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Chapter 4G R O W T H A N D D E V E L O P M E N T IN T R A D E M O D E L SRONALD FINDLAY *Columbia University

Contents

1. Ric ard ian theory 1871.1. A dynamic Ricardian model 1871.2. Lewison the terms of trade 1911.3. Unequal exchange 192

2. Neoclassical theory 1942.1. Comparative statics of growth and trade 1942.2. "Immiserizing" growth and foreign investment 1982.3. Steady state growth in the open economy 203

3. Develo pment and asymmetrical interde pendenc e 2123.1. Wagedifferentials and infant industry protection 2123.2. Two-gapmodels and export-led growth 2153.3. The open dual economy 2183.4. North-South models 221

References 232

*I would like to thank J. Bhagwati, R. Brecher, A. Burgstaller, R. Feenstra, R.W. Jones, J. Ruggieand A. Smith for comments, suggestions, and encouragement.Hand book of Internatio nal Economics, vol. I, E dited by R. W. Jones and P.B. K enen Elsevier Science Publ ishers B. V. , 1984

185

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Dostoevsky apparently once remarked that all of Russian literature emerged fromunder Gogors Overcoat. It is at least as true that all of the pure theory ofinternational trade has emerged from chapter 7 of Ricardo's Principles. Theincredibly simple example of the exchange of cloth and wine between Englandand Portugal went right to the core of the concept of comparative advantage andthe subsequent development of the subject has remained within the bounds set byRicardo in a manner symbolized by the offer curves of Mill, Marshall andEdgeworth intersecting between the domestic cost ratios of England and Portugalas established by the master.The determination of the terms of trade by reciprocal demand, the introductionof many goods, countries and factors, the analysis of tariffs, occupied theattention of subsequent writers down to the treatises of Viner (1937) and Haberler(1937). One topic, however, that was almost entirely absent from the formalliterature was any consideration of the connection between economic growth anddevelopment and internat ional trade, despite the famous quota tion from Marshallthat "t he catises which determine the economic progress of nations belong to thestudy of international trade". It has only been in the last two or three decadesthat the "dynamization" of trade theory has gotten underway and that anysystematic formal analysis of capital accumulation and technological change hasbeen undertaken in the context of open economies. All this of course runs parallelto the development of economics as a whole, with the emergence of dynamic trademodels following closely in the wake of neoclassical growth theory as developedby Solow, Swan, Uzawa, Phelps and others.

It is a strange irony, however, that Ricardo himself had constructed an implicitdynamic model of growth and trade, linked by the distribution of income, in hisEssay on the Influence o f a Low Price of Corn Upo n the Profits of Sto ck ) Hisinterest in the repeal of the Corn Laws was motivated not so much by a static"gains from trade" argument but from a "gains for growth" considerationunderlying the effect of the repeal in raising the rate of profit and reducing therent of land, capitalists being thrifty and landlords profligate in his stylizedrepresentation. The Ricardo of pure trade theory is a pale shadow of the real one.The very neatness and elegant simplicity of the chapter 7 analysis seems to havediverted attention from the more complex, but also in my opinion very rich anddeep ideas contained in the Essay, and also, for that matter, in the rest of chapter7. The formalization of these ideas was undertaken only rather recently byPasinetti (1960) and Samuelson (1959). I shall describe an explicit Ricardianmodel of trade and growth later in this chapter drawing upon the work of thesemodern commentators on his closed system and on the extension to openeconomies in Findlay (1974).

XTheEssay,originallypubfished n 1815, is available n VolumeIV, pp. 1-42, of Ricardo (1951), theSraffa edition of the collectedworks and correspondence.186

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Ch. 4: Growth and Development in Trade Models 187"Growth" and "development" are sometimes used interchangeably but I am

sure that the editors intended a distinction that is usually drawn between theseterms. "Growth" has the connotation of simply more of everything while "devel-opment" is taken to refer to some qualitative transformation or structural shift. Inpractice the "development" aspect of trade theory arises from the attempt toaddress problems regarded as of major significance for the less developed coun-tries of the world economy. These have ranged from the "infant industry"problem of Hami lton and List to the "terms of trade" problem of Prebisch (1950)and Singer (1950). The insights and concerns of these critics of orthodox doctrinehave led to a number of attempts, sympathetic and otherwise, to handle theseissues analytically.

Ever since the creation of a unified world economy as a consequence ofEuropean voyages of discovery of the fifteenth and sixteenth centuries and theIndustrial Revolution of the eighteenth century there has been a split between anadvanced "center", which generates the momentum of accumulation and innovaotion for the system as a whole, and a backward "periphery" which responds moreor less passively to or at least within the parameters set by the center. The patternof interdependence, which orthodox theory tends to view as one between quanti-tatively different but qualitatively similar national economies, is viewed by"dependency" theorists and other radical schools as fundamentally asymmetric incharacter, with a center and periphery, or a "North" and a "South", linkedtogether as "unequal partners" by the ties of trade and foreign investment. Thelast few years have seen some theoretical work on models of asymmetric interde-pendence or "North-South" models as I shall call them in this chapter.This chapter will be divided into three sections. The first, on Ricardian theory,begins by considering some neglected aspects of Ricardo's ideas on trade andgrowth, based on his analysis of the distributive shares. Subsequent sections takeup Arthur Lewis' three-good Ricardian model of the terms of trade andEmmanuel 's concept of "un equa l exchange". The second section, on neoclassicaltheory, contains the discussion of the major "mainstream" literature on growthand trade, with sections on comparative statics, dynamics and the concept of"immiserizing" growth and foreign investment. The final section is on varioustheoretical aspects of "trade and development" issues, including analyses ofinfan t industry protection, two-gap models, the open dual economy and lastly anextensive discussion of recent work on "Nor th -So uth" models.

1. Ricardian theory

1.1. A dynamic Ricardian modelIn the model of Ricardo's Essay the size of the labor force at any moment isdetermined by the wage-fund, a stock of corn, and the "natural" wage-rate, also

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188 R. Findlayfixed in terms of corn. There are two outputs produced, corn and manufactures,and the time elapsing between input of labor and the availability of final outpu t isfixed and equal in both sectors. Wages are paid at the beginning of eachproduction period. The output of manufactures is simply proportional to theinput of labor into that sector but in corn there is diminishing returns to laborbecause of the fixed supply of land. Given the wage-fund and the naturalwage-rate, the fixed supply of land and the two constant returns to scaleproduction functions a production-possibilities frontier that is concave to theorigin is obtained. At any given price-ratio perfec t competition equates the rate ofprofit between the sectors and thus the supply of each commodi ty is determined.

Writing r for the rate of profit, C and M for the two outputs, p for the relativeprice of manufactures in terms of corn, L c and L m for the inputs of labor in cornand manufactures, ~ for the natural wage and et for the productivity of labor inmanufactures we have

r ~ ~~L c wL m 'from which it follows that

1 OC (T, Lc) (1.1.2)P g aLewhich gives the supply of corn as the level of output corresponding to the value ofL~ that solves (1.1.2) and the supply of manufactures as a times the residual laborforce L m obtained by subtracting LJ r o m the wage-fund divided by ~. Increasingp must result in falling L c and hence C so that M and C both respond positivelyto an increase in their relative prices. The demand assumption is that a constantpropor tion of rent is spent on manufactures, regardless of relative prices. Thus asp rises L~ and hence total rents fall in terms of corn which means that thequantity of manufactures demanded by landlords declines. With all wages spenton corn this implies that the demand curve for manufactures is downwardsloping. Figure 1.1 depicts the momentary equilibrium of the system as de-termined by the intersection of the supply and demand for manufactures. Theequilibrium value o fp clearly determines Lo, L m, C, and r, which from (1.1.1) isequal to the difference between OC/OL~ and ~, divided by ~.

If all profits are re-invested, as Ricardo typically assumes, the wage-fund forthe next per iod will be (1 + r) times larger than initially and the analysis can berepeated and the sequence of momentary equilibria traced out. We first determinethe effect of accumulation on the relative price p of manufactures. To do thisobserve that from (1.1.2) it follows that at constant p we have the same value ofL~ and hence of C. Thus the expansion of the labor force due to accumulation

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Ch. 4." Growth and Development in Trade Models 189

" i F . . . . . . . . .

/i iII ' I0 Manufactures

Figure 1,1

does no t sh i f t the supp ly cu rve o f co rn a t a l l. The increase in the to ta l l abor fo rcem u s t t h e re fo re a ll b e ab s o rb ed i n t h e p ro d u c t i o n o f m an u fac t u re s , t h e s u p p l ycu rv e o f wh i ch t h e re fo re s hi f ts t o t h e r ig h t. Th e d em an d cu rv e fo r m an u fac t u re sdepends on ly upon the ren t tha t i s ea rned in the co rn sec to r and s ince th i s i s thesame a t each va lue o f p the de ma nd curve fo r manufac tu res does no t sh i f t a t a ll .Th u s t h e p r i ce o f m an u fac t u re s m u s t d ec l i n e a s a ccu m u l a t i o n co n t i n u es an d s oemployment in the co rn sec to r r i ses to sa t i s fy (1 .1 .2 ) . The fa l l in the marg ina lp roduc t iv i ty o f l abor in the co rn sec to r reduces the ra te o f p ro f i t s ince

OCOLc ( p ) - ~ drr = ~ , wi th ~pp > 0. (1.1.3 )

Accumula t ion thus d r ives down the re la t ive p r ice o f manufac tu res un t i l them arg i n a l p ro d u c t o f l ab o r i n t h e co rn s ec t o r b eco m es eq u a l t o t h e n a t u ra lwage-ra te , a t wh ich po in t the ra te o f p ro f i t as expressed in (1 .1 .3 ) becomes equa lt o ze ro an d t h e " s t a t i o n a ry s t a t e " i s r each ed .

In t e rn a t i o n a l t r ad e can r ead i ly b e i n t ro d u ced . F i r s t co n s i d e r th e " s m a l l o p eneco n o m y " ca se i n wh i ch t he R i ca rd i an eco n o m y h as t h e o p p o r t u n i t y t o t r ad e w i ththe res t o f the wor ld a t some f ixed p r ice- ra t io p* h igher than the va lue a t wh ichthe marg ina l p roduc t o f l abor in the co rn sec to r equa ls the na tu ra l wage . Tradewi ll t h en p e rm an en t l y r a i se t h e r a t e o f p ro f i t t o r* = r ( p * ) an d t h e g ro wt h r a te o fthe wage-fund and the l abor fo rce to r* as wel l . The "s ta t ionary s ta te" can thusbe aver ted i f the expand ing labor fo rce i s fed by ex tens ion o f the f ron t ie r o fcu l t iva t ion to empty lands overseas . The fa l l in the re la t ive p r ice o f the l and-in tens ive good co rn hur t s l andow ners s ince the marg ina l p ro duc t o f l and and

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190 R. Findlayhence rent per acre falls while the marginal product of labor rises. Workers ofcourse do not gain since they cannot earn more than the natural wage but thebenefit accrues to the capitalists in the form of a higher rate of profit which theirthrift, "Moses and the prophets", converts into a higher rate of growth. England'sagriculture is stationary but Manchester and Birmingham make her the "workshopof the world" which pays in food and pr imary products for the expanding outputof the "workshop". It was this possibility, and not so much the static gains fromtrade, that made free trade attractive to Ricardo.

The stationary state would however once again rear its ugly head once theglobal frontier ran out and the "regions of recent settlement", as the League ofNations quaintly referred to the Americas and Australia, filled up. This wouldrequire a two-country model that can readily be obtained from the previousanalysis by simply laterally summing the supply and demand curves of the twocountries and clearing the unified world markets. The countries might of coursediffer in any one of several respects-technology, demand, the level of thewage-rate, the supply of land or the size of the wage-fund. Eventually however thecommon relative price of manufactures would have to fall to a point at whichaccumulation ceased in both countries with the marginal productivities of labor incorn equal to the natural wage-rates and the profit-rates equal to zero.

In view of the subsequent development of the Heckscher-Ohlin factor propor-tions theory of comparative advantage it is interesting to see how our Ricardianmodel yields the same predictions once the corresponding assumptions are made.If we suppose that technology and demand are identical in both countries, andalso the natural wage-rates, it follows from the results established that the countrywith a higher ratio of the wage-fund to the supply of land would have to be ableto produce manufactures more cheaply in isolation and hence have a comparativeadvantage in that commodity. Also the equalization of commodity prices wouldimply the same marginal productivities of land and labor and hence equalizationof the rents per acre and the rates of profit. Our earlier "small open economy"analysis can already be seen to have established the Stolper-Samuelson proposi-tion that trade benefits the "scarce" factor and also the Rybczynski theorem forthe special case of land being used in only one sector, so that an expansion oflabor leads to an increase in the output of the labor-intensive commodity but notto a decline in the output of the land-intensive one.

It can therefore be seen that the model of Ricardo's Essay leads very naturallyand directly to both the Heckscher-Ohlin and the "specific factors" models sopopular today and extensively discussed by Jones and Neary in Chapter 1 of thisvolume. It would appear that there is good reason for Samuelson (1971) to havelabelled his second reconstruction of Ohlin the Viner-Ricardo modelfl Introduc-

2The reference to Viner is to the celebrated 1931 article on "Cos t Curves and Supply Curves". Seein particular pp. 58-64 of the reprinted article in Viner (1958) and the Supplementary Note, pp.79-84.

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Ch. 4: Growth and Development in Trade Models 191ing land and capital into a model of trade as Ricardo did in his Essay thusenables us to treat not only growth but its cessation due to the constraint of the"original and indestructible powers of the soil".

It is also of interest that the secular tendency of the terms of trade in this modelis for it to turn in favor of the exporter of primary products and againstmanufactures, contra Prebisch-Singer. British economists from Jevons to Keynes,Beveridge, Robertson, and E.A.G. Robinson have been concerned with thisproblem. 3

The model also indicates, however, that trade reduces the rate of growth (incomparison with autarky) in the country that exports corn, since the rise in rentsis absorbed in luxury consumption while the fall in the rate of profit reducesaccumulation. Thus critics of free trade orthodoxy, from List to the "dependency"theorists of today, may not necessarily have been totally off the mark in theirbelief that the free trade mechanism somehow benefited the already advancedcenter at the expense of the less developed periphery.

1.2. Lewis on the terms of tradeA Ricardian model also forms the basis of an intriguing analysis of the terms oftrade between advanced and developing countries that Arthur Lewis (1954) firstput forward in the second part of the celebrated paper on "unl imi ted supplies" oflabor and then more extensively in his Wicksell Lectures for 1969. Consider twoeconomies, in each of which labor is the only scarce factor of production. Oneregion, call it the North, produces Food and Steel while the other region, theSouth, produces Food and Coffee. Outputs are simply proportional to laborinputs for all three goods, with productivity in Food being higher in the North.Since both transformation curves are linear and all goods are tradeable it is clearthat the relative price of Steel and Coffee is determined strictly on the cost orsupply side, independently of demand, the price of each being fixed in terms ofFood by the relative labor productivities. The North exports Steel, the SouthCoffee, and Food is exported by whichever region has the deficit in the exchangeof Steel and Coffee.The consequences of productivity changes in all four sectors are easy to see.The "stylized facts" that Lewis introduces are that productivity growth is greaterin Food than in Steel in the North, while it is greater in Coffee than in Food inthe South. Thus a uni t of Food is worth increasingly less Steel in the North whileit is worth increasingly more Coffee in the South. I t therefore follows that a unitof Coffee exported by the South is worth less and less Steel over time, i.e., there isa secular tendency for the terms of trade of the South to deteriorate.3See Rostow (1958, chs. 8 and 9) for a valuable examinationof this literature.

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19 2 R. FindlayProductivity change in either Coffee or Steel, with Food productivities constant,clearly reduces the relative price of Coffee or Steel in the same proportion so that

the full benefit of the improvement is passed on to the importing country. Theexporter is benefited only to the extent that Coffee or Steel is consumed at home.Thus, for commodities such as Malayan rubber or Ghana's cocoa, where domesticconsumption is negligible, no significant benefit is received by technical progressin the export sector since the purchasing power in terms of importables does notchange. For the South modernization of the backward technology of Foodproduction would be doubly blessed since it would not only raise real incomesdirectly but also raise the relative price of Coffee in terms of Steel.

A more detailed analysis and critique of the Lewis Ricardian model is given inFindlay (1981, p. 430-434).

1.3. Unequal xchangeThe Ricardian model also provides a convenient framework within which todiscuss the concept of "unequal exchange" advanced by Emmanuel (1972). Twofundamental assumptions made by Emmanuel are that international capitalmobility equalizes the rates of profit and that real wage-rates are exogenous ineach country. The simplest model to contain these ideas, based on Bacha (1978),is one in which the North is specialized in Steel and the South in Coffee, with qNthe output of Steel per unit of labor in the North, qS the output of Coffee per unitof labor in the South, w N and w s the real wages in North and South respectively,both fixed in terms of Steel, p the relative price of Coffee in terms of Steel, and rthe common rate of profit. Production of each good takes one period with wagespaid at the beginning of each period. It therefore follows that:

r= (qN--wN) = (pqS--wS) (1.3.1)W N W S '

which implies:

w s qN (1.3.2)P = WN qS "

In this equation p represents the commodity or "ne t barter" terms of trade ofthe South. By "equal exchange" Emmanuel appears to mean a situation in whichthe "double factoral" terms of trade, i.e. the amount of foreign labor embodied in

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Ch. 4: Growth and Dev elopment in Trade Mo dels 193impor t s per un i t o f domes t ic l abor embodied in expor t s , i s equa l to un i ty . Thedoub le fac to ra l t e rms o f t rade , deno ted f , a re re la ted to p by :

f = _pqS w sqN w N" (1 .3 .3)

Thu s f i s equa l to un i ty i f and on ly i f w s = w N. Em ma nue l says tha t there i s"u ne qu al exchange " , b iased aga ins t the Sou th , because w S< w N, i .e . the Sou thge ts commodi t ies wor th l es s than a day ' s l abor in the Nor th in exchange fo rco m m o d k i e s wo r t h a d ay ' s l ab o r i n t h e So u t h .

Whi le there i s no po in t in a rgu ing abou t def in i t ions i t shou ld be no ted tha t thep e j o ra t iv e co n n o t a t i o n o f t h e t e rm "u n eq u a l ex ch an g e" can b e v e ry m is l ead in g ,as the fo l lowing exam ple i l lu st ra tes . Suppose to beg in wi th th a t w s = w N and tha tco n s eq u en t l y t h e re is n o "u n eq u a l ex ch an g e" . Le t q N an d w N b o t h i n c rea s e i n t h esame p ropor t ion , w i th no change in qS and w s. The r a te o f p ro f i t and theco m m o d i t y t e rm s o f t r ad e w il l r em a i n u n ch an g ed b u t t h e d o u b l e f ac t o ra l t e rm s o ft rade wi ll de te r io ra te be low the i r in i ti a l va lue o f un i ty . Exchan ge has thus beco meuneq ual e ven though there is no change in the wel fa re o f the Sou th which s t i ll ge t sthe same a mo unt o f S tee l per un i t o f Coffee expor ted . In fac t i t i s c lear tha t thecom mo di ty t e rms o f t rade wi ll improve fo r the Sou th i f w N does no t increase asmuch as qU does , whereas the doub le fac to ra l t e rms o f t rade mus t de te r io ra te dueto w s be ing co ns tan t and w N r is ing . Thus the So u th ' s ga in f rom t rade cou ld bei n c rea s in g a s a r e s u l t o f b eco m i n g a "v i c t i m " o f u n eq u a l ex ch an g e !

In our example the on ly way to p reven t unequa l exchange as a resu l t o f theprodu c t iv i ty increase in the N or th i s fo r w N to be he ld cons tan t , i . e. none o f thebenef i t passed on to No r th ern workers , o r fo r w s to increase par i passu wi th w N,i . e . an y b en e f i t t h a t No r t h em wo rk e r s g e t b e s h a red eq u a l l y w i t h So u t h e rnworkers .

One way o f in te rp re t ing unequa l exchange i s to say tha t in te rna t iona l d i s t r ibu -t ive jus t i ce requ i res a po l icy o f open borde rs wi th regar d to the m igra t ion o flabor . S imp ly ra i s ing wages in the So u th to impr ove the t e rms o f t rade wi l l no t d os i n ce i t co u l d h av e v e ry ad v e r s e co n s eq u en ces o n em p l o y m en t i f t h e No r t h ' sdemand fo r the Sou th ' s expor t s i s a t a l l p r ice-e las t i c . Free migra t ion o f l abor i sthe o n ly econom ica l ly v iab le , thoug h o f course po l i t i ca l ly and soc ial ly veryd i f fi cul t , so lu t ion . I have exp lo r ed the consequen ces o f f ree migra t ion fo r Marx ian ,Rawls ian , Libe r ta r ian a nd Ut i l i t a r ian con cep ts o f in te rna t io na l d i s t r ibu t ive jus t i cein F ind lay (1982) . Other exp lo ra t ions o f th i s top ic a re by Li t t l e (1978) and Sen(1981). Sec t ion 3 .4 be low no tes some consequen ces o f in te rna t iona l l abor m obi l i tyi n a " N o r t h - S o u t h " m o d e l o f c a p it a l a cc u m u la t io n .

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19 42. Neoclassical theory

R. Findlay

2.1. Comparativestatics of growth and tradeThe major impetus to the incorporation of growth into trade theory came in thefifties with the consideration of the long-run dollar problem and related issuesaddressed in the famous Inaugural Lecture on that topic by Hicks (1953). Thedifferential growth of productivity, both between sectors and national economies,was the focus of attention in that extremely stimulating paper. Hicks' lead wasquickly and energetically followed by Harry Johnson (1955), whose work in turninspired a number of other contributions, drawn together into a taxonomicsynthesis in Johnson (1959).

Johnson's initial work considered trade between two completely specializedeconomies, Mancunia and Agraria. Letting II1, M1 and Y2, M2 denote outputlevels and imports of Mancunia and Agraria respectively and p the terms of t radeof Agraria the requirement of balanced trade results in:

MM I ( P , Y 1 ) - 2 [ p (2.1.1)

Differentiating totally and substituting we obtain:EI~g'I - - e2Y2 (2 .1 .2 )P ( ~1+ ~2 - 1 ) '

in which the "hats" denote proportional changes, e1 and e2 are the income-elastic-ities of demand for imports and ~/1 and */2 the price-elasitcities. The denominatoris required to be positive by the familiar Marshall-Lerner stability condition.Thus the terms of trade will turn against whichever country has the higherproportional growth weighted by the income-elasticities of import demand. Thisanalysis would seem to indicate that the more "dynamic" country would experi-ence terms of trade, or balance of payments, difficulties as a consequence of itssuccess. This did not square well with the observation, explicitly made by Hicks,that i t was the greater dynamism (at tha t time of course) of the US economy thatcreated a "dollar shortage" for the then more sluggish rest of the world. Hickssaw that the greater dynamism was accompanied by a bias towards the import-competing sector in productivi ty growth that apparently reversed the outcome onthe deficit or terms of trade. Thus most of the subsequent literature concentratedon two-sector models that permitted different degrees of export or import bias inthe exogenous source of expansion.

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Ch. 4: Growth and Development in Trade Models 195Con side r no w the usual 2 x 2 x 2 mode l in which 1 and 2 refer to c ountr ies , X

and Y to goods, K and L to fac tors , a to a sh i ft param eter . Equ i l ib r ium in thewor ld marke t requ i res :

& ( p , = e x(p, e x(p) = o, (2 .1 .3)where Ex is wor ld excess supp ly o f X, E~ an d E~ the co r respo nd ing na t iona l l eve lsand p i s the re la t ive p r ice o f X. The e f fec t o f an exog enous change in Cou n t ry 1on p can be ob ta ined as :

dp - (OEXx/Oa)da OEx/O p

(2 .1 .4)

Th e d eno min a to r i s no th ing bu t O h + ~2 - 1 ) > 0 so the s ign o f the e f fec t on pdepen ds so le ly upo n the s ign o f the numera to r . Thu s suppose C oun t ry 1 is theex p o r t e r o f X an d t h a t:

OexO----a < O. (2 .1 .5 )At cons tan t p r ices th i s means tha t wor ld excess supp ly o f X i s nega t ive so tha t

p mus t increase to c lear the wor ld ma rke t i f i t i s s t ab le . Thu s Co un t r y 1 can havei t s t e rms o f t rade improve i f the exogenous source o f expans ion re f lec ted in thes h i f t p a ram e t e r c au s e s an ex ces s d em an d fo r i t s ex p o r t ab l e p ro d u c t a t co n s t an trelat ive prices .

W hat so r t o f change cou ld p ro duc e th is e f fec t? Le t X be the l abor- in tens ivegood and Y the cap i ta l - in tens ive good in the sense tha t kx[~(p)] < ky[o~(p)] fo ra l l va lues o f the wa ge -re n ta l ra t io o~. Def ine a as an increase in the f ixed amou n to f cap i ta l k wi th wh ich Coun t ry 1 i s endowed . We then have :

Xk x [~ o (p ) ] + ( 1 - X)ky[~O(p)] = k, (2 .1 .6)in wh ichindus t ry .co n s t an t ,

k i s the ra t io o f cap i ta l to l abor and X i s the f rac t ion o f l abor in the XDif fe ren t ia t ing wi th respec t to k and h o ld ing p , and hence w, k x an d k ywe ob ta in :

d2t 1d k - ( k x - k y ) " (2 .1 .7)Thus if k~, < ky i t mus t fo l low tha t l es s l abor (and consequen t ly cap i ta l ) mus t

be a l loca ted to X, the ou tpu t o f wh ich con t rac t s abso lu te ly , wh i le the ou tpu t o f Ymus t increase abso lu te ly . Th is i s the famous Rybczynsk i (1955) theo rem.

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196 R. Findlay

.L2

._J

Oy

a'

CapitalFigu re 2.1

The expansion therefore contracts the supply of the exportable good when thefactor that increases is used relatively more intensively in the import-competinggood. The higher national income at constant prices will increase the homedemand for the exportable good if inferiority in consumption is ruled out. Theexcess supply of the exportable must therefore become negative at constant pricesand the terms of trade of the expanding country must improve. The sameargument demonstrates that the terms of trade must deteriorate if the factor thatincreases is used relatively intensively in the exportable sector.

The other kind of expansion to consider is technical progress in either sector,which can be neutral in the well-known sense of Hicks or biased towards somefactor. The effects of technical progress of various kinds on the terms of tradehave been investigated in Findlay and Gruber t (1959). For simplicity I shall onlyconsider the case of Hicks-neutral technical change in detail here.

Figure 2.1 is the Edgeworth-Bowley production box for Country 1. Point a onthe efficiency-locus is the initial equilibrium with wage-rental ratio 0~ correspond-ing to the equilibrium product price ratio/~. Let Country 1 now experienceHicks-neutral technical progress in the import-compet ing sector Y. Note that theefficiency locus will not shift since each point on it will continue to have X and Yisoquants tangential to each other on it at slopes equal to their original values. Atpoint a the slope of the common tangent will continue to be equal to 0~, Y outputbeing larger and X output unchanged.

The Lerner diagram of Figure 2.2 shows the effect of the technical progress inY on the wage-rental ratio when relative product prices remain unchanged at/7,which can be put equal to unity without loss of generality. The Hicks-neutralprogress in Y implies that the uni t isoquant for that commodity is shiftedproport ionally downward along each ray from the origin. The common tangent to

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Ch. 4: Growth and Development in Trade Models 197t h e u n i t i so q u an t s m u s t t h e re fo re b e s t e ep e r t h an b e fo re s o t h a t t h e wag e - r en t a lra t io fa l l s and labor- in tens i ty increases in bo th sec to rs , wh ich impl ies tha t thepo in t on the e f f ic iency- locus in F igure 2 .1 co r respon d ing to /~ m us t b e to the l e f to f p o i n t a . Th e o u t p u t o f X m u s t t h e re fo re d ec l in e a t co n s t an t r e l at i v e p ro d u c tp r ices and excess supp ly o f X becom es nega t ive i f in fe r io r i ty in con sum pt ion i sru led ou t . Th e same reason ing shows tha t the t e rms o f t rade mus t de te r io ra te i fthe neu t ra l innova t ion occurred in the expor tab le sec to r .The cons idera t ion o f fac to r b ias in innova t ions in t roduces the in te res t ingposs ib il i ty tha t the t e rms o f t rade m ay impr ove even i f the innov a t ion takes p lacein the ex por t sec to r and , sym met r ica l ly , tha t they m ay de te r io r a te even if i t occursin the impor t -compet ing sec to r . The in tu i t ion i s tha t a cap i ta l - sav ing innova t ion ,fo r example , can be though t o f as a combina t ion o f a neu t ra l innova t ion and anincrease in the endowment o f cap i ta l . I f such an innova t ion were to occur in thelabor- in tens ive expor t sec to r X the t e rms o f t rade wou ld de te r io ra te on accoun t o fthe "n eu t ra l " t echno log ica l e f fec t bu t the no t iona l increase in the cap i ta l s tocktha t i s impl ied by the cap i ta l - sav ing chara c te r o f the innov a t ion wo u ld resu l t in anex p an s i o n o f t h e o u t p u t o f Y an d a co n t r ac t i o n i n th e o u t p u t o f X a t co n s t an tre la t ive p roduc t p r ices as a consequence o f the Rybczynsk i theorem. Th is e f fec twou ld work in the oppos i te d i rec t ion to improve the t e rms o f t rade . Thus aninnovat ion in the expor t sec to r tha t i s s t rong ly cap i ta l - sav ing bu t on ly weak lycos t - reduc ing cou ld resu l t in an improvement in the t e rms o f t rade . S imi la rreason ing would ind ica te tha t a l abor-sav ing innova t ion in the impor t compet ingsec to r cou ld cause a de te r io ra t ion in the t e rms o f t rade .

Th e o ther c oun t ry remains s ta t ic in a ll the resu l t s repo r ted so fa r in th i s sec t ionbu t i t i s c lear tha t any combina t ion o f changes in fac to r supp l ies and techn ica l

CapitalFigure 2.2

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198 R. Findlayprogress can be applied to both countries simultaneously and the consequencesfor the terms of trade deduced. Johnson (1959) provides an exhaustive diagram-matic analysis while Jones (1965) carefully works out the relevant algebra.

2.2. "Immiserizing'" growth and foreign investmentThe most striking result to emerge from the work of the fifties on the comparativestatics of growth and trade was the demonstration by Bhagwati (1958) thatgrowth in an open economy could be "immiserizing", i.e. that national welfarecould actual ly decline as a result of the expansion causing a sufficiently strongdeterioration of the terms of trade that exceeds the favorable effect on welfareof the expansion at constant relative product prices. This possibility hadbeen ant icipated by Edgeworth (1894) who referred to it as "damnifying" butBhagwati's demonstration is in a much more general setting.

Edgeworth's case is simply one in which a country produces a single good thatit does not consume domestically but exports in exchange for another good tha t itdoes consume. Think of Malaya or Ghana exporting rubber or cocoa in exchangefor food. An expansion of production and hence of exports (equal to all ofdomestic production in this example) would result in a smaller volume of foodimports if the price-elasticity of foreign demand is less than unity. The expansionhas thus reduced national welfare. It is clear that a necessary condition for thisresult is that both production and trade are conducted by atomistic perfectlycompetitive agents, i.e. there is no private monopoly or state intervention throughtariffs, export taxes or other measures that would restrict output optimally. Thisexample has the virtue of being possibly the simplest illustration of the proposi-tion that it does not always pay to rely solely on laissez fair e or the "magic of themarket".Bhagwati considers "immiserization" in the context of the standard 2 x 2 x 2model. A key role in the analysis is played by the "zero gain" decline in the termsof trade i.e. the amount that exactly off-sets the effect of the expansion at constantrelative prices. Compute the world excess supply for the importable at the "zerogain" level of the terms of trade. If it is negative then it is clear that stabilitywould require the terms of trade to deteriorate beyond the "zero gain" level, i.e.the country is immiserized.The condition for equilibrium in the market for the importable, prior to thechange is

S ( p , a ) + M ( p ) - C ( p ) =0, (2.2.1)in which S is domestic supply, M is imports, C is domestic consumption and p isthe relative price of the importable and a a shift parameter.

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Ch. 4: Growth and Deoelopment in Trade Models 199Diffe ren t ia t ing th i s express ion , pu t t ing /~ equa l to the zero ga in change in the

te rms o f t rade , y ie lds the fo l lowing express ion fo r the poss ib i l i ty o f immiser i -za t ion

C o+~r+rl /~ + -~--~ada < O, (2 .2 .2)in w hich o i s the p r ice-e las t i c ity o f the dom es t ic supp ly o f the impo r tab le , z is thepr ice-e las t ic i ty o f fo re ign supp ly o f impo r t s , ~ i s the com pens a ted p r ice-e last i c i tyo f d o m es t i c d em an d fo r t h e i m p o r t ab l e an d (OS/Oa)da is the shift in thedome s t ic supp ly o f the im por ta b le a t cons tan t re la t ive p r ices . S ince o , ~ and /~ axea l l pos i t ive i t fo l lows tha t immiser iza t ion can on ly occur i f e i ther z o r OS/Oa isnega t ive . A nega t ive va lue o f z means tha t the fo re ign supp ly o f the impor tab lerespon ds nega t ive ly to the r i se in i t s p r ice i .e . fo re ign dem and fo r hom e expor t s i sinelas t ic . A negat ive value of OS/Oameans tha t the expans ion i s s t rong ly b iasedaga ins t the im por ta b le a t co ns tan t re la t ive p r ices , i. e. a nega t ive R ybczy nsk i e f fec tsuch as an increase in cap i ta l occurr ing in an e con om y wi th l abor- in tens ivei m p o r t s o r a n eg a t i v e F i n d l a y -G ru b e r t e f fec t s u ch a s a H i ck s -n eu t r a l i n n o v a t i o nin the expor tab le sec to r .

Su p p o s e t h a t OS/Oa s negat ive and r is posi t ive, i .e . the foreign response to ar i se in the p r ice o f the i r expor t s i s "normal" . Thus a t cons tan t re la t ive p r ices thedomes t ic expans ion leads to a reduc t ion in the wor ld supp ly o f the impor tab lewhi le wor ld demand wi l l be unchanged i f rea l income (u t i l i ty ) in the expand ingcou n t r y is he ld cons tan t . T he re la t ive p r ice o f the impor tab le m us t there fo re r ise ifthe wor ld marke t i s to be c leared . The r i se in p r ice increases domes t ic supp ly ,r ed u ces d o m es t ic d em an d a t u n ch an g ed r ea l i n co m e an d i n c rea s e s fore i g n s u p p l yof the i mp ort ab le so al l the effects are wo rking to close the gap. If o , "r and ~ area l l small and the abso lu te v a lue o f the nega t ive OS/Oa s large, however, i t i s c leartha t these responses may no t be su f f ic ien t to c lose the gap when the p r ice r i se i sconf ined to the "ze ro ga in" va lue . Consequ en t ly the r i se in p wou ld ha ve toexceed th i s va lue i f equ i l ib r ium i s to be res to red so tha t immise r iza t ion resu l ts .

The su f f ic ien t cond i t ion fo r immiser iz ing g rowth to occur i s there fo re tha t thesum of al l four terms in (2 .2 .2) be negat ive. Since o and ~ are always posi t ive anecessary cond i t ion i s tha t e i ther r o r aS/Oa o r b o t h m u s t b e n eg a ti v e.

As in the Edgewor th case immiser iza t ion cou ld o f course never occur in thep re s en ce o f r a t i o n a l s t a t e i n t e rv en t i o n . Gro wt h acco m p an i ed b y o p t i m a l t r ad ein te rven t ion to sa t i s fy a l l the re levan t Pare to cond i t ions mus t l ead to an increasein na t iona l wel fa re .

An en t i re l y d i f fe r en t t y p e o f " i m m i s e r i z i n g " g ro wt h was an a l y zed b y J o h n s o n(1967) . Here the t e rms o f t rade a re f ixed fo r a two-sec to r , two-fac to r openeco nom y bu t there is a t a r i f f o r s imi la r d i s to r t ionary t rade re s t r i c t ion in p lace tha tresu l ts in the ou tpu t o f the impor t - com pet ing good be ing too la rge and o f the

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200 R. Findlayexportable good being too smal l . Suppose an expansion occurs that contracts theou tpu t o f the expor tab le and increases tha t o f the impor tab le a t cons tan t re l a tivedomest ic ( tar i f f- inclus ive) pr ices . Johnson shows that under some condi t ions i t i sposs ible for nat ional welfare to be reduced as a resul t .

The necessary and sufficient cond i t ion for immiseriza t ion of the John son type iseas i ly obtained. Observe that s ince domest ic relat ive product pr ices are f ixed bywor ld p r ices and the t a r if f the domes t i c wag e- re n ta l ra t io and hence a l l techn icalcoeff icients are unique ly determ ined also . The coeff icients in the e quat ions belowcan therefo re a l l be t rea ted "as i f " they were cons tan t s . The cond i t ions fo r fu l lu t i l izat ion of both factors g ive:

K = a11X-.t- al2Y, (2.2.3)L = a z l X + a22Y. (2.2.4)Suppose now that K increases wi th L constant and that X, the exportable , i s

labor- in tensive. The effects on the o utpu t levels are given by:d X a2 2- - < 0 , ( 2 . 2 . 5 )d K AdY a21 > 0, (2.2.6 )d K A

whereA = (a na 22 - azlax2 ) < 0, (2.2.7)

by the assumption that X is labor- in tensive.The effect on welfare , however , depends u po n w hat happ ens to the value of

domest ic product ion at world pr ices , s ince th is determines the purchasing powerof the econ om y in the wor ld m arke t and thus o f the l eve l o f u t i li ty the domes t i cconsum ers in the aggregate can at ta in wi th world pr ices given as p* and p~. Thecha nge in dom estic inco me eva luate d a t wo rld prices is th erefo re Px* d X + py* d Y.Immiserizat ion therefore impl ies that :

, dX , d Yp ; -d-g + p y -d--g < O, (2.2.8)

which, af ter subst i tu t ion, becomes:a22 -* a21 (2. 2.9 )

A"

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Ch. 4." Growth and Development in Trade Models 201

3O.

0>-

. . . . . . . I \\ '

I I. . . . . . . . . . I _ 1 . _ _

X outputFigure 2.3

Th is s ta tes tha t im miser iza t ion wi l l occur i f and o n ly i f the va lue a t w or ld p r iceso f the reduc t ion in the ou tpu t o f the expor tab le exceeds the va lue a t thosepr ices o f the increase in the ou tpu t o f the impor tab le .

The s i tua t ion i s i l lu s t ra ted d iag rammat ica l ly in F igure 2 .3 . Expans ion o f Kwi th L cons tan t moves the p roduc t ion po in t a long the f ixed labor cons t ra in t o rRybc zynsk i l ine in the d i rec t ion o f mo re Y ou tpu t and less X ou tpu t . T he va lue o fthe p roduc t ion bund le a t wor ld p r ices dec l ines i f the wor ld p r ice- ra t io i s s t eeperthan the s lope o f the Ry bczy nsk i line, wh ich is equ iva len t to the cond i t ion s ta tedabove .

In tu i t ive ly Johnson ' s immiser iza t ion occurs in th i s example because fac to rendow men ts change in such a way as to expan d the inef f ic ien t p ro te c ted sec to r a tthe expense o f the e f f ic ien t expor t sec to r . Any o ther type o f expans ion tha t hasth i s p roper ty cou ld be a po ten t ia l source o f immiser iza t ion . No te , however , tha treduc t ion in the ou tpu t o f the expor tab le i s on ly necessary , and no t su ff icient , fo rth i s ou tcome to occur . The d iag ram c lear ly shows tha t i f the wor ld p r ice- ra t io i sf l a t t e r than the Rybczynsk i l ine the va lue o f domes t ic p roduc t ion a t wor ld p r icesmust r ise .

Th e co n cep t o f s h ad o w p r i ce s fo r f a c t o r s o f p ro d u c t i o n i n d i s t o r t ed o p eneconom ies p rov ides a v a luab le too l in the ana lys i s o f immiser iza t ion . 4 I f V*deno tes the va lue o f domes t ic p roduc t ion a t wor ld p r ices the shadow pr ices o f

4See Findlay and Wellisz (1976) and Srinivasan and Bhagwati (1978) on the determination andinterpretation of shadow prices in distorted open econom ies and for references to the associatedfiterature of cost-benefit analysis in developingeconomies.

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202

cap i ta l and labor can be def ined as:R. Findlay

r* dV* . dX dY (2 .2 .10)= d K = P d -K + d---K'w* dV* , d X dY (2 .2 .11)- d L = P - d -L + d L '

whe rep* is the ra t io o f the wor ld p r ice o f the expor tab le to the wor ld p r ice o f theimportable . The derivatives of outputs with respect to factors are evaluated fromthe same tar if f-d is tor ted set of a ' s as before, ref lecting the inherently second-bes tna tu re o f the s i tuat ion . The m arke t p r ices o f the fac to rs , r and w, can be def inedin exac t ly the same way excep t tha t p* is rep laced by the domes t ic p r ice- ra t io /~which is :

1/7 (1 + t ) p* < p* ' (2 .2 .12)where t is the rate of tar if f .

S ince X is the labor - in tens ive good we have f ro m the R ybczynsk i Theorem tha t :d X d Yd K < 0, d---K > 0, (2.2 .13 )d X d Yd---L > 0, d ~ < 0. (2.2 .14 )

Fro m the def in i t ions and these inequal it ies it fo l lows immedia te ly tha t :r* < r, w* > w. (2.2.15)

Immiser iza t ion in Johnson ' s sense can be seen to be equ iva len t to r* be ingnegative, i.e. the d is tor t io n caused by th e tar if f is so pernicious as to m ake c apitalhave a negative marginal social product. Brecher and Diaz Alejandro (1977) haveshown tha t i f the add i t iona l cap i ta l i s owned by fo reigners , who ob t a in the m arke tp r ice as the reward , na t iona l welfa re mus t go down. Th is resu l t i s immedia te inview of the propert ies of shadow prices es tablished above s ince the change inna t iona l w elfa re is :

d V *d K r = (r* - r ) < 0 . (2 .2 .16)Thus add i t iona l cap i ta l tha t i s domes t ica l ly owned is on ly immiser iz ing i f r* i s

nega t ive whi le add i t iona l cap i ta l i s a lways immiser iz ing in the p resen t con tex twhenever i t is foreign owned.

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Ch. 4: Growth and Deoelopment in Trade Models 203Th e i m p ac t o f fo re ig n i n v es t m en t o n n a t i o n a l we l f a r e in t h e p re s en ce o f a t a ri f f

i s a l s o s h o wn t o b e n eg a t i v e i n t h e co n t ex t o f t h e V i n e r -R i ca rd o o r " s p ec i f i cfac to rs" model by Brecher and F ind lay (1983) . In th i s paper the na t iona l ly owneds tock o f cap i ta l in a t a r i f f -d i s to r ted smal l open e con om y is f ixed bu t i t is a l soava i lab le f rom abroad a t a f ixed (o r r i s ing ) p r ice . I t i s shown tha t an endoge-nous ly d e te rm ined un res t r i c ted in f low o f fo re ign cap i ta l lowers na t iona l w el fa re inco m p a r i s o n w i t h wh a t i t wo u l d b e i n t h e co m p l e t e ab s en ce o f i n t e rn a t i o n a l c ap i t almob i l i ty . An op t imal second-bes t t ax , g iven the t a r i f f d i s to r t ion , is der ived and i seq u a l t o t h e p ro p o r t i o n a t e d i f f e r en ce b e t ween t h e m ark e t an d s h ad o w p r i ce s ofcapi tal . This tax is necessari ly at a h igher rate than the rate of tar i ff , s ince themarke t p r ice o f cap i ta l i s shown to exceed the shadow pr ice by more than thelevel of the tar iff .Brecher and Choudhr i (1982) cons ider the impac t o f fo re ign inves tmen t onn a t i o n a l we l f a r e wh en t h e co u n t ry h a s m o n o p o l y p o wer i n i n t e rn a t io n a l t r ade .They show tha t na t iona l wel fa re wi l l r i se o r fa l l s imply as a consequence o f theef fec t o f the fo re ign inves tmen t on the t e rms o f t rade s ince na t iona l ly ow nedfac to rs a re f ixed and the i r wel fa re thus dependen t on ly on the t e rms o f t rade .

Th e re i s t h u s an i n t e re s t i ng co r r e s p o n d en ce b e t ween B re ch e r -D i a z an dJ o h n s o n , o n t h e o n e h an d , an d B rech e r -C h o u d h r i an d B h ag wa t i o n t h e o t h e r . I neach case the possibility of immiser iza t ion i s conver ted in to a necessity i f thesource o f the g rowth i s fo re ign -owned .

As p o i n t ed o u t b y B h ag w a t i (19 71 ) b o t h t y p es o f " i m m i s e f i za t i o n " a r i se d u e t othe fa i lu re o f the necessary Pare t i an cond i t ion o f equa l i ty be tween fo re ign anddomes t ic ra tes o f t ran s fo rm at ion to ho ld , as a resu l t o f the ta r i f f in the smal l openeco n o m y J o h n s o n ca s e an d a s a r e s u lt o f t h e absence of an op t imal t a r i f f in them o n o p o l y p o wer ca s e o f t h e o r i gi n a l d em o n s t r a ti o n .

2.3. Steady state growth in the open economyThe f i f t i es saw the emergence o f g rowth theory in bo th the neoc lass ica l andCam bridge var ie t ies . Th e fo r me r had a cons iderab le fa l lou t in t rade theo ry wh ichi s no t su rp r i sing in view o f the fac t tha t the 2 x 2 model was the c om m on p r ope r tyo f bo th these f i e lds . Ca l l one o f the goods a cap i ta l good , in t roduce a sav ingsfunc t ion to p rov ide the demand cond i t ions , l e t the l abor fo rce g row exogenous lyand the o ld t rade w ar ho rs e i s o f f to the races.

The co re o f neoc lassica l g row th the ory i s the one-sec to r mod el o f So low (1956)and Swan (1956), wh ich i s eas i ly adap ted to the case o f a smal l open e conom y. Asa mat te r o f fac t th i s se t t ing makes the hero ic aggrega t ion o f tha t model morepa la tab le s ince as we sha l l ind ica te t rade makes i t poss ib le to spec ia l i ze inp roduc t ion whi le permi t t ing as much d ivers i f i ca t ion and var ie ty in consumpt ionas one wishes .

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204 R. FindlayThus suppose that there are any number of commodities that an economy canproduce with two factors of production, capital and labor, according to constant

returns to scale production functions with the usual properties. The economy isembedded in a world market that determines the relative prices of all these goodsindependently of what goes on in the economy. With constant returns to scaleand fixed relative prices it is possible to define a composite or surrogate produc-tion function that will also have constant returns to scale and the usual propertiesby taking the inner envelope of a set of isoquants for the goods that have thesame value at world prices. I have called this the "foreign exchange" productionfunction in Findlay (1973, p. 105). Figure 2.4 is an illustration. Some goods willnever be efficient for the economy to produce at the given technology and relativeprices. Goods that are on the envelope for some segment would be effcient toproduce if the economy's factor proportions are within the relevant range.Given the initial capital and labor endowment of the economy, the growth rateof the labor force and the savings function, the composite production function isall that is needed to obtain the extension of the Solow-Swan model to an openeconomy. The same formal apparatus applies and it is unnecessary to repeat anyderivations. If a continuum of goods can be produced the "foreign exchange"production function would look just like the one-good function of the originalmodel except that a different good would be produced at each capi tal- labor ratio.If there are N goods produced then there will be ( N - 1) linear segments in the"foreign exchange" isoquant. Capita l-labor ratios corresponding to each segment

F

m

GLt~t . . )

LaborFigure 2.4

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Ch. 4: Growth and Development in Trade Models 205make it efficient to produce a combination of the two goods whose individualisoquants define the extremities of the segment.

Figure 2.5 depicts the solution in terms of the familiar diagram. The long-runequilibrium capital-labor ratio k* is where the n k line indicating the "widening"capital requirement cuts the savings function s y = s f ( k ) in which y = f ( k ) is theforeign exchange production function in per capita form. Thus given any k 0 theeconomy will converge to k* if the stability condition s f ' ( k ) < n is satisfied.The long-run equilibrium capi tal- labor ratio depends positively on the propensityto save and negatively on the growth rate of the "effective" labor force.

The model can illustrate the evolution of comparative advantage in response tochanges in factor proportions. Goods produced initially still correspond to what isefficient at k 0. As k increases over time the original goods will cease to beproduced, new ones will enter to be given up in turn until the economy settlesdown to a pattern of production corresponding to its "perma nent" or "long run"comparative advantage corresponding to k* given by the value of k that satisfiesthe equation

s f ( k ) = n k . (2.3.1)"Momentary" comparative advantage is therefore determined /t la

Heckseher-Ohlin by the k ( t ) prevailing at time t but "long run" comparative

0

0

/ nk

I ( k )

k0 k* "kCap i ta l - L a b o r R a t i o

Figure 2.5

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206 R. Findlayadvantage is defined by the "dynamic" determinants s and n, given the technol-ogy and the structure of relative prices in the world market. For further aspects of"dynamic" comparative advantage see Findlay (1973, ch. 7). Demand conditions(other than saving) are irrelevant since they only serve to determine how theincome that is efficiently produced at any moment is spent.

Figure 2.5 also can depict the "Golden Rule" capital-labor ratio /~ as de-termined by the condition f ' ( k ) = n that maximizes sustainable per capita con-sumption c = f ( k ) - n k . Note that in general the Golden Rule capital-labor ratiowill require the economy to specialize on only one good, unless the slope of thelinear segment of f ( k ) happens to be exactly equal to n.

The two-sector growth model, with one investment and one consumption goodand the relative price given in world markets has been very popular in theliterature on growth and trade. Analytically it is of course just a special case ofthe more general aggregation that has been described here by means of theconcept of a surrogate "foreign exchange" production function. There is stillhowever a great deal of insight that can be obtained from many of the papers inthis tradition such as Johnson (1971), Vanek (1971), Deardorff (1973) andBertrand (1975). A compact synthesis of much of this literature is provided inSmith (1977).

An intuitively satisfying result of Bertrand is that the locus of sustainable percapita consumption possibilities in a small open economy with free tradedominates that of the same economy when it is closed. This is easy to see. For theclosed economy a value of k defines a production possibility frontier and hence avalue of c after n k is allowed for. This function is concave and possesses a uniqueinterior maximum. The possibility of trade at fixed prices obviously raises c forany given value of k and hence dominates the consumption-possibilities frontierfor the closed economy. Varying the relative price p as a parameter generates afamily of free trade consumption-possibilities loci that have the closed economylocus as their inner envelope. This is the appropriate generalization of thestandard gains from trade theorem for a "small" open economy to a setting ofsteady growth.

Some other neat results along these lines can also be established easily. Vanekproved that an increase in the relative price of the consumption good, assumed tobe the more capital-intensive of the two, ~ raise the steady state capi tal- laborratio of a small open economy. In terms of our composite production function itis easy to see from the Lerner diagram that a rise in the relative price of thecapital-intensive good must reduce the real wage and raise the return to capitalf ' ( k ) , measured in terms of the capital good, when the economy produces bothgoods. The f ( k ) function in Figure 2.5 is shifted upwards, with a steeper slope ofthe linear segment associated with incomplete specialization. The steady statecondition s f ( k ) = n k can therefore only be satisfied at a higher value of k* thanbefore.

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Ch. 4: Growth and Development in Trade Models 207Deardorff pointed out that a closed economy with savings rate at the Golden

Rule value would always have its steady state per capita consumption raised byentering international trade. To see this observe that there is a unique productprice ratio p* that makes r( p) = n in the closed economy, the necessary conditionfor the Golden Rule. The per capita output of capital goods is determined by pand k, which we may express as q = q(p, k) with q depending negatively on kbecause of the Rybczynski theorem. With p* already given by r ( p ) = n theGolden Rule value k* is obtained as that which solves q(p*, k)= nk. Equi-librium in the closed economy under the Golden Rule can therefore be repre-sented by the tangency of p* with a per capita production possibility frontiercorresponding to k*. Now let trade be possible at any price-ratio other than p*.Per capita consumption must increase with investment maintained at nk*. Thusthe economy can increase per capita consumption even if it keeps k* unchanged.Changing k* to optimize under the trade opportunity can therefore only lead to afurther rise in per capita consumption.

We now leave the small open economy for the analysis of the two-countryequilibrium, in which the terms of trade have to be determined endogenously. Thefundamental contribution in this area is Oniki and Uzawa (1965), though much ofthe analysis was also done independently by Bardhan (1965). Both papers are ofcourse extensions to a two-country world economy of the Uzawa (1961) two-sector growth model of a closed economy, as is Stiglitz (1970), another importantcontribution. I t is convenient to begin with a simple diagrammatic exposition ofthe essential properties of the Uzawa model that makes the extension to thetwo-country world relatively plain sailing. The consumption good is assumed tobe always more capital-intensive than the investment good, as in all the paperscited. The investment good serves as the numeraire so that we have

y ( p , k ) =pc ( p , k ) +q( p , k ) , (2.3.2)in which y is per capita income and c and q are per capita consumption andinvestment. We also write

c = hf~(ko), q = (1 - h) fl (k i) ,k = ~kkc + ( 1 - ~ k ) k i,

(2.3.3)(2.3.4)

in which h is the share of labor in the consumption goods sector and thecapital-intensities k c and k I are increasing functions of the wage-rental ratio w,which in turn is a negative function of p. Factor allocations and output levels arethus all determined completely by p and k.

Given k the equilibrium value of p is determined by the condition that savingequals investment. The savings function makes savings proportional to income so

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208 R. Findlaythat we have

s y ( p , k ) = q ( p , k ) , (2.3.5)which can be solved for the unique value of p tha t satisfies this equation for anygiven value of k, which changes over time according to the accumulation equation

k = q (p , k ) -n k , (2.3.6)which has to equal zero in the steady state.In Figure 2.6 we plot k on the horizontal axis and the relative price of theinvestment good, which is the reciprocal of p, on the vertical axis. The curve QQindicates combinations of k and 1 /p for which (2.3.6) holds with k = 0. It ispositively sloped because q depends negatively on k by the Rybczynski theoremand positively on the relative price of the investment good 1/p. The curve SSindicates combinations of k and 1/p that make savings equal to the steady statelevel of accumulation nk. This curve is negatively sloped since

d(1 /p) ( n - s - ~ k )dk OyS -O ( l / p )

(2.3.7)

in which the denominator is negative and the numerator positive if the usual

1/p1/1/p3/Pz

0

s \. . . . . . . . . . . . . . . . L _ _

M - - - - - e ~

Q

ko k*

Figure 2.6

Q

~ M/

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Ch. 4: Growth and Development in Trade Models 209stability condition s ( O y / O k ) < n is satisfied. The intersection of QQ and S Sdetermine the steady state values p* and k* of the system.

How does the economy behave out of the steady state and does it converge tothe balanced growth path defined by p* and k*? To answer these questionsconsider the dashed curve M M that passes through the rest point (p*, k*),cutting QQ from above. This curve shows the value of p that satisfies the savingequal investment condition (2.3.5) for any given value of k. It thus depicts the"momen tar y" equilibrium value of p, and hence of ~, k c and ki , corresponding toany given value of k. Increasing k reduces the output of investment goods andincreases saving so that the reciprocal of p must increase for (2.3.5) to continue tobe satisfied. This shows why M M is positively sloped.

Why must M M cut QQ from above? Consider any value of k less than k*, sayk 0. Denote the prices corresponding to k 0 on S S and QQ by 1 / p 1 and 1 / p 2respectively. A little reflection will show that:

sy (P l , ko ) = nko < q ( P l , ko ) ,sy(P2, ko) > nko = q(P2, ko) ,

which means that investment exceedsexceeds investment at point (p2, ko).

(2.3.8)(2.3.9)

savings at point (P l, k0) while savingsConsequently savings can only equalinvestment at some point (P3, ko) where P3 is in between Pl and P2. This provesthat M M must lie above QQ at k 0 or any point to the left of k*.Since the relative price of the investment good is higher on M M than on QQ atk 0 it follows that k must be positive. The economy must thus move along M Mtowards the long run equilibrium point (p*, k*) with k and 1 / p both rising, sothat the wage-renta l ratio and the capital-intensities in bo th sectors rise as well.Similar reasoning would show that the model is stable in the other direction withk o > k* as well, though here of course the direction of change in relative priceswill be reversed.Internat ional trade in a two-country world can now be introduced very easily.Let countries A and B have identical technology and growth rates of the effectivelabor force. The population sizes may be different but for simplicity can be putequal to each other (it is trivial to allow for size differences). The only respect inwhich the economies differ is then in the savings propensities with s a > s b.In Figure 2.7 the QQ curve remains unchanged since it depends only on theidentical technology. The S S a n d M M curves will be different since they dependon the savings propensities. It is easy to see that the S S curve for A will be to theright of the S S curve for B while the M M curve for A will be above the M M curvefor B at equal values of k. Thus, in autarky, the high-saving country A will have ahigher equilibrium capital-labor ratio than the less thrifty B. The relative price ofthe labor-intensive good, the investment good, will be higher in A than in B underautarky.

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210 R. FindlayTrade in an integrated world market without borrowing and lending implies

that while saving must continue to equal investment in each economy separatelythe same is not t rue for the output of investment goods. The equil ibr iumcondit ion (2.3.5) for the closed econom y is replaced b y

S a Ya (P, ka ) + S b Yb (P , kb) = q a ( P , k a ) + q b ( P , kb)" (2.3.10)The equil ibr ium value l / p * for the world economy is determined at the point

where S S w, the S S curve for the world economy which is the simple average ofS S a and SS b, cuts the Q Q curve. This determines k* and k~ from S S a and S S bfor p = p* . Th e cap ital- lab or rat io for the world k* is the average of k* and k~.The M M w curve, the momentary equil ibr ium curve for the world economyshowing the combin at ions of p and ( k a + k b )/ 2 that sat isfy (2.3.10) passesthrough the long run equil ibr ium poin t (p* , k*) , cut t ing Q Q f rom above. Theworld economy thus behaves l ike a single closed economy, moving along i tsmomentary equil ibr ium curve and converging to the steady state .

International trade thus equalizes relative product prices and, assuming thatboth countr ies are not special ized in production, factor pr ices must be equalizedalso. The thr if ty and hence capital-abundant coun try A exports the capital- inten-sive consumption good while the labor-abundant B exports the labor- intensiveinvestment good. Note that t rade increases the capital- labor rat io of A above it sautarky level, while reducing that of B below i ts autarky level. The pre-trade

S W

. . . . . . . - - _ - - -~ - - z s : :MTM" - ~

Q J i S b

Q/ W

i \! \w l suI s

k~, k;Figure 2.7

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Ch. 4: Growth and Development in Trade Models 211differences in factor proportions, that give rise to trade, are themselves accentuatedas a result of trade.

It is interesting to note that the same effects of trade on capital stocks and percapita consumption levels as in this neoclassical growth model can also beobtained in stationary models with alternative technologies but in which factorproportions are also endogenously determined instead of simply taken as fixed asin the usual models of comparative advantage. An example is the "Austrian"model of Findlay (1978). In this model the country that has the lower rate of timediscount at any given stationary level of consumption has its per capita consump-tion and capital stock increase as a result of trade while those of its more"impatient" partner fall.

Further investigations of the dynamic two-sector neoclassical model are pro-vided in Hanson (1971), Fischer and Frenkel (1972, 1974) and many other papersFischer and Frenkel introduce t rade in debt (financial instruments) into the modeland link it in interesting ways to the "states of the balance of payments" an ideagoing back at least to J.E. Cairnes and expounded by Kindleberger (1968). Atechnical innovation that they introduce is an "adjustment costs" investmentfunction to break the indeterminacy that would otherwise occur in a small openeconomy's portfolio choice between physical capital and financial assets. Someother papers in this area that should be mentioned are Borts (1964), Hamada(1966), Onitsuka (1974) and Hori and Stein (1977). A very simple and analyticallyappealing model that considers many of these issues in a neat and concise fashionhas recently been presented by Ruffin (1979), who considers capital mobilitybetween two Solow economies that each produce the same good but with differenttechnologies and saving rates. Ruffin's model is extended to economies thatproduce different goods, with interesting consequences for the relationship be-tween capital mobility, the terms of trade and welfare in the steady state bySaavedra-Rivano (1982, ch. 1).

The relationship between money and growth, analyzed in the dosed economyby Tobin (1955) and others, has also given rise to some literature on the openeconomy. Examples are Allen (1972), Frenkel (1971), Find lay (1975) andRodriguez (1982). The last two papers consider two-sector growing open econo-mies in steady-state equilibrium, with given rates of monetary expansion in eachcountry. Rodriguez proves that under flexible exchange rates an increase in therate of monetary expansion by one country will raise its own capital-labor ratioand lower that of its partner, the net effect on the world capi tal- labor ratio beingpositive. The monetary and "real" sectors are therefore linked and money istherefore not a mere "veil" as in the usual static formulations, for reasonspointed out dearly by Marty (1961). This result is shown to hold not only forad hoc savings functions but also with intertemporal utility maximization byconsumers, under some restrictions on the demand functions for real balances.

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212 R. Findlay3. Development and asymmetrical interdependenceIn contrast to the tidy and systematic character of the "growth and trade"literature that has been our concern up to now the "t rade and development" areapresents a rather chaotic appearance, rich in historical anecdotes and intuitiveinsights but lacking any unified framework. Political preconceptions abound andpassions run high, with most mainstream economists favoring "outward looking"strategies and policies of development and most radicals stressing the dangers ofdependencia and consequently advocating "inward looking" policies and strate-gies to promote "self-reliance". The analytical task of assessing the relative costsand benefits of import substitution and export promotion as development strate-gies is in Anne Krueger's domain (Chapter 11) and I am happy to leave it in herexpert hands. My own task here I conceive to be the examination of the moreformal and theoretical aspects of the t rade and development literature, relating itwherever possible to the main body of trade theory, whether as "exception" or"rule". 5

The restriction to those aspects of the field that have undergone some formaldevelopment unfortunately excludes from discussion here many issues of greatimportance and interest. One example is the literature that has been inspired bythe historical development of export economies, which Myint (1958) has relatedto the "vent for surplus" view of foreign trade advanced by Adam Smith. Caves(1965) discusses these ideas in relation to the "staples thesis" of Canadianeconomic historians such as H.A. Innis. Also relevant in this connection are twopapers by Baldwin (1956, 1963) related to the development of mining economiesin Southern Africa. The work of all these authors is rich in insights andsuggestions that as yet await further analytical development. The technologicalcharacteristics of the major export products, the role of foreign capital, labor andentrepreneurship, the links between the modern export sector and the tradit ionalagrarian economy are all in principle capable of being modelled analytically onthe basis of the work already done by Baldwin, Caves and Myint.

3. 1. Wage differentials and infant industry protectionThe oldest controversial proposition in the field is of course the famous "infantindustry" argument of Hamilton and List, taken up by Mill and Bastable, thatmanufacturing in "young " countries should be protected until it could competeon an equal footing with the pioneers. During the inter-war years the RumanianManoilesco (1931) pu t forward the thesis that protect ion to indus try was justified

5See Nurkse (1961) and Kravis (1970) for moderate and balanced statementsof the "pessimistic"and "optimistic"positions respectivelyon the empirical aspects of the trade-developmentnexus andthe associatedpolicy mplications.

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Ch. 4: Growth an d Development in Trade M odels 213in less developed regions because the substant ial ur ba n-ru ral wage different ial inthose countr ies was a handicap that required off-set ting by a tariff . His boo k wasreviewed by n o less emin ent authorities than Viner and Ohlin, the latter giving, ina few sentences, the complete modern answer to the problem which is that theapprop riate intervention to off-set the distor t ion was a w age subsidy to manufac-tur ing and not a tariff . The Mano ilesco argument was taken up again af ter Wo rldWar II by Lewis (1954) , whose dual economy model gave the wage different ialargument an analyt ical underpinning by making the urban wage and hencemarginal product of labor , equal to the average product of labor in rural familyfarms and hence greater than the marginal product of labor in agr icul ture. Theargument was taken u p in a more formal way by Haberle r (1950) and H agen(1958), f inally leading to the emergence of a full-fledged theory of optimalintervention in the presence of domestic or foreign "distor t ions" in the work ofthe Delhi Trio of Jagdish Bhagwati, V.K. Ramaswami and T.N. Srinivasan, aswell as by Harry Johnson and Max Corden, whose chapter in this volume wil lcover this topic ful ly. Here al l I wish to do is to point out that a "development"problem has given r ise to a major extension of normative trade theory. Formaltrade theorists , who tend to scorn the development f ie ld for i ts messy andunrigorous character , should take note.

Another important but rather neglected formal extension of t rade theoryinspired by the infant industry problem is the work of Bardhan (1970, ch. 7) on"learning by doing" in a small open economy, inspired by the famous model ofArrow (1962). Consider an econo my endo wed with f ixed quantit ies o f capital andlabor , producing two goods, agr iculture A and manu factures M , the relat ive pr iceof which is f ixed from abroad. The agr icul tural production function is s implyconstant returns to scale in capital and labor but the manufactur ing productionfunction is of the form:

M = Q n F m ( K m , Lm) , (3.1.1)in which Q is the cumulat ive volume of outpu t of M so that

{ ) = M . ( 3 . 1 . 2 )The parameter n is a posi t ive f ract ion so that the elast ic i ty of output with

respect to "experience" Q is less than unity. The eco nom y's t ransformation curveshif ts over t ime, purely due to the effect of "experience" in raising productiv-i ty in manufactur ing, growth of the labor force and capital accumulat ion beingassumed away for simplici ty.An optimal c ontrol pro blem is posed, the object ive funct ion b eing the integralof the discounted f low of ut i l i ty f rom consumption of the two goods, assumed tobe homothetic , subject to balanced trade with the rest of the world at a f ixed

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214

relative price 7r, and a "dynamic" equation:R. Findlay

= M - 8Q, (3.1.3)in which 8 is the fixed rate at w hich experience depreciates or "forgett ing" occurs.The discount rate 8 is also assumed to be fixed. The necessary conditions for amaximum are easily seen to require that the marginal rate of substitution betweencapital and labor be equalized between industries i .e. for given Q the economyshould produce on i ts t ransformation curve and that the marginal rate ofsubstitutio n in con sum ption of A an d M be equa ted to ~r, the terms of trade. T hemarginal rate of transformation in production, however, should no t be equated tothe terms of t rade since production of M, in addit ion to direct ly contr ibuting toutil i ty by m aking m ore consum ption possible , a lso adds to experience and henceprovides a social benefit in enhancing future productivity. This positive external-i ty cannot be cap tured b y any single f irm in competi t ive industry and so we havethe result that the manufacturing sector would be too small under laissez faire.What has to be added to the marginal product of both capital and labor inmanufacturing is therefore the shadow price of the additional experience that isproduc ed. De notin g the marginal utility of M and C by/~ and 2% and the shadowprice of experience in term s o f utility by ~,, the marginal produ ctivity o f capital interms of utility in each sector is equated when

I z + y O A / n OM~ - a / Q = M R T ,OK,. (3.1.4)whereas

I I OU / OU- = M R S = ( 3 . 1 . 5 )O C m / O C a

The social ly optimal MRT therefore differs f rom the social ly optimal MRS by,/X, which yields the optim um subs idy ~" on ma nufact uring ou tpu t so that M R Tequa ls (1 + r)~r instead of ~r as it wou ld u nde r laissez faire. The Lag rangia ns/~and X are constants by vir tue of the a ssumption that the ut i li ty function ishomothetic but ~,, the shadow price of "experience", changes over time with thelevel of the stock, so that r also changes over time. Bardhan shows that theoptimal solution follows a saddle path converging to a stationary solutionchara cterized by Q and "y bein g at values Q * and ~,* that satisfy:

Q " Fm = ~Q, (3.1.6)(/~ + y ) r * /zr* (3.1.7)

"Y ( p + 8 )

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Ch. 4: Growth and Development in Trade Modelswhere

215

r * = n Q " - l F m = n 3. (3.1.8)is the marginal productivity of experience in manufacturing evaluated at Q*. Thestock of experiences is constant when the current output of manufactures is equalto the rate at which experience depreciates. The shadow price of experience "/*determined by (3.1.7) is equal to the current " flow" (/~ + 3')r* "capitalized" bythe sum of the discount rate and the rate of depreciation. The optimal subsidy r*in the stationary solution is given by:

r* Y* n3I ~ O + ( 1 - n ) 3 ' (3.1.9)which varies inversely with p and directly with n and 3 as one would expect.When Q < Q* it will follow that 3' > 7" and the shadow price of experience andhence r will fall over time towards r*.

Notice that the analysis is quite independent of whether manufactures areimported or exported. It is in fact consistent with manufactures being initiallyimported and later exported so that the infant can indeed grow up. The point isthat it is manufacturing output that should always be subsidized, since it is thisthat contributes to experience and provides the externality, rather than imports orexports of manufactures. Bardhan also modifies his analysis to account forcumulative output ceasing to influence productivity after a certain level isreached, so that the output subsidy need not be permanent in this case.

Related work in this area has been by Clemhout and Wan (1970) and Teubal(1973).

3. 2. Two-gap models and expor t -led growth

The early literature on development tended to emphasize domestic saving as themajor constraint on the growth rate that an LDC could achieve. This view aroseout of the wide-spread application of the Harrod-Domar model to problems ofdevelopment planning. The experience of many LDC's in the sixties, however,indicated that the balance of payments situation tended to be a critical constrainton the rate at which capital accumulation and development could take place.Hollis Chenery, who occupied influential advisory positions at the official USforeign aid agency and later at the World Bank, put forward a simple frameworkin which, depending upon the values of a few parameters, a particular LDCwould be identified as having its growth rate constrained by either a "domesticsavings" or a "foreign exchange" gap. "Two-gap" models, as they came to be

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216 R. Findlaycalled, were very much in vogue in the sixties and early seventies though interestin them a ppea rs to have dwindled in recent years. Che nery and Brun o (1962), andChenery and Strout (1966), are perhaps the most representative papers by theoriginator of this approach, McKinnon (1964) provides a detailed formalizationand Find lay (1973, ch. 10) an expos ition and critique of the logical basis.

The essential idea of the two-gap approach can be brought out with the aid ofFigure 3.1. Suppose that domestic output depends only on the capital stock,initially given. The distance O Y measures domestic output , which can be ex-changed at a fixed rate for imports of capital equipment. Total consumption issimply a f ract ion of domestic output and is equal to O C. Domestic investmentrequires imported capital equipment and the domestic good in f ixed proport ions.Levels of investment are indicated by a family of L-shaped isoquants with C asthe origin. The given propensity to save, C Y / O Y , determines V X as the amountof imported equipment, X Y the export of the domestic good required to pa y for i ta n d C X the domestic componen t of investment. The growth rate of output will beequal to the ratio of investment, the level corresponding to the isoquant at V,divided by the capital stock, assuming that the marginal and average capital-outpu t rat ios are equal. This is just a modif icat ion of Ha rro d- D om ar to an openeconom y, in which grow th is constrained b y the savings rate.

Assum e now that the maximum level of imports obtainable is U Z , regardless ofthe level of exports. This reduces the attainable level of investmen t to the iso quantat U. Exports of T Y will be sufficient to pay for the imports of capital equipment

.go0(. 9

g

0 C Z X YNational Income

Figure 3.1

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Ch. 4: Growth and Development n Trade Models 217and so Z T of domestic output will be "redundant" in the sense that it cannot beused for investment, either directly or through exports. The "foreign exchange"gap will be measured by V W , the difference between V X and U Z , while thesurplus of potential domestic saving is Z T .

Foreign aid is more growth-promoting when it is given to an LDC whosegrowth is constrained by the shortage of foreign exchange rather than bydomestic savings. In Figure 3.2 let the amount of foreign aid be measured by Y Y ' .If growth is constrained by savings investment will increase from V to V'. Noticethat all of the foreign aid will not be used to import capital equipment since X X 'of domestic output will be shifted from exports to the domestic component ofinvestment, to provide the complementary input for the additional capital equip-ment that is imported. When growth is constrained by the shortage of foreignexchange, however, all of the foreign aid can be used to increase imports ofcapital equipment, since domestic output for investment is available in the formof the otherwise redundant supply of domestic saving.

The foreign exchange gap can also be introduced into a simple mathematicalmodel. Let Y be domestic output, X exports, m the propensity to importconsumer goods and a the incremental output capital ratio. Assume that exportearnings increase over time at a constant rate g. We can therefore write:

d Y = ot[ X o e g t - m y ] (3.2.1)dt

C. )

EH

0 C XNational

X' YI ncome

Figure 3.2

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218 R. Findlaywhich is a simple differential equation that can be integrated to yield:

Y(t)=(g?am)Xoegt+{Yo (gLm)Xo}e-amt, (3.2.2)which shows that the growth rate of output will approach the growth rate ofexports in the limit. This is one meaning that can be attached to the rather looselyused term "export-led growth" in the development literature.

These simple examples that we have given illustrate a crucial limitation of thetwo-gap approach, which is its almost complete neglect of relative prices and alsoits tendency to assume that the constraint on the ability of LDCs to earn theforeign exchange that they undoubtedly need for economic development isexternal demand and not domestic supply. The external environment is similar towhat would be faced by an economic system that is undergoing a siege or ablockade. The experience of the expanding world markets of the sixties andseventies completely contradicted this ultra-pessimistic assumption about theexport possibilities of the LDCs.

3.3. The open dual economyThe issues connected with "export-led" growth have also been pursued within thecontext of the celebrated 1954 Lewis model of economic development withunlimited supplies of labor. Though Lewis himself has not "opened up" his ownanalysis of capital accumulation in an economy characterized by a fixed realwage, preferring to use instead the three-good Ricardian model described earlierin this paper for his analysis of the terms of trade, other writers have introducedtrade explicitly into this model in various ways. Examples include Fei and Ranis(1964), Hornby (1968), Dixit (1969), Bardhan (1970), Lefeber (1971), Paauw andFei (1973) and Findlay (1973).

One set of problems that have been posed in the context of an open dualeconomy is connected with long-run development strategy when the "modern"sector is controlled by a planning authori ty while the "tradi tional" sector consistsof small independent peasant producers. This situation is a relevant one for manycontemporary economies in S.E. Asia and Africa and is also similar to the SovietUnion in the twenties, except for the fact that foreign trade was not of anysignificance. The issues of "primitive socialist accumulation" debated at that timeby Bukharin, Preobrazhenski, Feldman and others and vividly discussed by Erlich(1960) cont inue to be relevant to contemporary developing economies and havebeen analyzed, with more sophisticated tools, by Hornby, Bardhan, Dixit andFindlay in the contributions listed at the end of the last paragraph. All of thiswork has also been influenced by the literature on development strategy andplanning by Maurice Dobb, A.K. Sen, P.C. Mahalanobis and Evsey Domar.

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Ch. 4: Growth and Development in Trade Models 2 1 9Among some of the specific issues examined in the open dual economy contextare the problem of the optimal "internal" terms of trade, or rate at which the

peasant sector should be taxed to finance capital accumulation in the modernsector, the optimal allocation of resources between capital goods and consumergoods in the modern sector itself and the optimal role of foreign trade in thedevelopment of the open dual economy over time. Findlay (1973, ch. 9) analyzesthis last problem in terms of the "turnpike" theorem that Dorfman, Samuelsonand Solow derived from the model of Von Neumann. This application predatesthe simpler application of the Von Neumann model to an open economy bySteedman (1979, ch. 13).

The composite production function for tradeable goods, used to extend theSolow-Swan model to an open economy in the previous section, is again thesimplest way in which to perform the analogous operation for the Lewis model,which can be thought of as a one-sector Von Neumann model. In Figure 3.3 theright hand panel is the factor-price frontier corresponding to the composite"foreign exchange" production function, which yields the rate of profit corre-sponding to the fixed real wage ~. The left-hand panel indicates the linearrelationship between the profit rate to and the growth rate g determined by the"Anglo-Italian" equation g = op where o is the propensity to save out of profit,the entire wage being spent on consumption. The growth rate of a small opendual economy therefore varies inversely with the real wage, directly with thepropensity to save out of profit a