the positive theory of international trade

8/13/2019 The Positive Theory of International Trade

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Chapter 1T H E P O S I T I V E T H E O R Y O F I N T E R N A T I O N A L T R A D ERONALD W. JONESUniversity of Rochester

and

J. PETER NEARYUniversity College Dublin

Content s1 Introd uct ion 22 Models of t rade 4

2.1. The exchange model 72.2. The Ricardian model 102.3. The Heckscher-Ohlin model 42.4. The specific-factorsmodel 212.5. Extensions 27

3 Multi level trad e 313.1. Trade in intermediates and natural resources 313.2. Trade in factors 373.3. Trade in technology 423.4. Trade in securities 43

4 Multi behavioral t rade 454.1. Market distortions 454.2. Increasing returns 484.3. Imperfect competition 505. Con cluding rem arks 53

References 53This paper was begun while the authors were visitors at the International Institute for AppliedSystems Analysis, Laxenburg, Austria. We are grateful to this Institute and to the national ScienceFoundation under grant no. SES-7806159 for support and to J.N. Bhagwati, A.V. Deardorff, A.K.Dixit, W. Ethier, M.C. Kemp, P.B. Kenen, F.P. Ruane, and L.P.F. Smith for helpful comments.

Handboo k of International Economics vol. I Edited by R. W. Jones and P.B. Ken en@ Elsevier Science Publisher s B. K 1984


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1 Introduction

The theory of international trade is one of the oldest subfields of economics andits central concerns remain those of Ricardo. Nevertheless, in recent years thefield has not stood still, but has exhibited an expansion of the range of topicsstudied and of the analytical tools brought to bear on them. In this chapter weattempt to present an overview of the present state of positive trade theory,concentrating on developments since the surveys of Mundell 1960), Bhagwati1964) and Chipman 1965-66) while at the same time drawing attention to thecont inuity in the development of the subject. We begin in this section by outliningthe scope of the field as we see it and the criteria which have guided our selectionof topics to be covered.

As the title of our chapter indicates, we confine our attention to the positivetheory of international trade, leaving normative questions for Chapter 2. Al-though the distinction is somewhat arbitrary, a reasonably clear line of demarca-tion can be drawn. As a rough guideline, questions concerning the effect ofexogenous or policy changes on the level of ggreg te real income or dealing withthe ranking of alternative policy instruments will be considered the province ofnormative trade theory. By contrast, questions concerning the effect of exogenousor policy changes on the composition of outputs, relative prices, trade flows, or onthe domestic distribution of real income will be considered within the realm ofpositive trade theory.While trade theory makes extensive use of general-equilibrium theory, with itsconcern for interactions among markets, the key feature which distinguishes it isits recognition that not all commodities and factors are equally mobile. Thisphenomenon of differential mobility can take many forms. From Ricardo on-wards, much of~ trade theory has been conducted in terms of the Classicalmobility assumptions: all final goods are tradeable between countries whereasprimary inputs are non-tradeable, though fully mobile between different sectorsof the domestic economy. However, a great deal of recent work has beenconcerned with examining the consequences of departures from these assump-tions.Another feature which characterizes international trade theory is its focus onapplied questions, making it natural to conduct analysis in the context ofrelatively small-scale models. This is not to say that trade theory is wedded to anyparticular model. For example, despite its dominance in the 1960s, theHeckscher-Ohlin model has not supplanted the Ricardian model, nor has it in itsturn been eclipsed by the recent revival of interest in the specific-factors model.Rather, positive trade theory uses a variety of models, each one suited to a limitedbut still important range of questions. While this eclectic approach is sometimes


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Ch. 1: Positive Theory of International Trade 3c r i t i c i z e d , s i n c e i t i s e a s y t o s h o w t h a t t h e p r o p o s i t i o n s d e r i v e d f r o m a n y o n em o d e l a r e n o t n e c e s s a r il y ro b u s t w i t h r e s p e c t to r e l a x a t io n s o f t h a t m o d e l ' sa s s u m p t i o n s , i t s e e m s t o b e a m o r e s a t i s f a c t o r y w a y o f y i e l d in g u s e f u l i ns i gh t s a n ds u g g e s ti n g h y p o t h e s e s f o r e m p i r i c a l t e st in g t h a n t h e a t t e m p t t o c o n s t r u c t ag e n e r a l m o d e l w h i c h e n c o m p a s s e s a l l o t h e r s a s s p e c i a l c a s e s. 1

A m o n g t h e is s u e s w i t h w h i c h p o s i t i v e tr a d e t h e o r y d e a l s is t h e q u e s t i o n o f th ed e t e r m i n a n t s o f t h e p a t t e r n o f t r a d e t o w h i c h t h e p r o x i m a t e a n s w e r u s u a l l y g i v e ni s st il l t h a t o f R i c a r d o : n a m e l y , t h e p r i n c i p le o f c o m p a r a t i v e a d v a n t a g e , w i t h i tsf o c u s o n a c o m p a r i s o n a m o n g a u t a r k i c r e l at i ve p ri c e s in d i f f e re n t c o u n tr i es . I n t h ec a s e o f tw o c o m m o d i t i e s a n d t w o c o u n t r i e s t h e p r i n c i p le is b o t h e a s y t o f o r m u l a t ea n d i n c o n t r o v e r t i b l y t r u e : 2 e a c h c o u n t r y w i l t t e n d t o e x p o r t u n d e r f r e e t ra d e t h a tc o m m o d i t y w h i c h h a s t h e l o w e r r e l a ti v e p r i c e i n a u t a r k y . H o w e v e r , w i t h m o r et h a n t w o c o m m o i t i e s t h e a p p r o p r i a t e w a y t o g e n e ra l iz e t h e p r i n c ip l e is n o ti m m e d i a t e l y a p p a r e n t . I t i s t e m p t i n g , f o r e x a m p l e , t o a r g u e t h a t i f c o m m o d i t i e sa r e r a n k e d b y t h e ir r e la t iv e p r ic e r a ti o s i n a u t a r k y i n t h e t w o c o u n t r i e s, d e m a n dc o n d i t i o n s w i l l d e t e r m i n e a c r i t i c a l r a t i o s u c h t h a t , w h e n t r a d e i s o p e n e d u p , t h eh o m e c o u n t r y w i l l e x p o r t a l l c o m m o d i t i e s w h o s e a u t a r k y r e l a t i v e p r i c e i s b e l o wt h i s r a t i o a n d i m p o r t a l l o t h e r c o m m o d i t i e s . T h i s a s s e r t i o n i s c o r r e c t i n t h eR i c a r d i a n c a s e o f c o n s t a n t c o s t s, b u t a s D r a b i c k i a n d T a k a y a m a ( 19 7 9 ) a n d D i x i ta n d N o r m a n ( 19 8 0, p p . 9 5 - 9 6 ) h a v e s h o w n , i t n e e d n o t h o l d i n l es s s p e c ia l c a se s .H o w e v e r , t h e m o r e p a r a d o x i c a l a s p e c t s o f t h e i r c o u n t e r - e x a m p l e s r e l y o n t h ep r e s e n c e o f s tr o n g c o m p l e m e n t a r i t y i n d e m a n d . I n a n y c a se , w h a t e v e r th e p a t t e r no f s u b s t i t u t a b i l i t y o r c o m p l e m e n t a r i t y , t h e p r i n c i p l e o f c o m p a r a t i v e a d v a n t a g em a y b e r e f o r m u l a t e d i n t e rm s o f a c o r r e la t i o n b e t w e e n d i f f e re n c e s i n a u t a r k y p r i c el e v el s a n d n e t e x p o r t v o l u m e s f o r d if f e re n t c o m m o d i t i e s , as D e a r d o r f f (1 9 8 0) a n dD i x i t a n d N o r m a n ( 19 80 ) h a v e s ho w n .

W h i l e t h e p r in c i p l e o f c o m p a r a t i v e a d v a n t a g e m a y t h u s b e d e f e n d e d a s a b a s i ce x p l a n a t i o n o f t r a d e p a t t e r n s , i t is n o t a p r i m i t i v e e x p l a n a t i o n , s i nc e it a s s u m e sr a t h e r t h a n e x p l a i n s i n t e r - c o u n t r y d i f f er e n c es in a u t a r k i c r e l a t iv e p r ic e s . M u c h o ft r a d e t h e o r y i s t h e r e f o r e c o n c e r n e d w i t h i n v e s t i g a ti n g a l t e r n a t iv e s o u r c es o f t h e s ed i f fe r e n c e s , a n d e a c h s u c h s o u r c e h a s i m p l i c a t i o n s i n t u r n f o r t h e e f f e ct o f t h eo p e n i n g u p o f tr a d e o n t h e s tr u c tu r e o f p r o d u c t i o n a n d o n t h e d o m e s t i cd i s t r i b u t io n o f in c o m e . T h e s a m e q u e s t io n s c a n a l s o b e p o s e d n o t i n t e r m s o f ac o m p a r i s o n b e t w e e n a u t a r k y a n d f r e e t r a d e b u t i n th e c o n t e x t o f d i s t u r b a n c e s t o

1This viewp oint is not sh ared by all trade theorists. For exam ple, Pearce (1970, p. 17) states Thereis but one world and only one m odel is needed to describe it .2Nevertheless, the principle, with its denial that absolute superiority in p roductive pow er determinesthe p attern of trade, remains suspiciously counterintuitive to m ost no n-econom ists. Sam uelson (1969)recalls the time he was challenged by the mathematician Stanislaw Ulam to nam e m e oneproposition in all of the social sciences wh ich is both true an d no n-trivial. Sam uelson remark s thatyears later he thought of the appropriate answer: the Ricardian the ory of comparative advantage.T ha t it is logically true need not be argued before a mathem atician; that it is not trivial is attested bythe thousands of imp ortant and intelligent men who have ne ver been able to g rasp the doctrine forthemselves or to b elieve it after it w as explained to them .


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4 R W Jones andJ P Nearyan initial trading equilibrium. In discussing these and other issues, our strategy isto present in Section 2 an overview of a number of alternative models, stressingthe complementari ty between them and the differences in the questions whicheach is well suited to answer. For the most part, this section stays within what wecall the Class ical paradigm. This encompasses not only the Classical assump-tions about goods and factor mobility already mentioned, but also neglectsintermediate stages in the production hierarchy and assumes that all agents areatomistic, operating in an undistorted and competitive environment in whichtechnology exhibits constant returns to scale. More recent work which relaxesthese assumptions, allowing for trade at different levels of the production spec-trum and for departures from competitive behavior, is reviewed in Sections 3 and4 respectively.Inevitably, throughout the chapter there is some overlap with other contribu-tions to this volume (though not on empirical matters, which we leave to Chapter10). In general, we go into less depth on individual topics than other contributors,attempting instead to fit recent extensions into an overall framework whichprovides a coherent view of the field. Moreo~,er, a survey of a wide field such asthis cannot hope to be anything other than highly selective. Without attemptingto provide a comprehensive coverage, therefore, we hope to give the flavor of asubject which remains a vibrant and fruitful source of theoretical insight andtestable hypotheses.

2 M od e l s o f t rad e

Although the theory of international trade combines dements of demand behav-ior with production structure in a general-equilibrium context, it is primarilyvariations in the specification of the production side that distinguish the basicmodels of trade. Section 2.1 describes the uses to which the exchange model hasbeen put; this model can be interpreted as one in which each of two factors isused to produce a separate commodity so that no intersectoral factor mobility isallowed. Section 2.2 describes the Ricardian model, the polar opposite of theexchange model in that only one productive factor (labor) is employed, but thisfactor can be freely reallocated between sectors so as to maximize its earnings.Section 2.3 presents the basic propositions of the Heckscher-Ohlin model, themodel most frequently used in positive trade theory, whereas Section 2.4 dealswith the specific-factors model, which focusses on asymmetry in the degree offactor mobility between sectors. Finally, Section 2.5 extends these models toconsider some properties of higher dimensional cases as well as the possibility ofjoint production

The production structures of the basic trade models discussed in this sectionhave many properties in common. For each country it is possible to relate thevalue of the nat ional product, Y to the vector of factor endowments, v, and the


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Ch. 1: Positive Theory of International Trade 5v e c t o r o f fi na l c o m m o d i t y p r ic e s, p , w h e r e c o m p e t i t i o n e n s u r e s t h a t t h e c o m p o s i -t i o n o f o u t p u t ( s h o w n b y t h e v e c t o r , x ) m a x i m i z e s t h e v a l u e o f Y a t t h o s e p ri c es . 3P r i c e - o u t p u t r e s p o n s e s a r e n o r m a l , i n t h e s e ns e t h a t n o c o m m o d i t y c a n f a ll i ns u p p l y i f i t s p r i c e r is e s ( a n d a ll o t h e r p r i c e s a n d e n d o w m e n t s r e m a i n c o n s t a n t ) .S i m il ar ly , a n i n c r e a se i n t h e e n d o w m e n t o f a n y f a c t o r o f p r o d u c t i o n c a n n o t r a i set h a t f a c t o r s r e tu r n i f c o m m o d i t y p r ic e s a n d a ll r e m a i n i n g e n d o w m e n t s a r e h e l dc o n s t a n t . F u r t h e r m o r e , a b a s i c r e l a t i o n s h i p - t h a t o f r e c i p r o c i t y - e q u a t e s t h e e f f e c tw h i c h a n i n c re a se i n t h e e n d o w m e n t o f f a c to r i 4 h a s o n t he o u t p u t o f c o m m o d i t y j( al l c o m m o d i t y p r i c e s c o n s t a n t ) t o t h e e ff ec t w h i c h a n i n c r e a se i n c o m m o d i t y j sp r i c e h a s o n t h e r e t u r n t o f a c t o r i.

T h e m o d e l s o f t r a d e d e s c r i b e d in S e c t i on s 2 . 1 - 2 . 4 d if fe r f r o m o n e a n o t h e r i nt h e s p e ci f i c at io n o f t h e n u m b e r s o f f a c to r s a n d c o m m o d i t i e s a n d t h e d e g re e o fi n t e r s e c t o r a l m o b i l i t y o f th e f a c t o rs . T h e y a ll s h a re , h o w e v e r , t h e r e q u i r e m e n t t h a tt h e e c o n o m y s d e m a n d f o r in p u t s t o p r o d u c e c o m m o d i t i e s n o t e x c e e d t h e av a il -a b i l it y o f f a c t o r s in t h e e n d o w m e n t b a s e , a n d t h e s t i p u l a t i o n t h a t i n a c o m p e t i t i v ee q u i l i b r i u m t h e u n i t c o s t s in a n y a c t i v it y d o n o t f al l s h o r t o f m a r k e t p r i c e .F u r t h e r m o r e , w e p o s t p o n e o u r d i sc u s s i o n o f i n t e r m e d i a t e g o o d s a n d j o i n t p r o d u c -t io n . s T h r o u g h o u t w e g e n e r a l l y a s s u m e t h a t f a c t o r e n d o w m e n t s a r e g iv e n. T h i sr u l e s o u t i n t e r n a t i o n a l t r a d e i n p r o d u c t i v e f a c t o r s ( s e e S e c t io n 3 . 2) , th e p o s s i b i l it yt h a t t h e l o c al s u p p l y o f f a c to r s m a y r e s p o n d t o c h a n g e s i n f a c t o r r e w a r d s , 6 o r t h ep o s s i b i l it y t h a t c u r r e n t p r o d u c t i o n a f fe c ts f u t u r e f a c t o r s u p p l ie s . 7 I f a l l f i na lc o m m o d i t i e s a r e t r a d e d o n w o r l d m a r k e t s , t h e c o m m o d i t y p r ic e v e c to r , p , a s w e llt h e f a c t o r e n d o w m e n t v e c to r , v, c a n b e t r e at e d a s e x o g e n o u s f o r a s m a ll o p e ne c o n o m y . B u t o f t e n t r a d e m o d e l s a l l o w a s u b se t o f c o m m o d i t i e s t o e n j o y o n l y an a t i o n a l m a r k e t ; e v e n f o r a s m a l l o p e n e c o n o m y th e p j s f o r n o n - t r a d e d g o o d st h u s d e p e n d e n d o g e n o u s l y u p o n l o c a l d e m a n d c o n d i t i o n s .

T h e s t u d y o f m o d e l s w i th n o n - t r a d e d g o o d s h as e x p a n d e d e n o r m o u s l y in r e c en ty e a rs , i n p a r t b e c a u s e o f th e ir r e l e v a n c e t o m a c r o e c o n o m i c p o l i c y i n s m a l l o p e n

3Formally , Y= g ( p , v ) = m a x x [ p x : F ( x , v) < 0], w her e the ag gregate production possibilities setdefined by the function F ( x , v ) is conv ex. The national pro duct function was introduced b ySamuelson (1953) and its properties have been examined under a variety of assumptions by C hipman(1972), Diewert (1974), and Dixit and No rm an (1980) among others.4The reciprocity relationship is due to Samuelson (1953) and discussed, inter alia, by Jones andScheinkm an (1977). Referring to the previous footnote, outputs and factor prices are reflected in thepartial derivatives of the national product function when these are well defined (as when the numberof factors is at le ast as great as the number of com modities): x = gp and w = gv. g is a concavefunction of v (implying gvv, or O w / O v , is negative semi-definite) and a convex function o f p (implyingO x / O p is positive semi-definite). Reciprocity follows from the symmetry of the matrix of secondderivatives of g.5Section 2.5 considers join t produc tion, w hile Section 3.1 allows the existence of intermediate goodsin the production spectrum as well as international trade in these goods.6For a d iscussion of variable labor sup ply, see Walsh (1956), Kem p and Jones (1962), and M artinand Ne ary (1980).

7This latter possibility is mad e explicit in neo -classical growth m odels in w hich capital is one of theproductive factors and is currently produced. See Onik i and Uzawa (1965) and the discussion ofFind lay (1970) in Section 2.3.


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6 R.W. Jones andJ.P. Nearye c o n o m i e s . 8 A l t h o u g h t h e t e r m s o f t r a d e ( t h e r e la t i v e p r i c e o f e x p o r t s t o i m p o r t s )a r e e x o g e n o u s f o r s u c h e c o n o m i e s , d o m e s t i c p o l i c y c a n n o n e t h e l e s s i n f l u e n c e t h el ev e l a n d c o m p o s i t i o n o f n a ti o n a l i n c o m e a n d ( if th e m o d e l i s e x t e n d e d t oi n c o r p o r a t e a m o n e t a r y s e c t o r ) t h e t r a d e b a l a n c e i f i t c a n a l te r t h e r e a l e x c h a n g er a t e ( d e f in e d a s t h e r e l a t iv e p r i c e o f t r a d e d t o n o n - t r a d e d g o o d s ) . A n y e x o g e n o u ss h o c k i n d u c e s c h a n g e s i n t h e p r ic e s o f n o n - t r a d e d g o o d s a n d t h e s e e ff e c ts a r es u p e r i m p o s e d o n t h e d i r e c t e ff e ct s o f t h e s h o c k i ts e lf . F o r e x a m p l e , E t h i e r ( 1 9 7 2 b )a n d J o n e s ( 1 9 7 7 ) s h o w t h a t a n i n c r e a s e i n t h e p r i c e o f o n e t r a d e d g o o d r e l a t iv e too t h e r t r a d e d g o o d s m a y l e a d t o a fa l l i n it s o u t p u t i n t h e p r e s e n c e o f a n o n - t r a d e dg o o d . M o r e o v e r , t h e i n d u c e d c h a n g e i n t h e p r i c e o f n o n - t r a d e d g o o d s m a y b e i ne i t h e r d i r e c t io n . C o n s i d e r , f o r e x a m p l e , t h e c a s e e x a m i n e d b y J o n e s ( 1 9 7 4 b ) o f a ni n c r e a s e i n t h e p r i c e o f i m p o r t a b l e s w i t h t h e p r i c e o f e x p o r t a b l e s h e l d c o n s t a n t .T o t h e e x t e n t t h a t s u b s t it u t io n e f fe c ts b e t w e e n i m p o r t a b l e s a n d n o n - t r a d e a b l e sa r e s t r o n g , t h e p r i c e o f t h e n o n - t r a d e d g o o d t e n d s t o r i s e , s i n c e d e m a n d i ss w i tc h e d a w a y f r o m i m p o r t s a n d r e s o u rc e s ar e b i d a w a y b y t h e im p o r t - c o m p e t i n gs e c t o r. B u t t h e r i s e i n t h e p r i c e o f i m p o r t a b l e s h a s a n e g a t i v e i n c o m e e f f ec t , a n d i fi t d o m i n a t e s , t h e n t h e d e m a n d f o r t h e n o n - t r a d e d g o o d f a l ls a n d i ts p r ic e ' i s l ik e l yt o f a ll . S i m i l a r co n f l ic t s b e t w e e n i n c o m e a n d s u b s t i t u t i o n e f f e c ts d u e t o t h ep r e s e n c e o f n o n - t r a d e d g o o d s a r i s e i n t h e a n a l y s e s b y B u r g e s s ( 1 9 7 8 ) o f f o r e i g nc a p i ta l i n fl o w s a n d C o r d e n a n d N e a r y (1 9 8 2) o f t h e D u t c h D i s ea s e .

F i n a ll y , a l th o u g h t h e g en e r a l p r o d u c t i o n f r a m e w o r k d e s c r i b e d a b o v e h o l d s f o ra ll t h e m o d e l s i n S e c ti o n s 2 . 1 - 2 .4 , t h e r e s p o n s e o f c o m m o d i t y o u t p u t s t oc o m m o d i t y p r ic e s is s m o o t h a n d w e l l d e f in e d o n l y i f t h e n u m b e r o f p r i m a r yf a c t o r s i s a t l e a s t a s g r e a t a s t h e n u m b e r o f f in a l c o m m o d i t ie s . 9 I f t h i s c o n d i t i o n i sn o t m e t , t h e p r o d u c t i o n p o s s ib i li ti e s f r o n t i e r in o u t p u t s p a c e c o n s is t s o f ru l e ds u r f ac e s , a n d o u t p u t l ev e l s a r e i n d e t e r m i n a t e f o r p r i c e r a t io s c o i n c i d e n t w i t h t h es lo p e s o f t h o s e s u rf ac e s. 1 T h e p h e n o m e n o n o f p r o d u c t i o n i n d e t e r m i n a c y i s b y n om e a n s a c u r i o s u m - i t a ris es i n th e R i c a rd i a n m o d e l , f o r e x a m p l e - a n d w h e n i to b t a i n s t h e a c t u al p r o d u c t i o n p a t t e r n c h o s e n w i ll b e d e t e r m i n e d b y c o n s i d e r a -t i o n s o u t s i d e t h e P a r t i c u l a r m o d e l b e i n g s t u d i e d , s u c h a s t h e t i m e p a t h b y w h i c ht h e e c o n o m y a p p r o a c h e s it s c u r r e n t e q u i li b r iu m o r d e m a n d c o n d i t i o n s a t h o m ea n d a b r o a d . A l t e rn a t iv e l y , p r o d u c t i o n i n d e t e r m i n a c y m a y b e r e s o l v e d if s o m e

8The implications of non-traded goods for trade models hav e been considered by McDougaU(1965), Kom iya (1967), Ethier (1972b) and Jones (1974b). Their application to macroeconom icpolicyhas been considered by man y writers, including Salter (1959), Pearce (1961), Dornbusch (1974), Jonesand Corden (1976), Helpman (1977), N om an and Jones (1979), Neary (1980c) and Neary and Purvis(1982).In models with oint production, he relevant comparison s b etween the num ber of primary factorsand the number of productiveactivities as W oodland (1977b) has po inted out. We return to this issuein Section 2.5 below.1The consequences of m ore comm odities than factors being produced w ere f i rs t noted bySamuelson (1953). Melvin (1968) studies the two-factor, three-comm oditycase in detail and Chang(1979) presents a comprehensiveanalysis of the g enera l case.


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Ch 1: Positive Theory of International Trade 7g o o d s a r e n o t t r a d e d o n w o r l d m a r k e t s s o th a t t h e i r e q u i l i b r i u m p r ic e s a r ed e t e r m i n e d b y t h e in t e r a c t io n o f d o m e s t i c s u p p ly a n d d e m a n d .

2 1 The exchan ge modelM a n y q u e s t i o n s i n t r a d e t h e o r y i n v o l v e t h e b e h a v i o r o f d e m a n d i n a c ru ci~ tl w a y .T o s t u d y t h e s e q u e s t i o n s i t p r o v e s u s e f u l t o s tr i p t h e p r o d u c t i o n s i d e o f t h e m o d e lt o a b a r e m i n i m u m . T h e r e su l ti n g m o d e l , o f t e n r e f e r r e d t o a s t h e e x c h a n g em o d e l , i s h e r e e n v i s a g e d a s a tw o - s e c t o r m o d e l in w h i c h e a c h p r o d u c t i sp r o d u c e d w i t h a s i n gl e f a c t o r s p e c if ic t o t h a t s e c t o r a n d e x o g e n o u s l y g i v e n i ns u p p ly . T h e v e r y s p a rs e n e ss o f t h e p r o d u c t i o n s t r u c t u r e - o u t p u t s d o n o t r e s p o n dt o p r i c e c h a n g e s - m a k e s t h e e x c h a n g e m o d e l a n i d e a l v e h i c l e f o r s t u d y i n gp r o b l e m s i n w h i c h d e m a n d b e h a v i o r is im p o r t a n t .

T h e f i r s t s u c h p r o b l e m i s t h e q u e s t i o n o f s t a b i l i t y o f e q u i l i b r i u m . G i v e n t h en o n - n e g a t i v e r e l a t i o n s h i p b e t w e e n p r i c e s a n d o u t p u t s n o t e d e a r l i e r , p r o d u c t i o nr e s p o n s e a l w a y s e n h a n c e s s t a b i l i t y . H e n c e t h e e x c h a n g e m o d e l i s o l a t e s t h e p o t e n -t ia l s o u r c e o f in s t a b i li ty , n a m e l y , a s y m m e t r i c i n c o m e e f fe c t s i n d e m a n d . O f c o u r s et h i s r o le o f i n c o m e e f f e c ts h a s b e e n w e l l - k n o w n a t l e a st s i n c e H i c k s ( 1 9 39 ) b u t i tt e n d s t o b e o b s c u r e d b y t h e u s u a l p r e s e n t a t i o n o f t h e M a r s h a l l - L e r n e r c o n d i t i o nf o r s t a b il it y . 11 O n l y w h e n t h e e l a s t ic i ti e s in t h is c o n d i t i o n a r e d e c o m p o s e d i n t oi n c o m e a n d s u b s t i t u t i o n e f fe c t s d o e s i t b e c o m e c le a r t h a t n o t h r e a t t o s t a b i l it ya r is e s u n le s s e a c h c o u n t r y h a s a h i g h e r m a r g i n a l p r o p e n s i t y to c o n s u m e it s o w ne x p o r t g o o d ; i n t h a t c a se , t h e i n c o m e e f f ec t o f a r i s e i n t h e r e l a t iv e p r i c e o f t h eh o m e c o u n t r y ' s e x p o r t g o o d , w h i c h r a i s e s r e a l i n c o m e a t h o m e a n d l o w e r s i ta b r o a d , t e n d s t o increase t h e w o r l d e xc e ss d e m a n d f o r th e h o m e c o u n t r y ' s e x p o r tg o o d . ( N o t e a n i m m e d i a t e i m p l ic a t io n : t h e M a r s h a l l - L e r n e r c o n d i t i o n m u s t b es a t is f i ed i f t a s t e s a r e t h e s a m e i n b o t h c o u n t r i e s . )

A s e c o n d p r o b l e m f o r w h i c h t h e e x c h a n g e m o d e l is e s p e ci a ll y a p p r o p r i a t e is t h ee f f e c t o f i n t e r n a t i o n a l g o o d s t r a n s f e r s o n t h e e q u i l i b r i u m t e r m s o f t ra d e . S i n c e th ea n s w e r t o t h i s q u e s t io n i s f o u n d b y e x a m i n i n g t h e s i gn o f w o r l d e x c es s d e m a n df o r e i t h e r g o o d a t t h e i n i t ia l t e r m s o f t r a d e , i t is p e r f e c t l y le g i t i m a t e i n m a n yc i r c u m s t a n c e s to c o n s i d e r t h e i s su e i n t h e e x c h a n g e m o d e l b e c a u s e e v e n w h e np r o d u c t i o n i s v a r i a b l e i t d o e s n o t a c t u a l l y c h a n g e u n t i l a f t e r th e t e r m s o f t r a d ea l te r . I t i s t h is c o n s i d e r a t i o n w h i c h l e a d s t o t h e i m p o r t a n t r e s u l t o f S a m u e l s o n( 1 9 5 2 ) t h a t t h e d i r e c t i o n o f c h a n g e i n t h e t e r m s o f t r a d e d e p e n d s s o l e l y o n i n c o m e

liT he M arshall-Lem er condition referred to in the text is that the sum o f the elasticities of the o ffercurves of the two c ountries (i.e. their general-equilibrium mp ort dem and elasticities) should exceedunity. T his should be distinguished fro m the special case (corresponding o infinite supply elasticitiesin both coun tries) of the partial-equilibrium Bickerdike-R obinson -Metzlercondition. Jone s (1974b)and Do rnbusch (1975) investigate the circumstances n wh ich the latter m ay be given a general-equi-librium interpretation. The decom positionof the offer curve elasticity into incom e and substitutioneffects is g iven in Jone s (1961a).


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R IV Jones and J P Nearye f fe c ts : sp e c i fi c a ll y , i n a t w o - c o u n t r y t w o - c o m m o d i t y f r e e - t r a d e w o r l d , t h e t e r m so f t r a d e o f t h e d o n o r c o u n t r y w i ll w o r s e n i f a n d o n l y i f i t h a s a h i g h e r m a r g i n a lp r o p e n s i t y t o c o n s u m e it s o w n e x p o r t g o o d t h a n h a s t h e r e c i p i e n t c o u n t r y . I ns u c h a c a s e t h e t r a n s f e r l e a d s , a t i n i t i a l p r i c e s , t o a n e t d e c l i n e i n w o r l d d e m a n df o r t h e d o n o r ' s e x p o r t s , w h i c h m u s t g i v e r i se t o a w o r s e n i n g o f i t s te r m s o f t ra d e .( N o t e t h a t t h i s c r i t e r i o n i s e x a c t l y t h e s a m e a s t h a t g i v e n a b o v e f o r t h e i n c o m ee f f ec t s o f a c h a n g e i n t h e t e r m s o f t r a d e t o b e d e s t a b i l i z in g . )

S a m u e l s o n c o n c l u d e d f r o m t h i s r e s u l t t h a t n o p r e s u m p t i o n c o u l d b e e s t a b l i s h e di n f a v o r o f w h a t h e c a ll e d t h e o r t h o d o x v i e w t h a t a d o n o r c o u n t r y w o u l d s u ff e ra s e c o n d a r y b u r d e n o f a d e c li n e i n i ts t e r m s o f t r a d e (o v e r a n d a b o v e th ep r i m a r y b u r d e n o c c a s i o n e d b y t h e d i r ec t l o ss o f p u r c h a s i n g p o w e r a r i s in g f r o mt h e t r a n s f e r i ts e lf ). 12 T h i s c o n c l u s i o n d e r i v e s f r o m t h e f a c t t h a t e c o n o m i c t h e o r yp l a c e s n o r e s t r i c t i o n s o n m a r g i n a l p r o p e n s i t i e s t o c o n s u m e , o t h e r t h a n t h a t t h e ym u s t l ie b e t w e e n z e r o a n d o n e i n t h e a b s e n c e o f in f e r i o r g o o d s. H o w e v e r , a s J o n e s( 1 97 0 a ) h a s p o i n t e d o u t , th e m a r g i n a l p r o p e n s i t i e s t o c o n s u m e in q u e s t i o n a r e f o rt h e g o o d e x p o r t e d b y t h e d o n o r c o u n t r y a n d w e w o u l d n o t i n g e n e r a l e x p e c t ta s t ed i f fe r e n ce s b e t w e e n c o u n t r i e s t o b e u n r e l a t e d t o t r a d e p a t t e r n s . O n t h e c o n t r a r y ,t h e c o u n t r y w i th t h e l a rg e r m a r g i n a l p r o p e n s i ty t o c o n s u m e a g i v e n c o m m o d i t y isl ik e l y t o b e t h e c o u n t r y w h i c h i m p o r t s t h a t c o m m o d i t y . I n a p u r e e x c ha n g e m o d e lw i t h e q u a l in i ti a l e n d o w m e n t s , t h is m u s t b e t h e o u t c o m e if m a r g i n a l a n d a v e r a g ep r o p e n s i t i e s a r e p o s i t i v e l y c o r r e l a t e d . T h i s l in e o f r e a s o n i n g t h e r e f o r e s u g g e s t s a na n t i - o r t h o d o x p r e s u m p t i o n t h a t t h e t r a n s f e r i s l ik e l y t o ra i se w o r l d d e m a n d f o rt h e d o n o r ' s e x p o r t s , a n d s o to i m p r o v e i ts t e r m s o f t r a d e .

W h i le m u c h c a n b e s a i d a b o u t t h e t r a n s f e r p r o b l e m u s i n g t h e e x c h a n g e m o d e l ,i t c a n n o t d e a l w i t h s i tu a t io n s w h e r e t h e t r a n s f e r in d u c e s c h a n g e s i n p r o d u c t i o nb e f o r e t h e t e r m s o f t r a d e a l t e r . O n e o b v i o u s i l l u s t r a t i o n o f t h i s i s w h e n t h e t r a n s f e ri s e f fe c t ed b y m e a n s o f p r o d u c t i v e f a c t o r s r a t h e r t h a n f in a l g o o d s . A n o t h e r i sw h e n t h e t r a n s f e r is e f f e c t e d v i a fi n a l g o o d s , b u t e i t h e r c o u n t r y a l s o p r o d u c e s an o n - t r a d e d g o o d . 13 T h e i s s u e o f p r o d u c t i o n c h a n g e s i s a l s o r e l e v a n t t o t h e e f f ec t so f a t r a n s f e r o n t h e r e a l i n c o m e s o f t h e c o u n t r i e s i n v o l v e d . F o r e x a m p l e , i f t h ea n t i - o r t h o d o x o u t c o m e e n su e s , c a n t h e s e c o n d a r y b e n e f i t a r is i n g f r o m t h e i m -p r o v e m e n t i n t h e d o n o r ' s t e r m s o f t r a d e b e s o g r e a t a s a c t u a l l y t o r a i s e i t s r e a li n c o m e ? I n a t w o - c o u n t r y e x c h a n g e m o d e l t h is p a r a d o x i s i m p o s s i b l e : t h ei m p r o v e m e n t i n t h e d o n o r ' s t e r m s o f t r a d e j u s t s u ff ic ie n t t o k e e p t h e r ea l in c o m e

12However, in a later paper [Samuelson 1954)] he show ed that artificial imped iments to trade(including tariffs thoug h excluding transport c osts which reflect the fact that international transporta-tion c onsum es real resources) go som e way tow ards salvaging the orthodox view.13The transfer problem in the co ntext of non-traded g oods has been considered by Johnso n (1956),M cDou gall (1965), Samuelson (1971a), Chipm an (1974) and Jones (1975a). Sam uelson considered thecase where the no n-traded com mo dity is leisure rather than a final good, but from a fo rmal point ofview the issues raised in the two cases are the sam e.


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Ch 1: Positive Theory of International Tradeo f b o t h c o u n t r i e s c o n s t a n t g i v e s r i s e t o s u b s t i t u t i o n e f f ec t s w h i c h r a i s e w o r l dd e m a n d f o r t h e d o n o r ' s i m p o r t g o o d . H e n c e t h e a c t u a l c h a n g e i n t h e e q u i l i b r i u mt e r m s o f t r a d e m u s t b e less t h a n t h a t s u f f ic i en t t o r e d i s t r i b u t e w o r l d r e a l i n c o m et o w a r d s t h e d o n o r . 14 H o w e v e r , i f t h e t r a n s f e r l e a d s t o o u t p u t c h a n g e s o f t r a d e -a b l e s a t t h e i n i t i a l t e r m s o f t r a d e , t h i s a r g u m e n t n e e d n o t h o l d . M o r e o v e r , e v e nr e m a i n i n g w i t h i n t h e c o n f i n e s o f t h e e x c h a n g e m o d e l , i t h a s r e c e n t l y b e e n s h o w nt h a t t h e d o n o r m a y g a i n i f t h e r e i s a t h i r d c o u n t r y e n g a g e d i n t r a d e , e v e n i f i t i sn o t a p a r t y t o t h e tr a n s f e r. T h e p r e s e n c e o f t h e t h i rd c o u n t r y d o e s n o t a l te r t h eS a m u e l s o n i a n c r i te r i o n f o r t h e d i r e c t io n o f c h a n g e i n t h e t e r m s o f t r a d e ( s in c e , a ti n i ti a l p ri c e s , t h e t h i r d c o u n t r y i s u n a f f e c t e d b y t h e t r a n s a c t i o n ) . H o w e v e r , i f t h et e r m s o f t r a d e i m p r o v e f o r th e d o n o r a n d t a s t e p a t t e r n s d i ff e r b e t w e e n t h e t h i r dc o u n t r y a n d t h e r e c i p i e n t ( w i t h t h e t a s t e b i a s i n t h e t h i r d c o u n t r y t o w a r d s i t se x p o r t g o o d ) , th e r e d i s tr i b u t i o n o f w o r l d i n c o m e m a y e n c o u r a g e s u c h a r is e i n t h ed o n o r ' s e x p o r t p r i c e t h a t i t s r e a l i n c o m e r i s es . 15

M o v i n g o n f r o m t h e t r a n s f e r p r o b l e m w e c o m e n e x t t o t h e t h e o r y o f t a r i f f s ,w h e r e o n c e a g a i n t h e e x c h a n g e m o d e l i s t h e i d e a l v e h i c l e f o r s t u d y i n g t h eq u a l i t a t i v e e f f e c ts o n t h e i n t e r n a t i o n a l e q u i l i b r i u m o f c h a n g e s i n t a r i f f r a t e s o nf in a l g o o d s , si n ce a n y i n d u c e d p r o d u c t i o n r e s p o n s e w o u l d m e r e l y e n h a n c e t h es u b s t i t u ti o n e f fe c ts i n d e m a n d o f p r i c e c h an g e s . W h i l e m u c h o f t a r if f t h e o r y i sc o n c e r n e d w i th n o r m a t i v e q u e st io n s , w e m a y m e n t i o n o n e i m p o r t a n t p o s it iv ei s s u e w i t h w h i c h i t d e a l s , n a m e l y , t h e e f f e c ts o f a t a r i f f o n w o r l d a n d ' d o m e s t i cp r ic e s . T h e n o r m a l o u t c o m e i n t h is ca s e is t h a t a t a r if f r a i se s t h e d o m e s t i cr e l a ti v e p r i c e o f t h e h o m e c o u n t r y ' s i m p o r t g o o d a n d l o w e r s it s re l a ti v e p r i c e o nw o r l d m a r k e t s . I n o t h e r w o r d s , t h e t a r if f i s p r o t e c t i v e i n t h a t it e n c o u r a g e si n c r e a s e d d o m e s t i c p r o d u c t i o n i n t h e i m p o r t - c o m p e t i n g se c t or , w h i l e a t t h e s a m et i m e i t i m p r o v e s t h e h o m e c o u n t r y ' s t e r m s o f t r a d e . H o w e v e r , e i t h e r o f t h e s en o r m a l o u t c o m e s c a n b e r e v er s e d i f e i th e r c o u n t r y ' s d e m a n d f o r i m p o r t s isp r i c e - i n e l a s t i c , r e q u i r i n g a l a r g e c h a n g e i n p r i c e s t o r e s t o r e w o r l d m a r k e t s t oe q u i l ib r i u m . T h u s , i f h o m e d e m a n d i s h i g h l y i n e la s t ic a n d a ll th e p r o c e e d s o f t h et a r if f r e v e n u e a r e s p e n t o n i m p o r t s , t h e r es u l ti n g i n c re a s e in i m p o r t d e m a n d m a yb e s u f f i c i e n t t o worsen t h e h o m e c o u n t r y ' s t e r m s o f t r a d e . A l t e r n a ti v e l y , if f o re i g nd e m a n d i s h i g h l y i n e la s t i c a n d a l l t h e t a r i f f r e v e n u e is s p e n t o n e x p o r t s , t h e t e r m so f t r a d e m a y i m p r o v e t o s u c h a n e x t e n t t h a t t h e d o m e s t i c r e l a ti v e p r i c e o f . i m p o r t s

4This argum ent is presented in Cav es and Jo nes (1981, pp. 64-65).lSThis result was dem onstrated in a num erical exam ple by Gale (1974), although the logic of theargum ent for both dono rs and recipients was earlier discussed in Jo hnson (1960), and criteria in theJohnson framework derived by Kom iya and Shizuki (1967). General criteria for this and relatedthree-agent transfer paradoxes were derived by Yano (1981), who show s that they are consistent withW alrasian stability and w ith som e degree of substitutability in demand. Som e of these results wereindependently obtained by Chichilnisky (1980) and Brecher and Bhagw ati (1981) in two-countrymodels wh ere one cou ntry consists of two groups w ith different taste patterns.


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10 R W Jones and J P Nearyf al ls . 16 T h e f ir s t o f t h e se p a r a d o x e s a d m i t t e d l y r e q u i r e s s o m e d e g r e e o f a s y m m e t r yi n t h e d i s p o s i t i o n o f t h e t a r i ff r e v e n u e : a d e t e r i o r a t i o n i n t h e t e r m s o f t r a d e isi m p o s s i b l e i n a t w o - c o m m o d i t y m o d e l if ta r i f f r e v e n u e is r e t u r n e d t o t h e p r i v a t es e c t o r i n a l u m p - s u m m a n n e r . H o w e v e r , th e p o s s i b i li t y o f t h e t a r i f f s b e i n ga n t i - p r o t e c t i v e su r v iv e s t h e r e la x a t i o n o f t h i s a n d o t h e r a s s u m p t i o n s , r e q u i r i n go n l y t h a t t h e f o r e i g n e l a s ti c it y o f d e m a n d f o r i m p o r t s b e le s s t h a n t h e h o m em a r g i n a l p r o p e n s i t y t o c o n s u m e e x p o r t a b l e s . 17

F i n a l l y , a l t h o u g h t h e e x c h a n g e m o d e l is a c r u d e v e h i c le f o r c o n s i d e r i n gq u e s t i o n s o f d o m e s t i c i n c o m e d i s t ri b u t i o n , it p e r m i t s a n e x a m i n a t i o n o f t h e e f fe c tso f e x o g e n o u s s h o c k s o n t h e d i s t r i b u t i o n o f r e a l i n c o m e b e t w e e n c o u n t r i e s . W h i l et h is i ss u e is c lo s e r to t h e c o n c e r n s o f n o r m a t i v e t h e o r y , w e m e n t i o n o n e a s p e c tw h i c h l in k s w i t h o u r e a rl ie r e m p h a s i s o n t h e i m p o r t a n c e o f i m p o r t d e m a n de l as ti c it ie s : n a m e l y t h e p h e n o m e n o n o f i m m i s e r i z i n g g r o w t h , f ir st p o i n t e d o u tb y E d g e w o r t h (1 8 9 4) a n d i n d e p e n d e n t l y r e d is c o v e r e d b y J o h n s o n ( 19 5 3, 1 9 5 5)a n d f u r t h e r d i s c u s s e d b y B h a g w a t i ( 1 9 5 8 ) . A s w i t h a n i n t e r n a t i o n a l t r a n s f e r ,g r o w t h im p o s e s a s e c o n d a r y b u r d e n o n t h e g r o w i n g c o u n t r y i f i t r a is e s t h ee x c e s s d e m a n d f o r i m p o r t s a t t h e in i t ia l t e r m s o f t ra d e . H o w e v e r , w i t h n om a t c h i n g c h a n g e i n s u p p l y a b r o a d , t h e r e s u l t in g d e t e r i o r a t i o n i n t h e te r m s o ft r a d e c a n b e s i g n if ic a n t e n o u g h t o l e a v e th e g r o w i n g c o u n t r y w o r s e o f f a s a r e s u lto f g r o w t h , p r o v i d e d t h e e la s t ic i ty o f t h e r e s t o f t h e w o r l d ' s d e m a n d f o r i m p o r t s issu f f i c i en t l y l ow .

2 2 The Ricardian modelI n t u r n i n g f r o m t h e ex c h a n g e m o d e l t o t h e R i c a r d i a n m o d e l , th e f o c u s m o v e st o w a r d s a m o d e l w h i c h p r ed i c t s e x tr e m e s h if ts in p r o d u c t i o n p a t t e r n s w h e n t r a d eis o p e n e d u p . T h e t w o m o d e l s a r e p o l a r o p p o s i te s b e c a u s e t h e e x c h a n g e m o d e le x c l u d e s c o m p l e t e l y t h e p o s s i b i li t y o f r e s o u r c e t r a n s f e r , w h e r e a s t h e R i c a r d i a nm o d e l p e r m i t s t h e m a x i m u m d e g r e e o f i n te r n a l f a c t o r m o b i l it y . M o r e o v e r , w h e r e a st h e e x c h a n g e m o d e l p i n s d o w n t h e q u a n t i fi e s o f d i f f e re n t g o o d s w h i c h a r ea v a i l a b le f o r t r a d e , t h e R i c a r d i a n m o d e l p i n s d o w n r e l a t i v e p r i c e s ( a t l ea s t, b e f o r et r a d e i s o p e n e d u p ) b y i t s a s s u m p t i o n s t h a t p r o d u c t i o n c o s t s a r e i n d e p e n d e n t o ft h e le v el o f o u t p u t a n d t h a t t e c h n i q u e s o f p r o d u c t i o n a r e i n d e p e n d e n t o f f a c to rp r ic e s a n d t h e c o m p o s i t i o n o f o u t p u t . T h i s m a k e s i t a n e x t r e m e l y u s e f u l m o d e l f o ri s o la t i n g t h e e f fe c ts o f i n t e r c o u n t r y d i f f er e n c e s i n t e c h n o l o g y o r i n s c a le ( w h e r et h e l a t t e r a r e n o t c o n f u s e d w i t h t h e e f fe c t s o f d i f f e r e n c e s i n t h e d e g r e e o f s c al e,

6Both of these outcom es are illustrated in Figure 4 of Lerner (1936) although the second case wasexamined in greater depth by M etzler (1949) and has com e to be associated w ith his nam e. Thepossibility of this M etzler paradox was disputed by Sode rsten and V ind (1968), but the ir analysiswas corrected by Jones (1969).17Komiya (1967) and Jones (1974a) extend the M etzler paradox to mo dels w ith intermediate andnon-traded goods.


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Ch 1: Positive Theory of International Trade 11which we consider in Section 4.2 below). At the same time, the Ricardian modelthrows no light on questions related to the internal distribution of income, since itassumes either a single mobile factor or many mobile factors which are used inequal proportions in all sectors so that they may be aggregated into a singleLeontief composite factor).Although mainly used by Ricardo to demonstrate the gains from trade, themajor interest of this model stems from its positive application in providing atheory of trade and production patterns. The reasoning leading to this theory inthe two-country, two-commodity case is straightforward. Since each sector uses asingle factor, competition ensures that output prices are directly linked to wagerates: e.g. in the home countrypj equals a L j W where commodities are indexed byj = 1 2 and aL j is the labor requirement per unit output in sector j). Internallabor mobility ensures that the same wage obtains in each sector, so that if acountry produces both goods their relative price must equal the ratio of unit laborcoefficients. The home country thus has a lower autarkic relative price of good 1,and so a comparative advantage in producing that good, if and only if:

aL___Z < a ~ 2.1)aL2 a~2

where an asterisk denotes variables relating to the foreign country. When barriersto trade are eliminated, competition therefore forces at least one country tospecialize in the production of the commodity which it produces relatively moreefficiently and trade patterns completely reflect comparative advantage.The Ricardian model isolates differences in technology as the basis for trade,but it does not rule out a role for demands. For example, of the four possibleequilibria in which at least one country specializes in production, the principle ofcomparative costs rules out only one: the inefficient case where both countriesspecialize according to comparative disadvantage . Depending on demand condi-tions, a free-trade equilibrium may occur at any of the other three points ofcomplete specialization, or at intermediate points where one or the other countryproduces both goods, a8 Moreover, demand takes on a special role if equilibriumoccurs at the point where countries specialize completely according to compara-tive advantage, since the equilibrium relative price ratio is then only bounded byrelative product ion costs. 19 Finally, although it is comparative rather than abso-

18This argument may be il lustrated using the world efficiency frontier , introduced by Whitin (1953).McKenzie (1954) showed that, irrespective of the number of countries and commodities, this frontieris defined by the set of l inear combinations of all efficient specialization patterns.a9Graham (1923) was highly critical of Mill (1848) for focusing on such limbo price ratios, andargued that with many commodities and countries such outcomes were highly unlikely. However, thework of McKenzie and others has shown that there is no general presumption as to whetherequilibrium will occur on a fla t or at a corner of the world efficiency frontier.


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2 R. W. Jones and J.P. Nearylute advantage which determines efficient patterns of trade and specialization,there is still a role for absolute advantage in determining relative wage rates (orthe "double-factoral" terms of trade). Since the price of any good cannot exceedits unit cost, whether the good is produced or not, it is easily shown that relativewage rates are bounded by the ratios of labor productivities for each commodityin the two countries, implying that:

aL_ l-* > _~w > a~.2 (2.2)aLl W aL2

with the wage ratio taking on its upper bound (where all the gains from tradeaccrue to the home country) when both countries produce good 1 and converselywhen both produce good 2.One of the attractive features of the Ricardian model is that its relatively simpleproduction structure allows virtually all the results we have stated to be extendedto many countries and many commodities. Some new features also emerge inhigher dimensions. For example, with many commodities but only two countries,commodities can be ranked by comparative costs in a "chain" of decreasingrelative labor costs:

a ~ 1 a ~ , 2 a ~ , j a ~ , ,- - > > . - - > > - . . > - - . 2 . 3 )a L l aL a L j aL nDemand conditions determine where the chain is broken, but the immutable costratios ensure that the home country must export all commodities to the left of thebreak and import all those to the right, with at most one commodity produced incommon. When more than two countries are considered explicitly, no such neatcriterion is available. Obviously, an efficient pattern of specialization must satisfybilateral comparisons such as (2.1) for all possible pairings of commodities andcountries. However, as McKenzie (1954) and Jones (1961b) have shown, thisrequirement is not sufficient to exclude inefficient production patterns. Regardlessof the number of countries or commodities, a general criterion for efficientspecialization is available which is the appropriate generalization of (2.1): theproduct of labor requirements in the efficient assignment of commodities tocountries must be less than the corresponding product in all other possibleassignments that allot the same number of countries to each commodity as doesthe efficient assignment.More recently, Dornbusch, Fischer and Samuelson (1977) have shown how atwo-country Ricardian model with an infinite number of commodities can beanalyzed using elementary geometry and calculus. The key to this simplicity is theassumption that the ratio of unit labor requirements in the two countries varies


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Ch. 1: Positive Theory of International Trade 13c o n t i n u o u s l y b e t w e e n c o m m o d i t i e s : i. e. i f c o m m o d i t i e s a r e i n d e x e d b y z , t h e r a t i oa * z ) / a z ) is a c o n t i n u o u s a n d m o n o t o n i c a l l y d e c re a s i n g f u n c t i o n o f z. T h i sf u n c t i o n i s th u s t h e c o n t i n u o u s a n a l o g u e o f t h e d i s c r e te c h a i n ( 2 .3 ) , a n d t h e p o i n ta t w h i c h it is b r o k e n b y d e m a n d d e t e r m i n e s n o t o n l y t h e p a t t e r n o f t r a d e b u t a ls o ,b y e x t e n s i o n o f t h e r e a s o n i n g w h i c h l e d t o ( 2 . 2 ) , t h e e q u i l i b r i u m d o u b l e - f a c t o r a lt e r m s o f t r a d e . A n a d d i t i o n a l s t r a t e g i c a s s u m p t i o n i s t h a t d e m a n d s t a k e t h eM i l l -G r a h a m f o r m ( i.e . p r e f e re n c e s c a n b e r e p r e s e n t e d b y a m o n o t o n i c t r a n sf o r -m a t i o n o f a C o b b - D o u g l a s u t il it y fu n c t i o n ) w i t h i d e n ti c a l ta s te s in t h e t w oc o u n t r i e s . T h i s m a k e s t h e f r a c t i o n o f w o r l d i n c o m e s p e n t o n h o m e - p r o d u c e dc o m m o d i t ie s a n i n c r e a s in g f u n c t i o n o f t h e i n d e x o f t h e b o r d e r l i n e c o m m o d i t y , Z ,a n d s o t h e d o u b l e - f a c t o r a l te r m s o f t r a d e c o n s i s t e n t w i t h b a l a n c e d t r a d e is a ls oi n c r e a s i n g i n ~ . ( T h e h i g h e r i s ~ , t h e g r e a t e r t h e s h a r e o f w o r l d i n c o m e s p e n t o nt h e h o m e c o u n t r y s g o o d s a n d s o th e h i g h e r, r e la t iv e l y , m u s t b e t h e h o m e w a g e . )C o m b i n i n g t h e se t w o f u n c t i o n s t h e r e f o r e p r o v i d e s a s i m p l e il l u s t r a ti o n o f h o w t h eu n i q u e e q u i l ib r i u m v a l u e o f t h e b o r d e r l in e c o m m o d i t y i s d e t e r m i n e d , a n d an u m b e r o f u s e f u l c o m p a r a t i v e s ta t ic s r e su l t s a re e a s il y d e r i v e d b y c o n s i d e r i n g h o wv a r i o u s c h a n g e s s h i f t e i t h e r o f t h e c u r v e s . 2

T h e t r a ct a b i li ty o f t h e c o n t i n u u m m o d e l h a s l e d t o it s e x te n s i o n in a n u m b e r o fd i r e c ti o n s . S a m u e l s o n ( 1 9 8 2 ) s h o w s t h a t t h e m o d e l e a s il y a c c o m m o d a t e s g e n e r a lh o m o t h e t i c t a s t e s w h i c h a r e t h e s a m e i n t h e t w o c o u n t r i e s : t h e v a l u e o f w / w *c o n s i st e n t w i th b a l a n c e d t r a d e n e e d n o l o n g e r b e a n i n c r e a si n g f u n c t i o n o f z b u ti t c a n n e v e r d e c r e a s e a t a f a s t e r r a t e t h a n a * z ) / a z ) . H e n c e e q u i l i b r i u m i s s t il lu n i q u e a n d m o s t o f t h e e a r l ie r c o m p a r a t i v e - s t a t i c s r e s u lt s c o n t i n u e t o h o l d . Am o r e e x t e n s i v e g e n e r a l i z a t i o n h a s b e e n c a r r i e d o u t b y W i l s o n ( 1 9 8 0) w h o a l lo w sf o r n o n - h o m o t h e t i c a n d n o n - u n i f o r m d e m a n d s a n d a n a r b i t r a ri l y l ar g e ( t h o u g hf i n i t e ) n u m b e r o f c o u n t r i e s . S i m p l e d i a g r a m m a t i c a n a l y s i s i s n o l o n g e r p o s s i b l e :e q u i li b ri a n e e d n o t b e u n i q u e n o r i s i t tr u e t h a t e a c h c o u n t r y p r o d u c e s o n l y t h o sec o m m o d i t i e s w h i c h l i e a l o n g a s i n g l e i n t e r v a l . H o w e v e r , W i l s o n s i m p l i f i e s t h em o d e l c o n s i d e r a b l y b y e x p r e s si n g t h e d e m a n d f o r e a c h c o u n t r y s p r o d u c t s i nt e r m s o f t h e d e r i v e d d e m a n d f o r it s l a b o r a n d t h u s e f f e c ti v e l y r e d u c e s t h e m o d e lt o a m a n y - c o u n t r y e x c h a n g e m o d e l w h e r e e a c h c o u n t r y su p p l ie s o n l y o n e g o o d( i . e . i t s o w n l a b o r ) . T o d e d u c e t h e c o n s e q u e n c e s o f a n y p a r a m e t e r c h a n g e i t i st h u s s u f f ic i e n t t o c o n s i d e r i n t h e f i rs t i n s t a n c e i t s e f f e c ts o n t h e e q u i l i b r i u m w a g er a t e in e a c h c o u n t r y , f r o m w h i c h t h e i m p l ic a t io n s f o r p r o d u c t i o n a n d t r a d ep a t t e r n s c a n b e i n f e r r e d .

2Trade theory is sometimes criticized for neglecting transport costs (although it is unlikely thatvery much of substance hinges on this, and, in any case, the y are just as imp ortant in dom estic as ininternational trade). The continuum m odel lends itself well to their inclusion, for it perm its smallchanges in de man ds or costs to alter endogenously he rang e of goods that are exported, not tradedinternationally, or imported. Sim ilar results ha ve be en ob taine d in. a simulation analysis ofI-Ieckscher-Ohlin-typemo dels by Helpm an (1976).


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14 R. W. Jones and J.P. NearyW hi l e t he c on t i nu um a pp r oa c h c l e a r ly pe r m i t s a t r a c t a b l e a na l y s i s o f s om e

is sues , the r e r em ain a nu m be r of ques t ion s wh ich i t i s no t we l l - su i ted to answer .On e of these conc erns the e f f ec t s o f t ech nolog ica l p ro gress in a s ing le sec tor. 21T h i s i s s ue wa s f i r s t e xa m i ne d i n a R i c a r d i a n m ode l by H i c ks ( 1953 ) , whoi n t r o d u c e d t h e i m p o r t a n t d i s ti n c ti o n b e t w e e n e x p o r t - b i a s e d a n d i m p o r t -b i a s e d i m p r ove m e n t s i n t e c hno l ogy . T he f o r m e r l owe r s c os t s i n e xpo r t i n -dus t r i e s , s o wor s e n i ng t he g r owi ng c oun t r y ' s t e r m s o f t r a de a nd be ne f i t t i ng t heres t o f the wor ld , whe reas the l a t t e r h as exac t ly o pp os i t e e f f ect s . 22 Jones (1979a)cons ide r s th i s ques t ion fur the r , no t ing tha t the Rica rd ian mode l wi th a f in i t en u m b e r o f c o m m o d i t i e s i s a c o n v e n i e n t f r a m e w o r k w i t h i n w h i c h t o i s o l a t ec ond i t i ons wh i c h g i ve r i s e t o e i t he r o f t he t wo pos s i b l e e x t r e m e ou t c om e s :i m m i s e r i z a t i on f o r t he g r owi ng o r t he l a gg i ng c oun t r y . T h i s i s s o be c a us e i n t h i sm od e l g r ow t h i n one s e c t o r c ha nge s a t m os t t wo r e l a ti ve p r i ce s : t ha t o f t heg r owi ng s e c t o r ' s ou t pu t r e l a t i ve t o o t he r hom e - p r oduc e d c om m od i t i e s , a nd t hedoub l e - f a c t o r a l t e r m s o f t r a de wh i c h de t e r m i ne t he r e l a t i ve p r i c e l e ve l s o fc om m od i t i e s p r oduc e d i n t he t wo c oun t r i e s .

2.3. The Hec ksc her -Oh lin modelW hi l e t he R i c a r d i a n m od e l i s o la t e s d i f fe r e nce s i n t e c hn o l ogy be t we e n c oun t r i e s a st he ba s i s f o r t r a de , t he He c ks c he r - Oh l i n m ode l f oc us e s i n s t e a d on d i f f e r e nc e sbe t we e n c oun t r i e s i n t he i r r e l a t i ve f a c t o r e ndowm e n t s a nd on d i f f e r e nc e s be t we e nc om m od i t i e s i n t he i n t e ns i t i e s w i t h wh i c h t he y u s e t he s e f a c t o r s . C os t s o fp r od uc t i o n t hus be c om e e ndoge no us a nd , i n ge ne ra l , w il l d i ff e r be t w e e n c ou n t r i e si n a u t a r ky , e ve n whe n a l l ha ve a c c e s s t o t he s a m e t e c hno l ogy f o r p r oduc i ng e a c hgood . T h i s m od e l t he r e f o r e p r ov i de s a n a l t e r na t i ve e xp l a n a t i on o f tr a d i ng pa t -t e r n s a nd a n e xp l ic i t ba s i s f o r c on fl i ct i n i n t e r na l i nc o m e d i s t ri bu t i on .

L a r ge l y due t o the wor k o f S a m ue l s on , t h is m ode l do m i n a t e d i n t e r na t i ona lt r a de t he o r y f o r m uc h o f t he pos t - wa r pe r i od , a nd i t s f ou r m a i n p r ope r t i e s o r

c o r e p r o p o s i t i o n s c a m e to b e v i ew e d a s t h e c e n t r al b o d y o f i n t e r n a t io n a l t r a d et he o r y . [ S ee C ha ng , E t h i e r a nd K e m p ( 1980) .] W e be g i n by s t a t i ng t hes ep r opos i t i ons f o r t he s t a nda r d ( m i n i m a l - s i z e d ) c a s e o f t wo c om m od i t i e s u s i ng t woin te rna l ly mo bi le p rod uc t iv e f ac tor s . 23

21Dombush, Fischer and Samuelson , Wilson , and Krugm an (1982), consider the effects in thecontinuum model of technological progress which takes the form of either a uniform improvement inall sectors in a given country or a convergence between the a z) schedules of two countries (whichmay be viewed as reflecting the international diffusion of technological knowledge).22Although Hicks expficitly used a Ricardian model, he did not specify the structure of trade andproduction in great detail, and most later formalizations of his approach adopted a Heckscher-Ohlinframework. (See footnote 35 below.)23The original sources for these propositions are : Lerner (1952) and Samuelson (1948, 1949) for thefactor-price equalization theorem; Stolper and Samuelson (1941) for the Stolper-Sam uelson theorem;


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Ch. 1: Positive Theory of International Trade 15(1) Fac tor -pr i ce equa l i za t i on t heorem. In its global form, this theorem states

that, under certain conditions, free trade in final goods alone brings aboutcomplete international equalization of factor prices. In its local form, the theoremasserts that, at cons tant comm odi ty prices, a small change in a cou ntry 's factorendowments does not affect factor prices.

(2) S t o l p e r - S a m u e l s o n t h e o r e m . An increase in the relative price of one com-modity raises the real return of the factor used intensively in producing thatcommodity and lowers the real return of the other factor.

(3) R y b c z y n s k i t h e o r e m . If commod ity prices are held fixed, an increase in theendowmen t of one factor causes a more than proportio nate increase in the outputof the commodity which uses that factor relatively intensively and an absolutedecline in the output of the other commodity.

(4) H e c k s c h e r - O h l i n t h e o r e m . A country has a production bias towards, andhence tends to export, the co mmodit y which uses intensively the facto r withwhich it is relatively well endowed.

To illustrate these propositions, we turn first to the model's implications for thedistribution of income, which are easily seen with the help of the unit cost curves,c 1 and c2, in Figure 2.1. 24 Eac h curve shows the combin ati ons of the wage rate wand the rental rate r which imply a unit cost of production equal to the outputprice of the sector in question. The coordi nates of point A are thus the only valuesof w and r compatible with zero profits in both sectors. Provided such anequilibrium is consistent with the econo my' s factor endowment, factor prices arethus determined solely by the location of the curves c I and c2, in othe r words, bytechnology and c ommo dity prices. To un derstand the caveat about consistencywith factor endowments we may note that the slope of the unit cost curve alwaysequals the cost-minimizing capital-labor ratio in the sector in question. More-over, for both factors to be fully employed, the eco nomy' s overall capital -lab orratio k must be a weighted average of the capital-labor ratios used in each sector:

k = ~ L l k l hL2k2, (2.4)where the weights, Xt.j, denot e the propor tion of the total labor force employed inRybczynski (1955) for the Rybczynski theorem; and Heckscher (1919) and Ohlin (1933) for theHeckscher-Ohlin theorem. The term core propositions was introduced by Ethier (1974) who alsopresents a vigorous defense of their robustness.24These curves were introduced by Samuelson (1962) and have been applied to trade problems by anumber of authors, including Schweinberger (1975), Burgess (1976), Woodland (1977a) and Mussa(1979), their increased use [along with that of the national product function] reflecting the recent driftfrom primal towards dual techniques. For an economywith more than one sector, we prefer the termunit cost curve to factor price frontier , since the latter usually refers to the locus of efficientfactor prices for the economyas a whole. In Figure 2.1 the factor price frontier is the outer envelope ofthe individual sectors' unit cost curves (illustrated by a heavy line). Another popular diagram used toillustrate properties of the Heckscher-Ohlin model is known as the Harrod-Jolmson diagram. SeeHarrod (1958), Johnson (1957), and earlier use by Samuelson (1949).


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16 R W Jones and J P Neary

O

Figure 2.1 . Un it cost curves.

s e c t o r j . H e n c e , j o i n i n g t h e o r ig i n O t o t h e p o i n t s B a n d D a t w h i c h e a c h s e c t o r' sc a p i t a l - l a b o r r a t io e q u a l s t h e e n d o w m e n t r a t io g i ve s r is e to t h e c o n e R O S , w h i c hw e m a y c a l l a c o n e o f d iv e r s if ic a t io n . 'z 5 P r o v i d e d t h e i n t e r s e c t i o n p o i n t A l ie sw i t h i n t h is c o n e t h e e c o n o m y p r o d u c e s b o t h g o o d s a n d f a c t o r p r ic e s a r e lo c a ll yi n d e p e n d e n t o f e n d o w m e n t s .W h i l e t h e f a c t o r - p r i c e e q u a l i z a t i o n t h e o r e m a s s e rt s t h a t f a c t o r p r ic e s a r ei n d e p e n d e n t o f e n d o w m e n t s , t h e S t o l p e r - S a m u e l s o n t h e o r e m i s c o n c e r n e d w i t ht h e n a t u r e o f t h e i r d e p e n d e n c e o n c o m m o d i t y p r i c e s. S p e c i fi c al ly , i t p r e d i c t s w h a tJ o n e s ( 1 9 6 5 ) h a s c a l le d a m a g n i f i c a t i o n e ff e c t : a g iv e n p r o p o r t i o n a l c h a n g e inc o m m o d i t y p r ic e s g i ve s r is e t o a g r e a t e r p r o p o r t i o n a l c h a n g e i n f a c t o r p r ic e s , s u c ht h a t o n e f a c t o r p r i c e u n a m b i g u o u s l y r i s e s a n d t h e o t h e r f a l l s r e l a t i v e t o othc o m m o d i t y p ri c es . T h i s m a y b e s e e n in F i g u r e 2 . 1 : t h e i n c r e a s e i n t h e p r i c e o fg o o d 1 s h i ft s c 1 t o c~ a n d t h u s l o w e r s t h e w a g e r a t e a n d r a is e s t h e r e n t a l b y ag r e a te r p r o p o r t i o n a t e a m o u n t t h a n t h e p r ic e i n c re a s e ( si n ce t h e n e w e q u i li b r iu mp o i n t G l ie s t o t h e f i g h t o f H w h i c h is o n t h e s a m e r a y f r o m t h e o r i g i n a s A a n d s or e p r e s e n t s a s i t u a t io n w h e r e t h e r e l a t iv e r e n t a l in c r e a s e j u s t m a t c h e s t h e i n c r e a s ei n t h e p r i c e o f g o o d 1 ) . M o r e f o r m a l l y , t h e c h a n g e s i n t h e u n i t c o s t a n d h e n c e i nt h e p r ic e o f e a c h c o m m o d i t y m u s t b e a w e i g h t e d a v e r a g e o f t h e c h a n g e s in t h et w o f a c t o r p r i c es ( w h e r e t h e w e i g h t s a r e t h e d i s t r i b u t i v e s h a re s o f t h e t w o f a c t o r si n t h e s e c t o r c o n c e r n e d a n d a c i r cu m f l e x d e n o t e s a p r o p o r t i o n a l c h a n g e : f f - -

25This concep t was discussed by M cKen zie (1955) in the context o f the prima l representation oftechnology wh ose geom etric depiction in the two-sector cas e was develope d by Lerner (1952) andPearce (1952). See also C hipman (1965-66).


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Ch 1: Posi t ive Theory o f ln tern at iona l Tradedw/w : 26

17

0Llw + 0/1r =/~ a, (2.5 )0/ .2ff + 0x zr =/~ 2. (2.6 )

S i nc e e a c h c o m m o d i t y p r i c e c ha n g e i s b o u n d e d b y t h e c h a n g e s in b o t h f a c to rp r ice s , th e S t o l p e r - S am u e l s o n t h e o r em f o l lo w s i mm ed i a t e ly , w i t h i ts p r ed i c t io n o fu n amb i g u o u s l y co n f l i c t i n g ch an g es i n r ea l f ac t o r r ew ar d s f o l l o w i n g a ch an g e i nco m m od i ty p r i ces. 27

C o r r e s p o n d i n g t o t h e mag n i f i ca t io n e f f ec t o f th e S t o l p e r - S am u e l s o n t h eo r em i sa s i mi l a r r e l a t i o n s h i p b e t w een en d o w men t ch an g es an d o u t p u t ch an g es i mp l i edb y t h e R y b czy n s k i t h eo r em, t h e d u a l i t y b e t w een t h e t w o t h eo r ems r e fl ect in g t h er ec i p r o c i t y r e l a t i o n s d i s cu s s ed ea r l i e r . A n i n c r ea s e i n t h e cap i t a l - l ab o r en d o w -m en t r a t i o le av es t h e w a g e - r e n t a l r a ti o , an d h en ce f ac t o r p r o p o r t i o n s i n eachs ec to r , u n a f f ec ted , p r o v i d ed r e l a ti v e co m m o d i t y p ri ce s d o n o t ch an g e an d b o t hg o o d s co n t i n u e t o b e p r o d u ce d . Eq u a t i o n ( 2.4 ) t h e r e f o r e i mp l i e s th a t t h e f r ac t io no f t h e l ab o r f o r ce emp l o y ed i n t h e l e s s cap i t a l - i n t en s i v e s ec t o r mu s t f a l l an d t h ef r ac t i o n i n t h e o t h e r s ec t o r mu s t r i s e b y a g r ea t e r r e l a t i v e amo u n t t h an t h een d o w men t ch an g e . Wi t h a co n s t an t c ap i t a l - l ab o r r a t i o i n each s ec t o r , t h i s i nt u r n i m p l ie s a s i m i l a r p a t t e r n o f o u t p u t ch an g es , w h i ch i s t h e e s s en ce o f t h eR y b czy n s k i t h eo r em. To s ee t h i s mo r e f o r ma l l y , w e t o t a l l y d i f f e r en t i a t e t h e t w of u l l - emp l o y men t co n d i t i o n s f o r t h i s mo d e l t o o b t a i n :

)kLl.~ 1 -t - )kL2.,~2 = L , (2 .7 ))kK l.~ 1 + )kK2.,~2 = g . 2 . 8 )

In a manner ana logous to (2 .5 ) and (2 .6 ) , t hese equat ions s t a t e t ha t endowmentch an g es a r e b o u n d ed b y o u t p u t ch an g es an d s o t h e h i g h ly a s y mm et r i c r e s p o n s e t oe n d o w m e n t c h a n g e s p re d i c te d b y t h e R y b c z y n s k i th e o r e m m u s t a p p l y .Th e f i n a l co r e p r o p o s i t i o n i s t h e H eck s ch e r - O h l i n t h eo r em i t s e l f , b u t t h i s i nf ac t is c l o s e ly r e l a t ed t o t h e R y b czy n s k i th eo r em. C o n s i d e r t w o co u n t r i e s w i t hd i f f e r en t r e l a t i v e f ac t o r en d o w men t s an d t h e s ame t ech n o l o g y f o r p r o d u c i n g b o t h

26These equa t ions fo l low from to ta l ly d i f fe rent ia t ing the com pet i t ive prof i t cond i t ions and in vokingthe enve lope prop er ty o f the uni t cos t func t ion . O ur a lgebra ic deve lopm ent of th is mo de l fo l lows theapproach of Jones (1965) .27A s t ronger form of the S to lp e r-Sa mu elson theorem (as i t was presented by i t s or ig ina tors ) is tha tprotec t ion m ust ra i se the rea l re turn to the fac tor used in tens ive ly in the impo rt -com pet ing sector . T hisrequi res the addi t iona l a ssumpt ion tha t pro tec t ion ra i ses the domest ic re la t ive pr ice of the import -c ompe t i ng good ; i n o t he r words , t ha t t he c ond i t ions fo r t he M e t z l er pa ra dox ou t l i ne d in S e c ti on 2 .1 d onot hold .


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18 R . IV . J o n e s a n d J . P . N e a r yg o o d s. I f b o t h c o u n t ri e s fa c e th e s a m e c o m m o d i t y p r ic e s t h en , b y t h e R y b c z y n s k it h e o r e m , t h e c o u n t r y w i t h t h e g r e a t e r re l a ti v e e n d o w m e n t o f c a p i ta l w i ll p r o d u c er e l a ti v e l y m o r e o f t h e c a p it a l -i n t e n s i v e g o o d . T h i s m a y b e s e e n b y s u b t r a c t i n g( 2 . 8 ) f r om ( 2 . 7 ) t o ob t a i n : 28

1 ~ K ,,X 1 - - .~ 2 = - ~ - ( L - ( 2 . 9 )

w h e r e 1 2 1 e q u a l s ( h L 1 - ~ kK 1 ) . P r o v i d e d t h i s p r o d u c t i o n b i a s i s n o t o f f se t b y ad e m a n d b i a s, t h e r e l a ti v e l y c a p i t a l - a b u n d a n t c o u n t r y w i ll e x p o r t t h e r e l a ti v e l yc a p i t a l - in t e n s i v e g o o d . W h e n i t i s e x p r e s s e d i n t e r m s o f a p h y s i c a l d e f i n i ti o n o ff a c t o r a b u n d a n c e , t h e H e c k s c h e r - O h l i n t h e o r e m is t h u s a s i m p l e c o r o l l ar y o f t h eR y b c z y n s k i t h e o r e m , a n d n o c o n s i d e r a t i o n o f a u t a r k y p r o d u c t i o n p a t t e r n s i sr e q u i r e d . A l t e r n a t i v e l y , t h e c o n c e p t o f f a c t o r a b u n d a n c e m a y b e f o r m u l a t e d i nt e r m s o f r e l a t i v e f a c t o r p r i c e s b e f o r e t r a d e t a k e s p l a c e . W h e n e x p r e s s e d i nt h is w a y , t h e H e c k s c h e r - O h l i n t h e o r e m r e q u i r e s i n a d d i t i o n t h a t t h e r e la t i o n -s h ip b e t w e e n r e l a ti v e c o m m o d i t y a n d f a c t o r p r ic e s p r e d i c t e d b y t h e S t o l p e r -S a m u e l s o n t h e o r e m h o l d . F r o m e q u a t i o n s ( 2 .5 ) a n d ( 2 .6 ) :

1, - e = j - p x - p 2 ) , ( 2 . 1 0 )w h e r e 1 0 1 e q u a l t o O L 1 - - 0 L 2 ) , h a s t h e s a m e s i g n a s I X l i n ( 2 . 9 ). 29 I n t he ab sen ceo f t r a d e , t h e r e l a t iv e s c a r c it y o f t h e l a b o r - i n t e n s i v e g o o d i n t h e c a p i t a l - a b u n d a n tc o u n t r y i s re f l e c te d i n i ts r e l a ti v e p r i c e b e i n g h i g h e r t h a n a b r o a d w h i c h , f r o m( 2. 10 ) , im p l i e s t h a t c a p i t a l w il l b e r e l a ti v e l y c h e a p i n t h e c a p i t a l - a b u n d a n tc o u n t r y . T h u s r e l a t i v e f a c t o r a b u n d a n c e i n e i t h e r t h e p h y s i c a l o r t h e v a l u e s e n s e i st h e s o u r c e o f c o m p a r a t i v e a d v a n t a g e i n t h i s m o d e l .

T h i s p r e d i c t i o n a b o u t t r a d e p a t t e r n s i s o n e o f t h e c e n t r a l f e a t u r e s o f t h eH e c k s c h e r - O h l i n m o d e l a n d i t h a s i n s p i r e d e x t e n s iv e e m p i r i c a l te s ti n g , b e g i n n i n gw i t h t h e f a m o u s s t u d y o f U . S . t r a d e p a t t e r n s b y L e o n t i e f ( 19 5 3). W e l e a v e f u r t h e rc o n s i d e r a t i o n o f t h e s e a n d o t h e r e m p i r i c a l m a t t e r s t o C h a p t e r 1 0 b e l o w a n dc o n c e n t r a t e h e r e o n s o m e t h e o r e t i r a l is su e s w h i c h h a v e a r i s en i n t h e p r o c e s s o fe x t e n d i n g t h e H e c k s c h e r - O h l i n m o d e l . O n e o f t h e se is t h e q u e s t i o n o f w h e t h e r,w h e n t h e n u m b e r o f c o m m o d i t i e s is in c r e a se d b u t t h e n u m b e r o f f ac t o r s a n dc o u n t r i e s r e m a i n s e q u a l t o t w o , i t is p o s s i b l e t o c o n s t r u c t a c h a i n o f c o m p a r a -

8The term IAI is the determinan t of the matrix of factor-to-sectorallocations,A / j , a n d is positive fand only if sector I is relatively abor-intensive in the sense of having a low er capital-labor ratio thansecto r 2, i.e. k 1 < k 2 ) .29[01 is the determinan t of the ma trix of factor sha res and is positive if and only if sector 1 isrelatively labor-intensive (in the sense that w ages constitute a larger proportion o f the v alue of itsoutput than in sector 2).


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Ch 1: Posi t ive Theory o f In ternat ion al Trade 19t i ve advan tage , s imi l a r t o t ha t wh ich ho lds i n t he R icard i an model [ eq . (2 .3 )above] bu t i n t e rms o f f a c to r i n t ens i t ies r a the r t han re l a t ive l ab or p rod uct iv i t ies . 3J o n es ( 1 9 5 6 ) a r g u ed t h a t r an k i n g co mmo d i t i e s b y t h e i r c ap i t a l - l ab o r r a t i o s( a s s u mi n g t h a t f ac t o r - in t en s i t y r ev e rs a l s d o n o t t ak e p l ace ) d o es i n d eed y i e ld s u cha cha in , wi th a l l commodi t i es hav ing cap i t a l - i n t ens i t i es h igher t han a cer t a in l eve lb e i n g ex p o r t ed b y t h e mo r e cap i t a l - ab u n d an t co u n t r y an d a l l o t h e r s b e i n gi mp o r t ed ; t h e l o ca t i o n o f t h e cu t - o f f p o i n t i n t h e ch a i n i s d e t e r mi n ed ( a s i n t h eR i ca r d i an mo d e l ) b y d eman d an d b y t h e r e l a t i v e s i ze s o f t h e t w o co u n t r i e s . Th ev a l i d it y o f t h is p r o p o s i t i o n h as b een d em o n s t r a t ed ex p l ic i tl y b y D ea r d o r f f (1 97 9) :p r o v i d ed f ac t o r p r i ce s i n t h e t w o co u n t r i e s co n t i n u e t o d i f f e r a f t e r t r ad e t ak esp l ace , t h e cap i t a l - ab u n d an t co u n t r y mu s t h av e t h e h i g h e r w ag e - r en t a l r a t i o an dh en ce mu s t s p ec i a l i z e i n an d ex p o r t t h e mo r e cap i t a l - i n t en s i v e g o o d s ( w i t h a tm o s t o n e c o m m o d i t y b e i n g p r o d u c e d i n c o m m o n b y b o t h c o u n tr ie s ). H o w e v e r ,t he p rov i so tha t t r ade does no t equa l i ze f ac to r p r i ces i s c ruc i a l here , as Melv in(1968) and Bha gw at i (1972) have p o in t ed ou t . 31 I f f ac to r p r i ces a re equa l i zed b yt r a d e t h e n t h e p a t t e r n o f p r o d u c t i o n i n e a c h c o u n t r y a n d h e n c e t h e p a t te r n o ft r ad e i s i n d e t e r mi n a t e an d s o th e ch a i n p r o p o s i t i o n n eed n o t h o l d in g en e r al . 32

A s w e w o u l d ex p ec t , w h en w e co n s i d e r a s ma l l co u n t r y f o r w h i ch r e l a t i v ec o m m o d i t y p ri ce s a r e f ix e d, t h e c a s e w h e r e m a n y c o m m o d i ti e s a r e p r o d u c e d w i t ho n l y t w o f ac t o r s i s s t r a i g h t f o r w ar d . A s s h o w n b y J o n es ( 1 9 7 4 c ) , s u ch a co u n t r yw i ll l o ca t e a l o n g t h e ch a i n a t a p o i n t d e t e r mi n ed b y i ts f ac t o r en d o w me n t ,p r o d u c i n g o n l y th o s e g o o d s ( o n e o r t w o ) w h o s e f ac t o r i n ten s i ti e s a re c l o s e t o i tso w n en d o w m en t r a ti o . Ev en i f t e ch n o l o g y i s t h e s ame a t h o m e a s i n an o t h e rs imi l a r smal l coun t ry , f ac to r p r i ces a re un l ike ly t o be equal i zed in t e rna t iona l ly i ns u ch a w o r l d s i n ce t h e m i x o f co m m o d i t i e s p r o d u ce d i s l ik e l y to d i f f e r b e t w een t h et w o co u n t r i e s u n l e s s t h ey h av e v e r y s i mi l a r en d o w m en t s . N ev e r t h e l e s s , t r ad ep a t t e r n s i n t h i s w o r l d r e f l ec t t h e H eck s ch e r - O h l i n t h eo r em i n t h e mo d i f i ed s en s et h a t t h e f ac t o r i n t en s i t i e s o f t h e s ma l l co u n t r y ' s ex p o r t s m i r r o r i t s en d o w men tr a t io , w h i le i t i mp o r t s g o o d s w h i ch a r e b o t h m o r e a n d l e ss cap it a l- i n ten s i v e t h ant h o s e i t p r o d u ces .

3 W e c o n f i n e a tt e n t i o n h e r e t o t h e c a s e w h e r e t h e n u m b e r o f c o m m o d i t i e s is f i n it e a n d s o t h ec h a in i s a d i s c r e te one . H ow e ve r , a s w i th t he R ic a r d i a n m ode l , i t i s pos s ib l e t o a s sum e in s t e a d tha tt h e n u m b e r o f c o m m o d i t i e s i s in f i ni t e, w i t h t h e c a p i t a l - l a b o r r a t i o o f e a c h c o m m o d i t y v a r y i n g a l o n g ac o n t i n u u m . S u c h a m o d e l h a s b e e n a n a l y ze d i n d e t a i l b y D o m b u s c h , F i s c h e r a n d S a m u e l s o n (1 98 0),a l t hough the pa y - o f f t o t h i s e x t e ns ion i s no t a s g r e a t a s i n t he R ic a r d i a n c a se , s i nc e t he d i s c r e t eH e c ksc he r - O h l in m ode l a l r e a dy a l l ow s c ons ide r a b l e s c ope f o r subs t i t u t i on be tw e e n f a c to r s .31T r a v i s ( 1964 , c h . 2 ) a nd D ix i t a nd N or m a n ( 1980 , pp . 114 - 121 ) g ive a u se f u l d i a g r a nm a a t i ct e c h n i q u e f o r d e t e r m i n i n g w h i c h a l l o c a t io n s o f a g i v e n w o r l d f a c t o r e n d o w m e n t a r e c o n s i s t e n t w i t hf a c to r - p ri c e e qua l i z a t i on w he n th e r e a r e tw o f a c to r s a nd th r e e goods .32 I n t h i s c a se , bo th c oun t r i e s p r oduc e a long the s a m e r u l e d su r f a c e o f t he i r p r oduc t ion pos s ib i l i t yf r on t i e r s ( e xc e p t f o r d i ff e r e nc e s i n s c a l e ) a nd b o th p r odu c e s t r i c t l y pos i t i ve a m o un t s o f a l l goods ( a pa r tf r om b ou nd a r y c ases ). ( R e c a l l ou r e a r l i e r d i s c us s ion o f r u l e d su r f a c e s a nd the r e f e r e nc e s g ive n the r e .)A n o p e n q u e s t i o n f o r r es e a r c h is w h e t h e r t h e i m p l i e d t r a d e p a t t e r n s c o n f o r m w i t h t h e p r e d i c t i o n s o f

t h e H e c k s c h e r - O h l i n t h e o r e m i f t h e p r o d u c t i o n i n d e t e r m i n a n c y i s r e so l v e d b y s p e c i f yi n g a n e x p l i ci td y n a m i c a d j u s t m e n t m e c h a n i s m f o r t h e t r a n s i t i o n f ro m a u t a r k y t o f r e e t ra d e .


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20 R W Jones and J P NearyT h e l o w d i m e n s i o n a l i ty o f t he s i m p l e H e c k s c h e r - O h l i n m o d e l h a s a t t r a c te d

m u c h a t t e n t i o n a n d w i l l b e c o n s i d e r e d f u r t h e r i n S e c t i o n 2.5 a n d i n C h a p t e r s 3a n d 1 0 . B y c o n t r a s t , a l i m i t a t i o n o f t h e m o d e l w h i c h i s a t l e a s t e q u a l l y s i g n i f i c a n tb u t h a s r e c e i v e d r a t h e r l e s s a t t e n t i o n i s i t s v i e w o f f a c t o r e n d o w m e n t s a s a ne x o g e n o u s d e t e r m i n a n t o f t r a d e p a tt e rn s . I n f a c t, e n d o w m e n t s m a y n o t b e

p r i m i t i v e i n th i s s en s e, b u t c a n b e in f l u en c e d b y t r a d e, b o t h i n s t a n t a n e o u s l y ( a sw h e n t r a d e a f fe c ts th e c h o i c e b e t w e e n w o r k a n d l e is u r e) a n d o v e r t i m e ( t h r o u g hc h a n g e s i n t h e r a te o f c a p i ta l a c c u m u l a t i o n ) . M o s t a t t e m p t s t o e x a m i n e t h e l a tt e ri s su e h a v e c o n s i d e r e d o p e n - e c o n o m y e x t e n s i o n s o f t h e t w o - s e c t o r g r o w t h m o d e lo f U z a w a ( 1 9 6 1 ) in w h i c h t h e c a p i t a l g o o d i s i n t e rn a t i o n a l l y t r a d e d . B y c o n t r a st ,F i n d l a y ( 1 9 7 0 ) p r e s e n t s a m o d e l w h i c h i s c l o s e r i n s p i r i t t o t h e H e c k s c h e r - O h i i na p p r o a c h i n t h a t b o t h t r a d e d g o o d s a r e u s e d f o r f in a l c o n s u m p t i o n w h i l ea d d i t i o n s t o t h e c a p i t a l s t o c k a r e p r o d u c e d b y a t h ir d , n o n - t r a d e d g o o d s , s e c t o r . 33T h e r e s u lt s h e o b t a i n s a r e r e c o g n i z a b l y H e c k s c h e r - O h l i n i n sp i ri t b u t r e l a t e n o tt o t h e e f fe c ts o f c h a n g e s i n e n d o w m e n t s b u t o f c h a n g e s i n t h e g e n u i n e l ye x o g e n o u s p a r a m e t e r s o f h is m o d e l , th e r a te s o f p o p u l a t i o n g r o w t h a n d o fs a v in g s . A r is e i n t h e f o r m e r l o w e r s th e e c o n o m y ' s s te a d y - s t a t e c a p i t a l - l a b o r r a t iow h i c h ( i n a m a n n e r s i m i l a r t o t h a t o f t h e R y b c z y n s k i e ff e ct ) l o w e r s t h e r e l a ti v eq u a n t i t y o f t h e c a p i t a l - i n t e n s i v e g o o d p r o d u c e d . B y c o n t r a s t , a ri s e i n t h e s a v i n g sr a t e m a y r a i s e o r l o w e r t h e r e l a t i v e o u t p u t o f t h e c a p i t a l - i n t e n s i v e g o o d i n t h es h o r t r u n , b u t m u s t r a i s e i t i n t h e l o n g r u n . A t l e a s t i n t h i s m o d e l , t h e r e f o r e , t h es p ir it o f th e H e c k s c h e r - O h l i n t h e o r e m i s p r e s e rv e d p r o v i d e d f a c t o r a b u n d a n c e isi n t e r p r e t e d n o t i n t e r m s o f e x o g e n o u s p h y s i c a l e n d o w m e n t s b u t o f t h e r a t e o fl a b o r f o r c e g r o w t h a n d t h e p r o p e n s i t y t o a c c u m u l a t e c a p i t a l. 34

I n c o n c l u s io n , t h e r el a ti v e ly r ic h p r o d u c t i o n s t r u c t u r e o f th e H e c k s c h e r - O h l i nm o d e l h a s m a d e i t a s o u r c e o f f r u i t f u l h y p o t h e s e s f o r e m p i r i c a l t e s t i n g ( w h o s eu s e f u ln e s s is n o t d i m i n i s h e d b y t h e f a c t th a t i n it s s im p l e s t f o r m - t w o g o o d s , t w of a c to r s a n d i d e nt ic a l t e c h n o lo g y w o r l d w i d e - t h e m o d e l ' s p r e d i c t i o n s a r e o v er -w h e l m i n g l y r e j e c t e d b y t h e d a t a ) a s w e l l a s a u s e f u l v e h i c l e f o r t h e s t u d y o f a w i d er a n g e o f t h e o r e t i c a l i ss u e s . 35 N e v e r t h e l e s s , t h e v e r y s t a r k n e s s o f i t s p r e d i c t i o n s ,a n d i n p a r t i c u l a r i ts r ig i d l in k i n g o f f a c t o r p r i c e s t o c o m m o d i t y p r ic e s , h a s l e d

33With only two factors perfectly mo bile betwee n all three sec tors, the fixity of traded good s pricespins dow n the price of the non-traded go od as well as domestic factor prices, exactly as in the staticmodels of K omiya (1967) and Ethier (1972b). A model with a n identical formal structure has beenused by Sam uelson (1965) to de mo nstrate that free trade equalizes not only the rental on c apital butalso the real interest rate betwee n countries, since the latter equ als (in equilibrium) the ren tal dividedby the price o f (non-traded ) mach ines. The prop erties of all these mo dels are extremely sensitive to theassumption that both traded goods continue to-be produced, and, as Ethier points o ut, this is m orestringent than requiring non-specialization n an otherw ise identical model with no non -traded goods.Dea rdorff (1974) show s that the produc tion sector of Find lay's mod el become s identical to that ofUzawa's closed-economygrowth model if only one traded goo d is produced.34For a related analysis, see Deardorff and Han son (1978).35To take just on e example of the latter, the analysis of the post-World W ar II dollar shortage byHicks (1953), me ntioned in Section 2.2, suggested that technological progress in a country's ex port


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Ch. 1: Positive Theory of International Trade 21m a n y e c o n o m i s t s t o q u e s t i o n i t s g e n e r a l i ty . P a r t l y fo r t h is r e a s o n , t r a d e t h e o r yh a s r e c e n t l y se e n a re v i v a l o f i n t e r e s t i n a n o l d e r m o d e l , w h i c h a b a n d o n s t h ea s s u m p t i o n o f c o m p l e t e i n t e r s e c to r a l m o b i l i t y o f a ll fa c t o rs a n d a s s u m e s i n s t e a dt h a t s o m e a r e s p e c i f i c t o p a r t i c u l a r s e c t o r s .

2 . 4 . T h e s p e c i f i c - f a c t o r s m o d e lT h i s m o d e l h a s i ts a n t e c e d e n t s i n t h e w o r k o f C a i r n e s a n d B a s t a b l e , a n d w a s u s

the positive theory of international trade

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