Capital Controversy 1

7/29/2019 Capital Controversy 1

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The Capital Controversy in Historical Perspective

Gary Mongiovi

St Johns University

Email: [email protected]

It is indeed a peculiarity of our science that its investigations

generally start from a point which is, so to speak, behind the zero

of ignorance. It is necessary to escape from error before

reaching positive truth. (F.Y. Edgeworth, 1925, p.273)

More than half a century has passed since the so-called Cambridge capital theory debateswere triggered by Joan Robinsons paper on The Production Function and the Theory ofCapital (1953). Several thoughtful efforts have been made to take stock of the debate,

and all of them begin by pointing out what is (for me, anyway) disappointingly evidentthat despite the attention paid to the debate in the 1960s and 70s, the ultimate impact of

the critique on economic thinking was negligible (see Birner, 2002; Elmslie & Sedgley,2003; Cohen & Harcourt, 2003). Contemporary mainstream economics treats the issues

as settled in its own favour, and deem the entire episode to have been much ado aboutnothing. In this paper I wish to assess the outcome of the controversy from a perspective

that remains to be fully explored. The capital theory debate is generally interpreted as atechnical controversy concerning the specification of capital in the neoclassical theory of

growth and distribution. Although Piero SraffasProduction of Commodities by Means ofCommodities (1960) is accorded a central role in the controversy, the connection of the

debate to Sraffas larger projectthe reconstruction of the theoretical approach of theclassical political economistsis not as well understood. It is perhaps only a slight

oversimplification to say that while one side in the debate was acutely aware of thishistorical dimension, the other was concerned mainly with technical issues. But the

technical dimensions of the problem themselves have a history that dates back to Ricardo,who encountered the problem of measuring capital in his attempt to explain the profit

rate. The problem was not fatal to Ricardos theory, which does not require that themagnitude of capital be specified prior to the determination of prices and the profit rate;

but its resolution in neoclassical theory requires a change in the object of analysisthat

is, the abandonment of the long-period method of analysis in favor of models ofintertemporal general equilibrium.Sraffas well-deserved reputation as a razor-sharp critic has overshadowed the

constructive project to which he devoted his career from at least 1927the revival ofclassical political economy. William Stanley Jevons famously wrote that Ricardo had

shunted the car of economic science on to a wrong line (1879, p. lvii). Sraffas worksuggests, though, that it was Jevons himself, along with Marshall, Walras and Menger,

who had knocked economic science off course, and that progress in economics would


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require the recovery and resuscitation of the classical political economy tradition ofSmith and Ricardo. This conclusion runs counter to the usual view of science as a

forward-moving process in which knowledge and understanding accrue over time as newtheories displace or assimilate old ones. Though modern discourse in the philosophy of

science is wary of the claim that science brings us ever-closer to some objective truth,

the argument that later theories areaccording to sensible criteria such as predictiveaccuracy, success at puzzle-solving, and so forthsuperior to their predecessors is lesscontroversial (see Kuhn, 1970, pp. 205207). The reappearance of a discarded paradigm

has no precedent in the history of science, and philosophers of science have, accordingly,not given the prospect much thought.

The central premise of the classical theory is that the distribution of the socialproduct is regulated not by the forces of supply and demand, but by historical and

institutional processes that reflect the interplay of class interests. The ratios at whichcommodities exchange were understood to depend upon the technical conditions of

production and the distribution of the social product between labor and the owners ofcapital. A difficulty arises in connection with the determination of the profit rate, which the

classicals regarded as the main influence on the rate of accumulation. They conceived thenormal rate of profit as the ratio of the social surplus (gross output less the

outputincluding wage goodsconsumed in production) to the capital utilized inproduction. Both the surplus and the capital stock, however, are vectors comprised of

heterogeneous wage goods and produced means of production. Calculation of the ratiobetween them requires that they be made commensurable. An obvious way to proceed

would be to weight the elements of the two vectors by their long-period prices ofproduction. The difficulty is that prices of production themselves depend upon the profit

rate. Ricardo (1821) thought he could get around the problem by supposing thatcommodities exchange approximately in proportion to the quantities of labor required to

produce them; the profit rate could then be calculated as a ratio of quantities of labor-time(Sraffa, 1951, pp. xxxxxxiii). This solution is unsatisfactory, however, since, as Ricardo

well understood, commodities do not generally exchange in proportion to quantities ofembodied labor-time: labor values deviate from long-period normal prices in a systematic

fashion, according to the degree in which different production processes utilize more orless labor relative to produced inputs.

1The puzzle vexed Ricardo until the end of his life

(he was working on it when he died; see Ricardo, 1823). We now know that the solutionrequires the simultaneous determination of relative prices and the profit rate (Sraffa,

1960, p. 6).The failure of the classical economists to resolve the difficulties posed by the

interdependence of prices and distribution partially explains why classical politicaleconomy faded from the scene over the half-century that followed Ricardos death. No

doubt the decline was hastened by the misappropriation of Ricardos labor value analysisby nineteenth century social reformers, who made it the basis of a claim that workers are

1Ricardo appears to have been the first economist clearly to grasp that the impact of a change in

distribution on relative prices depends upon the capital structures of different sectors of the

economy. Marx (186794, Vol. III, Part II) developed this insight further in his analysis of the

connection between sectoral differences in the organic composition of capital and the pattern of

price deviations from labor values. Sraffas work (esp. 1960, pp. 1415) showed that the effects

of distribution changes on prices are far more complex than either Ricardo or Marx supposed.


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entitled to the whole of the social product. Marx had no use for these so-called (but infact mislabeled) Ricardian socialists. In Capital(186794) and Theories of Surplus Value

(186263) Marx critiqued and elaborated Ricardos ideas, and demonstrated the richanalytical potential of the surplus approach. But he was no more successful than Ricardo

at reconciling his labor value analysis with prices conceived as long-period centers of

gravitation;

2

moreover, his rhetorical style and ideological stance were ill-designed topromote a sympathetic re-evaluation of the Ricardian approach among his less radicalcontemporaries. Nassau Senior (1836) and John Stuart Mill (1871; first edition 1848) had

already begun to nudge the discipline towards marginalismSenior with his argumentthat interest is a reward for abstention from consumption, and Mill with the wages fund

doctrine (which he later repudiated, but by then the damage was done) and with hisassignment of a prominent role to utility in the explanation of economic behavior.

By the start of the twentieth century the classical theory had been, as Sraffa (1960,p. v) put it, submerged and forgotten, its distinctive elements obscured in the wake of

marginalisms ascendance. Marshall (1920, pp. 420421; Appendix I) hadmischaracterized Ricardos theory as an embryonic version of the supply and demand

framework. Jevons, of course, recognized the classical approach to be different from themarginalist theory, but precisely on that account he thought it hopeless. These views have

informed modern interpretations that regard the classical theory essentially as a specialcase of neoclassical analysis, with the demand side of the story missing or inadequately

developed (see Arrow, 1993; Bliss, 1975; Hahn, 1982).The lack of attention to the historical background has also led the capital critique

to be confused with the problem of capital aggregation in empirical models aimed attesting neoclassical growth theory. They are in fact two distinct issues that intersect at

one juncture: the problem of the measurement of capital. In the case of the Cambridgedebates the measurement of capital is problematic because the prices of capital goods

change when distribution changes; in the standard production function literature onaggregation, the problem is whether production function can be constructed that exhibits

the properties needed to establish downward-sloping factor demand functions. Similarlythe assertion, by Christopher Bliss and others, that the aggregation problems associated

with labor and land are comparable to those associated with capital, is misplaced: theclaim exemplifies the muddling of the two kinds of measurement problems mentioned

above. Capital is problematic because its endowment must be specified independently ofdistribution in order to determine the profit rate. This problem doesnt arise in connection

with labor or land, though there may be other problems of aggregation involving themthat must be resolved when constructing models designed for empirical testing.

The degree of the misunderstanding arises with particular clarity in one of thestandard presentations of the logic of the reswitching phenomenon. This common

formulation is ill-designed to expose the nature of capital reversing; I not believe thedefect has hitherto been noticed: it came to my attention when I was had been asked to

read a draft of a paper on why the capital controversy fizzled, and was in fact the catalystfor the present note. The model is generally attributed to Ferguson (1969), but variations

2In Marx this manifested itself as the problem of transforming labor values into prices of

production.


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of it have been put forth by others, and it forms the basis of Birners summary of thelogic of the Cambridge critique.

Fergusons model contains but one capital good, so the circumstance that givesrise to capital reversing and reswitchinga multiplicity of capital goodsis not present.

Capital heterogeneity is alleged to be captured by the supposition that the different

techniques adopted at alternative profit rates utilize different types of capital goods (seeBirner, 2002, p. 15). But this sort of heterogeneity is not manifest in any of the formalfeatures of the model, and is not what gives rise to the perverse results. The latter stem

from the differences in input proportions between the consumption goods sector and thesector which produces the sole capital good, couples with the adoption of the

consumption good as numeraire. But this is a sleight of hand that misrepresents the rootcause of capital reversingagain, the multiplicity of capital goods.

The model writes the price equations as follows, on the assumption that constant

returns to scale prevail and all capital doesnt depreciate:

lMw + aMrpM= pM (1)lCw + aCrpM= pC (2)

where lM and lC are the unit labor input coefficients for the machine sector and the

consumption goods sector respectively, aM and aC represent the amount of the machinerequired to produce a unit of the machine and a unit of the consumption good

respectively; w is the real wage, ris the profit ratepM is the price of the machine andpCisthe price of the consumption good.

We have two equations with four unknowns. If we designate the consumptiongood as the numeraire, we can reduce this to two equations in three unknowns:

lM

w + aM

rpM

= pM

lCw + aCrpM= 1

This system has one degree of freedom, and its solution for the real wage is:

.

Thus we have the standard trade-off between the real wage and the profit rate. The trade-

off is in general nonlinear, and its precise shape will depend on the technical coefficientsofboth sectors. The nonlinearity of the trade-off according to Ferguson is what creates

the possibility of reswitching when two alternative techniques are counterposed againstone another.

But the model is seriously misleading as an explanation of reswitching. We doobserve that when the wage-profit trade-offs for two alternative technique (let us call

them and are graphed against one another in w-rspace the possibility arises that onetechnique can dominate at low rates of profit, be supersede by the other technique at

higher profit rates, and then dominate again at still higher rates of return. But this patternhas nothing at all to do with the heterogeneity of capital: it emerges because the two


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sectors utilize labor and the machine in different proportions, so that the wage curve isnonlinear: it would be just as apt to occur if the two techniques utilized exactly the same

sort of machine.Moreover, what ultimately accounts for the nonlinearity of the trade-off is the

adoption of the non-basic consumption good as numeriare. A consequence of this

decision the technical conditions of production in the consumption good sector influencethe trade-off between w and r, even though the consumption good is not basic in the senseof Sraffa. But the model is fully determined without the consumption good equation. In

effect, the model introduces a redundant equationthe price equation for theconsumption goodto determine a redundant unknownthe price ratiowhen in fact

the price equation for the machine is adequate to determine the wage curve if wedesignate the machine, that is, the sole basic commodity, as the numeriare. If we set pM=

1, we obtain from equation (1)

.

The wage curve is fully determined, is linear and its slope and intercept depend entirely

on the technical coefficients of the machine sector. Provided that 0 < r< 1/aM, the realwage will be nonnegative. Once we know rand w, they can be inserted into the price

equation for the non-basic consumption good to determine the pC. The solution value forpC enables a worker to purchase precisely the same amount of the consumption good per

unit of waged employment as the solution value, given r, forw when the wage curve wasderived using the consumption good as the numeraire. By making the (non-basic) wage

good the numeraire, the model gives the sector that produces it an artificial role in thesolutiona role that it could not have if the capital good were the numeraire.

3

Reswitching and capital reversing are not simply by-products of the choice ofnumeraire. Models such as this one obscure the important point that the capital theoretic

problems of orthodox theory stem from the possibility of reconciling the conventional

theory of distribution with a satisfactory specification of the endowment of capital. Themodel isnt really capturing reswitching or capital reversing, for the simple reason thatneither of these phenomena can occur when there is only one capital good. They arise

because, except for special cases, capital cannot be measured independently ofdistribution.

In their overview of the capital controversy, Cohen & Harcourt (2003, p. 200)remark that the debate involved three deep issues:

(i) the meaning and, as a corollary, the measurement of capital.

(ii) the usefulness of equilibrium as an analytical device; and(iii) the role of ideology and vision in fuelling controversy when the results of

simple models are not robust.

All of these issues are indeed tangled up in the late 20th

century discourse connected tocapital theory. But the second seems to me to be something of a red herring and the last

3To put it another way, Fergusson has in effect set up a corn model and then adopted some other

commodity besides corn as the numeraire!


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cannot be separated from the first, not so much because of ideology but because of thedifficulty of abandoning entrenched modes of thinking.

The early reactions to the capital critique combine an awareness that a seriousblow had been struck with a quite natural inclination to discount the magnitude of the

damage. Paul Samuelson, who has engaged the issues as directly as anyone on the

marginalist side, forthrightly declared in his Summing Up of the debate thatreswitching can be called perverse only in the sense that the conventional parables didnot prepare us for it (1966, p. 578). But a few pages later he characterizes reswitching

as a pathology [that] illuminates healthy physiology, in effect retracting his concession.And he reinforces this defensive maneuver by suggesting that capital reversing is

empirically rare. Stiglitz (1974) suggested that capital reversing and reswitching arephenomena akin to Giffen goods in the theory of consumer demand: theoretical

possibilities, but so unlikely as to be of no practical significance. This line of argumentmisses the point. The 19th century originators of the principle of factor substitution did not

derive it from observation of empirical regularities; they constructed it by deduction frompostulates ... now generally admitted to be invalid (Garegnani, 1970, pp. 424425).

The marginalist theory of value and distribution was not developed by inductivereasoning based on observations of behavior that reflects the existence of underlying

supply and demand functions. No economist has ever observed a factor demand function(or indeed any sort of demand function). What we observe are market phenomena, such as

pricequantity couplets, that require explanation. Providing an explanation is complicatedby the fact that observed magnitudes are conditioned by both accidental and systematic

causes. It is the job of theory to identify and isolate the systematic causesthat it, to findthe order in a highly complex reality. Here is where the role of vision comes into play. The

intuition of economists has been deeply penetrated by the idea that a decrease in the price ofa productive factor will cause the economy to use that factor more intensively, so that

alternative theoretical frameworks can only be interpreted as concerned with anomalies. Butthat conventional view of the relationship between distribution and the factor intensity of

production was not derived from empirical observation or common sense. Rather itemerged from a particular idea about how markets regulate the distribution of income, i.e.

from the idea that factor prices are the outcome of an allocative process that is essentiallydesigned to accommodate scarcity.

4From this premise follow all of the neoclassical notions

of downward-sloping factor and commodity demand functions, factor remunerationcorresponding to the marginal productivity of labor and capital. Without the premise, we

would never have been tempted to think about distribution in neoclassical terms: theoryshapes our conceptions of what is intuitive, what is common sense.

The basis for any theoretical proposition is the set of premises from which it isdeduced; if the premises are unsound, so must be the theory built upon them, and we ought

to look elsewhere for the regulating mechanism. Empirical evidence often runs counter toneoclassical propositions: declining real wages are not routinely associated with increases in

the labor intensity of production; lower interest rates (as the makers of Japanese and USmonetary policy have recently discovered) need not induce higher levels of capital spending.

These observations are accommodated within neoclassical theory by the introduction of

4The roots of the idea, I suspect, lie in the vulgar economy of the mercantilists, as channeled

through Malthus and Say.


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influences that interfere with the operation of the fundamental substitutionmechanismsprice rigidities, information asymmetries and the like.

Joan Robinson was not immune to this influence. Her 1953 article made little ofthe curiosum that Ruth Cohen had noticed concerning the possibility of the capital

intensity of production moving in the same direction as the interest rate. Indeed, she too

raised doubts about its empirical significance (1953, p. 106). Robinson, via Sraffa, waswell aware of the logic which supported that possibility, and of the connection of thephenomenon to the struggles of Ricardo and Marx to formulate a coherent theory of

value. But she appears not to have fully grasped the destructive potential of reswitching.She wrote in 1953 (p. 83) that the problem which the production function professes to

analyse, although it has been too puffed up by the attention paid to it, is a genuineproblem. We observe that developed countries tend to utilize techniques that are more

mechanized than techniques in use in underdeveloped economies. [I]t seems pretty clearthat the main reason for this state of affairs is that capital in some sense is more plentiful

in [developed countries] than in [underdeveloped] countries. The problem is a real one.We cannot abandon the production function without an effort to rescue the element of

common-sense that has been entangled in it. Elsewhere in the paper (p. 96) she makes asurprising statement: The neo-classical system is based on the postulate that, in the long-

run, the rate of real wages tends to be such that all available labour is employed. In spiteof the atrocities that have been committed in its name there is obviously a solid core of

sense in this proposition.I do not for a moment imagine that the resistance of orthodoxy to the capital

critique would collapse if only the critical argument were anchored more explicitly to theconstructive alternative of classical political economy as formulated by Sraffa, and

supplemented with a further development of Keynesian & Post Keynesian principles. YetI do think that the issues surrounding the debate would have been better understood if

that connection had been kept more constantly in focus. Robinsons insistence that themain issue concerned the inadequacy of comparative statics for dynamic analysis, astute

and accurate as it is, nevertheless weakened the impact of the critique. Contra Cohen &Harcourt (2003, p. 204) Capital theory is [no more] fundamentally intertwined with

issues of time than any other aspect of economic theory concerned with understandingreal world processes.

The aspect of Sraffas work that drew the most attention was the challenge itposed to foundational elements of neoclassical theory that had come to be regarded as

intuitively (if not empirically) evident. But once the neoclassicals walked away from thecapital theory debate the prospects for Sraffas constructive agenda receded.

Sraffas terseness did not help matters. In the Preface to Production ofCommodities he is explicit about his critical purpose: It is a peculiar feature of the set of

propositions now published that, although they do not enter into any discussion of themarginal theory of value and distribution, they have nevertheless been designed to serve

as a basis for a critique of that theory. He alludes to a more constructive purpose whenhe identifies the framework of his Parts I and II, in which no changes in outputs or

proportions are considered, as the standpoint of the old classical economists fromAdam Smith to Ricardo (1960, p. vi), and in his Appendix D on References to the

Literature. But these hints are, to say the least, faint, and most readers would have hadto work hard to grasp their significance.


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Sraffas reticence is all the more striking in light of what his manuscripts revealabout his intellectual activity during the 1920s, 30s and 40s. Paul Samuelson is fond of

an anecdote in which Keynes, upon being told that Nicholas Kaldor had contractedathletes foot, responds: I dont believe it. Next youll be telling me Piero has writers

cramp (Samuelson, 1990, p. 26). Samuelsons diagnosis of writers block is a case of

spurious induction. Though Sraffapublishedrelatively little over the decades since 1930,he in fact wrote hundreds of manuscript pages in preparation for Production ofCommodities.

In addition to voluminous notes relating to the working-out of the mathematicaland technical properties of the equation systems ofProduction of Commodities, the

manuscripts contain an enormous number of documents (including lecture notes) on thecharacter and evolution of classical political economy and its displacement by marginalist

theory. Sraffa was a perceptive and highly original intellectual historian, and takentogether these documents amount to a peerless exposition of the development of

economics from the seventeenth century through to the first three decades of thetwentieth (see Kurz, 1998, for thorough overview of Sraffas manuscript writings on the

history of economic thought).Evidence from the manuscripts suggests that Sraffas original plan was to publish

a larger work that would present a fully-developed account of his interpretation of theclassicals, and connect that interpretation to the analytics of his price equations and to his

implicit critique of orthodox capital theory. Indeed, at an early stage he appears to haveconsidered the historical dimension of the project to be more important than the formal

analytics. In notes (written in Italian) dated November 1927 he described the project ashe then envisioned it:

Approach of the book

The only way is to present history in reverse, and that is: the present state of

ec[onomics]; how it was arrived at, showing the differences and the superiority

of the old theories. Then to expound the theory. If chronol[ogical] order isfollowed, Petty, Physiocr[ats], Ric[ardo], Marx, Jevons, Marsh[all], it is

necessary that it be preceded by a statement of my theory in order to explain

what we are driving at. That means first expounding allof the theory. And

then there is the danger of ending up like Marx, who publ[ished] Cap[ital] first,

and then did not manage to complete the Histoire des Doct[rines]. And even

worse, he was unable to make himself understood, without the historical

explan[ation]. My plan is: I to lay out the history, which is really the essential

element II to make myself understood: for which it is required that I proceed

from the known to the unknown, from Marshall to Marx, from disutility to

material cost (D3/12/11; my translation).

Sraffa remarks in the Preface to Production of Commodities that while the book wasbeing put together out of a mass of old notes, little was added. In retrospect the remark

is pregnant with irony. Yes, little was added; but much was set aside. And what Sraffaset aside was the historical material that would have made the constructive purpose of the

project apparent.

References


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Arrow, K. (1991) Ricardos Work as Viewed by Later Economists,Journal of the History

of Economics Thought(Vol. 13), pp.7077.Birner, J. (2002) The Cambridge Controversies in Capital Theory: A Study in the Logic

of Theory Development(London: Routledge).

Bliss, C. (1975) Capital Theory and the Distribution of Income (Amsterdam: North-Holland).Burmeister, E. (2000) The Capital theory Controversy, in: H.D. Kurz (Ed.) Critical

Essays on Piero Sraffas Legacy in Economics (Cambridge: CambridgeUniversity Press).

Edgeworth, F.Y. (1925) Papers Relating to Political Economy, Vol. III (London:Macmillan).

Elmslie, B. & Sedgley, N. (2003) The Reswitching Debate: Whence It Came, Where ItWent,Intellectual History (Vol. 13, winter), pp. 6570.

Ferguson, C. E. (1969) The Neoclassical Theory of Production and Distribution(Cambridge: Cambridge University Press).

Garegnani, P. (1970) Heterogeneous Capital, the Production Function and the Theory ofDistribution,Review of Economic Studies (Vol. 37), pp. 407436.

Hahn, F. (1982) The Neo-Ricardians, Cambridge Journal of Economics (Vol. 6), pp. 353374.

Kuhn, T. (1970) The Structure of Scientific Revolutions, second edition (Chicago:University of Chicago Press).

Marshall, A. (1920)Principles of Economics, eighth edition (London: Macmillan).Marx, K. (186263) Theories of Surplus Value, Vols. IIII (New York: International

Publishers).Marx, K. (186794) Capital, Vols. IIII (New York: International Publishers, 1967).

Robinson, J. (1953) The production Function and the Theory of Capital, Review ofEconomic Studies (Vol. 21), pp. 81106.

Cohen, A.J. & Harcourt, G.C. (2003) Whatever Happened to the Cambridge CapitalTheory Controversy? Journal of Economic Perspectives (Vol. 17, no. 1), pp.

197214.Samuelson, P.A. (1966) A Summing Up, Quarterly Journal of Economics (Vol.80),

pp.568583.Sraffa, P. (1960) Production of Commodities by Means of Commodities (Cambridge:

Cambridge University Press).

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