Pattern of Trade and Economic Development

in the Model of Monopolistic Competition

Jeffrey Sachs

Center for International Development, Harvard University

Xiaokai Yang

Department of Economics, Monash University and

Harvard Center for International Development

and

Dingsheng Zhang

Research Center of Economics, Wuhan University and

Guanghua School of Management, Peking University

First submission: December 1999

Second submission: November 2000

JEL code: D30, F10, O10.

Key words: Income distribution, division of labor, dual structure, economic development, trade pattern, monopolistic competition, economies of scale, inframarginal analysis

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DE# 9184

Pattern of Trade and Economic Development

in the Model of Monopolistic Competition

REVIEW OF DEVELOPMENT ECO NOMICS

By: Jeffrey Sachs

- Center for International Development, Harvard University

Xiaokai Yang

- Department of Economics, Monash University and Harvard Center for International Development

and

Dingsheng Zhang

- Research Center of Economics, Wuhan University and Guanghua School of Management, Peking University

Contact author: Xiaokai Yang,

Email: [email protected],

Postal: Department of Economics, Monash University, Clayton, Vic. 3800, Australia. Phone: 61399052448,

Fax: 61399055499.

Coauthors: Jeffrey Sachs: [email protected]

Dingsheng Zhang: [email protected]

JEL code: D30, F10, O10.

Key words: Income distribution, division of labor, dual structure, economic development, trade pattern, monopolistic competition, economies of scale, inframarginal analysis

Abstract

The paper introduces differences in production and transaction conditions between countries into the model of monopolistic competition. It applies inframarginal analysis to show that as transaction conditions are improved, the general equilibrium may discontinuously jump across different patterns of trade and economic development. It shows that a country may export a good in which it has exogenous comparative disadvantage if its endogenous comparative advantage dominates this disadvantage. Countries will choose a trade and development pattern to utilize their net exogenous and endogenous comparative advantages in production as well as in transactions.

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1. Introduction

The purpose of this paper is twofold. First we introduce differences in transaction and production conditions between countries into a model of monopolistic competition to investigate trade pattern in this model. Second, we use the model with both final and intermediate goods to investigate the interplay between trade patterns and development strategies. Let us motivate the two tasks one by one.

In the past two decades, many general equilibrium models with economies of scale and monopolistic competition are developed to explain some trade phenomena that conventional trade models with constant returns to scale technology cannot explain. In particular, Yang (1994), Krugman and Venables (1995), and Fujita and Krugman (1995) introduce the trade-off between global economies of scale and transaction costs into this kind of models to explain productivity progress and an increase in trade dependence by improvements in transportation conditions.

In most of the models, symmetry is assumed (production and transaction conditions are the same for all agents) and therefore which country exports which goods is indeterminate. The current paper shall introduce asymmetric transaction and production conditions into the model of endogenous number of goods and economies of scale to investigate trade pattern.1

This research follows a tradition in trade theory represented by Bhagwati and Dehejia (1994), who suggested that the models with the CES production function and economies of scale may predict trade patterns that cannot be explained by the Heckscher-Ohlin (HO) theorem, the Stolper-Samuelson (SS) theorem, and factor equalization (FPE) theorem. These core trade theorems are at odds with empirical observations (Trefler, 1995, Grossman and Levinsohn, 1989). The current paper shall substantiate Bhagwati and Dehejia’s suggestion (1994, p. 44). In the face of a sufficiently large shift in relative factor prices, goods could switch over from being intensive in one factor to being intensive in the other (factor reversal). Scale economies could generate endogenous (ex

1Helpman and Krugman (1985) explore effects of economies of scale and monopolistic competition on trade pattern. For instance, Helpman (1987) shows that when economies become more similar in size, world trade increases. However, because of symmetry in the model, it is indeterminate which country exports which goods in equilibrium. Puga and Venables (1998) introduce difference in endowment between

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post) differences in technology and, in particular, could invalidate the SS theorem, causing both factors real wages to rise as scale efficiencies from trade swamp adverse effects on the scarce factor.

In addition the current paper shall synthesize two research lines of trade pattern. In the Ricardo model of exogenous comparative advantage (see Cheng, Sachs, and Yang, 2000), trade pattern is explained by exogenous comparative advantage in technologies. Here, exogenous comparative advantages come from ex ante differences between agents before they have made decisions. In the literature of endogenous specialization (see Yang and Ng, 1998 for a recent survey of this literature and references there), trade pattern is explained by endogenous comparative advan tage, which is generated by increasing returns and may exist between ex ante identical agents. As Yang (1991) shows, individuals trade those goods which have greater economies of specialization, better transaction condition, and/or are more desirable if not all goods are traded. But who sells which good is indeterminate in the models of endogenous specialization because of the assumption that all individuals are ex ante identical. The current paper shall investigate the implications of coexistence of endoge nous and exogenous comparative advantage and transaction costs for economic development and trade. As the difference in transaction and production conditions between countries (which generates exogenous comparative advantage) is introduced into the model with economies of scale (which generate endogenous comparative advantage), marginal analysis is not enough for managing the model. We will develop inframarginal analysis (total cost-benefit analysis across different patterns of trade and development in addi tion to marginal analysis of each pattern) of the model of monopolistic competition. The inframarginal analysis will generate much richer stories on patterns of trade and economic development than in other models of monopolistic competition and in the HO m odel.

We shall show that as relevant concepts change in response to changes in analytical framework, relevant empirical evidences may be changed too. As Albert Einstein stated (quoted in Heisenberg, 1971, p. 31), "It is quite wrong to try founding a theory on observable magnitudes alone. …It is the theory which decides what we can

countries into the model of monopolistic competition. But as they come to comparative statics of equilibrium, the difference is assumed away.

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observe." For instance, many economists take the notion of capital as granted. But its meaning in the model of endogenous number of intermediate (capital) goods is totally different from that in a neoclassical HO model. As the number of capital goods that are employed to produce a final good increases in response to improvements in transaction conditions, the equilibrium input level of capital and capital intensity increase even i f production conditions, tastes, and endowment of primary resources are not changed. Hence, in a model of monopolistic competition, outsourcing trade, disintegration, and variety of goods might be better concepts than the notion of capital for capturing th e essence of comparative statics of equilibrium. Hence, data sets that are designed according to the new concepts might be more appropriate for testing the new theory.

Many new models of monopolistic competition with transaction costs are used to analyze trade and development phenomena. For instance Krugman and Venables (1995) analyze industrialization and income distribution, Fujita and Krugman (1995) analyze urbanization by introducing difference of transaction conditions between industrial and agricultu ral sectors into the model of monopolistic competition. Puga and Venables (1998) analyze import substitution and geographical concentration of industrial production.2 As the essence of comparative statics of equilibrium in this kind of models is increasingly more appreciated, we can see that many conventional notions, such as import substitution, become out-of-date. Rethinking of the relationship between trade pattern and economic development pattern is needed.

Hence, the second purpose of the current paper is to investigate the interplay between trade pattern and development pattern in a model of monopolistic competition. Feenstra (1998) reviews empirical evidences for the relationship between increases in trade of intermediate inputs and economic developm ent. He points out that the distinction between effects of trade and effects of technological changes on income distribution becomes suspect if we consider equilibrium comparative statics in a model of endogenous number of intermediate goods. As transaction conditions are improved (due to new communication and transacting technology) the number of intermediate goods increases, final goods become more "capital intensive," and outsourcing trade increases.

2 The diffe rence between the transaction cost coefficients of final and intermediate goods is not a distinct feature of our model, since the Fujita and Krugman (1995) assume this difference too.

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Our general equilibrium comparative statics in the framework of monopolistic competition will assist clarifying the discussion in which vague logic and inaccurate terms are sometimes used.

As we introduce exogenous comparative advantage in production and exogenous comparative advantage in transactions into the model with monopolistic competition and endogenous comparative advantage, we can show that a country may export goods in which it has exogenous comparative disadvantage in production if its endogenous comparative advantages in production and exogenous comparative advantage in transactions dominate its exogenous comparative disadvantage. Also, final manufactured goods may become increasingly more capital intensive, as the number of capital goods increases in response to parameter changes. A country can ex port capital intensive goods even if it has exogenous comparative disadvantage in producing this good.

Our model will show that a country will trade goods in which it has net comprehensive exogenous and endogenous comparative advantage in production as well as in transactions. It will exploit substitution between trades of different types of goods to avoid trade that involves high transaction costs. Various possible substitutions between endogenous and exogenous comparative advantages and between comparative advantages in production and in transactions generate much more colorful picture of equilibrium trade and development patterns than in neoclassical trade models.

Section 2 specifies the model, identifies possible trade patterns, and solves for local equilibrium in each trade pattern. Section 3 conducts inframarginal analysis across different trade patterns and identifies parameter subspaces within each of which a local equilibrium is the general equilibrium. In section 4, our results are compared with the neoclassical theories of trade and economic development based on the models with constant returns to scale technology. Final section concludes the paper.

2. The Model and Local Equilibria and Marginal Comparative Statics in Various Trade Structures

Consider two countries. Population size in country i is M i. Migration between countries is prohibitively expensive. Agricultural good (such as food) z is produced from labor. Final

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(or light) manufactured good (such as car) y is produced from labor and n intermediate (or heavy manufactured) goods (such as car parts).

2.1. A consumer's decision

A representative consumer's decision problem in country i is

(1) Max: u i= (y i + k i y ji)α(z i +k i z ji)1-α s.t. p iy y i+ p jy y ji+ p iz z i + p jz z ji= w i

where u i is a consumer's utility level in country i, y i and z i are the respective quantities of the manufactured consumption good and the agricultural good, purchased from the domestic market in country i. y ji and z ji are the respective quantities of the two goods imported by an individual in country i from the other country. p is is the price of good s in country i. It is assumed that each individual is endowed with one unit labor, and labor in country 1 is the numeraire, so that w1= 1 and w2= w. Iceberg transaction cost is assumed, so that 1-k i∈ [0, 1] is the transaction cost coefficient and k i the transaction efficiency coefficient for importing one unit of food in country i. The transaction cost coefficient is determined by the geographical conditions, transportation technology, transportation infrastructure, institutional conditions, and tariff regime.3 We will discuss effects of tariff on the transaction cost coefficients in section 4. Since geographical and institutional conditions and tariff regime are country specifi c, the transaction cost coefficient may be different between the countries. If transportation technology changes, the transaction cost coefficient may be changed uniformly.

2.2. Production of agricultural good (food) z

The production function of food in country i is

Z i = θi L iz

where Z i is the output level of z, and L iz is the amount of labor allocated to the production of food in country i. For simplicity, we assume that θ2 =1 and θ1 = θ > 1. This implies that country 1 has exogenous absolute as well as comparative advantage in producing food, since in the next two subsections the production function of industrial goods y and x is assumed same for the two countries.

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2.3. Production of final (or light) manufactured good y

The production function for a representative car manufacturer's production function in country i is

Y i= [n i x iρ+(n-n i)(t i x ji)ρ]β/ρL iy1-β

where Y i is output level of good y produced by a representative firm in country i, n i and n-n i are the respective numbers of intermediate goods purchased by country i from domestic market and from the other country, x i is the amount of an intermediate good purchased by the firm in country i from domestic market to produce good y, x ji is that purchased by the firm in country i from the other country, and t i is the transaction efficiency coefficient for country i importing intermediate good from the other country. Elasticity of substitution 1/(1-ρ) is assumed to be larger than one, that is ρ∈(0,1). We have used the symmetry (x i or x ji is the same for each relevant intermediate good) and omit variety index of intermediate goods when no confusion is caused.

2.4. Production of intermediate (or heavy manufactured) goods

The production function for the monopolist producer of an intermediate good in country i is X i = (L i-a)/b,

where X i is the quantity of an intermediate good supplied by the monopolist in country i and L i is the amount of labor hired by the firm to produce the intermediate good. Again, we have used the symmetry and omit variety index of intermediate goods when no confusion is caused.

2.5. Possible trade structures

As we introduce the ex ante differences in transaction conditions between the two countries into the model, corner solutions are possible. Hence, standard marginal analysis for interior solutions does not work. We need a little bit of innovation of analytical method. We first apply the Kuhn-Tucker condition to identify the conditions under which a particular trade structure occurs in equilibrium. These conditions involve relative

3 Empirical evidence for effects of geographical conditions on a country’s transportation efficiency is provided by Gallup and Sachs (1998) and empirical evidence for effects of institutions on a country’s

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prices. Second, for a given structure, we solve for a local equilibrium using marginal analysis. We can plug the local equilibrium prices into the conditions identified in the first step. We can then partition parameter space into subspaces within each of which a particular structure occurs in equilibrium. This is called inframarginal analysis.

Let us take the first step of the inframarginal analysis. The Kuhn-Tucker condition for the two representative consumers' decision problems in the two countries indicates that some trade structures never occur in equilibrium and that each of the feasible trade structures occurs in equilibrium only if relative prices and relative transaction condition in the two countries satisfy a certain condition. Later, we can obtain similar result for trade pattern of intermediate goods using the Kuhn-Tucker condition for the decision of a firm producing the final manufactured good. The two sets of the Kuhn-Tucker conditions yield the following conditions for a certain trade pattern to occur in equilibrium, where x i is the amount of an intermediate good purchased from the domestic market in country i, x ji is the amount of an intermediate good imported in country i from country j, and t i is the transaction efficiency coefficient of importing intermediate goods in country i.

(2)

(A) If k1 and t1 and/or k2 and t2 are sufficiently small, the optimum decision requires that z ji = x ji = y ji = 0 and x i, y i,z i >0, which implies that no trade occurs between the countries or autarky structure, shown in Fig. 1(a), occurs in equilibrium.

(C1) For p1y/p2y ＜k2 and p1z/p2z >1/k1, the optimum decision requires z12 = x12 = y21 = z1 = y2 = 0 and x1, y1,z2, x21, z21, y12 >0. In this trade structure, called C1 and shown in Fig. 1(c), country 1 (for examp le Hong Kong) exports final goods and country 2 (for example the USA) exports food and intermediate goods.

(C2) For p1y/p2y > 1/k1 and p1z/p2z ＜ k2, the optimum decision requires z21 = x21 = y12 = z2 = y1 = 0 and x2, y2,z1, x12, z12, y21>0. This trade structure C2 is symmetric to C1.

(D0) For p1y/p2y∈(k2, 1/k1) and p1z/p2z∈(k2, 1/k1), the optimum decision requires z12 = y12 = z21 = y21 = 0 and x1, y1,z1, x2, y2, z2, x12, x21 > 0. In this trade structure, called D0 and

trading efficiency is provided by Sachs and Warner (1995), Barro (1997) and Easton and Walker (1997).

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shown in Fig. 1(d), the two countr ies have pure intraindustry trade, that is, they trade only intermediate goods.

(D1) For p1y/p2y∈(k2, 1/k1) and p1z/p2z ＜ k2, the optimum decision requires y12 = z21 = y21 = z2 =0 and x1, y1,z1, x2, y2, x12, x21, z12 > 0. This trade structure is called D1. The difference between D0 and D1 is that in there is international trade in food (z) in D1, but no such trade in D0.

(D2) For p1y/p2y∈(k2, 1/k1) and p1z/p2z > 1/k1, the optimum decision requires y21 = z12 = y12 = z1 =0 and x2, y2,z2, x1, y1, x21, x12, z21 > 0. This structure of trade D2 is symmetric to D1. (E1) For p1y/p2y ＜k2 and p1z/p2z∈(k2, 1/k1), the optimum decision requires x12 = z12 = y21 = z21 = x2 = y2 = 0 and x1, y1,z1, x21, y12, z2 > 0. In this trade structure, called E1 and shown in panel (e), country 1 (for example, Hong Kong) exports final goods and country 2 (for example, Germany) exports intermediate goods. If the production of y is interpreted as an assembly process to transfer intermediate inputs x into the final product, country 1 can be considered as an assembly enclave.

(E2) For p1y/p2y > 1/k1 and p1z/p2z∈(k2, 1/k1), the optimum decision requires x21 = z21 = y12 = z12 = x1 = y1 = 0 and x2, y2,z2, x12, y21, z1 > 0. This trade structure E2 is symmetric to E1. (F1) For p1y/p2y ＜k2 and p1z/p2z ＜ k2, the optimum decision requires x12 = y21 = z21 = x2 = z2 = y2 = 0 and x1, y1,z1, x21, y12, z12 > 0. In this trade structure, called F1 and shown in panel (f), country 1 (for example, China) exports final goods and food and country 2 (fo r example, Japan) exports intermediate goods.

(F2) For p1y/p2y > 1/k1 and p1z/p2z > 1/k1, the optimum decision requires x21 = y12 = z12 =x1 = z1 = y1 = 0 and x2, y2,z2, x12, y21, z21 > 0. This trade structure is called F2.

(a) Structure A (autarky) (b) A structure that does not occur in equilibrium

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(c) Structure C 1 (d) Structure D 0

(e) Structure E 1

(f) Structure F 2 Figure 1: Different Patterns of Development and Trade

Also, it can be shown that a trade pattern in panel (b) and other trade structures do not occur in equilibrium except for some razor edge cases where some of the inequalities involving relative prices in (2) become equalities.4 The markets for goods y and z are competitive because of constant returns to scale in production. But the market for intermediate goods is monopolistically competitive.

As shown in (2), ten market structures may occur in equilibrium in this model. We consider the local equilibrium in each of them.

2.6. Local equilibrium in structure A (autarky)

We first consider structure A where x i , y i , z i > 0, x ij = y ij = z ij = 0. A consumer's decision yields demand functions for goods y and z. Each consumer supplies one unit of labor and total supply of labor in country i is M i . The zero profit condition for the firm producing z gives the price of good z in terms of labor in country i p iz , The symmetry implies that quantities supplied or employed are the same for n i intermediate goods. The zero profit condition and a first order condition for the decision problem of the firm producing y yields 4 The complete partition of the parameter space when the razor edge cases are considered can be obtained from the authors upon request.

the equilibrium relative quantity of labor and intermediate goods and an equation that determines the equilibrium p iy/p ix. Using the production and demand functions of y, the market clearing conditions for y and labor, and the first order conditions for the decision problem of the firm producing y, we can find the demand function for x. Using the Dixit-Stiglitz formula for own price elasticity E = 1/(1-ρ), we can then work out the first order condition for the decision problem of the monopolist producer of an intermediate good. Then the zero profit condition for this firm yields the equilibrium n i. The local equilibrium and its marginal comparative statics in this structure is summarized as follows.

w i = 1, p1z = 1/θ, p2z = 1, p ix =b/ρ,

p iy = (1-β)β-1[a/(1-ρ)β]β/ρ[(1-ρ)b/ρa]β(αM i)β (1-1/ρ),

n i = M iβα(1-ρ)/a,

u1 = [θ(1-α)](1-α)ααp1y-α, u2 = (1-α)(1-α)ααp2y-α,

d p iy/d M i ＜ 0, d n i/d M i > 0, d u i/d M i > 0.

where i = 1, 2. The marginal comparative statics imply that as the population in an integrated market increases, the equilibrium price of final manufactured good d ecreases and the equilibrium number of intermediate goods and per capita real income increase. Since total factor productivity of the final manufactured good is an increasing function of the number of intermediate goods, this productivity increases with population size too. Ethier (1980) uses this result to show that the opening up of international trade can increase the population size in an integrated world market. This enlarges the scope for trading off economies of scale against productivity gains from more variety of intermediate goods and therefore generates gains from trade.

2.7. Local equilibrium in structure C

Next, we consider structure C1 where x1, y1,z2, y12,x21 > 0,x12 = y21= z12 = 0. The procedure to solve the corner equilibrium in this structure is the same as that for structure A except that the markets for x, y, z are jointly cleared for both countries. The corner equilibrium in this structure is summarized as follows.

w = t1ρ, p1z = 1/θ, p2z = t1ρ, p1x =b/ρ, p2x = t1ρb/ρ,

p1y = (1-β)β-1β-β/ρ(b/ρ)β[(1-ρ)α(M1+ k1ρM2)/a]β (1-1/ρ),

n1 = [(1-ρ)/a][M1(βα+1-α)-α(1-β)t1ρM2],

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n2 = [(1-ρ)/a][M2α-(1-α)t1-ρM1],

u1 = B(θk1)1-αt1-ρ(1-α)(M1+t1ρM2)αβ(1-ρ)/ρ,u2 = Bt1ραk2α(M1+t1ρM2)αβ(1-ρ)/ρ, where B≡ (1-α)(1-α)αα [(1-β)1-βββ/ρ(ρ/b)β]α[α(1-ρ)/a]αβ(1-ρ)/ρ. The differentiation of the solutions yields marginal comparative statics of the local equilibrium in structure C1.

(3) d n i/d M i > 0, d n i/d M j ＜ 0, d n2/d t1 > 0, d n1/d t1 ＜ 0,

d n/d t1 > 0, if (1-α)M1/α(1-β)M2 > t12ρ,

d n/d M1 > 0 iff t1>[(1-α)/αβ+1-α]1/ρ,d n/d M2 > 0,

d w/d t1 > 0, d u i/d M j > 0, d u i/d k i > 0, d u2/d t1 > 0.

where i, j = 1, 2 and n = n1 + n2 is the number of all intermediate goods available in the two countries. The marginal comparative statics of the local equilibrium imply that as t he transaction condition in country 1 improves, the production of intermediate goods will shift from country 1 to country 2. This relocation of industrial production increases utility levels in the two countries while the nominal income in country 1 relative to that in country 2 increases. The improvement of the transaction condition in country 2 has no effects on industrial structure and location of industrial production, though it increases utility of each individual in country 2. An increase in the popul ation size in country 1 will shift the production of producer goods from country 2 to country 1. But an increase in the population size in country 2 has opposite effect on location of industrial production. However, the increase in population size in either country will raise per capita real income in both countries.

As n1 or n2 tends to zero, the production of all intermediate goods becomes concentrated in country 2 or 1. A careful examination of the equilibrium solutions yields the following conditions for such concentration.

(4) n1 = n and n2 = 0 if t1 ＜ t a≡ [M1(1-α)/M2α]1/ρ

n1, n2∈ (0, n) if t1∈ (t a, t b), where t b≡ [M1(αβ+1-α)/M2α(1-ρ)]1/ρ

n2 = n and n1 = 0 if t1 > t b,

where t a＜ t b always holds. The marginal comparative statics of the local equilibrium in structure C1 are summarized in the following proposition.

Proposition 1:

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If the transaction efficiency of intermediate goods is very low in country 1, country 2 specializes in producing the agricultural good in the absence of industrialization. The production of all final and intermediate manufactured goods is located in country 1. As the transaction condition is improved in country 1, country 2 starts industrialization which relocates the production of intermediate goods from country 1 to country 2. The smaller the population size of country 1 relative to country 2, the faster is the relocation process. Per capita real incomes in both countries increase as a result of the relocation, although wage rate in country 2 increases compared to that in country 1. The wage difference between the two countries converges to 0 as transaction cost tends to 0. The per capita real income in country 1 is more likely to be higher than in country 2, the greater the income share of the final manufactured good, th e greater the elasticity of substitution between intermediate goods, and/or the higher the relative transaction efficiency of country 1 to country 2. An increase in the population size of a country will move the production of intermediate goods to this country from the other country, increasing per capita real income in this country.

The local equilibrium in structure C2 is symmetric to that in C1. Hence, a similar proposition can be obtained from the comparative statics of that local equilibrium.

2.8. Local equilibrium in structure D

We now consider structure D0 in which country 1 produces final goods y and z and n1 intermediate goods. It exchanges the n1 intermediate goods for n2 intermediate goods produced by country 2 which self-provides goods y and z as well. Hence, for this structure we have x i, y i,z i, x ij > 0,y ij= z ij = 0. The local equilibrium in this structure is summarized as follows.

w is given by f = M1 + t1ρ/(1-ρ) [M2w-ρ/(1-ρ)-M1w-1/(1-ρ)-M2w-(1+ρ)/(1-ρ) t2-ρ/(1-ρ)] = 0

p1z = 1/θ, p2z = 1, p1x =b/ρ, p2x = wb/ρ,

p1y = A(M1/t1)β [(t1ρ/(ρ-1)-t2ρ/(1-ρ))/(1-t2ρ/(1-ρ)w1/(1-ρ))]β [M1t11/(ρ-1)+M2wρ/(ρ-1)]-β/ρ

p2y = wAM2β[(t1ρ/(ρ-1)-t2ρ/(1-ρ))/(t1ρ/(ρ-1)w1/(1-ρ)-1)]β [M1t21/(1-ρ)+M2wρ/(ρ-1)]-β/ρ

n i = β(1-ρ)M i/a,

u1 = [θ(1-α)]1-α(α/p1y)α, u2 = (1-α)1-α(αw/p2y)α.

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where A≡ (1-β)β-1[a/(1-ρ)β]β/ρ[α(1-ρ)b/aρ]β. The market clearing conditions for intermediate goods and the first order conditions for producers of good y in the two countries require

w∈(t1ρ, t2-ρ).

where t1ρ＜ t2-ρ always holds. It is obvious that w converges to 1 as t1 and t2 tend to 1.

The differentiation of the solutions yields:

d w/d t1 = -(∂f/∂ t1)/(∂f/∂w) > 0, d w/d t2 = -(∂f/∂ t2)/(∂f/∂w) ＜ 0,

where ∂f/∂t1 > 0, ∂f/∂t2 ＜ 0, ∂f/∂w ＜ 0. The result implies that relative per capital nominal income of country 2 to country 1 increases as the transaction condition in country 1 improves or as the transaction condition in country 2 worsens.

Similar results can be obtained for the relationship between per capita real income in a country and the transaction conditions in the two countries. It can be shown that

(5a) d u1/d t1 = (∂u1/∂t1)+(∂u1/∂w)(d w/d t1) ＜ 0,

d u2/d t2 = (∂u2/∂t2)+(∂u2/∂w)(d w/d t2) ＜ 0,

where d w/d t1 > 0, d w/d t2 ＜ 0, ∂u1/∂w ＜ 0, ∂u2/∂w > 0, ∂u1/∂ t1 ＜ 0, ∂u1/∂t2 ＜ 0,∂u2/∂t2 ＜ 0.

Other marginal comparative statics in this structure are

(5b) d u i/d M i > 0, d u i/d M j > 0, d n i/d M i > 0, d n i/dρ ＜ 0, d n i/d a ＜ 0.

The Kuhn-Tucker condition for a producer of good y indicates that the first order derivative of profit with respect to quantity of an imported intermediate good is always negative if the transaction efficiency coefficient is zero in this country. Hence, the equilibrium will jump to another structure if t is sufficiently close to 0 in either country.

If 1-t i is interpreted as the import tariff rate in country i and all tariff revenue is exhausted by bureaucrats who collect it, then the marginal comparative statics in (5a) imply that each country has an incentive to impose tariff which increases per capita real income in the home country.5

Proposition 2:

5 Cheng, Sachs, and Yang (2000) consider the trade-off between dead-weight and government revenue created by tariff in a Ricardian model. We leave the trade-off in the model of monopolistic competition to future research.

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As the population size or import tariff rate increases in a country, the per capita real income in this country increases. Also, the number of intermediate goods produced in a country increases with its population size. Wage difference between the two countries converges to 0 as transaction cost tends to 0.

The local equilibrium in structure D1 is:

w is given by

f = αβM1-(1-α)wM2-αβt1ρ/(1-ρ)w-1/(1-ρ)M1 + w-ρ/(1-ρ)[(1-α+αβ)M2t1ρ/(1-ρ)+

(1-α)M2 t2-ρ/(1-ρ)-(1-α+αβ)M2w-(1+ρ)/(1-ρ) t1ρ/(1-ρ)t2-ρ/(1-ρ)] = 0

p1z = 1/θ, p2z = 1, p1x =b/ρ, p2x = wb/ρ,

p1y = A(M1/t1)β [(t1ρ/(ρ-1)-k2ρ/(1-ρ))/(1-t2ρ/(1-ρ)w1/(1-ρ))]β [M1t11/(ρ-1)+M2wρ/(ρ-1)]-β/ρ

p2y = wAM2β[(t1ρ/(ρ-1)-t2ρ/(1-ρ))/(t1ρ/(ρ-1)w1/(1-ρ)-1)]β [M1t21/(1-ρ)+M2wρ/(ρ-1)]-β/ρ

n1 = [αβM1-(1-α)wM2](1-ρ)/a, n2 = (1-α+αβ)M2(1-ρ)/a,

u1 = [θ(1-α)]1-αααp1y-α, u2 = (1-α)1-ααα (p2y/w)-α.

where A≡ (1-β)β-1αβ[a/(1-ρ)β]β/ρ[(1-ρ)b/aρ]β. The market clearing conditions for intermediate goods and the first order conditions for producers of good y in the two countries require

w∈(t1ρ,t2-ρ).

where t1ρ＜ t2-ρ always holds.

The local equilibrium in structure D2 is symmetric to that in D1. Marginal comparative statics in structure D1 or D2 are similar to that in D0.

2.9. Local equilibrium in structure E

The local equilibrium in structure E1 is:

w = p2z = t1ρ, p1z = 1/θ, p1x =b/ρ, p2x = wb/ρ,

p1y = (1-β)β-1β-β/ρ(b/ρ)β[(1-ρ)α(M1 +M2t1ρ)/a]-β(1-ρ)/ρ

p2y = (1-β)β-1β-β (b/ρ)β[(1-ρ)αM2/a]-β(1-ρ)/ρ

n1 = [αβM1-(1-β)α t1ρM2](1-ρ)/a, n2 = αM2(1-ρ)/a,

u1 = θ1-αB(M1+t1ρM2)αβ(1-ρ)/ρu2 = B(M1+t1ρM2)αβ(1-ρ)/ρk2αt1αρ.

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where B≡αα(1-α)1-α [(1-β)1-β(ρ/b)βββ/ρ]α[α(1-ρ)/a]αβ (1-ρ)/ρ. The marginal comparative statics in this structure are

(6) d u i/d M i > 0, d u i/d M j > 0, d u i/d t1 > 0, d u2/d k2 > 0

d n i/d M i > 0, d n1/d M2 ＜ 0, d n1/d t1 ＜ 0.

The local equilibrium in structure E2 is symmetric to that in E1. The marginal comparative statics in the two structures are summarized in the following proposition.

Proposition 3:

As transaction efficiency and population size increases in either country, per capita real incomes in both countries increase. The number of intermediate goods produced in a country increases with the population size in this country. The number of intermediate goods produced by the country importing intermediate goods decreases with the population size in the other country and with the transaction efficiency coefficient in this country.

2.10. Local equilibrium in structure F

The local equilibrium in structure F1 and its marginal comparative statics are:

(7) w = p2z = t1ρ, p1z = 1/θ, p1x =b/ρ, p2x = wb/ρ,

p1y = (1-β)β-1(b/ρ)ββ-β/ρ[(1-ρ)α(M1+t1ρM2)/a]

p2y = (1-β)β-1β-β (b/ρ)β[(1-ρ)M2/a]-β(1-ρ)/ρ

n1 = [αβM1-(1-αβ)t1ρM2](1-ρ)/a, n2 = M2(1-ρ)/a,

u1 = θ1-αB(M1+t1ρM2)αβ(1-ρ)/ρ, u2 = B(M1+t1ρM2)αβ(1-ρ)/ρt1ρk2.

d u i/d M i > 0, d u i/d t1 > 0, d u2/d k2 > 0

d n i/d M i > 0, d n1/d M2 ＜ 0, d n1/d t1 ＜ 0.

where B≡αα(1-α)1-α [(1-β)1-β(ρ/b)βββ/ρ]α[α(1-ρ)/a]αβ (1-ρ)/ρ.

The local equilibrium in structure F2 is symmetric to that in F1. The marginal comparative statics in the two structures are consistent with proposition 3.

3. General Equilibrium and Inframarginal Comparative Statics

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Inserting the local equilibrium values of prices into (2), we can partition the twelve dimension parameter space (θ, b, a, ρ, M1, M2, α, β, t1, t2, k1, k2) into subspaces, within each of which a local equilibrium is the general equilibrium. This analysis needs the equilibrium value of domestic price of some good in a country which does not produce this good in some structure. But we can calculate the shadow price of this good in this country from the first order condition of a firm, assuming that this firm is active in producing this good. This analysis yields the following inframarginal comparative statics of general equilibrium.

(8a) The local equilibrium in structure A (autarky) is the general equilibrium if either k1 and t1 or k2 and t2 are sufficiently small.

(8b) Suppose that M1 is not too small compared to M2 and that k2 and t1 are not too small. (8b-I) the local equilibrium in structure C1 is the general equilibrium if t1ρ ＜ k1/θ.

(8b-II) the local equilibrium in structure E1 is the general equilibrium if t1ρ∈(k1/θ, 1/θk2). (8b-III) the local equilibrium in structure F1 is the general equilibrium if t1ρ >1/θk2.

(8c) Suppose that M1 is close to M2 and t1 is close to t2.

(8c-I) the local equilibrium in structure D0 is the general equilibrium

if k1 ＜ θt1ρ and k2 ＜ t2ρ/θ

(8c-II) the local equilibrium in structure D1 is the general equilibrium if k2 > 1/θt1ρ.

(8c-III) the local equilibrium in structure D2 is the general equilibrium if k1 > θ/t2ρ.

(8d) Suppose that M2 is not too small compared to M1 and that t2 and k1 are not too small. (8d-I) the local equilibrium in structure C2 is the general equilibrium if t2ρ＜ θk2

(8d-II) the local equilibrium in structure E2 is the general equilibrium if t2ρ∈(θk2, θ/k1). (8d-III) the local equilibrium in structure F2 is the general equilibrium if t2ρ > θ/k1.

Here, we have used the upper and lower bound of the local equilibrium value of w to find sufficient conditions for D i to occur in equilibrium since the local equilibrium value of w in

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D i cannot be solved analytically. But these conditions may not be necessary. Hence, the parameter subspace (8c) is not completely partitioned.

In words, the i n framarginal comparative statics state that three factors determine trade patterns: exogenous technological comparative advantage (its degree is represented by θ); endogenous comparative advantage (its degree is represented by 1/ρ, reciprocal of elasticity of substitution); exogenous comparative advantages in transactions which relate to relative transaction efficiencies of final and intermediate goods in country 1 compared to that in country 2 (k i/k j, t i/t j, k i/t i, k j/t j) and absolute level of transaction efficiency. Here, we need more explanation about the connection between 1/ρ and the degree of endogenous comparative advantage. 1/ρ represents the effect of the number of intermediate goods on the total factor productivity of y (the small the elasticity of substitution, the greater the positive effect of the number of intermediate goods on the total factor productivity). Hence, a larger 1/ρ implies that the endogenous change in the total factor productivity is more sensitive to changes in the number of intermediate goods. Since an increase in total factor productivity generates endogenous difference in productivity between different specialist firms, 1/ρ represents degree of endogenous comparative advantage between different specialists.

If the absolute lev el of transaction efficiency is low for all goods, autarky is equilibrium. As transaction efficiency is improved, the general equilibrium jumps from autarky to a structure with trade. It is the interplay between exogenous and endogenous comparative advantage in production and transactions that determines to which structure the equilibrium will jump.

In order to understand the complicated comparative statics, we take a three-step analysis. We first consider inframarginal analysis between structures, then m arginal analysis for each structure. For inframarginal analysis, we first compare between cases (8b), (8c), and (8d), then compare between different structures in each case. The comparison between the cases indicates that when transaction conditions of intermediate goods are similar in the two countries, each country exports and imports intermediate goods. That is, a structure D occurs in equilibrium. Otherwise, the country with the better transaction condition of intermediate goods imports such goods. This is case (8b) or (8d). Case (8b) in which only country 1 imports intermediate goods, is more likely to occur in

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equilibrium than case (8d) in which country 2 imports intermediate goods, if the transaction efficiency of intermediate goods relative to that of final goods is higher in country 1 than in country 2 and/or if the population size in country 1 is larger.

We now take the second step. We consider case (8b) first. Suppose that the transaction condition and exogenous comparative advantage change in the following way. k1 decreases and/or k2 increases, and/or θ (degree of exogenous comparative advantage) increases, and t1 increases over three periods of time. Hence, in period 1 k1>t1ρθ, which implies that country 1's transaction efficiency of final goods is high, its transaction efficiency of intermediate goods is low, and exogenous comparative advantage is not significant. Hence, the local equilibrium in structure C1 is the general equilibrium (see (8b-I). In this structure, country 1 imports z and x and country 2 imports y. Then, these parameters change: k1 decreases, θ increases, and/or t1ρincreases, such that in period 2, t1ρk2θ ＜ 1 ＜ t1ρθ/k1. Hence, the equilibrium jumps to structure E1 where country 1 no longer imports the final good z (see (8b-II)). In period 3, k2 increases, and/or t1ρ, θ further increase, such that k2θt1ρ > 1. Then the equilibrium jumps to structure F1 where country 2 imports one more final good z (see (8b-III)). This implies that as the degree of exogenous comparative advantage increases and as country 2's relative transaction efficiency of importing final and intermediate goods increases compared to that for country 1, the equilibrium trade pattern shifts as to increase country 2's imported final goods compared to country 1. Al so, the equilibrium trade pattern shifts from exporting goods with exogenous comparative disadvantage in production to exporting goods with exogenous comparative advantage.

Repeating this analysis for other cases, we can obtain similar results. In summary, if exogenous and endogenous comparative advantages in production and transactions go in the same direction, then a country exports its comparative advantage goods. If it has endogenous comparative advantage in production and exogenous comparative advantage in transactions, but exogenous comparative disadvantage in production for exporting a good, then it will export this good if the advantage dominates the disadvantage. Otherwise, it imports this good. In other words, a country exports a good with net comprehensive endogenous and exogenous comparative advantage in production and transactions. It will use substitution between trades of different types of goods to avoid

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trade with low transaction efficiency. Inframarginal comparative statics of general equilibrium are summarized in Table 1. Here, A is autarky, C is a structure in which a country is an assembly enclave and the other exports food and intermediate goods, E is a structure in which a country is an assembly enclave and the other exports intermediate goods, F is a structure in which a country is an assembly enclave exporting food and the other exports intermediate goods, and D is a structure of intraindustry trade.

Table 1: Inframarginal Comparative Statics of General Equilibrium

Trading efficiency small

k1, t1,

k2, t2

large k i, t2,

small t1,

large M1/M2

large k i, t1,

small t2,

small M1/M2

large t i,,

small k i,

M1/M2 close

to 1

large t i, k2,

small k1,

M1/M2

close to 1

large t i, k1,

small k2,

M1/M2

close to 1

Equilibrium

structure A C1 C2 D0 D1 D2

Trading efficiency k2, t1 are not too small,

k1, t2 are very small, M1/M2 is large

k1, t2 are not too small,

k2, t1 are very small, M1/M2 is small t1ρ ＜ 1/k2θt1ρ > 1/k2θt2ρ ＜ θ/k1t2ρ > θ/k1

Equilibrium

structure E1 F1E2F2

The CES production function is essential for endogenizing the number of intermediate goods, which represents the degree of industrialization. Without the CES function, we cannot figure out the relationship between trade pattern and industrialization pattern. The assumption of θ≠ 1 is essential for predicting a trade pattern where a country exports a good in which it has exogenous comparative disadvantage. This assumption generates exogenous comparative technology advantage in addition to exogenous comparative endowment advantage, which is based on the difference in population size between the countries. The assumption of global economies of scale, which generates endogenous comparative advantage, is essential for the trade-off between economies of scale and transaction costs. The trade-off yields positive effects of an increase in the trading efficiency coefficient on industrialization and trade dependence.

Table 2: Marginal Comparative Statics of Local Equilibria

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Structure A C1 D0 E1 n1n2p1y p2y u1u2n1n2w n u1u2n1n2w u1u2n1n2u1u2 Variable

Parameter

M1+ 0 - 0 + 0 + - 0 + + + 0 + + + 0 + + M20 + 0 - 0 + - + 0 + + + 0 + + + - + + + t10 0 0 0 0 0 - + + + + 0 0 + - - 0 + + t20 0 0 0 0 0 0 0 0 0 0 0 0 0 - - 0 0 0 0 k10 0 0 0 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 0 0 k20 0 0 0 0 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 +

Structure F1

n1n2p1y p2y u1u2

Variable

Parameter

M1+ 0 - 0 + +

M2- + 0 - + +

t10 0 + 0 + +

t20 0 0 0 0 0

k10 0 0 0 0 0

k20 0 0 0 0 +

Marginal comparative statics of each local equilibrium are summarized in Table

2. Since marginal comparative statics in structures D1 and D2 are similar to that in structure D0, structure C2 is symmetric to C1, E2 is symmetric to E1, and F2 is symmetric

to F1, we omit these structures in Table 2. Sign + (- or 0) in this table represents a positive (negative or zero) derivative of an endogenous variable with respect a parameter. For instance, “+”in column 8 and row 3 in Table 2 implies that d n1/d M1 > 0 in structure C1.

Put marginal comparative statics for structure C given in (3), and inframarginal comparative statics, given in (8), together, we can see that if the local equilibrium in structure C1 is the general equilibrium, then the conditions for d n/d t1 > 0 and d n/d M1 > 0, given in (3), are satisfied. Hence, d n/d t1 > 0 and d n/d M1 > 0 holds if structure C1 occurs in equilibrium. All marginal and inframarginal comparative statics are summarized in the following proposition.

Proposition 4:

(1) If transaction efficiencies for all goods a re low, then autarky structure is equilibrium in which no international trade occurs though the number of intermediate goods, productivity,

and per capita real income in each country increases with its population size. As transaction efficiency is improved, the equilibrium jumps to a structure with trade. In an equilibrium

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trade pattern, a country exports goods with net endogenous and exogenous comparative advantages in production and transactions. It exports a good if its endogenous comparative advantage in production and exogenous comparative advantage in transactions dominate its exogenous comparative disadvantage in producing this good. Otherwise, it imports this good. Each country will exploit the substitution between trades of different types of goods to avoid trading goods that are associated with low transaction efficiency.6

(2) If a country exports the agricultural good and imports the final manufactured good (structure C), as the transaction efficiency of intermediate goods in the other country increases from a very low to a high level, this country shifts from specialization in producing the agricultural good to exporting increasingly more intermediate goods. Changes in relative population size will shift the production of producer goods to the country with increased relative population size. Improvements in transaction conditions of final goods benefit both countries too. Improvements in transaction conditions and increases in population size raise per capita real incomes in both countries and the t o tal number of producer goods in the whole economy.

(3) If a country specializes in producing producer goods (structure E or F occurring in equilibrium), an increase in population size and/or in transaction efficiency in either country raises per capita real income. But an increase in a country's transaction efficiency or in the population size in the other country will relocate the production of producer goods from the former country to the latter.

(4) If the two countries trade producer goods (structure D occurring in equilibrium), then an increase in the transaction efficiency in a country may reduce its per capita real income although increases in population sizes may have positive effects on industrialization and per capital real income. This implies that the government in each country may have an incentive to impose a tariff (reduces transaction efficiency for importing goods) to improve terms of trade and raise home residents' per capita real income.

In many models of endogenous network size of division of labor (see a survey of this literature by Yang and Ng, 1998), the two following results in proposition 4 hold.

6The effects of transaction conditions on economic development are verified by historical evidences documented in North (1958) and by empirical evidences provided in Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997), Gallup and Sachs (1998), Sachs and Warner (1995, 1997).

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The equilibrium network size of division of labor, the number of traded goods, and aggregate productivity increase as the trading efficienc y coefficient increases; Individuals will exploit the substitution between trades of different types of goods to avoid trading goods that are associated with low transaction efficiency, meanwhile getting them involved in the division of labor. Also, Sachs, Yang, and Zhang (2000) and Cheng, Liu, and Yang (2000) show that a country may export a good with exogenous comparative disadvantage if endogenous comparative advantage dominates this disadvantage. Hence, these three results in Proposition 4 are not sensitive to those changes of model specification that have been already explored in the existing literature of endogenous network size of division of labor. Other results are model specific. They may not be robust to changes in model specification.

4. Comparison with the Models with CRS

In this section, we compare our analysis of pattern of trade and economic development with the conventional theories of trade and economic development. We first show that our theory may make the core theorems of neoclassical t rade theory irrelevant and then compare it with neoclassical development economics based on the models with constant returns to scale.

We first show that our theory may make the HO theorem irrelevant. It is interesting to see that our comparative statics may generate prediction that is empirically equivalent to rejecting the HO theorem. If we interpret intermediate goods as capital or producer goods, then empirically, the aggregate output level of intermediate goods in our model can be considered to be total value of capital. With this interpretation, good y is capital intensive and z is labor intensive (which needs no capital goods for production). Hence, as the number of intermediate goods endogenously increases in response to improvements of transaction condition or to population growth, capital intensity of good y increases. There is no reason that the country producing a lot of capital goods must export good y in our model. Hence, it is perfectly reasonable that from empirical observation, a country producing a lot of capital goods exports labor intensive goods z and imports capital intensive goods y. This analysis is consistent with the proposition

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made by Bhagwati and Dehejia (1994) that as increasing returns and intermediate goods are introduced, the neoclassical core trade theorems may become irrelevant.

Next, we compare our results with the SS theorem. Using the results in (3)-(7), it can be shown that if structure C, E, or F occurs in equilibrium, we have

d(p ix/w i)/d t i = 0 and d(p iy/p iz)/d t i ＜ 0.

d(p ix/w i)/d M i = 0 and d(p iy/p iz)/d M i ＜ 0.

d(p ix/w i)/d M j = 0 and d(p iy/p iz)/d M j ＜ 0.

Also, if structure D occurs in equilibrium

d(p ix/w i)/d t j = 0 and d(p iy/p iz)/d t j ＜ 0.

d(p ix/w i)/d M i = 0 and d(p iy/p iz)/d M i ＜ 0.

d(p ix/w i)/d M j = 0 and d(p iy/p iz)/d M j ＜ 0.

All of these marginal comparative statics imply that as relative prices of goods and inputs change in response to changes in parameters, the direction of the changes of relative prices are inconsistent with the SS theorem. In other words, the final manufactured good y is capital intensive and the agricultural good is labor intensive. As relative price of the two final goods decreases in response to changes of transaction conditions, the relative price of capital goods to labor does not change.

The SS th eorem has been used to show that tariff can be used to redistribute income toward the scarce factor. But the common sense is inconsistent with the logic of the SS theorem. The common sense says that as tariff increases in a country that exports capital intensive goods and imports labor intensive goods, labor will marginally benefit. But this tariff forgone opportunity to increase productivity by expanding trade network. Hence, it is the net effect that determines if labor can benefit from the increased tariff.

Our model substantiates this common sense. From (8b), we can see that if k2 and t1 are large, structure C1 occurs in equilibrium. Assume that country 1 is the US and country 2 is Taiwan. Now the government in the US increases import tariff rate, so that t1 decreases. Its inframarginal effect is to make the equilibrium jump to autarky. From (2) and the local equilibrium in autarky, we can see that the relative wage rate of the US to Taiwan is 1/t1ρ>1 in C1, and is 1 in autarky. Hence, inframartinal effect of the tariff increase is to reduce relative wage of the US. But marginal effect of a decrease in t1 is to raise the relative wage rate in the US since d(1/w)/d t1 = d(1/t1ρ)/d t1 ＜ 0. Also, from (2),

25

the terms of trade of the US p1y/p2z marginally increases as t1 decreases (or as tariff rate in the US increases). These are positive marginal effect of this tariff increase on terms of trade and wage rate in the US. But it generates negative marginal effect by reducing trade and productivity gains that can be exploited. The net marginal effect of this tariff increase is represented by resulting changes in per capita real incomes (equilibrium utility). From (2) and (3), it is obvious, this net marginal effect is negative since per capita real income decreases as a result of the tariff increase in the US (d u1/d t1, d u2/d t1 > 0). If we take into account of the negative inframarginal effect of the tariff increase which reduces the relative wage rate of the US, the total net effect of the tariff increase is to hurt labor in the US. We have conducted similar analysis for other structures C, E, F and obtained similar results.

It is interesting to see that in this example, labor in the US benefits from a decrease in tariff rate, even if this tariff reduction marginally deteriorates US’s terms of trade. This is because productivity gains from expanded network size of trade (an increase in the number of traded intermediate goods n) may outweigh the negative effect of deteriorated terms of trade.7

But the analysis of stru cture D indicates that the net marginal effect of a tariff increase in the US is positive (u1 increases as t1 decreases), though it marginally deteriorates terms of trade p1x/p2x and relative wage 1/w. But total net marginal and inframarginal effect could be still negative.

It is straightforward from the local equilibria in C, D, E, and F, that the factor price equalization does not hold in general since the equilibrium value of w is not 1 in general, though it tends to 1 as transaction cost goes to 0. Hence, transaction costs explain the difference in factor prices between the countries. As transaction conditions are improved, the factor price tends to be equal for a given structure. But inframarginal comparative statics (jumps of equilibrium between stru ctures) will invalidate the generalized FPE theorem. For instance, as k2 increases, the equilibrium may jump from

7 Empirical evidence to support this prediction can be found from Sen (1998). In the literature of development strategy, a decrease in k(associated with an increase in tariff on imported final goods) in structure D0 is considered as first-stage import substitution. A decrease in t is considered as second-stage import substitution.

26

D0 to C1, which may cause an increase in the difference in wage rates between the two countries.

It is not appropriate to directly compare ou r comparative statics with the core trade theorems in the HO model because of different specifications of model structures. Hence, we should pay more attention to the distinct features of comparative statics of our model which are summarized in propositions 1-4 and Tables 1, 2. The effects of changes in transaction conditions on the number of traded goods and intermediate goods (degree of industrialization), productivity, and per capita real income and on discontinuous jumps of trade patterns are much more important than their effects on structure of relative prices. No much regularity of comparative statics that relate to changes of structure of relative prices stands out in general in our model. Anything is possible even if a specific model is explicitly s pecified. The regularity of comparative statics that relates to price structure is not only model specific, but also trade structure specific (or parameter subspace specific). Hence, it is inconsequential to try finding the counterparts of the SS theorem.

We now consider comparison between our comparative statics and conventional development economic theories. We first consider the development trap, then the relationship between industrialization, income distribution, and evolution of dual structure, and finally development strategy.

Assume that food z is a necessity and its minimum per capita consumption must be not smaller than 1 for subsistence. Suppose all labor is allocated to the production of z. Then per capita output and therefore per capita consumption of z is θi, which is not greater than 1 if and only if θi≤ 1. Hence, for a value of θi that is small enough to be close to 1, the equilibrium number of intermediate goods must be at its minimum value 1. In other words, each intermediate good is not necessity individually for the production of the final manufactured good y and therefore labor must be concentrated in the production of food rather than dispersed in producing many intermediate goods if productivity of food is very low. If transaction efficiency for international trade is very low too, then importing food is not an optimum choice. Therefore, a country with very low transaction efficiency and low productivity of the agricultural goods will be locked in the development trap where the number of available producer goods is very small,

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productivity of the final manufactured goods is low, and trade dependence and per capita income is low.

It is not difficult to show that as transaction conditions are improved, the relative output of industrial goods x and y to the agricultural good z increases though the income share of industrial goods is always a constant regardless of the degree of industrialization (an increase in the number of intermediate goods and a decrease of price of final manufactured goods). As industrialization continues, changes in the difference in per capita real income between countries have no much general regularity.

Suppose structure C1 occurs in equilibrium, then from (2) and (3), we can see that per capita real income in country 1 is higher than in country 2 if and only if (θk1)1-αt11-ρ-α> (k2t2)α. Suppose this inequality holds, the difference in per capita real income between the two countries increases with θ and k1, and decreases with k2 and a. Its relationship with t1 is ambiguous. Hence, there are many determinants of the relationship between trade and inequality of income distribution between countries. Suppose industrialization and increases in trade are driven by improvements in transaction conditions. Relative change speed of transaction conditions in the two countries affects changes in the difference in per capita real income between the two countries. There is no monotonic correlation, nor simple inverted U curve between the difference and trade, which increases with transaction efficiency and with industrialization. If marginal comparative statics in other structures and inframarginal comparative statics are considered, our conclusion will be strengthened: no much general regularity of the relationship between i n equality and economic development and related trade exists. This prediction is supported by recent empirical evidences in Ram (1997), which rejects inverted U curve for the relationship between inequality and per capita income, and in Jones (1998, p. 65) which shows that the ratio of GDP per worker in the 5th-richest country to GDP per worker in the 5th-poorest country fluctuated from 1960 to 1990. This result differentiates our model from the Krugman and Venables (1995) which predicts an inverted U-curve.

We now consider the implications of our comparative statics for development strategies. Again, we may take country 1 as the US and country 2 as Taiwan. Suppose that transaction efficiency for international trade in the initial period of time is very low in both countries, then autarky occurs in equilibrium. Assume further that the US has a quite large

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autarky equilibrium number of intermediate goods (quite high degree of industrialization) due to the relatively large population size and Taiwan is in the development trap. We consider the two cases. In case (a), Taiwan is in the development trap due to low relative productivity of the agricultural sector (bad climate condition and limited arable land). In case (b) Taiwan’s relative productivity of the agricultural sector is high, but its population size is too small.

Assume that in period 2, transaction efficiency for international trade is slightly improved. The equilibrium will jump to structure F1 for case (a) since (8a) and (8b-III) indicate that for a large θ (country 2’s relative productivity of the agricultural good is low), as transaction conditions are slightly improved, the equilibrium jumps from autarky to F1. For case (b), as transaction conditions are improved, the equilibrium jumps from autarky to structure C1 since (8b-I) indicates that for a small θ (country 2’s relative productivity of the agricultural good is high), structure C1 is more likely to occur in equilibrium. Suppose that the slight improvement of transaction condition is not enou gh to ensure t1 > t a, so that n2 = 0 as shown in (4). This implies that Taiwan completely specializes in producing and exporting the agricultural good (without industrialization) though it can gain from exogenous comparative advantage in production.

In period 3, Taiwan has several options, dependent on the transaction cost coefficient or tariff rate in the US (1-t1). Suppose 1-t1 decreases over time due to liberalization reforms or preferential tariff rate to Taiwan in the US. Then Taiwan starts industrialization. The production of intermediate goods relocates from the US to Taiwan, increasing per capita real incomes in both countries and the relative wage rate in Taiwan (see (3) and (4)). This increase of n2 in C1 looks like an export oriented development pattern, pursued by Taiwan in the 1960s - 1980s. The driving forces of this industrialization are the open door policy of the US (an increase in t1 and k1, see (3) and (8b-I)) and Taiwan’s liberalization and internalization policy (a large k2, see (8b)). In the literature of development economics, structure C1 with a small n2 is sometimes called development pattern of dependence (see Myrdal, 1957, Nelson, 1956, Palma, 1978, for instance).

But if k2 is small compared to t1 and t2 because of a high tariff of imported final goods and a low tariff of imported producer goods in Taiwan, then the equilibrium will jump from C1 with a small n2 to D0 as Taiwan lows its import tariff of producer goods. This

29

policy regime is just like the import substitution strategy carried out in Taiwan in the 1950s (see, for instance, Balassa, 1980, Chenery, Robinson, and Syrquin, 1986, Meier, 1989, pp.297-306,and Bruton, 1998). The jump from C1 with a small n2to D0 is just like an import substitution process. The difference between export oriented and import substitution development patterns lies in the fact, shown in propositions 1-4, that all countries have incentives to raise import tariff rates in structure D0 which will reduce per capita real incomes in both countries, while in structure C, E, or F, both countries have incentives to reduce tariff rates.

In other words, if a government distorted tariff structure to pursue structure D (import substitution), D itself will justify a more distorted tariff structure which impends economic development. Hence, this distorted tariff policy could generate a particular type of development trap. In the absence of such distorted tariff, structure D may occur naturally in equilibrium as a consequence of certain pattern of endogenous and exogenous comparative advantages in production and transactions. Since utilities of both countries increase with transaction efficiencies in structures C, E, and F, liberalization and internationalization policy is easier to carry out in these structures. This explains why export oriented development pattern is more successful than the pattern of import substitution. But the notion of import substitution is inaccurate, since this pattern of trade and development relies on increases in imported intermediate goods, though it promotes domestic production of final manufactured goods.

Another interesting difference in development patterns is between structure E1 or F1 and structure E2. F1 is like that the less developed country (country 2) imports final goods and exports parts and components of the final manufactured goods. Taiwan does not export automobiles but exports a lot of parts and components of automobiles and computers. In structure E2, the less developed country imports intermediate goods and exports fina l manufacture goods, similar to Hong Kong’s development pattern in the 1970s and 1980s. However, if E1 or F2 occurs in equilibrium in the absence of the government intervention, which of them takes place is determined by natural endogenous and exogenous comparative advantage in production and transactions. It is counter-productive to pursue a particular one of them by using tariff policy. Any improvements in transaction efficiencies

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will promote productivity progress and increase per capita real income, reg ardless which one among E and F occurs in equilibrium.

Following Yang and Heijdra's method (1992), we can show that all local equilibria may not be Pareto optimal. Ignoring the conditions that marginal revenue equals marginal cost for firms producing intermediate goods, we can use all conditions for a local equilibrium in a structure to express utilities as functions of n1 and n2. Maximizing utility of one country with respect to n1 for given n2 and maximizing utility of the other country with respect to n2 for given n1 yields the Pareto optimum n1 and n2, which may be either greater or smaller than their local equilibrium values. Nobody gains from such distortions caused by monopoly power and coordination problems of the industrial linkage network. Hence, a cheap talk among members of an industrial association may reduce such distortions. Kemp (1995) shows that if identical share holders’decisions are spelt out in this kind of models, the distortions caused by coordination problems can be avoided since consumers as shareholders do not gain from such distortions while they suffer from them. In the presence of interest conflict between countries which occurs in structure D when governments can manipulate transaction conditions via tariff policies, the coordination difficulty cannot be solved via cheap talks. Hence, structure D (import substitution pattern) cannot survive competition in the long-run if tariff policies are used to manipulate terms of trade.

5. Concluding Remarks

We develop the model of monopolistic competition to provide a unified framework for the analysis of patterns of trade and economic development. Coexistence of exogenous and endogenous comparative advantages in production and differences in transaction conditions between countries distinguishes our model from other models of monopolistic competition. Inframarginal comparative statics distinguishes our results from marginal analyses of other models of monopolistic competition. Our model shows that a country exports goods with net endogenous and exogenous comparative advantage in production and transactions. It may export a good with exogenous comparative disadvantage in production, if its endogenous comparative advantage in producing this good and its comparative advantage

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in transactions dominate this disadvantage. Decision makers will use substitution between trades of different types of goods to avoid trade with high transaction costs.

Improvements in transaction conditions or increases in population sizes will promote industrializatio n, increase productivity, per capita real incomes, and trade dependence. But increases in the population size in a country may relocate the production of intermediate goods to this country from the other country. In an asymmetric trade pattern which looks like an export oriented development pattern, improvements in transaction conditions in a country has positive effects on per capita real incomes in all countries. But in a symmetric trade pattern which looks like a development pattern of import substitution, a decrease in transaction efficiency in a country may increase per capita real income in this country. This creates incentives for manipulating terms of trade by imposing import tariff. This tariff war will impend economic development in all countries.

No much general regularity exists for the relationship between inequality of income distribution between countries and economic development and related trade, nor for the relationship between relative prices of goods and relative prices of inputs.

The shortcoming of this model is that it predicts two types of scale effects. Type I scale effect implies that industrialization, economic development, and trade will be promoted by an increase in population size in the whole economy. The scale effect is rejected by empirical evidences surveyed in National Research Council (1986) and Dasgupta (1995). Also, our model generates Type II scale effect which implies that productivity of manufactured goods goes up if and only if the average size of the manufacturing firms increases. The scale effect is rejected by empirical evidence provided by Liu and Yang (2000). There are two ways to avoid the scale effects. One is to specify local economies of scale. This makes the algebra very complicated due to feedback loops between positive profit and consumers' demand functions. The other way is to develop the models with endogenous levels of specialization for individuals (Sun, 2000, Yang and Ng, 1995, Shi and Yang, 1995, and Liu and Yang, 2000). These models of endogenous specialization formalize the argument of irrelevance of the size of the firm, proposed by Coase (1937), Cheung (1983), Stigler (1953), and Young (1928). According to this argument, if division of labor develops between firms, productivity increases while averag e size of firms declines (outsourcing, down-sizing, contracting out, disintegration, focusing

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on core competence). If division of labor develops within each firm, then the average size of firms and productivity increase simultaneously.

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