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Philosophical and Scientific Issues in Dispute
 
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Disputed term/author/ism Author
Entry
Reference
Aggregate Production Function Champernowne Harcourt I 29
Aggregate production function/equilibrium/CampernowneVsRobinson/Campernowne/Harcourt: Champernowne [1953-4] accepted the logic of Joan Robinson's approach and measure but objected to the possibility that the same physical capital could have a different value as between two situations 'merely' because it was associated with a different set of equilibrium rates of wages and profits. >Aggregate production function/Robinson, >Aggregate production function/Solow.
Harcourt I 30
HarcourtVsChampernowne: This objection is valid from the point of view of the theory of production, i.e. the ability to predict the rate of flow of output from a knowledge of factor supplies, but it is neither valid nor relevant for 'capital' viewed as value property, i.e. as reflecting the institutions of capitalist society. There is a real difference between the two situations and value capital ought to reflect it. The economic significance of a given plant may vary from one economic environment to another.
Harcourt: Nevertheless Champernowne appears to have been searching for a unit which could do both tricks at the same time.
Measure of capital: Thus he further felt it would be convenient - and more in keeping with the orthodox neoclassical tradition - to have a measure of capital such that the rewards to the factors of production could be obtained by partial differentiation of the relationship between output and capital (so measured), on the one hand, and labour, on the other.
Comparability: Furthermore, despite the strictures on using comparisons to analyse processes, he was keen to analyse the process of accumulation and deepening, tracing the development of capitalism over time, approaching its 'crisis' as real wages rose and rates of profits fell.
Even if, in fact, equilibrium were ruptured repeatedly, Champernowne hoped to make the process slow enough to proceed as if this had not occurred, to measure capital each step on the way and to provide a means of comparing capital stocks over time as well as between different situations of stationary equilibrium.
Measurements: Such an all-purpose measure is provided in a chain index whereby the 'normal' concave relationship between output per head of a constant labour force and capital per head would be established, provided that any one technique, having been the most profitable or equi-so at a given rate or range of interest rates, could never reappear again at another rate or range of rates, and that, of two techniques which are equi-profitable at a given rate of interest, it is the one with the higher output per head and higher value of capital per head that is the more profitable at a lower rate of interest.
Harcourt I 32
Formalization/indexes: This series of index numbers shows the changes in the 'quantity' of capital after the effects on the value of capital of different rates of wages and profits have been removed. Output/labour: Output may now be expressed as a unique function of labour and chain index capital and the rewards of the factors of production correspond to the partial derivatives of the appropriate branches of the function. In the 'pure' cases, the coefficients of the production function set the upper or lower limits to the factor prices: see Champernowne [1953-4](1), p. 127.)
Equilibrium wage rate: The partial derivative of output with respect to labour equals the equilibrium wage rate and the partial derivative of output with respect to capital equals the equilibrium rate of profits multiplied by the 'price' of 'capital'.
Price: The price itself is a chain index price since the chain index removes, as it were, the 'quantity' of capital from the coefficient of the capital term.
Capital/ChampernowneVsRobinson/Harcourt: In effect Champernowne has removed the 'zigs' - the horizontal stretches - from Joan Robinson's real-factor-ratio curve (…) and changed the slopes of the 'zags' - the upward-sloping stretches - so that they now equal the relevant equilibrium values of the 'price' of 'capital'.
>Method/Champernowne.

1. Champernowne, D. G. [1953-4] 'The Production Function and the Theory of Capital: A Comment', Review of Economic Studies, xxi, pp. 112-35.

Champernowne I
David Gawen Champernowne
Uncertainty and estimation in economics (Mathematical economics texts) Edinburgh 1969


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972
Aggregate Production Function Solow Harcourt I 29
Aggregate production function/equilibrium/SolowVsRobinson/Solow/Harcourt: „It doesn't seem to bother her [Joan Robinson] much that on [her] definition two physically identical outfits of capital equipment can represent different amounts of 'capital'. It wouldn't bother me either except that from the point of view of production two identical plants represent two identical plants.“ (Solow [1956a](1), p. 101.) >Aggregate production function/Robinson, >Equilibrium/Robinson, >Aggregate production function/Champernowne.
Harcourt I 30
HarcourtVsSolow: This objection is valid from the point of view of the theory of production, i.e. the ability to predict the rate of flow of output from a knowledge of factor supplies, but it is neither valid nor relevant for 'capital' viewed as value property, i.e. as reflecting the institutions of capitalist society. There is a real difference between the two situations and value capital ought to reflect it. The economic significance of a given plant may vary from one economic environment to another.
1. Solow, R. M. [1956a] 'The Production Function and the Theory of Capital', Review of Economic Studies, xxin, pp. 101-8.

Solow I
Robert M. Solow
A Contribution to the Theory of Economic Growth Cambridge 1956


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972
Capital Solow Harcourt I 7
Capital/Measurements/return on investment/Fisher/SolowVsFisher/Solow/Harcourt: Solow [1963a(1), 1966(2), 1967(3), 1970(4)]: Solow's purpose was, in part, to get away from the obstacles of the measurement of capital and its related problems by developing instead the concept of the rate of return on investment. His own contributions were to graft technical progress on to Fisher's analysis and to apply the resulting concepts empirically, in order to obtain estimates of the orders of magnitude of the rates of return on investment in post-war U.S.A. and West Germany.
>Irving Fisher.
Joan RobinsonVsSolow: It is argued that neither in theory nor in empirical work has Solow been able completely to escape from the need to define and measure aggregate capital and to work within the confines of a one-commodity model.
>Aggregate Capital.
Harcourt I 46
Capital/SolowVsRobinson/Solow/Harcourt: Solow's comment in Solow [1956a](5) on Joan Robinson's [1953-4](6) article: Solow investigated the conditions under which it would be legitimate to aggregate heterogeneous capital items into a single figure, no doubt having in mind his subsequent econometric studies. >Econometrics.
He found that the conditions were very stringent - the rate at which one capital good could be substituted for another had to be independent of the amounts of labour which subsequently would be used with each. (He discusses in this context a neoclassical model in which continuous substitution is possible, not the discrete case of Joan Robinson's article, but he also looks at the latter towards the end of his article.)
>Neoclassical economics.
His conclusion is quoted in full below because it is an extremely clear statement of the stand that he takes in the debates that followed:
„I conclude that discreteness is unlikely to help matters. Only in very special cases will it be possible to define a consistent measure of capital-in-general.
Some comfort may be gleaned from the reflection that when capital-labour ratios differ widely we hardly need a subtle index to tell us so, and when differences are slight we are unlikely to believe what any particular index says.“ (p. 108.)(5)
Harcourt: For Solow, 'Capital as a number is not an issue of principle. All rigorously valid results come from n-capital-good models. In particular there is no justification ever for supposing that output can be made a function of labour and the VALUE of capital whose partial derivatives do the right thing.' Capital as a number is purely an aid to empirical work 'and you want to get away with the smallest dimensionality possible' (Solow [1969](7)).
>Capital, >Economic models.
Harcourt: Had the contestants been content to leave the discussion here, the literature of the following years might have served to generate far more light - and certainly a lot less heat.*
>Cambridge Capital Controversy.
Harcourt I 92
Capital/Solow/Swan/Harcourt: Solow's basic puzzle concerning a simple, unique measure of capital which in fact has many dimensions and characteristics has been put splendidly by Swan [1956](10) as follows: „That there should be great difficulties in handling the concept of Capital in a process of change is not surprising. A piece of durable equipment or a pipe-line of work-in-progress has dimensions in time that bind together sequences of inputs and outputs jointly demanded or jointly-supplied at different dates. The aggregation of capital into a single stock at a point of time is thus the correlative of an aggregation of the whole economic process, not only in crosssection (which gives rise to the ordinary index-number problems), but also in time itself: in other words, the reduction of a very highorder system of lagged equations - in which each event, its past origins and its future consequences, could be properly dated and traced backward and forward in time-to a more manageable system with fewer lags. This second kind of aggregation introduces a further set of ambiguities, similar in principle to those of indexnumbers, but as yet hardly investigated . . .
From the idea of capital as a single stock there is in principle no sudden transition to 'the enormous who's who of all the goods in existence'. Between the two extremes lies an ascending scale of nth-order dynamic systems, in which capital like everything else is more and more finely subdivided and dated, with ascending degrees of (potential) realism and (actual) complexity. In fact, most of us are left at ground-level, on ground that moves under our feet.“ (p. 345.)
Solow/Harcourt: As a self-confessed middlebrow, Solow sees the rate of return on investment as the link between highbrow capital theory -
Harcourt I 93
the microeconomic theory of resource allocation and prices which allows for the fact that commodities can be transformed into others over time and which is only complete when it also explains the distribution between factors - and lowbrow theory, which is concerned with aggregation and approximation and relates to the empirical implications of saving and investment decisions. By analysing these problems in terms of a rate of return, i.e. a price, we take cognizance of the fact that 'the theory of capital has as its "dual" a theory of intertemporal pricing . . .' (Solow [1963a](11), p. 14.)
>Return on investment/Solow.

* Solow's latest statement of these views is in Solow [1970](8), pp. 424 and 427-8 (but see, also, Pasinetti [1970](9), pp. 428-9).

1. Solow, R. M [1963] 'Heterogeneous Capital and Smooth Production Functions: An Experimental Study', Econometrica, xxxi, pp. 623-45.
2. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115.
3. Solow, R. M. [1967] 'The Interest Rate and Transition between Techniques', Socialism, Capitalism and Economic Growth, Essays presented to Maurice Dobb, ed. by C. H. Feinstein (Cambridge: Cambridge University Press), pp. 30-9.
4. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti.Economic Journal, LXXX, pp.423-8.
5. Solow, R. M. [1956a] 'The Production Function and the Theory of Capital', Review of Economic Studies, xxin, pp. 101-8.
6. Robinson, Joan (1953-4). 'The Production Function and the Theory of Capital', Review of Economic Studies, xxi.
7. Solow, R. M. [1969] Letter to author.
8. Solow, R. M. [1970] 'On the Rate of Return: Reply to Pasinetti Economic Journal, LXXX, pp.423-8.
9.Pasinetti, L.L. [1970] 'Again on Capital Theory and Solow's "Rate of Return" ', Economic Journal, LXXX, pp. 428-31.
10.. Swan, T. W. [1956] 'Economic Growth and Capital Accumulation', Economic
Record, xxxn, pp. 334-61.
11. Solow, Robert M. [1963a] (Professor Dr. F. De Vries Lectures, 1963) Capital Theory and the Rate of Return (Amsterdam: North-Holland).

Solow I
Robert M. Solow
A Contribution to the Theory of Economic Growth Cambridge 1956


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972
Capital Stock Austrian School Coyne I 17
Capital stock/Austrian School/Coyne/Boettke: The concept of the capital structure stands in contrast to the idea of a "capital stock," which refers to an aggregate measure of all capital at a point in time. >Capital structure/Lachmann.
Obtaining a single measure of the capital stock requires that capital be added together using a common denominator such as money.
Cf. >Capital/Joan Robinson.
LachmannVsRobinson: Ludwig Lachmann, however, argued that this approach does not make sense because it assumes that prices are in equilibrium.
>Equilibrium.
Given subjective expectations and valuations, whether someone values a good as a capital good is not objectively observable. Moreover, human expectations will often be incorrect because of the three factors discussed above.
See >Capital structure/Lachmann.
Coyne I 18
The notion of a capital stock only makes sense in a world where equilibrium has been achieved, meaning that all plans and expectations align perfectly. But, in a disequilibrium world characterized by constant error and change, the idea of a capital stock is not useful. It is for this reason that Lachmann, and other Austrian economists, focus instead on the capital structure. In disequilibrium, what matters is how heterogeneous and multi-specific capital goods fit together in production plans and how capital substitution occurs in the face of error and changing conditions.


Coyne I
Christopher J. Coyne
Peter J. Boettke
The Essential Austrian Economics Vancouver 2020
Economic Growth Swan Harcourt I 5
Measurements/Economic growth/factor rewards/marginal products/Swan/Harcourt: In 1956 Swan(1) published one of the first of a spate of neoclassical models of economic growth in which the equality of factor rewards with marginal products plays a crucial role. >Factors of production, >Factor prices, >Capital, >Factor market,
>Production theory, >Capital structure.
In the appendix to his article he provided a rationale for his procedure. It contained two strands.
1) The first was the device of using a primary unit, namely, a one all-purpose commodity - his famous meccano sets model - so that capital may be measured in terms of its own unit, i.e. itself.
The commodity is, moreover, malleable so that both specificity and heterogeneity - two essential characteristics of capital goods - may be abstracted from, and the implications of disappointed expectations in the sense of actual quasirents differing from expected ones may be avoided.
In effect it is 'as if perfect foresight always prevailed. 'Capital' as an aid to production and as privately owned property, whether held or invested by its owners, become indistinguishable.
A theory of production and of distribution may thus be invoked simultaneously.
That is to say, the level of output and its distribution between labour and 'capital' are explained simultaneously by the same set of factors.
2) The second defence was to examine the neoclassical procedure of considering notional changes at equilibrium points in a stationary state.
SwanVsChampernowne: Swan argues that the Champernowne chain index measure of capital is peculiarly suited to cope with this procedure in the analysis of a process of accumulation over time.
>Capital/Champernowne.
RobinsonVsSwan: This viewpoint was (…) vigorously disputed by Joan Robinson, who argues that comparisons of equilibrium positions one with another are not the appropriate tools for the analysis of out-of-equilibrium processes or changes, and that the neoclassical procedure is singularly ill-equipped to cope with the problem of 'time'
Cf. >Time/Rothbard.
Harcourt I 34
Economic growth/Swan/Harcourt: In Swan's model of economic growth, Swan [1956](1), capital-labour ratios need to change considerably as accumulation occurs over time, in order that both stable equilibrium capital-output and capital-labour ratios may be re-established following a change in a parameter, for example, the saving ratio.
Harcourt I 35
In this manner, considerable processes occur, or, rather, are analysed. Moreover, he uses a Cobb-Douglas production function, and assumes that saving determines investment, and that there are constant returns to scale, full employment, static expectations and perfect competition, so that the wage of labour equals its full-employmerit marginal product and the rate of profits on capital equals its marginal product. >Production function, >Cobb-Douglas Production function.
RobinsonVsSwan.
Capital/SwanVsRobinson: His first line of defence is to suppose that capital consists of meccano sets which can be costlessly and timelessly transformed into any desired form, as given by the latest booklet of instructions (so incorporating technical progress), in order to co-operate with labour in response to the pull of changes in relative factor prices and to technical advances. Relative prices: The relative prices of products (including meccano sets) never change, no matter how rates of wages and profits (and, sometimes, rents, when land, which we ignore, is considered) do.
Aggregation: In this way the aggregation of heterogeneous items of capital, both as cross-sections and over time, where they are both 'infinitely durable and instantaneously adaptable', is possible in terms of their own technical unit and 'the basic model of [his] text could be rigorously established in a form which deceived nobody' - an answer which proceeds by abolishing the question.
For, with malleability, disappointed expectations and imperfect foresight can be avoided since the capital stock can be made into any form that is wanted and adapted to any labour supply that is forthcoming.
Thus it is hoped that the long-run implications of capital-labour substitution may be analysed independently of any troublesome shortrun Keynesian and other puzzles.

1. Swan, T. W. [1956] 'Economic Growth and Capital Accumulation', Economic Record, xxxn, pp. 334-61.

Swan I
Trevor W. Swan
Trevor Winchester Swan, Volume I: Life and Contribution to Economic Theory and Policy (Palgrave Studies in the History of Economic Thought) London 1922


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972
Equilibrium Price Samuelson Harcourt I 20
Equilibrium/Modigliani/Samuelson/Swan: Capital/rate of interest/value/measurement/Robinson/Harcourt: (…) it is impossible to conceive of a quantity of 'capital in general', the value of which is independent of the rates of interest (or interchangeably, profits, given the present assumptions) and wages. Yet such independence is necessary if we are to construct an iso-product curve showing the different quantities of 'capital' and labour which produce a given level of national output, or, as is more usual in the theory of economic growth, if we are to construct a unique relationship between national output per man employed and 'capital' per man employed for any level of total national output. That is to say, if we are to construct the neoclassical production function (…). The slope of this curve plays a key role in the determination of relative factor prices and, therefore, of factor rewards and shares.
Problem: However, the curve cannot be constructed and its slope measured unless the prices which it is intended to determine are known beforehand; moreover, the value of the same physical capital and the slope of the iso-product curve vary with the rates chosen, which makes the construction unacceptable.
SwanVsRobinson/SamuelsonVsRobinson/ModiglianiVsRobinson: (…) critics have suggested that this particular set of arguments shows a failure to understand both the nature of the solution to a set of simultaneous equations, such as is, for example, the essential nature of the Walrasian general equilibrium system, and the lack of any necessary link between the variables in which the equilibrium values of key magnitudes are expressed, on the one hand, and causation, or determination, or explanation, or what you will, on the other. See, for example, Swan [1956](1), p. 348 n14; Samuelson and Modigliani [1966a](2), pp. 290-1 n1.
>Causation, >Equilibrium/Walras.
RobinsonVsVs/Harcourt: This criticism is, however, unfair. Thus, for example, to argue that, in equilibrium, the wage rate equals the marginal product of labour is not to argue that one is the cause of the other, or that one determines the other.
Moreover, it is abundantly clear from the manner in which Joan Robinson's version of the production function is derived (…) and the constructions which are used, that these are not the points at issue.

1. Swan, T. W. [1956] 'Economic Growth and Capital Accumulation', Economic
Record, xxxn, pp. 334-61.
2. Samuelson, P. A. and Modigliani, F. [1966a] 'The Pasinetti Paradox in Neoclassical and More General Models', Review of Economic Studies, xxxm, pp. 269-301.

EconSamu I
Paul A. Samuelson
The foundations of economic analysis Cambridge 1947


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972
Extraversion Ackerman Corr I 168
Extraversion/intelligence/Ackerman: The associations between Extraversion and intellectual abilities, and Conscientiousness and intellectual abilities appear to be of a negligible magnitude. Small positive correlations between these traits and abilities are found as often as small negative correlations. However, it is important to keep in mind a central issue with respect to these two personality traits that differs from either the intelligence-related personality constructs or even Neuroticism. >Neuroticism, >Personality traits, >Method.
That is, what one considers to be ‘normal’ or optimal is not found at one end of the continuum of the traits, but rather somewhere near the middle.
>Neuroticism/intelligence/Ackerman.
Theorists who have asserted that individuals who are neither too high nor too low on such traits are optimally adjusted (see e.g., Robinson 1989(1); though cf., Matthews 1985(2) for a differing view (personality traits/MatthewsVsRobinson), have hypothesized that linear correlations are not appropriate measures to assess the relationship between the personality traits and intellectual abilities.

1. Robinson, D. L. 1989. The neurophysiological bases of high IQ, International Journal of Neuroscience 46: 209–34
2. Matthews, G. 1985. The effects of extraversion and arousal on intelligence test performance, British Journal of Psychology 76: 479–93

Phillip L. Ackerman, “Personality and intelligence”, in: Corr, Ph. J. & Matthews, G. (eds.) 2009. The Cambridge Handbook of Personality Psychology. New York: Cambridge University Press


Corr I
Philip J. Corr
Gerald Matthews
The Cambridge Handbook of Personality Psychology New York 2009

Corr II
Philip J. Corr (Ed.)
Personality and Individual Differences - Revisiting the classical studies Singapore, Washington DC, Melbourne 2018
Neuroticism Ackerman Corr I 168
Neuroticism/intelligence/Ackerman: A broad factor of Neuroticism (which usually is considered to include broad Anxiety, Stress Reaction, Negative Affect or Negative Emotionality) shows consistent negative correlations with an array of both general and specific intellectual abilities (e.g., on the order of r = −.15 with general intelligence). Correlations between Neuroticism related traits and mathematical abilities are typically larger in magnitude than are correlations between Neuroticism and verbal abilities, though the differences are not large. >Personality, >Stress, >Intelligence.
Theorists who have asserted that individuals who are neither too high nor too low on such traits are optimally adjusted (see e.g., Robinson 1989(1); though cf., Matthews 1985(2) for a differing view (personality traits/MatthewsVsRobinson), have hypothesized that linear correlations are not appropriate measures to assess the relationship between the personality traits and intellectual abilities.
>Ability, >Performance.

1. Robinson, D. L. 1989. The neurophysiological bases of high IQ, International Journal of Neuroscience 46: 209–34
2. Matthews, G. 1985. The effects of extraversion and arousal on intelligence test performance, British Journal of Psychology 76: 479–93


Phillip L. Ackerman, “Personality and intelligence”, in: Corr, Ph. J. & Matthews, G. (eds.) 2009. The Cambridge Handbook of Personality Psychology. New York: Cambridge University Press


Corr I
Philip J. Corr
Gerald Matthews
The Cambridge Handbook of Personality Psychology New York 2009

Corr II
Philip J. Corr (Ed.)
Personality and Individual Differences - Revisiting the classical studies Singapore, Washington DC, Melbourne 2018
Wicksell Effect Swan Harcourt I 39
Wicksell effect/Swan/Harcourt: Wicksell demonstrated that an increase in social capital is partly 'absorbed by increased wages . . ., so that only the residue ... is really effective as far as a rise in production is concerned'. Swan: Swan is concerned to show in terms of Wicksell's own examples (the point-input-point-output case and the analysis of Ackerman's problem, see Swan [1956](1), pp. 352-61) that "the Wicksell Effect is nothing but an inventory revaluation' (p. 355).
SwanVsRobinson: In establishing this point, he accused Joan Robinson of confusing the change in the value of a stock of capital with the value of the change, a charge which she understandably took rather amiss, see Robinson [1957](2), p. 107 n6.
As Swan shows (see pp. 352-3) this implies that the marginal product of capital (in Wicksell's point-input-point-output case) is less than the rate of interest, an obstacle in the way of the acceptance of 'von Thünen's thesis' (which was its main interest to Wicksell).
>Wicksell effect/Harcourt.

1. Swan, T. W. [1956] 'Economic Growth and Capital Accumulation', Economic
Record, xxxn, pp. 334-61.
2. Robinson, J. [1957] 'Economic Growth and Capital Accumulation - A Comment', Economic Record, xxxm, pp. 103-8.

Swan I
Trevor W. Swan
Trevor Winchester Swan, Volume I: Life and Contribution to Economic Theory and Policy (Palgrave Studies in the History of Economic Thought) London 1922


Harcourt I
Geoffrey C. Harcourt
Some Cambridge controversies in the theory of capital Cambridge 1972


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