determined by full employment, that is: n=

L α + β xi

(9)

Figures 2 to 4 illustrate the determination of pi/w and ci. The ZZ curve represent the locus of ci and pi/w where the zero-profit condition holds (equation 8). It is downward sloping because higher levels of output (for a given number of consumers, L) implies lower unit costs and therefore a lower break even price. The PP curve represents the ci and pi/w values that satisfy equation (7), the profit-maximization condition. Its slope will depend on the elasticity of substitution between differentiated goods (εi). The cases when the elasticity of substitution is decreasing, constant and increasing will be considered separately. a) Case 1: Decreasing elasticity of substitution (∂ε/∂ci<0) The interception of PP and ZZ determine the equilibrium price of each good (which is the same for all goods) and the equilibrium per capita consumption of each variety (which is also the same for all goods). In can be seen from equations (7) and (8) that an increase in L, will, all other things equal, will shift the ZZ curve down, but not the PP curve, since as we can see from equation (7), L has no effect on PP.

pi/w

Z'

(pi/w)

Z

P

A

A'

(pi/w)' P Z' c'

c

Z ci

Figure 2.2: Decreasing elasticity of substitution case Figure 2: Decreasing elasticity of substitution case It is shown in section A.5 of the appendix A that, when ∂εi/∂ci<0, the increase in L will imply that: 7

8

(1) d(pi/w)/dL<0 (2) dci/dL<0 (3) dxi/dL>0 (4) dn/dL>0 In other words, an increase in L when the elasticity of substitution between differentiated goods is negative will shift the equilibrium point in figure 2. from A to A' and imply a decrease in the price level (from (pi/w) to (pi/w)') and a decrease in the per capita consumption of each variety (from c to c'). In this case, it can also be seen from (8) that xi=α/[pi/w)-β], so that an decrease in (pi/w) implies an increase in the output per firm. Finally, an increase in population will also imply an increase in the number of varieties available to consumers, n. b) Case 2: Constant elasticity of substitution (∂εi/∂ci=0)

When considering constant elasticity of demand (as in Krugman (1980) and Dixit and Norman (1980)), the outcome will be different. Figure 3 illustrates the case when the elasticity of substitution between any two differentiated products is constant and therefore with the PP curve drawn flat.

pi/w

Z'

Z

(pi/w) P

P

Z' c'

c

Z ci

Figure 2.3: Constant elasticity of substitution case Figure 3: Constant elasticity of substitution case It also shown in section A.5 of the appendix that when ∂εi/∂ci=0, an increase in L will imply: (1) d(pi/w)/dL=0 (2) dci/dL<0 (dci/dL=-1) (3) dxi/dL=0 (4) dn/dL>0 An increase in population, L, when the elasticity of substitution is constant will also shift the ZZ curve to Z'Z'. However, since the PP schedule is horizontal, an 8

9

increase in L will not imply a decrease in pi/w. Therefore, the output of each variety, xi, will remain constant. The consumption per capita falls from c to c'. In order to satisfy the increased demand, the number of varieties, n, will also have increased at the new equilibrium point.

c) Case 3: increasing elasticity of substitution (∂εi/∂ci>0) The case when the elasticity of substitution between differentiated goods is increasing (as in the Goto (1986) model), is depicted in the figure 4 below: Z'

pi/w

Z

P

(pi/w)' (pi/w) P Z' c'

Z

c

ci

Figure 2.4: Increasing elasticity of substitution case Figure 4: Increasing elasticity of substitution case

In this case, the PP curve is downward sloping and is assumed to be flatter than the ZZ curve 10 . An increase in population, L, the ZZ curve shifts to Z'Z', with equilibrium shifting form A to A'. The increase in population will imply 11 : (1) d(pi/w)/dL<0 (2) dci/dL<0 (3) dxi/dL<0 (4) dn/dL>0 At the new equilibrium, the price levels increase from (pi/w) to (pi/w)' and the consumption per capita decreases from c to c'. We can see from (8) that an increase in pi/w must decrease the output per firm, xi. Naturally, this decrease in the output per firm and the decrease in consumption per capita must be compensated by an increase in the number of varieties available, n.

10 This assumption is in accordance with Helpman and Krugman (1989). Although using a slightly different model, they also used the PP-ZZ analysis. They required that when decreasing, the PP curve must be flatter than the ZZ curve. In terms of the present analysis (see section A.5 of the appendix A), this assumption ensures that even when the elasticity of substitution is increasing (εi>0), the number of varieties available to consumers will increase (since it ensures that dci/dL<0 and therefore dn/dL>0). 11 See section A.5 of appendix A for proof.

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10

We are now ready to consider the open economy. Suppose that, in addition to the Home country, there also is a Foreign country, identical to the Home country in every respect. Assuming that there are no transportation costs, the symmetry of the model will ensure the wage rates and prices in both countries will be same. In this scenario, the effects of opening to trade will be the same as in the case of a population increase illustrated in figures 2 to 4. Each consumer will now be maximizing the following utility function: n

n + n*

i =1

i = n +1

U = ∑ v ( ci ) +

∑ v(c ) i

(10)

where * denotes foreign country, with goods 1,...,n being produced in the Home country and goods n+1,...,n+n* being produced in the foreign country. Since every good enters the utility function symmetrically, welfare in both countries will increase because the number of varieties available to consumers increases to n+n* [where n is defined as in (9) and n*=L*/(α+βxi)]. This result is independent of the value of the elasticity of substitution 12 . In addition, since the increase in the market size implies larger economies of scale, there will be welfare gains in terms of lower unit costs. However, the effects of prices on welfare will depend on the elasticity of substitution between differentiated goods (Lower, equal and higher for decreasing, constant and increasing elasticity of substitution, respectively). Since there are no incentives for firms to produce the same variety, each good will be produced in only one country. Which country produces which varieties is not, however, determined in this model. In other words, the direction of trade is undetermined. In conclusion, in the love-of-variety approach, contrary to the traditional H-OS theory, shows that, intra-industry trade in (horizontally) differentiated goods will occur even when countries are similar in every respect (factor endowments, tastes, technology, among others). This is due to economies of scale and due to the way consumer's utility function is constructed. Because there is no incentive for firms to produce the same variety, different countries will produce different goods. Since consumer's utility is maximized when they consume the highest possible number of available varieties, intra-industry trade will occur, with each country's consumption being proportional to its size. However, in this model, product variety is solely determined by factor supply and production conditions, with the demand having no role whatsoever. When countries differ in size, we can see from (8) that the larger country will produce more varieties. In this case, the smaller country will realize the larger gains from trade because the increase in the number of varieties available to its consumers will be larger than for the larger country. Extensions of the basic model Dixit and Norman (1980) introduced a second sector in the Krugman model (corresponding to the homogeneous goods sector). As referred earlier, they also 12 On the assumption that in the case 3 (ε >0), the PP curve is flatter than the ZZ curve, as explained in i footnote 8.

10

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introduced a new utility function (see p. 6) which like Krugman (1980) implies constant elasticity of substitution between differentiated goods. The conclusions of this model are similar to Krugman (1980), that is, even though the number of varieties produced in each country doesn't change after trade, welfare in both countries will increase because the number of varieties available to consumers will increase with trade (from n (n* in the case of the foreign country) to n + n*). Furthermore, interindustry trade is explained by factor endowment differentials (like in the traditional H-O-S theory), that is, trade between homogeneous and differentiated goods only occurs if the two countries have different factor endowments. In the case that the 2 countries are similar, all trade will be intra-industry trade, therefore suggesting that the intra-industry trade will be higher the more similar two countries are. Lawrence and Spiller (1983) base their model in a utility function in the same format as Dixit and Norman (1980) and like them, they consider 2 sectors. However, in Lawrence and Spiller (1983), the homogeneous sector is assumed relatively labourintensive and the differentiated goods sector is assumed relatively capital-intensive. They also assume that firms entering the differentiated goods sector need to incur in substantial fixed costs (in the form of market research outlays). Finally, they also assume different factor endowments between the 2 countries. After trade, like Krugman (1980) and Dixit and Norman (1980), the number of varieties produced remains unchanged (In this model, the elasticity of substitution between differentiated goods is also assumed constant). However, in Lawrence and Spiller (1983), n and n* are determined by the absolute value of capital stock in each country (whereas in Krugman (1979,1980), it was determined by L and L*). Unlike Krugman (1979,1980), the inclusion of factor endowment differences and differences in factor intensities, allows the determination of the direction of trade, with the relatively capital-abundant country specializing in the production of differentiated goods and the relatively labour abundant country specializing in the production of homogeneous goods. Goto (1986) introduced the possibility of increasing elasticity of substitution between differentiated products (he studied the case of the automobile trade between Japan and the United States). The general equilibrium model developed by Goto (1986) in a Chamberlinian monopolistic competition setting (following Krugman (1979,1980) and Dixit and Norman (1980)), also incorporated labour market imperfections in the differentiated goods sector (the labour market in that sector is assumed to be controlled by a single labour union). Goto (1986) model, identified the same gains from trade as in the basic framework (namely, increased welfare due to increase in the number of varieties available, a decrease in the monopolistic power of firms (through increased competition) and a decrease in the unit costs (due to the existence of economies of scale). Furthermore, he showed that by introducing labour market imperfections and increasing elasticity of substitution in the model, two extra gains from trade can be identified, namely, a decrease in unemployment in the differentiated goods sector due to reduced imperfections in the labor market and a contribution to economic growth through a release of capital resources from the distorted sector. 2.3 Horizontal differentiation models: product specification approach

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Another way of modelling the demand for variety is due to Lancaster (1979, 1980). This approach has also been labelled has neo-Hotelling approach, since Lancaster developed this model based on his previous work (see for example Lancaster (1975)), on the characteristics approach to consumers theory, which has its bases in Hotelling (1929). The main difference between this approach and the love-ofvariety approach is that, while in the latter all differentiated products enter the utility function symmetrically, the product specification approach assumes asymmetry. Each product is seen by consumers as having its own collection of characteristics (for example, a car represents a bundle of characteristics such as safety, comfort, size, speed, and so on) which will define its specification. Products that have the same characteristics (although in different proportions), will form a group of products (for example, all passenger cars, although of different sizes, colours and shapes, will form a group of products). Product specifications are assumed to vary in a continuous manner over a convex (corresponding to the product spectrum for that group), and in this sense, the group will have an infinite number of potential products. Figure 5 illustrates the simplest two-dimensional case: A

B a1

a2

a3

Figure 2.5 Figure 5

Then, assume that a given product embodies only 2 product characteristics, which are continuously variable over the spectrum AB. If each point of the spectrum represents a variety specification, the number of potential products is infinite. Goods around a1 will be A-intensive and goods around a2 will be B-intensive. An alternative way of presentation is given by Helpman (1981) and is presented in figure 6: a a

a

d

b

c Figure 2.6

Figure 6

12

13

Instead of using a line, Helpman (1981) uses a circle where each variety of a given product is represented by a point in the circle. This method has the advantage of avoiding having to make special assumptions about the specifications located at the edge of the line in figure 5. In this approach, individuals are assumed to have preferences (which are assumed uniform among consumers) over a certain specification rather than over a collection of goods. These goods characteristics are 'non-combinable', that is, consumers cannot obtain a certain specification by combining two or more goods (in the example of figure 5, this means that if the only two available varieties are a1 and a2, a consumer whose ideal is specification a3, cannot obtain his ideal variety by combining quantities of available specifications a1 and a2). Each individual will have a 'most preferred good' or 'ideal product', that is, each consumer will have a certain product specification that he will prefer over all the other products. The essence of this approach is that, in a given economy, different consumers will have different most preferred varieties or ideal specifications. For simplicity, uniform density of consumers over the spectrum is assumed, so that, the same aggregate demand exits for every variety. Therefore, if the number of varieties actually produced is less than the number demanded (which is the case in this model since it is assumed that each variety is produced under increasing returns to scale), some consumers will be able to consume their ideal variety while others will be forced either to consume a variety which is not ideal or not consume the product at all. In the event that a consumer has to settle for a variety which is not his ideal, the price he will be willing to pay for that variety (for a given income) is negatively related to the distance of this variety from his ideal. That is to say that, the further away is the available variety from his ideal, the lower the price he is willing to pay. In order to illustrate this effect, Lancaster introduced the concept of compensating function, which is depicted in figure 6 below:

Compensation required

S*

Product specification

Figure 2.6 Figure 7 Thus, the further away an available variety from the consumer's ideal, the more compensation is required. The steeper is this curve, the more it takes to keep consumers indifferent between alternative models. It is also assumed that this 13

14

compensating function is symmetrical, that is, whether the available variety is located to the left or to the right of the ideal variety (obviously at the same distance of s*), the same compensation will be required for the consumer to buy it. On the supply side, Lancaster (1980) assumes increasing returns to scale in the production of each specification, so that there will be decreasing costs "for some range of output commencing at the origin" (p. 156). Furthermore, it is assumed that the economies of scale are lost if the good is changed in specification. When firms enter the market, they not only have to decide the price of the good but also what specification their variety will be. This is an essential difference from the decision of firms under the usual monopolistic competition setting (where firms set their price, P, equal to the marginal cost, MC). In this model, firms are seen as having two half-markets (in the example of figure 6, a firm that produces the specification a will have an half-market to the left, corresponding to the range [ a ,a] and an half-market to the right, corresponding to the range [a, a ]). In this setting, the profit market solution for each firm, will be a joint pricespecification pair, such that, MR[ a ,a] = MR[a, a ] = MC. In other words, firms will set their price and choose their specification where the marginal cost is equal to both the marginal revenue of the half-market to the left and to the right, simultaneously. This condition will ensure that: (1) No two firms will produce the same specification (2) The specification of the goods will be at equal distances along the product spectrum. (3) The market areas of all goods will be the same (4) All goods will sell at the same price and quantities. Furthermore, this model also assumes free-entry of firms so that in equilibrium, profits will be driven by zero (therefore, in equilibrium price will be equal to the average cost). The market structure here described is what Lancaster (1980) calls 'perfect monopolistic competition' since "it represents the Nash equilibrium of perfectly informed firms facing perfectly informed consumers under conditions of perfect flexibility in choice of specification, absence of collusion, and free and willing entry" (p. 157). In this model, there is also a sector producing homogeneous goods (agriculture), under constant economies of scale. In order to demonstrate the effects of trade, Lancaster (1980) assumes the existence of a second country (foreign country), identical to the Home country in every respect and exhibiting all the above characteristics. Therefore, each country will, before trade, have the same number of firms, consumers and number of varieties available to consumers. After the opening to trade, the conditions discussed above will ensure that each specification will be produced by only one firm and hence in only one country. Half of the output of each variety produced will be sold in the Home country, with the other half being consumed in the Foreign country. Also, since the countries are similar in every respect, the number of varieties produced in each country will the same, that is, n1=n2, where the subscripts 1 and 2 denote the home and foreign countries, respectively. However, because of the existence of increasing economies of scale, the total number of varieties produced, n1+n2, may after trade, have increased.

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15

The post-trade equilibrium for two identical countries (home + foreign), producing one homogeneous good X (agriculture), under constant economies of scale and one differentiated good Q (manufactures), under increasing returns to scale, can be formally described as follows: The incomes of the ith country, Yi, is given by: Yi = Xi + 2nipQ

(11)

and its resource constraint, V, is given by: V = Xi + niC(2Q)

(12)

where C is the cost function in manufacturing. Since each country is identical, the income and resource constraint are the same for each country. Under the assumptions of the model (profit maximization and free entry in the manufactures sector), price must be equal to average cost (P=AC). The price is given by: pi = C(2Q)/2Q

(13) This will imply that: Yi = V, for all ni.

(14)

In other words, the level of income is independent of the division of the economy between agriculture and manufacturing. The trade balances for the two countries are given by: T1 = X1 - X + 2pn1Q - p(n1+n2)Q

(15)

T2 = X2 -X + 2pn2Q - p(n1+n2)Q

(16)

and

Given the resource constraint in (12), these can be rewritten as: T1 = (V-X) - [n1C(2Q) - p(n1-n2)Q]

(17)

T2 = (V-X) - [n2C(2Q) - p(n1-n2)Q]

(18)

and

By setting T1=T2 for balanced trade, we obtain what Lancaster (1980) calls the 'balance condition': (n1-n2)(2pQ - C(2Q))=0

(19)

Assuming constant returns to scale in the agriculture sector, any combination of n1 and n2 is consistent with this condition being fulfilled. Furthermore, as long as the elasticity of demand for differentiated goods (ε) is equal of greater than 1, all of the

15

16

possible equilibrium conditions will be stable 13 . When ε>1 (the normal case), there will be no trade in agriculture, and thus with all trade being intra-industry trade and the volume of trade being equal to half of the production of manufactures. When ε=1, manufacturing may be divided in any way between the two countries and trade can be anything from pure intra-industry trade to exchange of agricultural goods for manufactures. This model shows that, intra-industry trade occurs as a consequence of preference variety and economies of scale, as in the love-of-variety approach. However, the gains from trade from greater product variety are qualitatively different. In the love-of variety approach, since all goods enter the utility function symmetrically, an increase in the number of varieties available increases consumer's welfare for all individual consumers. In this model, an increase in variety, will be beneficial for some consumers but harmful to none. Some consumers will, after trade, be able to consume products much closer to their ideal specification than before trade, since the average distance between varieties on the spectrum is smaller with trade than without. However, for the consumers that were consuming their ideal variety before trade, opening to trade will not increase their welfare. It is important to note that this model implies that preference variety is the only reason for the existence of intra-industry trade. If preferences were equal for all individuals in each country, all consumers would have the same 'most preferred good' and thus, the output for this group of products would be a homogeneous product made to this specification. Extensions of the basic model Both Lancaster (1980) and Helpman (1981) extend the basic model by relaxing the assumption that countries are of equal size. When countries are allowed to vary in size (as measured by the number of consumers), the larger country will, in autarky, produce a larger number of varieties, due to the existence of larger economies of scale. Hence, in equilibrium, (and since no trade in agriculture will occur) the smaller country will import more than half the total number of varieties available in each group of products, the quantity of each being less than half the total output and will export less than half the products but in quantities more than half their total output. This immediately implies that the level of intra-industry trade will be higher the more similar in size countries are. Also, although the pre-trade per capita incomes differed (obviously the larger country had a higher per capita income), after trade per-capita incomes will be the same. This has the interesting implication that, the smaller country will 'reap' the larger gains from trade (in terms of per-capita income). Also, the smaller country will have the larger potential gain from trade (in terms of consumers welfare), since the increase in the number of varieties available to consumers will be bigger for the smaller country than for the larger country. Lancaster (1980) and Helpman (1981) have also extended the basic model into an H-O-S framework where differences in factor endowments between the two countries exist (with the Home being relatively capital-abundant and the foreign country being labour-intensive) and also different factor intensities between manufacturing and agricultural goods (with the manufacturing good being relatively capital-intensive and agricultural good being relatively labour-intensive). This implies that the Home country will produce a higher manufacturing to agriculture goods ratio 13

If the elasticity of demand for manufactures is less than one, the equilibrium will be unstable and the long run equilibrium will be one where all manufacturing goods will be produced in only one country. 16

17

than the foreign country. Therefore, the Home country will be a net exporter of manufacturing goods while the foreign country will be a net exporter of agricultural goods. While in the traditional H-O-S analysis all trade would be inter-industry trade, in this model, in addition to the exchange of agricultural goods for manufacturing goods, intra-industry trade will also occur since each variety is only produced in one country. The relative importance of intra-industry trade (in relation to total trade), will depend on the initial differences in factor endowments. In, this model, intra-industry trade will be higher the more similar (in terms of factor endowments and market size) are the trading economies. In conclusion, in the product specification approach, trade only occurs because of preference diversity and the existence of economies of scale. Contrary to the H-OS theory, intra-industry trade will occur even when countries are equal in every respect. In fact, in this approach, the potential for intra-industry trade will be higher the more similar any two countries are in terms of size and initial factor endowments. As in the love-of-variety approach, consumers welfare will increase after trade due to an increase in the number of varieties available. However, in this model, the gains from increased variety are qualitatively different from the love-of-variety approach. While in the latter, an increase in the number of varieties will increase all individuals welfare equally, in the product specification approach, increased number of goods will enable some consumers to buy goods which are closer to their 'most preferred good' than in autarky. However, if before trade some consumers were buy their 'most preferred good', trade will not increase (but also not reduce) the welfare for this particular group of consumers. Obviously, since some consumers will better off than before trade (and none will be worse off), the total consumers welfare (in both countries) will have increased after trade. Also as in the love-of-variety models, this approach does not predict the direction of trade (unless extended to include differences in initial factor endowments). 2.4 Homogeneous goods models: 'reciprocal dumping' approach The possibility of two-way trade in perfectly homogeneous goods (also called "cross-hauling"), has been first studied by Brander (1981) and Brander and Krugman (1983). All the models considered up until now, assumed free-entry of firms and that markets are integrated rather than segmented.

Brander (1981) developed a model with a single industry consisting of two firms, each in a different country, that behave in a Cournot setting, i.e., firms are assumed to be able to choose separately their deliveries to each national market and take the other firm's deliveries to each market as given. If trade is non-existent, both firms will act as monopolists in their home markets, restricting output in order to sustain monopolistic profits (setting the price where MC=MR). If trade is possible, however, firms will have the incentive to sell small amounts in the other firm's market, as long as prices exceed marginal cost. Since the foreign market is smaller than the domestic market, each firm sees itself facing a higher elasticity of demand on its exports than it does on its domestic sales. This implies that each firm is willing to sell abroad at a lower price than at its domestic market. This phenomenon is what Brander and Krugman (1983) called 'reciprocal dumping'. In this model, because symmetry is assumed, firms will invade each other markets until each firm has captured a 50% share of each market. 17

18

When considering transportation costs (in this model, transportation costs are assumed to 'shrink' the volume of exports, which implies that, the higher the transportation costs, the less exports will reach the foreign market), the outcome will not be as extreme. Since a country imports are negatively related to transportation costs, higher costs will imply a lower level of (intra-industry) trade. However, this model shows that even with transportation costs, two-way trade in homogeneous goods may still happen. From the fact that marginal revenue in the exports market is higher than the marginal revenue in the domestic market, in turns out that firms will be able to bear this extra cost and sell in the other firm's market (at a lower price than it sells in the domestic market). Moreover, Brander (1981) and Brander and Krugman (1983) show that despite the waste involved in transporting the same good in two directions, trade can still be welfare improving (by diminishing each firm's monopolistic power and thus increasing efficiency). In conclusion, this approach has the merit of showing that when markets are segmented, intra-industry trade in identical commodities can occur as a result of 'reciprocal dumping' of oligopolist firms that behave in a Cournot fashion. When considering transportation costs, the volume of "cross-hauling" will not be as large but will nevertheless be possible. One obvious limitation to this approach is the fact that this model relies on the assumption that firms take the other firm's output as given. Some authors have criticized this model on the grounds that the assumption that firms behave in a Cournot environment, is not realistic and lacks of empirical foundation. However, when considering industries where the output decision is taken only once a year, a given firm will take the output level of the other firms as given, or at least as being 'sticky'. In these cases, this model may be considered as a reasonable approximation to reality. 3. Conclusions All the approaches discussed in this chapter presented models that explain the phenomenon of intra-industry trade in different (and sometimes conflicting) ways. We have seen that, alternative assumptions on the nature of product differentiation and consumers behaviour, can lead to competing hypothesis on the effects of the level of development and market size of trading partners on their level of intra-industry trade. More specifically, while in the vertical differentiation models (differentiation by quality approach) differences in the initial factor endowments are a prerequisite for the existence of IIT, in the horizontal differentiation models (both the love-of-variety and the product specification approaches), similarity in factor endowments as well as in the market size, are more likely to be associated with intra-industry trade. Since a country capital to labour ratio is positively related to its income per capita, the horizontal differentiation models suggest that the "more similar countries are in per capita income, the larger the share of intra-industry trade in their bilateral trade volume" (Helpman and Krugman (1985), p.173.). On the other hand, as the number of varieties produced in each country is proportional to its market size (because of economies of scale) and since only preference diversity leads to IIT, the horizontal differentiation models predict that the more similar any two countries are in terms of market size, the higher the potential for IIT.

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APPENDIX A: A.1 In order to prove that ∂U/∂n>0, I will make use of an example set by Vousden (1990). If each individual's income equals the wage rate w, then the utility from consumption of n varieties is 14 : U = nv(c) then: dnv(c) = v(c) + nv(c' ) dn ⎡ ⎛ w ⎞⎤ = v(c) + n ⎢v' (c).⎜⎜ − 2 ⎟⎟⎥ ⎝ pn ⎠⎦ ⎣ = v(c) − v' (c).c when v''<0 and v'(0)≥0, the average utility (v/c) is always larger than the marginal utility [v'(c)]. This implies that: dU >0 dn A.2 Consumers will maximize the utility: n

max U = ∑ v ( ci ) =v ( c1 ) + v ( c2 ) + ... + v ( cn ) i =1

p1c1 + p2 c2 + ... + pn cn = w

s. t .

where w = income (which is equal to the wage by assumption) and pi = price of variety i. The Lagrangian function is: L=

n

∑ v(c ) + λ( w − p c i

1 1

+ p2 c2 + ... + pn cn )

i =1

which implies: ∂L = v '( ci ) − λpi = 0 ∂ci so that: dci λ = dpi v ' ' ( ci )

then:

εi = −

v '( ci ) dci pi λ pi =− =− v ''( ci ) ci v ''( ci ). ci dpi ci

(equation 4)

A.3 14Note

that because w=pnc, c is equal to w/pn. 19

20

From the previous note we have v ' ( ci ) = λpi which for the specific case when ci=ciθ, implies that v'(ci)=θciθ. We then obtain the value of ci: 1

⎛ λ ⎞θ −1 ci = ⎜ ⎟ piθ −1 ⎝θ ⎠ 1

From the consumer's budget constraint, we know that ci =

w n

∑p

. θ

i

i =1

Then, by substituting in the previous expression, we obtain: λ wθ −1 = θ − 1 θ θ ⎞ ⎛ ⎜ ∑ piθ −1 ⎟ ⎟ ⎜ ⎠ ⎝ By substituting this expression for (λ/θ) into equation v'(ci)=λpi, we obtain the following solution for ci: 1

ci =

wp θ −1 n

∑p

θ θ −1

i

i =1

which in the logarithmic form corresponds to: ⎛ n θ ⎞ 1 log pi − log⎜⎜ ∑ piθ −1 ⎟⎟ log ci = log w + θ −1 ⎝ i =1 ⎠ then by differentiating with respect to pi: ⎛ θ ⎞ d log ci dci 1 1 1 ⎛ θ ⎞ ⎜⎝ θ −1 −1⎟⎠ = − n θ ⎜ ⎟ pi dci dpi θ − 1 pi θ −1⎠ θ −1 ⎝ ∑ pi i =1

θ θ −1

1 pi dci p ⎛ θ ⎞ = − n i θ ⎜ ⎟ θ −1⎠ ci dpi θ − 1 θ −1 ⎝ ∑ pi i =1

n

If we let

∑p

θ θ −1

i

θ θ −1

= npi

, then:

i =1

pi dci 1 1 θ = − ci dpi θ − 1 n θ − 1

If we assume n to be very large, 1/n becomes zero which implies that: 1 εi = (since the above expression corresponds to -εi) 1− θ

A.4 In section A.2 we saw that: pi = λ-1 . v'(ci) when n is very large, λ-1 becomes negligible, so that: 20

21

pi = v'(ci) The representative firm profits are given by: πi=pixi-(α+βxi)w then by differentiating with respect to xi, we obtain: dπ i d (v' (ci ) = xi − βw dxi dxi = v ' ( ci ) + v ' ' ( ci )

dci xi − β w dxi

Since xi=Lci, dci/dxi=1/L, so that: dπ i = v ' ( ci ) + v ' ' ( ci ). ci − β w dxi ⎛ v' ' (ci ).ci ⎞ ⎟⎟ − βw = pi ⎜⎜1 + p i ⎝ ⎠ ⎛ 1⎞ = pi ⎜⎜1 + ⎟⎟ − βw ⎝ εi ⎠ pi ⎛ ε i ⎞ ⎟β =⎜ w ⎜⎝ ε i − 1 ⎟⎠

(equation

7)

A.5 By differentiating equation (9) with respect to L, we obtain: dn L ' ( α + β xi ) − L ( α + β xi )' = dL ( α + β xi ) 2 substituting xi by Lci and deriving, we obtain: dc ⎞ ⎛ α + βLci − βL⎜ ci + L i ⎟ dn dL ⎠ ⎝ = 2 dL (α + βLci ) dc α − βL2 i dL = (α + βLci )2 Clearly, the result depends on the sign of dci/dL. In order to determine the result of dci/dL, we need to find the total derivatives of curve PP (equation 7) and curve ZZ (equation 8).

The PP curve is given by:

21

22

pi ⎛ ε (ci ) ⎞ ⎟β =⎜ w ⎜⎝ ε (ci ) − 1 ⎟⎠ and the ZZ curve is given by: pi α =β+ w Lci Their total derivatives are: ε ' (ci ) β ⎛p ⎞ d⎜ i ⎟ = − dc (ε (ci ) − 1)2 i ⎝w⎠

α ⎛p ⎞ {− dci − dL} d⎜ i ⎟ = 2 ⎝ w ⎠ (Lci ) For simplicity, let: ε ' (ci ) β =φ (*) (ε (ci ) − 1)2

α

(Lci )2

= δ (**)

Then, the expression becomes: ⎛p ⎞ d ⎜ i ⎟ = −φ .dci ⎝w⎠ ⎛p ⎞ d ⎜ i ⎟ = −δdci − δdL ⎝w⎠

Transforming we get the values of d(pi/w) and dci: φδ ⎛p ⎞ d⎜ i ⎟ = .dL ⎝ w ⎠ φ −δ δ dci = − . dL δ−φ It is clear from (**) that δ >0. From (*) we can see that the value of φ will assume the same sign of the elasticity of substitution, ε'(ci). This results imply that: When ε'(ci)<0 [case 1] d(pi/w)/dL>0 dci/dL<0 dn/dL>0 When ε'(ci)=0 [case 2] d(pi/w)/dL=0 dci/dL<0 (it is equal to -1) dn/dL>0

22

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When ε'(ci)>0 [case 3] d(pi/w)/dL<0 dci/dL<0 (when δ >φ) dn/dL>0 The condition that δ >φ states that when PP is downward sloping [case 3], the PP curve must be flatter than the ZZ curve, otherwise dci/dL will not be lower than zero and therefore dn/dL will not be positive 15 . On the other hand, since xi=Lci: dxi = dL + dci = [1-(dci/dL)]dL −φ dL = δ−φ which implies that: when εi<0, dxi/dL>0 εi=0, dxi/dL=0 εi>0, dxi/dL<0

It is important to note, however, that when δ < φ, the results for case 3 will be the opposite, that is, d(pi/w)/dL>0, dci/dL>0 and therefore dn/dL<0. In accordance to Helpman and Krugman (1989), I will restrict the analysis to the case when the PP curve is flatter than the ZZ curve, or when δ > φ. 15

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Helpman, E. and Krugman, P. (1985) "Market structure and foreign trade: increasing returns, imperfect competition and the international economy", Cambridge, MIT press. Helpman, E. and Krugman, P. (1989) " Trade policy and market structure", London, MIT press. Hoteling, H. (1929), "Stability in competition", Economic journal, 39, pp. 41-57. Hughes, K. S. (1993) "Intra-industry trade in the 1980s: a panel study", Weltwirtschaftliches Archiv, 130, 1994, pp. 561-572. Krugman, P. (1979), "Increasing returns, monopolistic competition and international trade", Journal of international economics, 9, pp. 469-479. Krugman, P. (1980), "Scale economies, product differentiation and the pattern of trade", American economic review, 70, pp. 950-959. Krugman, P. (1990), "Rethinking international trade", London, MIT press. Lancaster, K.J. (1975) "Socially optimal product differentiation", American economic review, 66, pp. 567-585. Lancaster, K.J. (1979) "Variety, equity and efficiency", Oxford, Basil Blackwell. Lancaster, K.J. (1980) "Intra-industry trade under perfect monopolistic competition", Journal of international economics, 10, pp. 151-175. Lawrence, C. and P. T. Spiller (1983) “Product diversity, economies of scale and international trade”, Quarterly journal of economics, 97, pp. 63–83. Shaked, A. and Sutton, J. (1984), “Natural Oligopolies and International Trade”, In Kierzkowski, H. (ed.) (1984), “Monopolistic Competition and International Trade”, London, Claredon. Somma, E. (1994) "Intra-industry trade in the European computer industry", Weltwirtschaftliches archiv, 130, pp.784-799. Stone, J.A. and Lee, H-H (1995) "Determinants of intra-industry trade: a longitudinal, cross-country analysis", Weltwirtschaftliches archiv, 131, pp. 6785. Verdoon (1960) "The intra-block trade of Benelux". In Robinson, E.A.G. (1960), "Economic consequences of the size of nations", London, Macmillan. Vousden, N. (1990) "The economics of trade protection", Cambridge, Cambridge university press.

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