smithian growth

8/13/2019 Smithian Growth

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A Formal Outline of A Smithian Growth ModelAuthor(s): Haim BarkaiSource: The Quarterly Journal of Economics, Vol. 83, No. 3 (Aug., 1969), pp. 396-414Published by: Oxford University PressStable URL: http://www.jstor.org/stable/1880528.

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A FORMAL OUTLINE OFA SMITHIAN GROWTH MODEL *

HAIMBARKAII. The aggregate production function, 396. II. The determinants of thestate of technology, 398. III. The long-run pattern of social product, 400.-IV. Capital and the profit rate, 404. -V. Investment and saving, 406.- VI.Saving, investment, and Say's law, 408.- VII. The pattern of growth, 410.-VIII. The availability of resources for investment, 412.

Smith's vision of the economic system as an entity which couldbe represented by a small set of variables and their interrelatedfunctional relationships - social product, labor, capital, technology,"accumulation" (investment), saving, the profit rate - is the con-ceptual framework of aggregate economics to this day. In whatfollows below, we attempt to single out the strategic hypotheses andtheorems of his growth model, and restate them formally. We canthus study the nature of the relationships involved, follow the linkswhich forge the various building blocks into a whole, and finallytrace the workings of the integrated structure.The specification of the Smithian aggregate production func-tion indicates the dominant role attributed to capital, and the stra-tegic position of technology, specified as an endogenous variable, inhis scheme. An analysis of the saving relation shows that it is dif-ferent in a crucial sense from the conventional saving function at-tributed to the classics. The properties of the (implicit) investmentfunction, and the assumed saving investment relationship bringsinto the open a specifically Smithian version of Say's law. Finally,the study of the time pattern of the model as a whole clarifies thesignificance of the Smithian version of the "infinity" of invest-ment outlets hypothesis. This puts Smith's belief in the eternalityof economic progress into its proper conceptual context.

I. THE AGGREGATEPRODUCTIONFUNCTIONSmith identifies scarcity as the fundamental economic factfacing society and thus underlines the nature of the resource restric-tion which limits the size of the social product. He also clearly* The comments of J. Atieh on several drafts, and of D. Levhari and thelate R. Szereszewski on an early draft are gratefully acknowledged. Thanksare also due to an anonymous referee for helpful criticisms.

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A SMITHIAN GROWTHMODEL 397specifies the variables which determine its level. The nature of thisbasic relationship is forcefully put in the Wealth of Nations, asfollows:... the annual produce of the land and labour of the country .... can neverbe infinite but must have certain limits .................................[It] can be increased in its value by no other means, but by increasing eitherthe number of its productive labourers, or the productive powers of thoselabourers who had before been employed. The number of its productivelabourers . .. can never be much increased, but in consequence of an increaseof capital .... The productive powers of the same number of labourers can-not be increased, but in consequence either of some addition and improve-ment to those machines and instruments which facilitate and abridge labour;or of a more proper distribution of employment. In either case an additionalcapital is almost always required .... When we compare, therefore, thestate of a nation at two different periods, and find, that the annual produceof its land and labour is evidently greater at the latter than at the former ...we may be assured that its capital must have increased during the inter-val.... 1

Capital and technology are both specified as strategic deter-minants of aggregate product - the relevance of the latter and itsdependence on endogenous variables of the model are particularlyunderlined. The Smithian aggregate production function accord-ingly relates social product to capital, labor, and the state of tech-nology. Thus, writing Y for social product (national income), andK, N, and T for capital, labor, and the state of technology respec-tively, we have:(1) Y=Y[K, N, T(t, m)]where Y is assumed to be an increasing function of each of its argu-ments.

To trace the leading strains of Smith's argument, in whichcapital has been cast into a major role, it is advisable to follow hislead in diagrammatical presentation. In Figure I (p. 405) we thusmeasure the stock of capital and of social product on the horizontaland vertical axes respectively. The rising product curve such asY(Ta) in Figure I represents obviously one section only of the pro-duction surface specified by equation (1). Since Smith does notoffer a proposition on the rate of change of product in response to

1. A. Smith, The Wealth of Nations, ed. E. Cannan (New York: ModernLibrary, 1937), pp. 315 and 326. The italics are mine. Subsequent referencesto the Wealth of Nations will refer to this edition. Most elements of thissummary statement on the nature of the aggregate relation between inputsand outputs are repeated by Smith elsewhere.



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398 QUARTERLY JOURNAL OF ECONOMICSthe growth of one input - others constant - any form of risingproduct curves would be consistent with his approach.

Smith also never assumed fixed capital-labor ratios - theclassical concept of a dose of capital and labor is alien to his ap-proach. He definitely allowed for changes in capital-labor ratios,and thus for corresponding changes in the level of product in re-sponse to a change in the size of the labor force only. A change inthe size of the labor force, ceteris paribus, would be expressed by acorresponding shift of the product curve in Figure I. The severalproduct curves in Figure I could thus represent alternative productlevels due to differing sizes of the labor force for given levels ofcapital.

II. THE DETERMINANTSOF THE STATEOF TECHNOLOGYChanges in the state of technology affect the relevant product

curves of Figure I similarly -they will shift in response to cor-responding changes in technology, from say Y(Ta) to Y(Tb). Twoaspects of this variable are identified -the "extent of the market"and what could be dubbed as the "technical efficiency of equipment."Each of these two determinants of the state of technology are re-lated to other endogenous and exogenous variables.A. The Extent of the Market

Smith underlines the strategic relevance of the size of the mar-ket to the state of technology in his well-known title of ChapterThree of Book I of the Wealth of Nations - "That the Division ofLabour is Limited by the Extent of the Market." Institutional andpolitical factors and the level of social product, are specified as thedeterminants of the "extent of the market."The reduction in the barriers imposed on foreign trade - apolitical and hence an exogenous determinant in our context -isrepresentative of the set of institutional factors.2 The hypothesiswhich specifies the dependence of the size of the market on socialproduct is forcefully put as follows:... the revenue of all the inhabitants of the country is necessarily in pro-portion to the value of the annual produce of their land and labours; . . . Thegreater the . . . revenue of the inhabitants . . . the more extensive is themarket . .. 3

2. See Wealth of Nations, p. 415.3. Ibid., pp. 347, 356.



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A SMITHIAN GROWTH MODEL 399Writing m for the extent of the market, we have accordingly:(2) m=m (Y) and m'(Y)>O.The extent of the market increases with the increase of social prod-uct, and also in response to changes in the institutional data. Thelatter change would be expressed in terms of a change in the formof the function specified in (2).An increase in the stock of capital which according to theproduction function generates an increase of product, thus triggersoff the technology mechanism through the extension of the marketaccording to (2). In terms of Figure I this means that an increasein the stock of capital from, say, Ko to K1 implies not only a movealong a product curve such as Y (Ta). In response to a change intechnology induced by the extension of the market the curve itselfshifts upwards at one and the same time to, say, Y (Tb). The prod-uct corresponding to K1 is accordingly Y2 at B on Y (Tb) and notYj on Y(Ta), which would have been its value in the constant tech-nology case.4B. The Technical Efficiency of Equipment

Consider now the other facet of technological change -theincrease in the technical efficiency of equipment-"improvementto those machines and instruments which facilitate and abridgelabour" as Smith put it. In addition to inventions induced by "phi-losophy and speculation" both of which are exogenous factors, Smithunderlines the relevance of capital, as a crucial determinant in thiscontext. He writes:. . labour can be more and more subdivided in proportion only as stock

is more and more accumulated .... and as the operations of each workmanare gradually reduced to a greater degree of simplicity, a variety of new ma-chines come to be invented .... in order to give constant employment to anequal number of workmen, an equal stock of provisions, and a greater stockof materials and tools than what would have been necessary in a ruder stateof things, must be accumulated beforehand.5

4. This formulation pinpoints at once the reversibility dilemma. Thus,what happens if capital decreasesfrom K1 to Ko? Would this shift the productcurve back from Y(Tb) to Y(T.), or is technological change nonreversible?In the latter case, income would not fall to Yo n responseto a reductionin thesize of capital K -it will decrease to Y', on Y(Tb) only.Though valid analytically and of some historical significance videthe universal decline in the state of the arts in the wake of the dissolution ofthe Roman Empire-the reversibility issue seems to be out of context in aSmithian growth model, the focus of which is capital accumulation.5. Wealth of Nations, p. 260.



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400 QUARTERLY JOURNAL OF ECONOMICSThe "technicalefficiency"of equipmentis accordinglyspeci-fied as an increasingfunctionof the capital-laborratio. Writing tfor the technicalefficiencyof equipmentwe have accordingly:

(3) t -t ;and t ( )> 0."Technicalefficiency"(of equipment) increases with the in-creasein the ratio of capital to labor. It also increases n responseto "inventiveness"nducedby pure speculationor by the ingenuityof the men on the job. The latter are exogenousvariables. If they

vary this will changethe form of the technical efficiency unction(3). The impactof institutional and social factors,and of motiva-tions, which Smith identified, among others, as relevant determi-nantsof specialization,will also changethe formof (3).6Capital accumulation,when it involves also an increasein thecapital-labor ratio, thus brings into motion technology via thesupply facet of economicactivity, accordingto (3). In terms ofFigure I, this, similarly to the extent of the market case, impliesthat an increase of social capital does not signify only a movementalong a product curve such as Y(Ta). If accumulationoutpacesthe growthof the labor force, it may also imply an upwardshiftof the curve itself.

III. THE LONG-RUN PATTERN OF SOCIAL PRODUCTA. The Long-Run Product CurveLet us now put together the various building blocks of theSmithianmacroeconomic onceptof production, pecified by (1) -the production unction,and by (2) and (3) -the relationswhichspecify the endogenousdeterminantsof technology.This set of equations sets the equilibrium pattern of socialproductin a context of continuous"accumulation."Thus, an in-creasein the size of capital stock, generatesaccordingto the pro-duction function an increase in product. Since by (2) a higherproduct level implies an increase in the extent of the market, ac-cumulationnducesconcomitantlychanges n technology. The tech-nology argument n the productionfunction, therefore, pushes thelevel of product beyondthe point which it would have reached in

6. An interesting study of this facet of Smith's analysis of the determi-nants of the division of laboris given in N. Rosenberg,"Adam Smith on the Di-vision of Labour: Two Views or One?"Economica, XXXII (May 1965).



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A SMITHIAN GROWTH MODEL 401responseto the growthof capital stock under the conditions of agiven technology.The growthpotential of social product due to the direct im-pact of capital on product, and to its indirect effect in responseto extensionof the market, may be even greaterthan the one notedabove. This will happen if the growth of the capitalstock proceedsfaster than that of the labor force. The resultant rise in the ratioof capital to labor, increases, by (3), "the technical efficiency ofequipment." This pulls the technology argumentof the productionfunction upwards, and correspondinglygenerates an even greaterproductfor the givenlevel of capital stock.The same argumentcouldbe put in terms of FigureI. Supposethat the capital stock grows from Ko to K1. Output would thusincrease from Yoto Y1 on the Y(Ta) curve. This, however, doesnot take into accountthe effect of changes in these two variableson technology. This increase n product ncreases,by (2), the valueof m which pulls the productcurveY(Ta) upwards romits originalposition. This upward motion may or may not be reinforced,byforces emanating from the technical efficiencyrelationship (3),according o the ensuing changein the capital-laborratio.Thus investmentwhich increases productiondirectly activatesat one and the same time a technologyvariablewhich pushesthecurveupwards, o a level of say Y(Tb). The correspondingncreaseof income in response o the growthof capital stock fromKo to K1is (Y2- Y0), of which (Y2- Y1) may be attributed o induced ech-nological change.

The Ye curve,joining points like A, B and C, drawninto thecapital product plane of Figure I, is accordingly the long-runcapital-product urve. It expresses he direct and indirectresponseof the entireproduction urfaceto "accumulation."Changes n theexogenousvariables such as relaxation of feudal and mercantilerestrictions,or spurtsof inventive activity broughtabout by "purespeculation"of the late eighteenthcentury genre affect the formof technologyrelations (2) and (3), and hence the location of the(constant technology) productcurve similarly. A change inducedby any of these exogenousparameterscould obviously also shifta curve as Y(Ta) towards Y(Tb) or Y(T,).

7. Smith's well-known comparisons of China and England could beeasily understood by means of this apparatus. The former country's productcurve for given levels of the capital stock may be lower due to institutionalfactors such as strict restrictions of foreign trade, difficulties in the legal en-forcement of contracts, and the nature of Chinese abstract speculation whichconcentrates on semantics and shies away from natural philosophy. Theseimply low values of m and t and correspondinglyof product.



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402 QUARTERLY JOURNAL OF ECONOMICSB. The Long-Run Capital Product Curve - A Special Case

A special case, for which we could specify the structural subsetof relations (1), (2) and (3) may offer additional insights on theproperties and feasible values of the strategic parameters of theSmithian long-run capital product curve -the Y curve of FigureI. Thus, assume a Cobb-Douglas constant returns aggregate pro-duction function(1') Y=TKa Ni-a.Assume also that the extent of the market, one of the determinantsof technology, is proportional to the current size of per capita prod-uct. We have accordingly

y(2') m = a - where0 < a


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A SMITHIAN GROWTH MODEL 403This expression, deduced from the structural relations, reflects theSmithian equilibrium values of social product corresponding to thevalues of the endogenous technology variables and to the exoge-nously given parameters. The expression is finite and positive only ifthe denominator is positive, and this requires that the factorac( -) shouldbe smallerthan unity.

Assume now that a, the extent of the market coefficient, is notsignificantly different from unity. This premise, which means thatmost of any additional income is spent, is a dominant feature ofSmith's approach, and imposes a restriction on the value of c, the(total) technology coefficient. The latter must be significantlysmaller than unity, unless the capital-labor ratio, and the elasticityof product with respect to capital are very small.

With a capital-labor ratio of say 2 and a of about 0.3, to usesome empirically relevant orders of magnitude, the denominator of(1") would approach zero if c is of an order of 0.7. It will turnnegative if larger than that. If we do not assume that the systemexplodes, in other words, that capital formation will generate atonce an infinite growth of product, we must assume values of cwhich are significantly smaller than 0.7. This restriction on thevalue of c -the technology coefficient, underlines the nature of abasic restriction imposed on technology. Induced technologicalchanges must be assumed to be small.9

This result holds presumably for any form of the aggregateproduction function. The specific case presented here underlinesthe induced effect of capital accumulation on technology. Thedistinctive feature of this process is thus not only its direct impacton production, but also its multiplicative effect on the productionpotential due to induced technical change. The latter implies a so-called "technology multiplier" as an element of the model.

9. The form of the extent of the market function (2') adopted above,where the extension of the market is assumed to be proportional to thechange in per capita income, is not the only one consistent with the Smithianhypothesis. A more general form would be one which assumes that the extentof the market is an increasing function of social income. In the latter case,though not in the case studied in the text, an increase in social income whichleaves per capita income constant would activate the technology factor ofthe model. This, however, does not change the nature of the results deducedon the basis of the more restrictive assumption. It rather strengthens theconclusion that for a stable system induced changes in technology must beassumed o be small.



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404 QUARTERLY JOURNAL OF ECONOMICS

IV. CAPITAL AND THE PROFIT RATE

The capital-profit-rate relationship, the "law of the fallingprofit rate" in the terminology of classical economics, is obviouslya strategic element in Smith's model. The property of this relation-ship is concisely stated:The increase of stock ... tends to lower profits . .. The diminution of thecapital stock of the society . . . raises the profit of stock.1

Unlike West and Ricardo, who deduced the law of the fallingprofit rate from their hypothesis on the diminishing returns propertyof the production function in agriculture, Smith does not derive thisrelationship from an underlying productivity hypothesis. His rea-soning is in terms of the common-sense rule of competition:As capitals increase in any country, . . . there arises in consequence a com-petition between different capitals, the owner of one . . . can hope to justlethat of the other out of . . . employment, . . . by dealing upon more reason-able terms. He must not only sell . . . somewhat cheaper, . . . he must some-times too buy ... dearer .... profits which can be made by the use of acapital are in this manner diminished ... at both ends. ..2

Smith, who does exclude diminishing returns as an explanatoryvariable, nevertheless assumes the relevance of an economic vari-able per se in this context - the nature of demand for final prod-ucts. A negatively sloped market demand curve, does obviouslyimply lower price in response to an increase in supply - and hencegenerates a downward pressure on the price for factors. Thus thoughthe Smithian profit rate theory is seriously weakened because of theabsence of an explicit background productivity hypothesis, it isnevertheless anchored within the conceptual framework of economicbehavior.3

Profits, are, by implication, related also to one other endogenousvariable of the model - technology. In the course of his discussionon "Inequalities of Profit" Smith makes the following remark:The establishment of any new manufacture ... of any new practice in agri-culture, is always a speculation from which the projector promises himselfextraordinary profits .... If the project succeeds, they are commonly at

1. Wealth of Nations, pp. 87, 94.2. Ibid., pp. 336-67. In the course of a historical survey of colonizationthough, Smith makes a passing reference to productivity as a determinant ofprofit. He writes: "When the most fertile and best situated lands have allbeen occupied, less profit can be made by the cultivation of what is inferiorboth in soil and situation."Ibid., p. 93.3. The macroeconomic behavioral hypothesis which Smith uses here,is admittedly somewhat out of place in the macroeconomic context of theprofit rate discussion.



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A SMITHIAN GROWTH MODEL 405

y(...Tc)y

-- y~~~~(..Tb) y So(y) Sy

.I Y8 Sy(..To7C.

-O - - - ----- Yo/yo -~AY /I /

Figure I IKo Kd K Figure ; I ? Sl I

'IO~~~~

Ko K Io__ _Figure m Figure 1Z

FIGURE I-IV

first very high. When the trade or practice becomes thoroughly established. . . competition reduces them to the level of other trades.4This statement definitely indicates that Smith did visualize thatprofits and hence the profit rate, for specific projects, do rise inresponse to a change in technology -the latter being identified aseither a change in the method of production, or in the product mix.Moreover, he identifies this (expected) rise as the very mechanismwhich attracts resources into these novel activities.The statement leaves admittedly one crucial point open: Itdoes not indicate the direction in which the equilibrium profit rate

4. Op. cit., p. 115.



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406 QUARTERLY JOURNAL OF ECONOMICSmay be expected to move in response to changes in technology. Theobservation made in the last sentence of the above passage that theinitially extraordinary high profit rates due to changes in technologyare in due course reduced to "the level of other trades," does notnecessarily imply that the overall equilibrium rate itself is unaf-fected. In other words, the statement is certainly consistent withthe possibility - though this in not explicitly mentioned - that thepost-technological change equilibrium profit rate would be higherthan the pre-technological change rate. This is also fully in line withthe general bent of his thought on the implications of technologi-cal change on total product. Thus, writing r for the profit rate, theSmithian profit rate function is accordingly:(4) r=f (K, T) wherefKO.

The "law" of the falling profit rate which is expressed by thenegative sign of the derivative with respect to the first argumentof (4), is represented by the negative slope of the curve in theprofit rate capital stock plane drawn as Figure III. The level ofthis curve is determined by the value of T - the level of technology.A more advanced technology shifts the curve from, say, f (Ta)towards a curve such as f(Tb). An alternative and economicallymore meaningful way to put the same idea would be to say that thelevel of the profit rate which is consistent with a given capitalstock would be higher, the greater the value of T -the higher isthe level of technology applicable in this economy.

Smith's dicta offers no hypothesis on the rate at which theprofit rate is supposed to fall in response to capital accumulation.In other words, we have no specification on a feasible value or valuesof the slope of profit rate curves such as are drawn into Figure III.And this, though the economic implications of curves that have asmall slope (in absolute terms) are prima facie quite different fromthose of curves that have a large slope. We shall, however, arguebelow, that this point is of minor significance in the context of themodel as a whole.

V. INVESTMENTNDSAVINGA. The Investment Curve

The investment capital relation is clearly defined by Smith.He uses the contemporaneous term "accumulation" as a synonymfor our present day investment. Accordingly investment and capi-



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A SMITHIANGROWTHMODEL 407tal are by definition positively related: "the capital . . . of a nationis increased . . . by continually accumulating and adding to it." 5A relation between the profit rate and investment is to the best of myknowledge not explicitly mentioned. Yet by applying the investmentcapital relation it is possible to deduce at once a Smithian "invest-ment profit rate" relationship. Since the profit rate is a decreasingfunction of capital and the stock of the latter is positively relatedto investment -the profit rate is consequently a decreasing func-tion of investment too. Thus, we have(5) r=g(I, T) where g1(I, T) 0.

The investment curves of Figure IV - in which the profit rateand investment are measured on the vertical and horizontal axescorrespondingly, are accordingly negatively inclined. Similarlyto the case of the capital profit rate relationship, higher profitrates are consistent with the same level of investment if technologyis more advanced. Hence the upward shift of the investment curvein Figure IV, from g(Ta) to, say g(Tb) in response to changes intechnology.B. The Saving Relation

Consider now Smith's dicta on saving. The term is explicitlyused, and hypotheses relating saving to other variables are timeand again stated. Yet significantly he never specifies a relation-ship between saving and the profit rate or its money market repre-sentative -the interest rate.A conventional positive saving interest rate relation, whichhas been identified as a sine qua non of classical economics, is ac-cordingly not an inherent element of the Smithian structure. Arising saving curve which figures in the diagrammatical presenta-tions of the models of the classical economists from Ricardo onward,does not appear consequently in Figure IV.

The level of income is identified by Smith as the strategic de-terminant of saving. This point is forcefully put as follows:The capital of . . . a nation ... is likely to increase the fastest, therefore,when it is employed in the way that affords the greatest revenue to all theinhabitants of the country, as they will thus be enabled to make the greatest

5. Op.cit., p. 347.6. Blaug underlinesthis point. See M. Blaug, Economic Theory in Retro-spect (Homewood, Ill.: Irwin, 1962), p. 54. I doubt, however, whether Blaug'sstatement, made in this connection, that "Smith never suggests that saving isa function of . . . net revenue" is warranted. It is certainly inconsistent withSmith's statement quoted in the next paragraphof the text.



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408 QUARTERLY JOURNAL OF ECONOMICSsavings ... the revenue of all the inhabitants of the country is necessarilyin proportionto the value of the annual produce of their land and labour.7

Savingsis thus specifiedas a positive functionof income thesocial product. The corresponding aving relation could hence bewritten:(6) S=S(Y) whereS'(Y) >0.We have accordinglydrawn a rising saving curve into Figure II,wheresocial productand saving are measuredon the vertical andhorizontalaxes correspondingly.

The location of this curvein the saving income plane, reflectsthe (average) propensity to save, and depends on behavioral andinstitutionaldata. Smithsuggeststhat individualsdo differ in theirsaving behavior due to personal characteristics "frugals"and"prodigals" re Smith'sextreme cases. The same applied to socialand political groupings the notorious"extravaganceof govern-ment"set againstthe net frugalityof the private sector, is Smith'scase in point. Smith'swell-knownrealistic presumption hat pro-pensitiesto save out of wages, rent, and profitsdiffer significantly,impliesthat changes in income distributionalso affect the locationof the saving curve. Thus, a redistributionof income from rent toprofit would shift the saving curve of Figure IV from say Sa Y)to S(Y).Differentpropensitiesto save of entire societies and politicalentities are also mentioned,China and England serving as repre-sentativeexamples. These differencesare attributed o institutionalfactors such as the rule of law which could enforcethe sanctityof propertyand of contract and also to national characteristics.The average propensity to save varies accordingly n time and inspace.VI. SAVING, NVESTMENT,AND SAY'S LAW

Consider now Smith's handling of saving and investment.FigureIV brings nto the openthe essential element of the problem.It portraysthe demand facet of the (real) capital market in theform of a negatively inclinedinvestment-profit ate curve. It doesnot feature, however, as we have arguedin the previous section, asavings-profitrate curve. The structureof the Smithianmodeldif-fersconsequentlyon this crucialpoint from the commonrun of clas-7. Wealth of Nations, p. 347.



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A SMITHIAN GROWTH MODEL 409sical models. Yet the saving investment frameworkis the veryframeworkwhich servesin more than one sense as the heart of theseformalstructures. It is the very mechanismwhich,within a morecomprehensive ontext, settles, so to speak,the equilibrium evel ofone of the fundamentalvariables of the system the profit (in-terest) rate. To put Smith'saggregatemodel lightheartedly underthe classicalumbrella s thereforeunwarranted.The implication of the absence of a saving curve in FigureIV is therefore of far-reaching significance, since it prevents thespecificationof the equality of saving and investment as an equi-libriumconditionin the sense of an intersectionof two schedules.Yet if these two variables aresomehowmade equal,as Smith arguesthey are, they must be brought into this relationshipin the onlyalternativesense possible in termsof an identity.This is, as a matter of fact, Smith'smessageon the natureofthis relationship.It is undoubtedly he identity, and not the equal-ity, variant of the saving investment relationshipto which Smithrefers when he asserts:As the capital of an individual can be increased only by what he saves fromhis annual revenue . . . so the capital of society, which is the same with thatof all the individuals who compose it can only be increased in the samemanner .... What is annually saved, is as regularly consumed as what isannually spent.8The messageof this passage,presumablyhe most extreme n formu-lation among several others in a similar vein, is clear cut. Savingand investment at the macro - as at the micro - level are identicalall along the line. Thus we have the fundamental dentity of theSmithianmodel, namely:(7) SaI.

Hence though the income flow decomposes nto two flowsconsumptionexpenditureand a residual flow of saving Smithassumes hat the latter which "forthe sake of profitis immediatelyemployedas capital"9 generates by definition an identical expen-diture on investment. The sequenceof output-income-expenditure-output is consequentlynot liable to interruption rom the savinginvestmentmechanism. Even a growingsystemwould consequentlynever be chokedby an overflowof savings they are ipso factoinvestment. The continuously ncreasingflow of output would ac-cordinglyalways be absorbedby consumersand capitalists qua in-8. Ibid., p. 321.9. Ibid., p. 321.



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410 QUARTERLY JOURNAL OF ECONOMICSvestors. This evidently reduces to the assertion dubbed later on asSay's Law.The Smithian version is, however, an extreme version of this"law." It is obviously one thing to claim that saving could notgenerate a gap between the value of social product (at remunera-tive prices) and the expenditure flow, since the profit (interest) ratewould vary in response to any (ex ante) gap between the two soas to adjust the two flows. This "conventional" classical line ofreasoning assumes a positively sloped savings curve which, in thesavings investment plane, assures intersection of the supply and de-mand scissors. It is, however, quite a different story if, as Smith'smodel implies, the respective saving and investment curves ofFigure IV are identical so that these two are identical at any rateof interest.'In other words, the Smithian variant of Say's Law does not as-sume the existence of an economic mechanism which reacts to adisturbance by adjusting the appropriate variables -particularlythe interest rate - so as to bring these flows and hence the systeminto equilibrium. Any disturbance related to these activities isassumed away in the first place, which means in effect Say's Lawwith a vengeance.

VII. THE PATTERN OF GROWTHA. Stationary Conditions

Consider now the growth pattern of the system as a whole.Let us start from a given position - a position where the capitalstock is say - Ko (Figure I). By employing the given labor forceat the current level of technology, this generates a social productYo. Now suppose that the relevant savings curve in Figure II isthe Sa curve, which intersects the product axis at the current levelof product Yo. By the saving investment identity this zero savinglevel implies that at the current profit rate ro - read off the profitcapital curve of Figure III - investment is zero too. We haveaccordingly a corresponding investment curve such as g - in FigureIV, which intersects the vertical axis at a zero level of investment.1. This sounds queer analytically speaking, since the identity conditionand the property of the investment curve, implies prima facie a negativelysloped saving curve. This should, however, not be taken too literally. Whilstthe negatively sloped investment curve could be deduced from a backgroundstructural relation - the saving curve in the profit rate investment plane hasno behavioral significance whatsoever. This underlines the previously men-tioned lacuna in the Smithian structure.



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A SMITHIAN GROWTH MODEL 411The constant stock of capital - assuming a constant laborforce - implies constant levels of the other endogenous variables -

social product, saving, the profit rate, technical efficiency of equip-ment, the size of the market. Economic activity will accordinglybe going on in a recurrent and intermittent flow at a constant level,unless one or more of the exogenous variables - say invention in-duced by pure speculation or institutional factors such as betterenforcement of the rule of law - pull the system off this track.This is a Smithian variant of the stationary state.

Note that this account accords in more than one sense withSmith's interpretation of the case of China. His reading of thethen current economic conditions of this country are neatly formu-lated as follows:China seems to have been long stationary, and had probably long ago ac-quired that full complement of riches which is consistent with the nature of itslaws and institutions. But.this complement may be much inferior to what,with other laws and institutions, the nature of its soil, climate, and situationmight admit of. A country which neglects or despises foreign commerce ....in a country too, where, though the rich or the owners of large capitals enjoya good deal of security, the poor or the owners of scarce capitals enjoyscarce any . . . the quantity of stock employed . . . can never be equal towhat the.nature and the extent of that business might admit.2B. The GrowingSystem

Smith's statement in the passage above puts the finger on twostrategic factors which lead to stationary conditions. The one re-lates to an institutional determinant of the saving function; theother to an institutional factor which affects the "extent of themarket" and hence factor productivity. A change in any of thesetwo could start the system along a growth path.

Thus a rise in productivity due to the lifting of restrictionson foreign trade would generate a greater output for the given levelof capital Ko. Now even if the relevant savings curve in Figure IIis the same Sa curve as before, the higher income level of say Y'on Y(Tb) will generate positive saving, hence positive investment.Similarly an increase in the propensity to save, in response to achange in an institutional factor, initiated by, say, the gradual im-position of the rule of law and the sanctity of contract, would alsodo the trick. This would be expressed in terms of a shift of thesaving curve to the right and would thus generate positive capitalformation at the current level of social product Yo.

2. Wealth of Nations, p. 95. The italics are mine.



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412 QUARTERLY OURNALOF ECONOMICSLet us pursue the latter line of reasoning somewhatfurther.Thus supposethat the average propensityto save at Yo is the one

presentedby the S curve of FigureII. Savingwould accordinglybeSo, whichby (7) is identicalto 1. This investmentlevel will alsobe consistent with the ruling profit rate determinedby the givenlevel of the capitalstockK0.The level of activity would thus not stay constant. Whetherthe labor force grows,at a similar rate,or not, the resulting ncreasein the stock of capital generates a greaterproductin the comingperiod. Thus even for a given labor force the system wouldmoveto the right along the product curve such as Y(Ta) which repre-sents the constanttechnology aggregateproduction unction.A simultaneouslyincreasinglabor force, implies at one andthe same time an upwardshift of the productcurve towards sayY(Tb), and hence along the Y path. This obviously increasestherate of increaseof producteven more.Oneis therefore nevitably temptedto ask whetherthis processcouldgo on infinitely. Oncesaving,whichis ipso facto investment,is at a positive level, wouldthe recurrentprocessof capacity crea-tion pushthe systemalong a growingpatternforever? It is at thispoint that we must put into the analysis the effect of the fallingprofit rate. Capitalaccumulation mplies a move along the profitrate curveof FigureIII - a falling trend of the profitrate.Smith clearly relates stationaryconditions and low profits:In a country which . . . could . . . advance no further, and which was notgoing backwards, ... the profits of stock would probably be very low.3Since growth generatespressureon the profit rate, this must even-tually choke this very process. Stationaryconditions are thereforepresumably inevitable.

VIII. THE AVAILABILITYFRESOURCESOR NVESTMENTA. Capital, Product, Technology

Smith was, nevertheless,not bothered by this prophecy ofdoom which primafacie follows directly from the structure of hismodel. In more than one sense the basic message of the WealthofNations is rather that capital accumulationcould ensure eternal"progress."The reasonwhy Smith was not after all worried est thedepressing effect of capital accumulation on the profit rate reducethe growth potential of the system to nought, is due to a leading3. Ibid., p. 94.



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A SMITHIAN GROWTH MODEL 413strain of his thought. This is his belief, which we have alreadyunderlined,n the strategic functionof technologicalchange,andtheincorporation of technology as an endogenous variable of hismodel. Ouranalysis in the previoussection, in which we studiedtheworkingsof the model as determinedby the interactionsof capital,social product saving, and investment, must therefore be extendedto incorporate he effectsof endogenously nducedtechnicalchange.An inspection of the specification of the productionfunctionin (1) and the two technology equations (2) and (3) indicates atonce the nature of the other mechanism at work. Thus positivesaving - hence investment - creates greater capacity and thereforea greatersocial product. The growingcapital stock generatespres-sureon the profit rate. The movementalong a product curve suchas Y(Ta) in Figure I, also impliesa movementalong (Ta) in FigureIII. Yet since technical efficiency of equipment - t - is a positivefunctionof the capital-laborratio,an inspectionof (3) and (1) sug-gests at once that if capital formationproceeds faster than thegrowthof the laborforce,the value of T - the technology variablein the production unction rises correspondingly.This, however,shifts the productcurve of Figure I upwards towards, say, Y(Tb)and correspondinglyhe profitrate curvein FigureIII to the right,towards,say, f (Tb).This is, however,not the end of the story. We haveyet to studythe effect of these comingsand goings on m -the extent of themarketvariable. The latter, accordingo (2), is positively relatedtosocial product. Consequentlya growing product in response tocapitalaccumulationriggersoff the technologyvariablein boththeproduction unctionand the profitrate functionthrough ts impacton the extent of the market. Thus even if a movementalong aproduct curve such as Y(Ta) fails to operateon the technical effi-ciencyvariable dueto the fact that capitalaccumulation ndpop-ulation growth proceed at the same rate the growing marketwouldstill do the trick. The market inducedtechnologicalchangewill shift the productcurve of Figure I towards Y(Tb) and cor-respondinglyhe profitrate curve of FigureIII towardsf (Tb) . Themotion along these curvesproceeds accordinglypari passu with ashift in them even assuminga constant t.The Smithianvision of eternalprogress s thus obviously notbased on the oversimplifiedassumptionof unlimited investmentoutlets, in the sense that the investmentand capital curves of Fig-ures III and IV are asymptoticto the horizontalaxis. Accordingto this variantof the unlimited nvestmentoutletshypothesis,some-



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414 QUARTERLY JOURNAL OF ECONOMICStimes attributedto the classics, the profit rate could never fallto nought. Smith's belief that the profit rate, hence investment(and also saving), will not fall to zero as an inevitableconsequenceof growth,is, as we have seen, deducedfrom a more sophisticatedand thus morecomplexview of the natureof the economicprocess.The capital and investmentcurvesare not asymptoticto the hori-zontal axis at a positive interest rate. They could intersect it at afinitelevel of capital stockandinvestment.What the structuralpremisesof the Smithianmodel do implyis that growthgeneratesforceswhich continuouslyshift these twocurvesto the right. It is obviouslytechnologywhich does the trickand prevents stagnation, by constantly removingthe depressingpressureon the system, thus allowingit to lift itself continuously,so to speak, by its ownbootstraps.B. Smith'sEulogy of Capital

Ourrestatementof Smith'smodel indicateswhy it was capitalwhich Smithidentifiedas the strategicfactor in the process of eco-nomic evolution. Capital is not only an input that togetherwithothers generatesthe social product. Capital accumulationfiguresalso as the sine qua non of technologicalprogress. It operates,onthe one hand, throughthe production ncomenexus to extend themarket,and hence to inducedivision of labor. On the other hand,by making possiblea risingratio of capital to laborit makes"em-bodied" echnologicalchanges,to use a modernterm, possible.The technology relations that figure as integral elements ofthe Smithianstructureare admittedlyoversimplified.This is, how-ever,much less important han the fact that Smithposed the capi-tal technology issue right on the agenda of political economy.After all, one may doubt whether we have in between improvedupon his insights. To this day we are short of a meaningfulandtestable hypothesisfor technology,which on most occasions is stilldefined n empiricalwork as a somewhatmysteriousresidual.Oncewe realizethe cardinalposition of technologyin Smith'svision, the reason for his worshipof capital and of saving, whichmadean ineradicable mprinton the intellectualatmosphereof theprofession o this day, comesinto its own.

THE HEBREW UNIVERSITYJERUSALEM

smithian growth

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