No CrossRef data available.
Article contents
A Robinsonian Growth Model*
Published online by Cambridge University Press: 07 November 2014
Extract
A Robinsonian model is a two-sector model with fixed technical coefficients. Aside from Mrs Robinson's own work, similar models, without technical change, have been discussed in two major papers, one by I. M. D. Little and the other by R. Findlay. Mrs Robinson has criticized both these contributions on the ground that they do not treat the rate of growth or accumulation as an exogenous variable, but rather regard it as endogenous, emerging from the model after the real-wage rate has been given. In the first section of this paper I explore the conditions for stable equilibrium growth on Mrs Robinson's assumption of a desired rate of accumulation (a function of “animal spirits” and the rate of profit), and then add to the model neutral technical change of an appropriate sort.
In section II, the effects of introducing biased technical change are examined. I show that the model has “technological stability,” by which I mean that there is a tendency for technical change to be neutral. Predictions and tests about the movement over time of the consumption-good price of capital are made in section III. Finally, I end with a short comment on stability in the short run.
Un modèle de croissance robinsonien
Un modèle robinsonien est un modèle à deux secteurs et à coefficients techniques fixes dans lequel le désir d'accumuler du capital est à l'origine de la croissance. On établit d'abord les conditions de stabilité du modèle et les taux de croissance d'équilibre des diverses variables dans le cas d'un changement technique neutre. A la base de la dynamique du modèle, se trouve l'hypothèse suivante: le prix du capital, en terme du bien de consommation, s'élève si le taux d'accumulation désiré excède le taux des épargnes. La croissance d'équilibre est stable si le changement du taux de profit amène une modification du taux désiré d'accumulation du capital qui est inférieure (ou supérieure) au changement du taux des épargnes, compatible avec un coefficient capital-travail relativement plus élevé (ou moins élevé) dans le secteur du bien de capital.
Dans la deuxième partie de l'article, l'auteur examine les effets d'un progrès technique non-neutre. Dans le cas d'un secteur du bien de capital qui serait relativement d'une haute intensité de capital, un progrès technique économiseur de travail (labour-saving) conduirait à un taux de profit croissant et à une préférence pour des techniques à plus haute intensité de travail; par contre, un progrès technique consommateur de travail (labour-using) résulterait en un taux de profit décroissant et à une préférence pour des techniques à plus faible intensité de travail. Il existe donc une tendance favorisant la neutralité du changement technique.
D'autres études ont dégagé une tendance séculaire à la hausse du prix du capital, exprimé en terme du bien consommation, dans un certain nombre de pays développés. L'auteur indique en une troisième partie de cet article qu'un tel changement dans les prix relatifs est conforme aux prévisions d'un modèle robinsonien et d'un progrès technique neutre. En outre, un progrès technique économiseur de travail tend à accélérer l'augmentation du prix du capital (en terme du bien de consommation) tandis qu'un progrès technique consommateur de travail tend à réduire son taux d'augmentation. Ce système de relations entre les différentes catégories de changement technique et les variations des prix relatifs semble être confirmé par l'expérience américaine.
- Type
- Research Article
- Information
- Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 32 , Issue 4 , November 1966 , pp. 499 - 509
- Copyright
- Copyright © Canadian Political Science Association 1966
Footnotes
*
This paper was presented to the annual meeting of the Canadian Political Science Association in Sherbrooke, June 9, 1966. I want to thank Professor H. A. J. Green for helpful comments and guidance on an earlier version.
References
1 The Accumulation of Capital (London, 1958)Google Scholar, and Essays in the Theory of Economic Growth (London, 1962).Google Scholar
2 “Classical Growth,” Oxford Economic Papers, IX, no. 2 (06 1957).Google Scholar
3 “The Robinsonian Model of Accumulation,” Economica, XXX (02 1963), 1–12.Google Scholar
4 The first in “Accumulation and the Production Function,” in her Collected Economic Papers (Oxford, 1960), II, 132–44Google Scholar; the second in “Findlay's Robinsonian Model of Accumulation: A Comment,” Economica, XXX, 409–411.Google Scholar
5 See The Accumulation of Capital, 43; also Little, , “Classical Growth,” 154 Google Scholar and Findlay, , “The Robinsonian Model,” 4.Google Scholar
6 This follows, of course, the pioneering work of N. Kaldor on “Keynesian” distribution theory (see “Alternative Theories of Distribution,” Review of Economic Studies, XXIII, no. 2 (1955–1956)Google Scholar). It is sometimes overlooked that in a two-sector model such as this, this may not be a theory of distribution. As Findlay showed (“The Robinsonian Model,” 5), if the consumer-goods sector is the more capital-intensive sector, the direction of change of the share of capital or labour with a rising rate of profit is indeterminate.
7 With r = 1/a 11, the share of wages drops to zero.
8 On the assumptions leading to equation (17A) it is clear that, for a given rate of capital accumulation, a higher savings propensity on the part of profit earners will result in a lower rate of profit. Findlay's argument leads him to conclude “that the rate of profit is independent of the thrift of the capitalists” (“The Robinsonian Model,” 4).
9 This is different from the dynamic assumption made by MrsRobinson, (cf. Essays in the Theory of Economic Growth, 48 and 49).Google Scholar She assumes that if the desired accumulation exceeds the savings generated, the rate of profit will always rise and so permit (with no savings out of wages) additional accumulation. This assumption has the rather peculiar implication that with a relatively capital-intensive capital-good sector, Pk will necessarily rise, but with a relatively labour-intensive capital-good sector, Pk will necessarily fall.
10 This diagram is similar to one used in a more casual manner by Mrs. Robinson in ibid., 48. Her A curve is equivalent to my GS curve, and her I curve to my Gd curve.
11 The rate of profit, r, and the rate of interest in the economy, which rate is determined by monetary policy, have no necessary connection in this model. The assumption of perfect competition merely serves to ensure the equivalance of profit rates across all capital and not the equivalance of the profit rate and the interest rate. Thus the elasticity (or lack of it) of the desire to invest with respect to the rate of interest has no necessary bearing on the plausible elasticity of the Gd curve.
12 Not a movement in the rate of profit. See the preceding footnote.
13 See The Accumulation of Capital, 48.
14 See ibid., 133. Mrs Robinson's definition of neutral change amounts to the same thing as R. F. Harrod's definition.
15 For a discussion on the relative profitability of techniques at different rates of profit see Essays in the Theory of Economic Growth, Part III.
16 Possibly with the help of John W. Kendrick's productivity study, which shows, over the period 1899–1953, rising outputs per unit of capital input, especially in the transportation and the communications and public utilities sectors. See his Productivity Trends in the United States (Princeton, 1961) Table 45, pp. 166–7.Google Scholar
17 “Differential Changes in the Prices of Consumers' and Capital Goods,” American Economic Review, LI (12 1961), 937–57.Google Scholar
18 “Biased Efficiency Growth and Capital-Labor Substitution in the U.S., 1899–1960,” American Economic Review, LV, no. 3 (06 1965), 383.Google Scholar A greater Hicks-labour-saving bias is also a greater Harrod-labour-saving bias.
19 Gordon, , “Differential Changes,” 939.Google Scholar