Readings in the theory of growth: a selection of papers from the "Review of Economic Studies"

No distinction is here made between the interest rate and the rate of profit on capital. Since the models contain ho financial sector, it is obvious why no distinction is required. '' Harrod-neutrality '' of steady-state technical progress not by an appeal to the Harrodimpartiality of the inventor's muse, but through the choice of economic agents. The pace at which investment grows, if not consistent with a constant investment output ratio, will also thereby change the profitability of investment by changing the rate of growth in output Professor Joan Robinson has drawn my attention to certain difficulties which arise when net saving's are taken as proportional to net income or net profit. profit, thriftiness and the rate of growth. Pasinetti was able to show that on certain assumptions the equality between the rate of profit and the rate of growth, divided by a certain saving propensity, would continue to be true for steady state even if wage-earners saved. In this work he postulated that the saving propensities differed by class rather than by type of income (a sociologically appealing idea) and that the classes were intergenerationally stable. His steady state required the distribution of ownership of capital between classes to be constant. He also required to assume that the saving propensity of workers was less than the share of profits in income multiplied by the capitalist's propensity to save. This last condition has given rise to an extended controversy (Samuelson and Modigliani [10], Robinson [8], Kaldor [3], Pasinetti [6]) which is too lengthy to reproduce. Mr. Sato's paper makes the point rather shortly. The point, of course, is that the economy may have two steady states: one where both classes own a constant positive fraction of the capital stock per man, and one where the fraction of this capital stock per man owned by capitalists becomes zero (which, of course, does not mean that they own no capital). The third possibility, that the fraction of the capital stock owned by workers become zero, is not possible. If, then, the Pasinetti condition is violated, there is effectively only one class, and so the steady state is again of the Harrod-Domar variety. However, Samuelson and Modigliani were not only concerned to establish this latter possibility but also convergence to this steady state. This cannot be shown for complicated von Neumann-type models, and they relied rather heavily on macro-economic production function-type arguments which cannot be shown to be generally valid. This, however, in no way invalidates their main point, which has nothing whatever to do with '' neoclassical '' arguments. This main point is very simple: even when there are fixed coefficients everywhere, the value-capitaloutput ratio is not given by technology but by market conditions combined with technology. The Pasinetti condition depends on this ratio which is not independently given. Hence as far as logic and steady states are concerned, one steady-state solution has as much claim on our attention as another. Nor is it hard, say, for a Leontief technology to show that both solutions may exist for specified thriftiness conditions. All this has nothing to do with an allegedly inverse relationship between capital per man and the rate of profit-and that relation may be as irregular as we care to make it. This, of course, does not mean that for particular ('' realistic '') saving propensities and technologies, the Pasinetti steady state may not turn out to be the proper one. Before leaving this matter it may be worth while to note a related matter. The line which runs from von Neumann through Kaldor to Pasinetti is undoubtedly of importance and establishes an impressive, possible, direct and simple relationship between the rate of growth and the rate of profit. However, it is not a theory of relative shares. This requires one to know the investment-output and so the capital-output ratio in value terms which for any economist is an unknown of the model. To find its steady-state value requires a theory of the choice of techniques by investors. This may be of the von Neumann kind, it may be " parable-macro-economic " or it may be the pay-off period convention. But some micro-theory is required before we can say that we have a theory of relative shares. Returning to the main line of steady-state theory, one cannot leave it without remarking how little Keynesian economics has any bearing on it. This is not surprising, since steadystate theories have been concerned with the question: what must be postulated in order that steady state be possible? Mostly the situation to be analysed was to be one of full 1 Except the possibility that the steady-state value-capital-output ratio with proportional savings need not uniquely determine a rate of profit on this technique. qualify. This observation brings out very well the main difficulties. In Solow (56), the future had no effect on the present since neither savings, investment nor choice of technique today depended on the values of variable tomorrow. This is not true if there are many capital goods (or if savings are governed by '' lifetime '' utility maximisation). However, there are not available sufficient current markets for future goods to make it at all sensible to suppose that all future transactions can be decided upon '' now ''. That being the case, and in any event it also being assured that all assets are always tradable, current behaviour will be governed by '' myopic '' expectations with the results already noted. It should be emphasised that the discussion here-as in all '' equilibrium dynamics '' -is not a description of the world. Indeed, it should rather be taken as confirmation that this methodology is not very sensible. However, the connection with the planning-like nature of the problem is well brought out by Kurz. In the context of a Leontief model, the problem of multi-sectoral stability is further explored by Jorgenson. A further point is worthy of brief notice. It can be shown that it is not generally true that permitting the degree of disequilibrium implied by ''static expectations '' will lead the resulting paths to the steady state. The reason is connected with a matter which has been of much concern to Professor Robinson: there is not necessarily a well-behaved relationship to be found between an aggregate index of capital and the rate of profit [7]. (The rate of profit is well defined with static expectations even out of steady state.) Mr. Atkinson investigates the time taken by the various paths discussed before they are ''near enough'' to steady state. The result is not exactly encouraging to this kind of theory. The forces driving an economy to the steady state have received rather different treatment from Kaldor, and the paper by Meade is a contribution to this discussion. As is known, Kaldor relies on changes in profit margins as one of the major mechanisms of adjustment. The spirit is quite different from that of the earlier construction discussed and makes it a much more hopeful approach to a theory which could actually be confronted with the facts. He has, however, been perhaps too keen to argue that his mechanism always performs in the desired way. Where there is excess demand, not only prices but money wages will tend to rise. Where the profit margin does rise, and so the rate of profit on investment, not only may savings be higher but so may be investment. Professor Meade shows that the final outcome depends on the relative strengths of the forces at work, and that is how it should be. The whole problem of actual as opposed to warranted paths is still largely a matter 1 A Model of General Economic Equilibrium 1 J. VON NEUMANN 1 This paper was first published in German, under the title Vber ein Okonomisches G!eichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes in the volume entitled Ergebnisse eines JHathematischen Seminars, edited by K. Menger (Vienna, 1938). It was translated into English by G. Morgenstern. A commentary note on this article, by D. G. Champernowne, is printed below. fJ ( = 1 + ~, z being the rate of interest in % per unit of time. Front Matter....Pages i-xv A Model of General Economic Equilibrium....Pages 1-9 A Note on J. von Neumann’s Article on “A Model of Economic Equilibrium”....Pages 10-18 On a Two-Sector Model of Economic Growth....Pages 19-26 Note on Uzawa’s Two-Sector Model of Economic Growth....Pages 27-30 On the Stability of Growth Equilibria in Two-Sector Models....Pages 31-47 The Classification of Inventions....Pages 48-52 Disembodied Technical Change in a Two-Sector Model....Pages 53-60 Tentative Notes on a Two-Sector Model with Induced Technical Progress....Pages 61-67 Neoclassical Growth with Fixed Factor Proportions....Pages 68-102 On Putty-Clay....Pages 103-130 The Economic Implications of Learning by Doing....Pages 131-149 Extensions of Arrow’s “Learning by Doing”....Pages 150-164 A New Model of Economic Growth....Pages 165-183 Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth....Pages 184-196 The Neoclassical Theorem and Distribution of Income and Wealth....Pages 197-201 The Adjustment of Savings to Investment in a Growing Economy....Pages 202-217 The General Instability of a Class of Competitive Growth Processes....Pages 218-237 On Warranted Growth Paths....Pages 238-247 The Timescale of Economic Model How Long is the Long Run?....Pages 248-263 Stability of a Dynamic Input-Output System....Pages 264-275