A comparison of two models of intra-industry trade

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A comparison of twomodels of intra-industrytradeYingfeng XuPublished online: 09 Dec 2010.

To cite this article: Yingfeng Xu (2002) A comparison of two models ofintra-industry trade, The Journal of International Trade & EconomicDevelopment: An International and Comparative Review, 11:4, 405-427,DOI: 10.1080/0963819022000014258

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A comparison of two models ofintra-industry tradeYingfeng XuUniversity of Alberta, Edmonton, Canada

Abstract

A direct comparison is made between two models of intra-industry trade: the love-of-varieties model and the Armington model. The former is a textbook model that istheoretically appealing, but seldom used in applied studies of trade policy. The latterhas been widely used in CGE modelling, but is barely mentioned in textbooks. We� nd that what really differentiates the two models empirically is not the incorporationof increasing returns and monopolistic competition, but the elasticity of substitutionbetween domestic and foreign differentiated products. The Armington model with anin� nite elasticity of substitution can mimic the love-of-varieties model.

Keywords

Intra-industry trade, Armington model, love-of-varieties model.

1. INTRODUCTION

Intra-industry trade has increasingly grown to become much more importantsince Balassa (1966) and Grubel and Lloyd (1975) extensively documentedits presence. Indeed, new trade theories based on imperfect competition andincreasing returns to scale are speci� cally designed to explain the pattern ofintra-industry trade, as traditional theories of comparative advantage accountfor only inter-industry trade. In the general equilibrium setting, intra-industry trade is usually analysed with models of monopolistic competition.In particular, based on the work of Spence (1976) and Dixit and Stiglitz(1977) and popularized by Helpman and Krugman (1985), the love-of-varieties (LOV) model has become a standard textbook model for intra-industry trade in horizontally differentiated products.

However, the new trade theories do not provide the only explanation ofintra-industry trade. Within the framework of classical trade theories ofcomparative advantage, intra-industry trade can be modelled by incorporat-ing the Armington (1969) speci� cation that the same products produced bydifferent economies are treated as differentiated. Of course, the Armingtonmodel is often regarded as a less satisfactory ad hoc construct, it is not even

Address for CorrespondenceDepartment of Economics, University of Alberta, Edmonton, Alberta T6G 2H4,Canada. E-mail: [email protected]

J. Int. Trade & Economic Development 11:4 405–427

The Journal of International Trade & Economic DevelopmentISSN 0963-8199 print/ISSN 1469 9559 online © 2002 Taylor & Francis Ltd

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mentioned in most trade textbooks (e.g. Wong, 1997). However, theArmington model of intra-industry trade has been widely adopted incomputable general equilibrium (CGE) studies of trade policy. In contrast,despite its appealing theoretical features, the LOV model of intra-industrytrade has seldom been applied in empirical studies of trade policy.

How different is the Armington model from the LOV model? What arethe consequences of using the Armington model, if the LOV model shouldbe the better alternative? Is the LOV model really superior to the Armingtonmodel in that it can better explain empirical patterns of trade? These areimportant questions, especially for applied studies of trade policy. However,most trade textbooks provide no clear answers. The objective of the presentpaper is to make a direct comparison of the LOV and Armington models ina general equilibrium setting of two economies, two sectors, and two factors.We pinpoint the essential difference between these models. We also com-pare how these two models would behave in response to changes in thedeterminants of comparative advantage – differences in factor endowmentsand in technology – and to changes in trade policy. Since we want to knownot only the differences between the two models, but also the magnitude ofsuch differences, we make use of numerical simulation in our comparison.

Our main � nding is that the LOV model and the Armington model areactually very similar to each other in their predictions with regard to tradepatterns. The incorporation of increasing returns to scale and imperfectcompetition in the LOV model is not, however, the critical factor thatdifferentiates the two models. What we � nd, but which is seldom mentionedin trade textbooks, is that the main difference between the two models liesin how sensitively the production structure responds to changes in thedeterminants of comparative advantage and trade policy. In simple terms,the main difference between the two models can be encapsulated by the factthat, in the LOV model, relative supply determines relative demand, whereasin the Armington model, relative demand determines relative supply. In turn,the critical parameter for that difference is the elasticity of substitutionbetween the home-produced and foreign-produced differentiated products.With respect to the response to changes in the determinants of comparativeadvantage, the Armington model with an elasticity of substitution approach-ing in� nity can mimic the LOV model very well. In this sense, the LOVmodel can be regarded as a special limit case of a more general Armingtonmodel that may have an elasticity of substitution ranging from zero toin� nity. Furthermore, with respect to the response to changes in trade policy,the Armington model with a small elasticity of substitution resembles theLOV model. The optimal tariff argument applies to both models. As far aspredictions of trade policy effects are concerned, the LOV model does notoffer any more than what can be provided by a simpler Armington model. Insum, despite a more appealing explanation of the micro-foundation, theLOV model does not really offer, as is usually claimed in the trade literature,

406 The Journal of International Trade & Economic Development

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a superior way to analyse intra-industry trade and evaluate the effects oftrade policy, especially when the practical dif� culties in applying the LOVmodel in CGE studies are recognized.

The rest of the paper is organized as follows. Section 2 describes theLOV model, while Section 3 describes the Armington model. Section 4 thencompares the two models on the basis of identical benchmark equilibrium.Section 5 concludes the paper.

2. THE LOVE-OF-VARIETIES MODEL

Consider a standard textbook model. There are two sectors. Sector 1 iscapital-intensive and produces differentiated products that generate two-wayintra-industry trade. Sector 2 is labour-intensive and produces a homoge-neous good for which there is only inter-industry trade. With productdifferentiation, the number of products can potentially be very large.However, as is discussed in Lloyd (1994), we can reduce the dimension oftradable goods down to three: the home-produced differentiated product, theforeign-produced differentiated product, and the homogeneous product. Theworld consists of two economies. A complete LOV model is speci� ed asfollows.

Let s1, w and r be the output of the differentiated product per � rm, thewage rate, and the rental rate. Following common practice in the literature,we consider a symmetric equilibrium in which all � rms are assumed to beidentical. The total cost function is assumed to have the form of TC 5 ( f 1

s1)A1w12 a 1 ra 1, where f is the � xed cost parameter, s1 is the output of a

representative � rm/variety, A1 is a scale parameter, and a 1 is a parameter thatdetermines the cost share of capital (capital intensity). A1 w12 a 1 r a 1 is theconstant marginal cost that depends only on factor prices, while f A1w

12 a 1 r a 1

is � xed cost. The presence of � xed cost generates increasing returns to scalethat is an essential feature of imperfect competition models of trade.

The preference for the differentiated good is represented by a CES sub-utility function:

D1 5 S O ni 5 1

di

s 2 1s D s

s 2 1,

where D1 is the sub-utility of differentiated products, di are the demand pervariety and s is the elasticity1 of substitution between differentiated prod-ucts. If the equilibrium n is large, s can approximate the demand elasticity.2

In that case, marginal revenue is related to price in the familiar way: MR 51 1 2 (1/ s )2 p, where MR is marginal revenue. The equilibrium of monopolis-tic competition is characterized by the equality of marginal revenue andmarginal cost on the one hand, and the equality of price and average cost onthe other. The pair of these conditions implies:

Two models of intra-industry trade 407

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s1 5 (s 2 1) f (1)

In other words, s1 is independent of n, determined only by s and f .3 Theother condition of monopolistic equilibrium is the � rst-order condition forpro� t maximization:

p1S 1 21s D # A1w

12 a 1 r a 1, n $ 0, nF p1S 1 21s D 2 A1w

12 a 1 r a 1G 5 0 (2)

Equation (2) provides a general speci� cation that incorporates complemen-tary slackness. It allows for the possibility that a feasible equilibrium valueof n may be zero, i.e. the economy becomes completely specialized in thelabour-intensive homogeneous good.

The speci� cation of the perfect competition equilibrium for Sector 2 ismuch simpler. it is the relation between price and average cost.

p2 5 1 # A2w12 a 2 r a 2, S2 $ 0, S2_ 1 2 A2w

12 a 2 r a 2+ 5 0 (3)

Again, equation (3) provides a general speci� cation that allows for thepossibility that the output of good 2 may be zero in equilibrium when aneconomy is specialized in good 1.

Another set of conditions on the supply side is given by the equilibriumin factor markets. The derivatives of the unit cost functions with respect tothe wage rate and the rental rate give the demand functions for labour andcapital per unit of output. Therefore, the equilibrium conditions for thelabour and capital markets are:

S f

s1

1 1D (1 2 a 1)S wr D 2 a 1

ns1 1 (1 1 a 2)S wr D 2 a 2

S2 5 L (4)

S s

s1

1 1D a 1 S wr D 12 a 1

ns1 1 a 2S wr D 12 a 2

S2 5 K (5)

where L and K are the supplies of labour and capital.The foreign economy has a similar structure. Therefore, equations

(6)–(10) are the corresponding equations for the foreign economy.

s*1 5 (s 2 1) f * (6)

p*1 S 1 21s D # A1w*12 a 1 r* a 1, n*$ 0, n* F p*1 S 1 2

1s D

2 A1 w*1 2 a 1 r*a 1G 5 0 (7)

p*2 5 1 # A2w*1 5 a 2 r* s 2, S*2 $ 0, S*2 _ 1 2 A2w*12 s 2 r* a 2 + 6 0 (8)


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S f *s*1

1 1D (1 2 a 1) S w*r* D 2 a 1

n*s*1 1 (1 2 a 2)S w*r* D a 2

S*2 5 L* (9)

S f *s*1

1 1D a 1S w*r* D 12 a 1

n* s*1 1 a 2S w*r* D 12 a 2

S*2 5 K* (10)

To simplify analysis, we consider only the trade policy in the form oftariff levied on the imports of the differentiated good. Income consists of thesum of factor income and import tariff revenue. It is de� ned as follows forthe two economies:

Y 5 wL 1 rK 1 t(n* p* f1) (11)Y* 5 w* L* 1 r* K* 1 t* (npd*1) (12)

where f1 and d*1 are the home demand for a typical foreign variety and theforeign demand for a typical home variety as de� ned below, t and t* are thehome and foreign tariff rates on the imports of good 1.

Let the aggregate utility take a simple Cobb–Douglas form: U 5D1

u D212 u , where U is and D2 is the demand for the homogenous good. Such

utility has the property that the expenditure shares of the two goods areconstant. Let d1 and f1 be the demand of the home economy for the homeand foreign differentiated products. It can be shown that they have thefollowing form:

d1 5p12 s

np12 s 1 n*(1 1 t)p*12 s · u Yp

(13)

f1 5(1 1 t)p*1 2 s

np12 s 1 n*(1 1 t)p*12 s · u Y

(1 1 t)p*(14)

Similarly, let d*1 and f *1 be the demand the foreign economy for the homeand foreign differentiated goods. They are as follows:

d*1 5(1 1 t*)p12 s

n(1 1 t*)p12 s 1 n* p*12 s · u Y

(1 1 t*)p(15)

f*1 5p*12 s

n(1 1 t*)p12 s 1 n* p*12 s · u Yp*

(16)

In the present model, there are three distinct markets: the market forhome-produced differentiated products, the market for foreign-produceddifferentiated products, and the market for the homogeneous good. Accord-ing to Walras’ law, only two of the three goods market equilibriumconditions are independent. We choose to use the equilibrium conditions forthe two differentiated goods. They are speci� ed as follows:

s1 5 d1 1 d*1 (17)s1* 5 f1 1 f*1 (18)


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The set of structural equations (1)–(18) forms a complete model thatdetermines the values of 18 endogenous variables: s1, s*1, w, w*, r, r*, n, n*,S2, S*2, Y, Y*, d1, d*1, f1, f*1, p1 and p*1, with p2 5 1 being the numeraire.Once their values are solved, other endogenous variables can be computed.Equation (19) de� nes the � ow of inter-industry trade (NT), while equation(20) shows the extent of intra-industry trade (IT) in the differentiated good.NT measures the exports of good 2, or the balance of the intra-industry tradein good 1 (the differentiated product). IT is a conventional measure of intra-industry trade. IT varies between 0 and 1. When IT 5 0, there is onlyinter-industry trade; when IT 5 1, there is only intra-industry trade; when ITis in between 0 and 1, there are intra- as well as inter-industry trade. In fact,the difference, 1 – IT, measures the proportion of total trade in good 1 thatis inter-industry trade.

NS 5 S2 2 D2 5 n* p* f1 2 npd*1 (19)

IT 5 2min(n* p* f1, npd *1)/(n* p* f 1 1 npd*1) (20)

Equations (22)–(24) calculate the levels of aggregate utility and the sub-utility of the differentiated good for the two economies.

U 5 D1u D2

12 u (21)

D1 5 S nd1

s 2 1

s 1 n* f 1

s 2 1

s D s

s 2 1 (22)

U* 5 D*1u D*2

12 u (23)

D*1 5 S nd*1

s 2 1

s 1 n * f*1

s 2 1

s D s

s 2 1 (24)

3. THE ARMINGTON MODEL

The Armington model of intra-industry trade can be speci� ed by making afew modi� cations to the above model. The essential idea of the Armingtonmodel is product differentiation by country. To make the comparisonbetween the two models as close as possible, the Armington model has asimilar structure. There is intra-industry trade only in sector 1 and sector 2produces a homogeneous good. The complete model is speci� ed as follows.One major difference from the LOV model is that the sectoral output ofgood 1 is not broken down into the number of varieties/� rms and output pervariety/� rm. Therefore, S1 (the sectoral output of good 1) replaces ns1. Thismodi� cation means that equations (1) and (6) can be deleted. A correspond-ing change in the cost function is that the presence of � xed cost is no longerneeded. The average cost function for sector 1 becomes A1w

12 a 1 r a 1, which isthe same as marginal cost. Accordingly, the labour and capital demand perunit of output in sector 1 also need to be modi� ed accordingly.


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To summarize the modi� cations, the equations (25)–(32) specify the setof structural equations on the supply side for the two economies. Equations(25)–(26) and (29)–(30) relate product prices to factor prices for the twoeconomies through the condition of perfect competition. Equations (27)–(28)and (31)–(32) specify the full employment conditions in labour and capitalmarkets for the two economies.

p 5 p1 5 A1w12 a 1 r a 1, S1 $ 0, S1_ p1 2 A1w

1 2 a 1 r a 1+ 5 0 (25)p2 5 1 5 A2w

12 a 2 r a 2, S2 $ 0, S2_ 1 2 A2w12 a 2 r a 2+ 5 0 (26)

(1 2 a 1)S wr D 2 a 1

S1 1 (1 1 a 2)S wr D 2 a 2

S2 5 L (27)

a 1S wr D 12 a 1

S1 1 a 2 S wr D 12 a 2

S2 5 K (28)

p* 5 p*1 5 A1w*1 2 a 1 r a 1, S*1 $ 0, S*1 _ p* 2 A1w*12 a 1 r a 1 + 5 0 (29)p*2 5 1 5 A2w*12 a 2 r a 2, S*2 $ 0, S*2 _ 1 2 A2w*1 2 a 2 r a 2+ 5 0 (30)

(1 2 a 1)S w*r* D 2 a 1

S*1 1 (1 2 a 2) S w*r* D 2 a 2

S*2 5 L* (31)

a 1S w*r* D 12 a 1

S*1 1 a 2S w*r* D 12 a 2

S*2 5 K* (32)

Let D1 (D*1) and F1 (F*1) be the demand of the home (foreign) economy forthe home-produced and foreign-produced good 1. Similarly to the LOVmodel, a tariff is levied only on the imports of good 1. Therefore, incomeconsists of factor income and tariff revenue for both economies:

Y 5 wL 1 rK 1 tp*F 1 (33)Y* 5 w* L* 1 r* K* 1 t pD*1 (34)

Once the budget constraint is known, the four demand functions4 for good1 are computed as follows:

D1 5d p1 2 s

d p12 s 1 (1 2 d )(1 1 t)p*12 s

u Yp

(35)

F 1 5(1 2 d )(1 1 t)p*12 s

d p12 s 1 (1 2 d )(1 1 t)p* 12 s

u Y(1 1 t)p*

(36)

D*1 5d (1 1 t*)p*12 s

d (1 1 t*)p12 s 1 (1 2 d )p*1 2 s

u Y*(1 1 t)p

(37)

F*1 5(1 1 d )p*12 s

d (1 1 t*)p12 s 1 (1 2 d )p*1 2 s

u Y*p*

(38)

where d is a parameter that determines the mix of the expenditure shares onthe home- and foreign-produced good 1.


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Similarly, in this model, there are three distinct markets: the market forthe home-produced good 1, the market for the foreign-produced good 1, andthe market for good 2. Only two of the three goods market equilibriumconditions are independent. We choose to use the following two.

S1 5 D1 1 D*1 (39)S*1 5 F 1 1 F*1 (40)

The complete model as speci� ed by the set of equations (25)–(40)determines the values of 16 endogenous variables: w, w*, r, r*, S1, S*1, S2,S*2, Y, Y*, D1, D*1, F 1, F*1, p1 and p*1. Once they are solved, equation (41)measures inter-industry trade (NT) and equation (42) intra-industry trade(IT), similar to equations (19) and (20).

NT 5 S2 2 D2 5 p*1 F 1 2 p1D*1 (41)IT 5 2min(p*1 F 1, p1D*1)/(p*1 F 1 1 p1D*1) (42)

Finally, equations (43)–(46) calculate the levels of aggregate utility and thesub-utility of good 1 for both economies.

U 5 U1u D2

12 u (43)

U1 5 S D1

s 2 1

s 1 F1

s 2 1

s D s

s 2 1 (44)

U* 5 U*1u D*2

12 u (45)

U*1 5 S D*1

s 2 1

s 1 F*1

s 2 1

s D s

s 2 1 (46)

4. COMPARISON

How do the LOV model and the Armington model differ from each other?An apparent difference is that in the LOV model, the sectoral output of good1 (S1) is further decomposed into the number of varieties/� rms (n) andoutput per variety/� rm (s1). How signi� cant is this feature? The answerdepends on three considerations.

First, the decomposition of S1 into n and s1 affects welfare evaluation.Furthermore, the value of the elasticity of substitution, s , plays a signi� cantrole here. To illustrate this point, consider a symmetric equilibrium in whichthe demand per variety is the same for all varieties. The sub-utility ofconsuming good 1 is D1 5 n

ss 2 1d1. Observe the difference in the way a

change in n and that in d1 affects utility. Since s is assumed to be larger than1.0, a given percentage increase in n raises utility more than that in d1. Inother words, the contribution to utility of a given percentage increase in D1

depends on how it comes about. Only in the limit case of s approachingin� nity does D1 become linear in n and the distinction between n and d1disappears. Of course, this is a feature central to the idea of monopolistic


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competition. With given resources, aggregate consumption of good 1 wouldbe larger if less varieties are produced due to the presence of increasingreturns to scale. Therefore, if a premium is placed on the number ofvarieties, the optimal number of varieties would be something greater thanone, the minimum value for s .

Although the decomposition is of some theoretical interest, it does notfollow that the LOV model necessarily offers a superior explanation of howthe sectoral output of the differentiated good is determined. Note that, in theLOV model, s1 is determined by only two parameters, s and f , and isindependent of all the other variables. Therefore, s1 is invariant to changes inthe determinants of trade pattern such as factor endowments and technolo-gies, it is also invariant to changes in trade policy. It implies that any changein the sectoral output, S1, is effected only through changes in the number ofvarieties/� rms, n. Intuitively, this feature does not appear to be quiterealistic. Operationally, the substitution of n for S1 does not yield any newinsights.

Second, the decomposition does not provide variables that are directlyobservable and measurable. While the decomposition of S1 into n and s1 ina symmetric equilibrium can be rationalized as a theoretical simpli� cation, itis dif� cult operationally to translate n and s1 into measurable data. Ad hocprocedures must be adopted to � t the model to the real world.

Finally, as demonstrated by the Armington model, the decomposition ofS1 into n and s1 is not indispensable for explaining intra-industry trade. Thecritical piece in the story of intra-industry trade is product differentiation.And that is separable conceptually from increasing returns to scale andmonopolistic competition. In sum, the decomposition does not necessarilymake the LOV model a superior explanation of intra-industry trade, althoughit appears to provide a more appealing story of � rm behaviour.

As well as the decomposition feature analysed above, there is a materialdifference between the LOV model and the Armington model in the way theratio of the demand for the home-produced differentiated products tothe demand for the foreign-produced differentiated products is determined.In the LOV model, the [n(d1 1 d*1)]/[n*(F1 1 F*1)] ratio (for the homeeconomy) is not affected directly by the price ratio, p1/p*1, and dependsmainly on the ratio, n/n*. To better see this property, consider a symmetricequilibrium in which demand per variety is identical. In that case, weobserve that s1/s*1 5 (d1 1 d*1)/(f1 1 f*1) 5 (p1/p*1)

2 s . Because therelative supply ratio, s1/s*1, is independent of the relative price ratio, p1/p*1,the causality in the above relationship runs from s1/s*1 to p1/p*1. Accord-ingly, the [n(d1 1 d*1)]/[n*(f1 1 f*1)] ratio is proportional to the n/n* ratio.It follows that, in the LOV model, for the differentiated products, relativesupply determines relative demand in the one-way direction. Any factorsthat affect n and n* on the supply side affect relative demand accordingly. Inother words, preferences do not impose any independent in� uence on the


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ratio of the supply of the home-produced products and that of the foreign-produced differentiated products. This peculiar nature resembles theHeckscher–Ohlin model of a small open economy. With exogenouslydetermined product prices, production structure is entirely determined byfactors on the supply side. It follows that production structure as re� ected inthe S1/S2 ratio is highly sensitive to any factor that affects the demand andsupply in the labour and capital markets.

In contrast, the (D1 1 D*1)/(F 1 1 F*1) ratio in the Armington model isdetermined uniquely by the p1/p*1 ratio. In turn, the relative supply, S1/S*1,is constrained by the relative demand, (D1 1 D*1)/(F 1 1 F*1), in the worldas a whole. This relationship can be summarized as relative demanddetermining relative supply. Any factor that affects the S1/S*1 ratio mustwork its way through its impact on the p1/p*1 ratio. This is a normalbehaviour of most general equilibrium models of a closed economy. In thiscontext, the elasticity of substitution, s , plays an important role. It determi-nes how a sensitive production structure (S1/S2) would change in response toa shift in an exogenous variable through its effect on the relative productprice (p1/p2).

The above comparison suggests that the critical factor that differentiatesthese two models is the size of s . In the LOV model, the productionstructure as re� ected by the S1/S*1 ratio would respond sensitively tochanges in any exogenous factors that affect the supply side. With an sapproaching in� nity, the Armington model would resemble a LOV model.How similar would these two models be in predicting trade patterns andevaluating the effects of trade policy? This is a natural question to ask, giventhe resemblance between the models. Since it is dif� cult to obtain anunambiguous general analytical answer, we resort to numerical simulationfor comparison.

The present study focuses on comparing how the two models respond tochanges in three exogenous variables: differences in factor endowments,differences in technology and trade policy. Following the common percep-tion, we assume that good 1 is more capital-intensive than good 2.Speci� cally, we assume that a 1 5 0.7 and a 2 5 0.3. To facilitate a closecomparison, the production structure and trade pattern in the benchmarkequilibrium are the same for both models. The benchmark equilibrium iscalibrated to produce the following set of endogenous variables: p 5 p* 5w 5 w* 5 1, r 5 r* 5 0.1, S1 5 S*1 5 S2 5 S*2 5 100 for both models,and n 5 n* 5 s1 5 s*1 5 10 for the LOV model. The benchmarkequilibrium implies that the factor supplies are: L 5 L* 5 100 and K 5 K*5 1000; the expenditure share for differentiated products is u 5 0.5; for theLOV model, f 5 10, A1 5 2.51, and A2 5 2.00; for the Armington model,A1 5 5.01 and A2 5 2.00. Since neither country has comparative advantagein the two goods, there is only intra-industry trade in differentiated productsbut no inter-industry trade in the benchmark equilibrium.


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4

As explained above, the elasticity of substitution ( s ) is the criticalparameter that affects the extent to which these two models resemble eachother. What value should we choose for s ? Our tentative choice is s 5 10.This value is much higher than the typical values that have been used inmany CGE models that incorporate the Armington model of intra-industrytrade, but is far from in� nity. For example, the range of the elasticities ofsubstitution used in a recent study of trade liberalization among APECcountries (APEC, 1997) is from 1.9 (trade and transport, construction, publicand private services) to 5.2 (transport equipment). Such estimates of theelasticity of substitution come mainly from econometric studies. Anyway,the particular value chosen for s is not crucial for our � ndings, because ourobjective is not to perform accurate simulations of trade policy in a realisticsetting, but to explore how the difference in the behaviour of the two modelsis systematically related to the value of s . To spotlight the differencebetween the LOV and Armington models, two comparisons are made. In onecomparison, we assume that both models have the same s 5 10. We intendto show, with this comparison, that the production structure in the LOVmodel tends to be much more sensitive to changes in the determinants oftrade pattern than in the Armington model. In the other comparison, weassume that the LOV model has an s 5 10 but the Armington model has ans 5 50. This comparison is designed to demonstrate that, with a suf� cientlylarge s , the Armington model can be made to resemble closely thebehaviour of the LOV model.

4.1 Factor endowments

To show how the difference in factor endowments affects trade pattern, weraise the capital supply of the foreign economy by 100 per cent from 1000to 2000. In other words, the home economy becomes labour-abundant andthe foreign economy becomes capital-abundant. Table 1 presents the com-parison results. Column 1 shows the values of all the endogenous variablesfor the benchmark equilibrium that is identical for both models. Column 2reports the new equilibrium for the LOV model. Column 3 shows the newequilibrium for the Armington model with the same s 5 10, while column4 shows the new equilibrium for the Armington model with s 5 50.

Turning to the comparison, let us � rst examine the effects on p1 and p*1,the relative prices of the home- and foreign-produced differentiated productsin terms of good 2. The common behaviour of the two models is that bothp1 and p*1 fall, re� ecting the impact of the increased world supply of capital.In the LOV model, p1 and p*1 fall from 1.00 to 0.85. In the Armingtonmodel, p1 and p*1 fall from 1.00 to 0.90 and 0.82 with and to 0.86 and 0.84with respectively. However, the two models differ in that in the LOV model,the p1/p*1 ratio remains unchanged, while in the Armington model, thep1/p*1 ratio increases, so the foreign-produced good 1 becomes cheaper


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Tabl

e 1

The

rol

e of

the

dif

fere

nces

in

fact

or e

ndow

men

ts

Vari

able

sSy

mbo

lB

ench

mar

keq

uili

briu

mLO

V m

odel

wit

hs

= 1

0A

rmin

gton

mod

elw

ith

s=

10

Arm

ingt

on m

odel

wit

h s

= 5

0

The

pri

ce o

f go

od 1

, H

ome

p1.

000.

850.

900.

86T

he p

rice

of

good

1,

fore

ign

p*1.

000.

850.

820.

84O

utpu

t pe

r �r

m,

sect

or 1

, H

ome

s 110

.00

10.0

0N

umbe

r of

�rm

s/va

riet

ies,

sec

tor

1, H

ome

n10

.00

5.53

S 110

0.00

55.3

472

.36

59.7

4O

utpu

t pe

r �r

m,

sect

or 1

, fo

reig

ns*

110.

0010

.00

Num

ber

of �

rms/

vari

etie

s, s

ecto

r 1,

for

eign

n*10

.00

21.0

3S*

110

0.00

210.

3019

4.35

206.

40T

he s

uppl

y of

goo

d 2,

Hom

eS 2

100.

0014

1.17

126.

2613

7.40

The

sup

ply

of g

ood

2, f

orei

gnS*

210

0.00

84.7

098

.00

88.0

0T

he w

age

rate

, H

ome

w1.

001.

131.

081.

12T

he w

age

rate

, fo

reig

nw

*1.

001.

131.

161.

14T

he r

enta

l ra

te,

Hom

er

0.10

0.08

0.08

0.08

The

ren

tal

rate

, fo

reig

nr*

0.10

0.08

0.07

0.07

GD

P, H

ome

Y20

0.00

188.

2219

1.58

188.

98G

DP,

for

eign

Y*20

0.00

263.

5125

6.94

261.

83T

he d

eman

d fo

r th

e ho

me

vari

ety,

Hom

ed 1

5.00

4.17

D1

50.0

023

.06

30.9

125

.04

The

dem

and

for

the

fore

ign

vari

ety,

Hom

ef 1

5.00

4.17

F1

50.0

087

.62

83.0

186

.52

Sub-

util

ity o

f di

ffer

entia

ted

prod

ucts

U1

139.

5015

9.34

56.3

455

.60

The

dem

and

for

the

hom

e va

riet

y, F

orei

gnd*

15.

005.

83D

* 150

.00

32.2

841

.45

34.7

0T

he d

eman

d fo

r th

e fo

reig

n va

riet

y, F

orei

gnf*

15.

005.

83F

* 150

.00

122.

6711

1.33

119.

88Su

b-ut

ility

of

diff

eren

tiate

d pr

oduc

ts,

For

eign

U* 1

139.

5022

3.08

75.5

677

.04

Dem

and

for

good

2D

210

0.00

94.1

195

.79

94.4

9D

eman

d fo

r go

od 2

, Fo

reig

nD

* 210

0.00

131.

7612

8.47

130.

91In

ter-

indu

stry

tra

de,

volu

me

NT

0.00

47.0

630

.47

42.9

1In

tra-

indu

stry

tra

de i

n go

od 1

, pe

r ce

ntIT

1.00

0.54

0.67

0.57

Not

e:In

thi

s co

mpa

riso

n, K

* =

200

0 an

d K

= 10

00.

The

oth

er p

aram

eter

s an

d va

riab

les

are:

a1

= 0

.7 a

nd a

2=

0.3

; L

= L*

= 1

00;

the

expe

ndit

ure

shar

e fo

r go

od 1

is

u0.

5; f

or t

he L

OV

mod

el,

f=

10,

A1

= 2.

51 a

nd A

2=

2.0

0; f

or t

he A

rmin

gton

mod

el,

A1

= 5

.01

and

A2

= 2.

00.


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relative to the home differentiated product. What accounts for this differ-ence? This is because, in the LOV model, the p1/p*1 ratio depends, asexplained above, only on the s1/s*1 ratio. Since the latter is unaffected bychanges in factor supplies, the p1/p*1 ratio remains constant. In contrast, inthe Armington model, the initial impact of the increase in the foreign supplyof capital is to expand the supply of the foreign-produced good 1 through theRybczynski effect, reducing the relative price of the foreign-produced good1. Because of the imperfect substitution between the home- and foreign-produced good 1, the price of the home-produced good 1 also falls, but notby as much as the fall in the price of the foreign-produced good 1. Hence therise in the p1/p*1 ratio. However, as shown in Table 1, the size of sconditions the extent to which the p1/p*1 ratio rises. In the case of s 5 10,the p1/p*1 ratio rises to 1.10 but only to 1.03 in the case of s 5 50. It isapparent that as s gets larger, the Armington model resembles more theLOV model.

Now let us compare the response of the production structure. Since theforeign economy becomes capital-abundant, it possesses comparative advan-tage in good 1 and exports good 1 on the net basis and imports good 2.Therefore, there is inter-industry trade between good 1 and good 2 as well asintra-industry trade in good 1. This is the common aspect between the twomodels. A useful indicator is the index of intra-industry trade in sector 1(IT). This index is reduced from 1.00 to 0.54 in the LOV model, and to 0.67in the Armington model with s 5 10 and to 0.57 in the Armington modelwith s 5 50. In both models, the home economy shifts resources to producemore good 2, while the foreign economy now produces more good 1.Speci� cally, the S1/S2 ratio falls from 1.00 to 0.39 in the LOV model, to 0.57in the Armington model with s 5 10 and to 0.43 in the Armington modelwith s 5 50. Correspondingly, the S*1/S*2 ratio rises from 1.00 to 2.48 inthe LOV model, to 1.98 and 2.35 in the two Armington models with the twodifferent s s. Within sector 1, the foreign economy produces more varieties(or aggregate output in the Armington model), while the home economycontracts the production of good 1. The S1/S*1 ratio falls from 1.0 to 0.26 inthe LOV model, but to 0.37 in the Armington model with a s 5 10 and to0.29 in the Armington model with a s 5 50. Again, the pattern is clear: thetwo models become more alike if the value of s in the Armington modelapproaches in� nity.

The same conclusion applies when the responses of factor prices to thechange in factor endowments are compared between the two models. Whenthe world has more capital as a whole, the rental rate would fall and thewage rate would rise. This pattern can also be deduced from the correspond-ing changes in relative product prices, p1 and p*1, due to the Stolper–Samuelson effect. This is the common aspect between the two models. Thedifference between the two models lies in the fact that, in the LOV model,factor prices are equalized but in the Armington mode, they are not. As


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explained above, the factor price equalization property of the LOV model isattributable to the peculiar feature that the p1/p*1 ratio depends only on thes1/s*1 ratio, which is independent of factor endowments. However, with asuf� ciently large s , the Armington model can replicate such a property. AsTable 1 shows, the w/w* and r/r* ratios are 0.93 and 1.19 with s 5 10, butmove to 0.98 and 1.04 as s increases to 50.

To summarize the above comparison, the LOV and Armington modelsare similar qualitatively with respect to the role played by factor endow-ments. The LOV can be regarded as the limit for the Armington model as sapproaches in� nity. With a small value of s close to unity, the two modelscan behave quite differently. In the LOV model, most of the adjustment inresponse to a change in factor endowments is accomplished through reallo-cation of resources in the production of the two goods in an economy; while,in the Armington model, part of the adjustment takes place through changesin relative product and factor prices.

4.2 Ricardian technological differences

As well as the differences in factor endowments as analysed by theHeckscher-Ohlin model, comparative advantage may also arise from thedifferences in technology. According to the Ricardian model, trade can stillbe bene� cial even though one economy is less ef� cient in both sectors thanthe other economy, provided that it is not equally less ef� cient in bothsectors. To explore how the LOV and Armington models would respond totechnological differences between the two economies, we reduce A*1 to 90per cent of A1. For this comparison, the two economies have the same factorsupplies: L 5 100 and K 5 1000. In other words, we let the home economybe equally ef� cient in producing good 2 as the foreign economy, but lessef� cient in producing good 1. Thus, the foreign economy possesses compar-ative advantage in producing good 1. Table 2 shows the comparisonresults.

Qualitatively speaking, the effects of a fall in A*1 are similar to those ofthe increase in K* that we have just discussed. In both LOV and Armingtonmodels, p1 and p*1 decrease because of the productivity gain in sector 1 ofthe foreign economy. The difference between them is that, in the LOVmodel, the p1/p*1 ratio remains unchanged at 1.00, while in the Armingtonmodel, the p1/p*1 ratio rises to 1.03 in the case of s 5 10 and to 1.01 in thecase of s 5 50.

Since the foreign economy has comparative advantage in producing good1, it exports good 1 on the net basis and imports good 2 from the homeeconomy. The index of intra-industry trade for sector 1 is reduced from 1.00to 0.83 in the LOV model, and in the Armington model, to 0.87 in the caseof s 5 10 and to 0.84 in the case of s 5 50. To generate this trade pattern,the output of sector 1 contracts and that of sector 2 expands in the home


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Tabl

e 2

The

rol

e of

the

dif

fere

nces

in

tech

nolo

gy

Vari

able

sSy

mbo

lB

ench

mar

keq

uili

briu

mLO

V m

odel

wit

hs

= 1

0A

rmin

gton

mod

elw

ith

s=

10

Arm

ingt

on m

odel

wit

h s

= 5

0

The

pri

ce o

f go

od 1

, H

ome

p1.

000.

950.

960.

95T

he p

rice

of

good

1,

fore

ign

p*1.

000.

950.

930.

94O

utpu

t pe

r �r

m,

sect

or 1

, H

ome

s 110

.00

10.0

0N

umbe

r of

�rm

s/va

riet

ies,

sec

tor

1, H

ome

n10

.00

8.56

Supp

ly o

f go

od 1

, H

ome

S 110

0.00

85.6

089

.87

86.6

4O

utpu

t pe

r �r

m,

sect

or 1

, fo

reig

ns*

110

.00

10.0

0N

umbe

r of

�rm

s/va

riet

ies,

sec

tor

1, f

orei

gnn*

10.0

012

.59

Supp

ly o

f go

od 1

, fo

reig

nS*

110

0.00

125.

8912

1.75

124.

90T

he s

uppl

y of

goo

d 2,

Hom

eS 2

100.

0011

4.01

109.

9411

3.03

The

sup

ply

of g

ood

2, f

orei

gnS*

210

0.00

86.3

590

.25

87.2

9T

he w

age

rate

, H

ome

w1.

001.

041.

031.

04T

he w

age

rate

, fo

reig

nw

*1.

000.

960.

970.

96T

he r

enta

l ra

te,

Hom

er

0.10

0.09

0.09

0.09

The

ren

tal

rate

, fo

reig

nr*

0.10

0.11

0.11

0.11

GD

P, H

ome

Y20

0.00

195.

1119

6.44

195.

42G

DP,

for

eign

Y*20

0.00

205.

6220

3.93

205.

21T

he d

eman

d fo

r th

e ho

me

vari

ety,

Hom

ed 1

5.00

4.87

D1

50.0

041

.68

44.1

042

.26

The

dem

and

for

the

fore

ign

vari

ety,

Hom

ef 1

5.00

4.87

F1

50.0

061

.30

59.7

460

.93

Sub-

util

ity o

f di

ffer

entia

ted

prod

ucts

U1

139.

5014

4.54

51.8

651

.58

The

dem

and

for

the

hom

e va

riet

y, F

orei

gnd*

15.

005.

13D

* 150

.00

43.9

245

.78

44.3

8T

he d

eman

d fo

r th

e fo

reig

n va

riet

y, F

orei

gnf*

15.

005.

13F

* 150

.00

64.6

062

.01

63.9

8Su

b-ut

ility

of

diff

eren

tiate

d pr

oduc

ts,

For

eign

U* 1

139.

4951

152.

3253

.83

54.1

6D

eman

d fo

r go

od 2

D2

100.

0097

.56

98.2

297

.71

Dem

and

for

good

2,

Fore

ign

D* 2

100.

0010

2.81

101.

9610

2.60

Inte

r-in

dust

ry t

rade

, vo

lum

eN

T0.

0016

.46

11.7

215

.32

Intr

a-in

dust

ry t

rade

in

good

1,

per

cent

IT1.

000.

830.

870.

84

Not

e:In

thi

s co

mpa

riso

n, A

* 1=

0.9

A1.

The

oth

er p

aram

eter

s an

d va

riab

les

are:

a1

= 0

.7 a

nd a

2=

0.3;

L=

L*

= 1

00;

K*

= K

= 10

00;

the

expe

ndit

ure

shar

e fo

r go

od 1

is

u0.

5; f

or t

he L

OV

mod

el,

f=

10,

A1

= 2.

51 a

nd A

2=

2.0

0; f

or t

he A

rmin

gton

mod

el,

A1

= 5

.01

and

A2

= 2.

00.


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economy, and conversely in the foreign economy in both models. Withinsector 1 itself, the S1/S*1 ratio falls to 0.68 in the LOV model, but to 0.74 inthe Armington model with s 5 10 and to 0.69 in the Armington model withs 5 50. To sum up this comparison, it is clear that the LOV model can beregarded, again, as the limit for the Armington model with s approachingin� nity.

4.3 Trade policy

Now we turn to a comparison of the effects of trade policy in the twomodels. In particular, we examine the speci� c case in which the homeeconomy imposes tariffs on the imports of the foreign-produced good 1.Theoretically, the optimality of free trade applies only to a small openeconomy for which world prices are exogenous. When intra-industry trade isintroduced through product differentiation, neither of the two economies inour models can be considered as small open economies.5 In both models, theexport supply of the imported good 1 is a positive function of the price ofthat good. Therefore, the optimal tariff argument applies to both models.Free trade is no longer the optimal policy. Provided that the foreigneconomy does not retaliate, a small import tariff would increase domesticwelfare by improving the terms of trade. As far as the optimal tariff rategoes, there is no essential qualitative difference between the two models.

Are there any essential differences in the effects of trade policy betweenthe LOV and Armington models? Helpman and Krugman (1985) alsodiscuss two other ways in which a protective trade policy may improvedomestic welfare in the LOV model. One is the production ef� ciency effect.Speci� cally, if there is a sector-speci� c factor in sector 1, such as skilledlabour, that is required to undertake research and development, the protec-tion that expands the domestic production of good 1 can be welfare-enhancing because it raises the rent that the sector-speci� c skilled labourreceives. However, this argument is not unique to the LOV model. it canalso be incorporated into the Armington model. Therefore, it is not arelevant factor that distinguishes the LOV model from the Armingtonmodel. The other way import protection may improve domestic welfare isthe home market effect. In the presence of a signi� cant transport cost, theimport protection would improve domestic welfare if the distortion cost ofprotection is less than the transport cost that can be saved by importsubstitution. This argument is not built on the inherent properties of theLOV model. It requires the additional assumption of signi� cant transportcost. In principle, the same argument can be applied to the Armingtonmodel. Therefore, the LOV model is also not distinct from the Arming-ton model on that account.

How should we compare these two models with regard to the effects oftrade policy? One way is to impose the same tariff rate on the imports


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of good 1 in both models and then compare how the two models wouldrespond. Another way is to compute the optimal tariff rate for both modelsand then compare the effects of the optimal tariff rate. Either of the twocomparison methods would work, but the second method of comparisonyields more interesting information. It would demonstrate not only howtrade policy affects production structure and trade pattern, but also showhow the optimal tariff rates in the two models could be compared to eachother. In view of this consideration, we choose to compare the two modelsby computing the optimal tariff rate. The comparison results are presented inTable 3.

The optimal tariff rate is computed for the given set of parameters andfactor supplies that produce the benchmark equilibrium. In other words, thetwo economies are identical in terms of size, factor endowments, andtechnologically. The optimal tariff rate is computed numerically as the valuethat maximizes home welfare as measured in equation (21) for the LOVmodel and equation (44) for the Armington model. It is reported in the � rstrow of Table 3. The optimal tariff rate is 12 per cent for the LOV model, 10per cent for the Armington model with a s 5 10, and 3 per cent for theArmington model with a s 5 50. It follows that, in the Armington model,the optimal tariff rate is inversely related to s . The more elastic thesubstitution between the home and foreign-produced good 1, the lessthe optimal tariff rate. In the limit, as s approaches in� nity, the optimal tariffrate becomes zero and free trade is the optimal policy. The pattern of oursimulation may lead to the speculation that the LOV model may be regardedas the limit for the Armington model as s approaches zero. But thisspeculation turns out to be false. The optimal tariff rate for the Armingtonmodel becomes 12 per cent, the same as that in the LOV model, when sdecreases to 5.18. Therefore, as s becomes smaller than 5.18, the optimaltariff rate would be even higher.

Why would the optimal tariff rate be higher in the LOV model than in theArmington model with the same s The intuition for this peculiarity lies inthe fact that, in the LOV model, s in� uences only the ratio of the demandfor the home-produced differentiated product per variety to that for theforeign-produced differentiated product per variety, but it does not affectthe n/n* ratio directly from the demand side. Therefore, the aggregatedemand ratio, (D1 1 D*1)/(F1 1 F*1), is much less sensitive to a change ins in the LOV model than in the Armington model. Hence the higher optimaltariff rate in the LOV model.

How does trade policy affect trade in the two models? In both models, theimposition of tariffs on the imports of good 1 in the home economy raisesthe price of the home good 1, p1, but less than the increase in the domesticprice of the imported good 1, (1 1 t)p*1. In other words, foreign exportersbear part of the tariff cost. In the LOV model, p1 rises to 1.03 but p*1 fallsto 0.97. In the Armington model, p1 rises to 1.02 but p*1 falls to 0.98 with


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Tabl

e 3

The

eff

ects

of

trad

e po

licy

Vari

able

sSy

mbo

lB

ench

mar

keq

uilib

rium

LOV

mod

el w

iths

= 1

0A

rmin

gton

mod

elw

ith s

= 1

0A

rmin

gton

mod

elw

ith s

= 5

0

Opt

imal

tar

iff

rate

0.12

0.10

0.03

The

pri

ce o

f go

od 1

, H

ome

p1

1.03

1.02

1.01

The

pri

ce o

f go

od 1

, fo

reig

np*

1.00

0.97

0.98

0.99

Dom

estic

pri

ce o

f th

e im

port

ed g

ood

1,H

ome

q1.

001.

091.

081.

02

Dom

estic

pri

ce o

f th

e im

port

ed g

ood

1,Fo

reig

nq*

1.00

1.03

1.02

1.01

Out

put

per

�rm

, se

ctor

1,

Hom

es 1

10.0

010

.00

Num

ber

of �

rms/

vari

etie

s, s

ecto

r 1,

Hom

en

10.0

010

.64

Supp

ly o

f go

od 1

, H

ome

S 110

0.00

106.

4510

4.05

101.

44O

utpu

t pe

r �

rm,

sect

or 1

, fo

reig

ns*

110

.00

10.0

0N

umbe

r of

�rm

s/va

riet

ies,

sec

tor

1, f

orei

gnn*

10.0

09.

16S*

110

0.00

91.6

594

.36

98.1

8T

he s

uppl

y of

goo

d 2,

Hom

eS 2

100.

0093

.47

95.9

298

.56

The

sup

ply

of g

ood

2, f

orei

gnS*

210

0.00

108.

2210

5.58

101.

82T

he w

age

rate

, H

ome

w1.

000.

980.

991.

00T

he w

age

rate

, fo

reig

nw

*1.

001.

021.

021.

01T

he r

enta

l ra

te,

Hom

er

0.10

0.10

0.10

0.10

The

ren

tal

rate

, fo

reig

nr*

0.10

0.09

0.10

0.10

GD

P,

Hom

eY

200.

0020

6.36

205.

0520

1.43

GD

P,

fore

ign

Y*20

0.00

197.

0219

7.95

199.

32T

arif

f re

venu

e, H

ome

T0.

003.

783.

450.

88T

arif

f re

venu

e, F

orei

gnT*

0.00

0.00

0.00

0.00


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Tabl

e 3

cont

inue

d.

Vari

able

sSy

mbo

lB

ench

mar

keq

uilib

rium

LOV

mod

el w

iths

= 1

0A

rmin

gton

mod

elw

ith s

= 1

0A

rmin

gton

mod

elw

ith s

= 5

0

The

dem

and

for

the

hom

e va

riet

y, H

ome

d 15.

006.

28D

150

.00

66.8

863

.33

66.5

2T

he d

eman

d fo

r th

e fo

reig

n va

riet

y, H

ome

f 15.

003.

47F

150

.00

31.8

435

.50

33.1

8Su

b-ut

ility

of

diff

eren

tiate

d pr

oduc

tsU

113

9.50

137.

0049

.22

49.7

9T

he d

eman

d fo

r th

e ho

me

vari

ety,

For

eign

d*1

5.00

3.72

D* 1

50.0

039

.57

40.7

234

.92

The

dem

and

for

the

fore

ign

vari

ety,

For

eign

f*1

5.00

6.53

F* 1

50.0

059

.81

58.8

665

.00

Sub-

util

ity o

f di

ffer

entia

ted

prod

ucts

, Fo

reig

nU

* 113

9.50

137.

9449

.71

49.9

1D

eman

d fo

r go

od 2

D2

100.

0010

3.18

102.

5210

0.72

Dem

and

for

good

2,

Fore

ign

D* 2

100.

0098

.51

98.9

799

.66

0.00

70.

005

0.00

2U

tility

, H

ome

UH

118.

1111

8.89

71.0

370

.82

–0.0

13–0

.008

–0.0

03U

tility

, Fo

reig

nU

F11

8.11

116.

5770

.14

70.5

3In

ter-

indu

stry

tra

de,

volu

me

NT

0.00

–9.7

1–6

.61

–2.1

6In

tra-

indu

stry

tra

de i

n go

od 1

, pe

r ce

ntIT

1.00

0.86

0.93

0.97

Not

e:In

thi

s co

mpa

riso

n, t

he p

aram

eter

s an

d va

riab

les

are:

a1

= 0

.7 a

nd a

2=

0.3;

L=

L*

= 1

00;

K*

= K

= 10

00;

the

expe

nditu

re s

hare

for

goo

d 1

isu

0.5;

for

the

LO

V m

odel

, f

= 1

0, A

1=

2.5

1 an

d A

2=

2.0

0; f

or t

he A

rmin

gton

mod

el,

A1

= 5

.01

and

A2

= 2.

00.


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s 5 10, while p1 rises to 1.01 but p*1 falls to 0.99 with s 5 50.Consequently, the ratio falls but the p1/p*1 ratio rises. The differencebetween the two models is merely quantitative, depending only on the levelof the optimal tariff rate.

In both models, home consumers now spend more money on the homegood 1 because of the fall in p1/[(1 1 t)p*1], and foreign consumers spendmore money on the foreign-produced good 1 ratio because of the rise in thep1/p*1 ratio. Consequently, the volume of intra-industry declines. In bothmodels, the decrease in the home imports of foreign-produced good 1exceeds the decrease in the foreign imports of the home good 1. As a result,inter-industry trade is generated compared with the benchmark equilibrium.The home economy exports differentiated products on the net basis andimports the homogeneous product. In other words, the imposition of thetariff on the home imports of the foreign-produced differentiated productshas the expected protection effect, expanding sector 1 at the expense ofsector 2. The size of this protection effect is related to the size of the optimaltariff rate. In the LOV model, the 12 per cent tariff rate induces the homesector 1 to expand from 100 to 106.45. In comparison, in the Armingtonmodel, the 10 per cent tariff rate in the case of s 5 10 induces the homesector 1 to expand to 104.05 and the 3 per cent tariff rate in the case ofs 5 50 induces the home sector 1 to expand to 101.44, marginally.Alternatively, we can compare the effects on production structure ofimposing the same tariff rate in the two models. As an illustration, we havecomputed the effects of a 10 per cent tariff rate. In the LOV model, ns1

increases from 100 to 105.3 and S2 decreases from 100 to 94.6. In theArmington model with s 5 10, s1 goes up to 104.08 and S2 down to 95.89.In the Armington model with s 5 50, s1 goes up to 105.06 and S2 down to94.89. Here again it can be seen that the LOV model is approximated closelyby an Armington model with a very large elasticity of substitution.

How does trade policy affect welfare in the two models? In both models,home welfare improves at the expense of foreign welfare. But the optimaltariff rate affects welfare only marginally. In the LOV model, home welfareimproves by 0.7 per cent while foreign welfare is reduced by 1.3 per cent. Inthe Armington model with s 5 10, home welfare improves by 0.5 per centwhile foreign welfare is reduced by 0.8 per cent. In the Armington modelwith s 5 50, home welfare improves by 0.2 per cent while foreign welfareis reduced by 0.3 per cent. Since the levels of home and foreign welfare areidentical in the benchmark equilibrium, the gain in home welfare is less thanthe loss in foreign welfare in both models. Consequently, world welfaredecreases as a whole. It is in this sense that an interventionist trade policy isnot optimal for the world as a whole, even though it improves the welfare ofthe economy that adopts it. It is apparent that such trade policy invites tradewars, making both economies worse off in the end.


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To recapture the above comparison, the LOV model and the Armingtonmodel behave similarly in their analytical properties. In both models, a tariffon the imports of the foreign-produced good 1 discourages trade by makingthe home-produced differentiated products more attractive to home con-sumers and the foreign-produced differentiated products more attractive toforeign consumers. In addition, it increases home welfare by improving theterms of trade for the home economy. The LOV model resembles anArmington model with a smaller s .

5. CONCLUSIONS

To conclude, there are two main differences between the LOV model andthe Armington model. The � rst difference is that, in the LOV, model thesectoral output of good 1 is further decomposed into the number of varieties/� rms and output per variety/� rm. Although it is an integral part of the storyof increasing returns to scale and imperfect competition, this difference isnot essential to modelling intra-industry trade. What matters is productdifferentiation, and that is shared by both models. Furthermore, the decom-position requires variables that are not directly observable and measurable.This aspect poses serious operational dif� culties for CGE modelling.

The second difference lies in the way the ratio of the demand for thehome-produced differentiated product to the demand for the foreign-produced differentiated product is determined. Production structure is moresensitive to changes in the determinants of comparative advantage in theLOV model than in the Armington model with the same elasticity ofsubstitution. In essence, relative supply determines relative demand inthe LOV model, while relative demand determines relative supply in theArmington model. The LOV model can be adequately mimicked by anArmington model with an elasticity of substitution approaching in� nity. Inthis sense, the LOV model can actually regarded as a special case of theArmington model.

So far, our comparison has highlighted the differences and similaritiesbetween the two models. However, nothing has been said about which of thetwo models is superior, especially for applied studies of trade policy. It isbeyond the scope of the present paper to answer this question adequately.However, as discussed above, the crucial parameter that distinguishes thetwo models is the elasticity of substitution between domestic goods andforeign goods. There have been numerous studies that estimate the Arming-ton elasticity. A recent review of the empirical estimates by McDaniel andBalistreri (2001) � nds that estimates of the Armington elasticity generally liewithin the range of 1.0 to 5.0. If this consensus for the Armington elasticityis accepted, then we may reach two important conclusions. First, if theobjective of an applied study is to assess the effects of trade policy,the choice of the two models does not matter much. Their predictions are


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close to each other. Second, if the objective of an applied study is to assessthe impact on trade pattern of changes in factor endowments and technolo-gies, then the LOV model would yield implausible predictions.

NOTES

1 In this paper we examine a symmetric equilibrium in which the elasticity ofsubstitution between domestic and foreign differentiated products is the same as thatbetween domestic differentiated products. Such a symmetric equilibrium is what iscovered in most trade textbooks. However, it is plausible to introduce an ‘asym-metric’ CES sub-utility function that allows these two elasticities of substitution tobe different. Indeed, this is often what is done in applied CGE studies. However, theadoption of an asymmetric CES sub-utility function amounts to bringingthe Armington model through the back door. In other words, on top of productdifferentiation by � rms, we also add product differentiation by country, which isessentially the Armington model. Since the objective of the present paper is a directcomparison of a stylized LOV model and an Armington model, not an applied studyof actual intra-industry trade pattern, we focus only on the symmetric CES sub-utility function.

2 The full expression for the own price elasticity of demand is

h 5 s 1(1 2 s )pi

12 s

ojpj

12 s 2pi

E1

E1

pi

.

As the number of varieties approaches in� nity, the last two terms approach zero. Soh » s .

3 Actually, this property is an unattractive restrictive feature of the LOV model witha CES sub-utility. With more general functional forms, IT is possible to generate theresult of a variable elasticity of substitution so that the output of a typical � rm mayrespond to changes in the trade regime other than the size of � xed cost.

4 The implicit utility function for good 1 has the following shape:

U1 5 S d D1

s 2 1

s 1 (1 2 d )F1

s 2 1

s D s

s 2 1,

where U1 is the sub-utility, D1 and F1 are the demand for home and foreign-produced good 1, and d is a parameter that helps to determine the expenditure sharesfor the two goods.

5 The property that both economies have market power to in� uence the terms of tradeis also due to the homothetic utility function we use here. For differentiatedproducts, the CES sub-utility implies that the demand for any variety, home orforeign, is strictly positive.

REFERENCES

Asia Paci� c Economic Cooperation (1997) ‘The impact of trade liberalization inAPEC.’

Armington, P. S. (1969) ‘A theory of demand for products distinguished by place ofproduction’. International Monetary Fund Staff Papers 16(1), 159–78.

Balassa, B. (1966) ‘Tariff reductions and trade in manufactures among the industrialcountries’. American Economic Review 56, 466–73.


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Dixit, A. K. and Stiglitz, J. E. (1977) ‘Monopolistic competition and optimum productdiversity’. American Economic Review 67, 297–308.

Grubel, H. G. and Lloyd, P. J. (1975) Intra-industry Trade: The Theory and Measurementof International Trade in Differentiated Products. New York: Wiley.

Helpman, E. and Krugman, P. (1985) Market Structure and Foreign Trade. Cambridge,MA: MIT Press.

Lloyd, P. J. (1994) ‘Aggregation by industry in high-dimensional models’. Review ofInternational Economics 2(2), 97–111.

McDaniel, C. A. and Balistreri, E. J. (2001) ‘A discussion on Armington tradesubstitution elasticities.’ US International Trade Commission, Of� ce Of EconomicsWorking Paper No. 2002–01–A.

Spence, H. (1976) ‘Product selection, � xed costs, and monopolistic competition’. Reviewof Economic Studies 43, 217–36.

Wong, K. (1997) International Trade in Goods and Factor Mobility. Cambridge,Massachusetts: the MIT Press.


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A comparison of two models of intra-industry trade

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Transcript of A comparison of two models of intra-industry trade