recent developments in the theory of economic growth

AUSTRALIAN ECONOMIC PAPERS

JUNE-DECEMBER, 1964

RECENT DEVELOPMENTS IN THE THEORY OF ECONOMIC GROWTH*

K. S. FREARSON Monash University

The literature of economic theory since 1950 has been dominated by an increasing proliferation of growth models, the great majority of which have appeared as journal articles. The two major books on the subject have been provided by Professor Lewis and Mrs. Robinson.1 These models (which have inevitably become embroiled with the theory of capital) are extremely diverse in character, and their categorization and summarization in a unified treatment is exceedingly difficult. Moreover, new models appear much faster than one can digest them. “A Complete Theory of Growth Involving Heterogenous Models” would be beset with index number problems no less formidable than those involved in the theory of capital (though perhaps it is not to be too sanguine to hope that, like capital, interest would be an organic growth out of it). The divergence of views on the subject is exemplified in papers delivered by most of the leading protagonists in the field at a recent symposium, “Production Functions and Economic Growth”;Z and an extra dimension of difficulty is added by Solow’s illuminating confession that “I have long since abandoned the illusion that the participants in this debate actually communicate with each other”. The other problem is that in essence a review should provide some answer to the question, “What are the results so far?”; but this question I shall unashamedly dodge. This is not because I believe that growth theories

This paper was presented in January 1964 to the Canberra Meeting of the Australian and New Zealand Association for the Advancement of Science, as one of a series entitled “Recent Developments in Economic Theory”. It is discursive rather than analytical; it is not intended to be a survey of modem growth theories, but rather an examination of the problems involved in the formulation of a theory of economic growth.

1 W . A. Lewis, The Theory of Economic Growth (London, Allen & Unwin, 1955); Joan Robinson, The Accumulation of Capital (London, Macmillan & Co., 1956). An excellent introduction to the theoretic treatment of the subject is provided by D. M. Bensusan- Butt, On Economid Growth (Oxford University Press, 1960).

2 The Review of Economic Studies, Vol. XXIX (3). No. 80, June 1962.

1 A

2 AUSTRALIAN ECONOMIC PAPERS JUNE-DEC.

have as yet achieved nothing. Growth has now become a stated objective of current economic policy, and growth theory does help to provide a method of thinking about current problems in the context of an expanding economy. But the theories themselves are still in the ferment of ideas which is necessary before settled conclusions can begin to emerge. “Traditional treatments and traditional solutions are being questioned, improved and revised. In the end this activity of research should clear up controversy. But for the moment controversy and doubt are increased.”s

In this paper, then, I shall first take refuge in a brief discussion of the common problems associated with growth theory, and, for illustrative purposes, examine the models of growth propounded in The Accumu- lation of Capital. There are several reasons for doing this. First, the models can serve as a plane of reference for other models; secondly, there seems to linger still what seems to me to be an irrational prejudice against Mrs. Robinson’s analysis (and certainly some of her critics have misunder- stood what it is that she is trying to say); thirdly, I myself find these models the easiest to understand, and as Samuelson has remarked, because of a Gresham’s Law that operates in economics, easier expositions get more listeners than hard ones; and lastly, simple models are designed primarily as an aid to clear thinking, and I am optimistic enough to believe that they do have considerable heuristic value in providing an insight into the fundamental elements of an extremely complex process.

I Growth theory is nourished by intellectual curiosity, and sustained by

the fact that growth has (for better or for worse) become an overriding consideration of economic policy. But because it is the most ambitious of all types of economic theory, the severe limitations of both the purpose and practical application of growth theory must be kept constantly in mind. A model of economic growth does not purport to be a description of reality, but rather an abstraction from it. I t is merely “a device for sorting out our ideas” which provides a framework within which the innumerable complications of reality can be discussed. It is “a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct con~lusions”.~ The formulation of the model requires assumptions which are either heroic or absurd (depending on one’s nature), and upon which it is only too easy to pour scorn. I t may be argued that a true theory of economic growth should be able to explain why it is that particular societies have had different rates of growth at different times, and why different societies have had different rates of growth at the same time; but the complexity of the growth process is such that the answers to a J. M. Keynes, quoted by Mrs. Robitlaon in Collected Economic Pupcrs, Vol. 11, p. 88. 4 J, M. Keynes, Introduction to the Cambridge h n o m i c Handbooks.

1964 RECENT DEVELOPMENTS I N GROWTH THEORY 3

these questions are not to be found in pure economic theory, but must be couched in t e r n of mental attitudes, of institutions, and of historical experience. But still it remains true that if growth theory is to be more than just an academic exercise it must have some application to the practical needs of policy-makers, and as an instrument of interpretation it must be able to explain the characteristic features of the process of growth as we find them in reality. No one model can provide a complete explanation of the different phases of economic development; the problems of “developed“ and “underdeveloped” economies are different in kind, they require theories of “stages of development”, and cannot be generalized in a set of equations which are expected to hold good for years on end. What is required is not a synthesis of growth theories, but a collection of models which taken together will illuminate the problems of immediate interest. It is by con- centrating on the purely economic strands in the process of development that economists can shed light in corners that would otherwise remain dark, and so provide a practical guide to the understanding of history, and an indication to planners about how best they might set about their task.

In its widest context, the economic growth of a society can be said to depend on the one hand upon its natural resources, and on the other upon human behaviour-in so far as this behaviour manifests itself in the ability and willingness to exploit and increase the bounty provided by nature. Natural resources consist of physical resources and labour resources. The first of these we may regard as being given and fixed in supply; but the second has two important characteristics: it is augrnentable in supply, and its productivity (measured by output per man) can be increased by the accumulation of capital entailing the use of labour-saving techniques of production. A technique of production is defined by the ratio of capital to labour used in the productive process, and the conventional production function of economic theory summarizes a given state of technical knowledge by providing a blueprint for the continuous range of techniques currently available. A higher output per man can be obtained either by increasing the capital-labour ratio (that is, increasing the “degree of mechanization” of the technique employed), or by an improvement in technical knowledge, which in some mysterious way enables a higher output per man to be obtained from the use of the same technique. (Unless capital changes its form, the increased productivity must be due wholly to improve- ments in labour efficiency.) The first entails the exploitation of known techniques which for economic reasons have not been previously used, and involves a movement along the production function; the second requires application of new knowledge, and involves an upward shift in the production function. The distinction between these two methods of increasing productivity is in practice extremely difficult, since new investment gen- erally involves some qualitative change in the coefficients of production as


well as a quantitative change in the existing stock of capital. But conceptually they are distinct, and (by loose fractional analogy) we may call them Vulgar Technical Progress and Technical Progress Proper, respectively.

Analysis involving the use of production functions can be applied to comparisons of different economies, each using a single technique of production chosen from the book of blueprints; but its straightforward application to the process of development experienced in a single economy is exceedingly treacherous. It is not only that capital must be regarded as a homogeneous and transmutable entity, “a single abstract capital substance that transmutes itself from one machine to another like a restless reincar- nating soul”.6 But since new techniques can be introduced only through investment in new capital, then no matter how capital is measured (whether it be in tons of steel, or as meccano sets, or in terms of its value), increases in productivity must entail an increase in the overall capital-labour ratio, regardless of whether technical progress is of the Vulgar or the Proper kind (unless of course all existing capital is scrapped as a new technique is introduced, so that there is instantaneous adjustment to the new technique). This is one of the fundamental differences between labour and capital as factors of production. It is feasible to postulate an improvement in the quality and skill of existing labour, but not so for the quality of the past labour which is embodied in the existing stock of capital. Con- siderations of this kind have led Mr. Kaldor to eschew any distinction between Vulgar and Proper technical progress, and to postulate instead a “technical progress function” describing the relationship between the annual rates of growth in output and capital per workefl-though even here capital accumulation and technical progress remain separate and distinct elements in the growth process.

The fundamental forces which condition the rate of economic growth of a society are thus the growth of population, the accumulation of capital, and technical progress. This is not meant to imply that these are the basic causal factors of growth; all three are the product of social forces and institutional environments, and are an objective expression of the process of development rather than the reason for it.

The distinguishing feature of capital is that on the one hand i t is a factor of production contributing to total output, but on the other, addi- tions to capital are themselves provided from total output, so that there is an intimate interaction between the growth of capital and the growth of output. The growth of capital is thus more amenable to economic analysis than are the other two growth elements, and unlike classical theory, 6 P. A. Samuelson and R. M. Solow, “A Complete Capital Model Involving Heterogeneous

6 N. Kaldor, “A Model of Economic Growth”, Economic Journal, December 1957. Capital Goods”, Quarterly Journal of Economics, 1956.

1964 RECENT DEVELOPMENTS IN GROWTH THEORY 5

modern theories of growth usually take the increase in these latter as parameters of the model.

As long as population is increasing then, it is necessary for total output to increase at the same rate, if real income per head of population is not to decline. This means that if the labour force is a constant proportion of the total population (so that we can identify “population” with “labour force”), output per worker must be consistently maintained. Whether or not this situation is properly to be identified with economic growth is a point which rattles the skeleton in the utility closet. It is preferable, I think, to foIlow Professor Lewis in associating economic growth with the growth of output per head; in which case increasing productivity becomes the rationale and the sine qua non of the whole process of development. Increases in output per man are effected through investment in labour- saving machinery, and are thus reflected in the productive equivalent of a given volume of saving. This involves a re-examination of the initial Keynesian premise of growth models, that saving is a function of income, and saving and investment are identically equal in value. In its simplest form, this is expressed

S = s Y = I Here saving, income and investment must all be measured in the same

units. This presents no problem in the Keynesian theory, which is concerned with the expenditure effects of investment; here it is only the process of investment that matters, and not its fruits.

But the growth of output hinges on the fact that investment is an addition to the existing capital stock, and hence represents an addition to the productive capacity of the community. The ensuing growth postulate is thus that

dK I = x

As soon as we do this, however, i t becomes vital to observe the fundamental distinction between saving and investment as they affect the growth process. Since saving means to refrain from consumption, it is logically measured in terms of consumption goods; but since investment means an addition to capital, it is logically measured in terms of “capital” units. If, for instance, the existing stock of capital consists of machines of a certain type, then it is only logical to measure investment in terms of these machines. In this event, we must write S = PI, where p is the price of a machine in terms of consumption goods. This price is of first importance in determining the number of machines to be obtained from any given volume of saving.7

The second relevant consideration is of course the state of technical

7The influence of the price of capital upon the value of capital required for a given method of production has been termed by Mn. Robinson the “Wicksell Effect”.

6 AUSTRALIAN EOONOMIC PAPERS JUNE-DEC.

knowledge, which determines the productive capacity of the machines. “The productive contribution of a piece of technical equipment, such as a steam engine, is determined not by its cost but by the horse-power which it develops”.8 Suppose that the productive capacity of each machine is given by

dP dt - = qz

Then (dP /d t ) = ( q / p ) S; the productive equivalent of a given volume of saving varies directly as the productivity of new machines, and inversely as the price of them. This is an important consideration to bear in mind, if saving as such is identified with the process of capital accumulation.

Since growth theories are concerned with the analysis of aggregates, they are faced at the outset with Keynes’s problem of “the choice of the units of quantity appropriate to the problem of the economic system as a whole”. The three prime variables of growth theory are the total output produced (9, the labour force employed (L) and the stock of capital (K). I n reality, the problem of their measurement is insoluble; the composition of output, the characteristics and skills of the labour force, and the techniques of production embodied in capital goods are continually changing through time, and our knowledge of the actual values of these quantities cannot ever be complete or exact. In growth theory, however, the concern is not so much with the measurement of these variables, as with the consequences of the growth in them, and the assumptions which are necessary to introduce homogeneity into what are essentially non-homogeneous complexes are perhaps not so drastic in their implications as i t may seem. I t is, for instance, not too heroic for analytic purposes to assume that all workers are alike, and of equal skill, nor even that output consists of a single homogeneous commodity. If however we consider the basic division of product between consumption and investment goods, then these mag- nitudes must be measured in the same units, to obtain the value of total output. A discussion of the problems associated with the measurement of the stock of capital would take us too far into the realms of capital theory. But “capital is whatever it is, no matter what we call it”, and there is more importance in dealing with the thing itself rather than becoming involved in argument about the proper use of its name. The meaning of capital is really an epistemological problem, and there is no common agreement about the way in which it should be measured. Various ways that we shall consider are to measure capital:

(a) In its own technical unit, such as robots, or machines of a certain type.

8K. Wicksell, Lectures in Political Economy, Vol. I.

1964 RECENT DEVELOPMENTS IN GROWTH THEORY 7 (b) As a fluid factor of production, capable of adapting its form to

meet changing circumstances. Professor Swan’s all-purpose meccano sets provide the most brilliant example of how capital may be treated in this way.n

(c) As a quantity of value in terms of commodities. Strictly speaking, the value of capital should include its wages cost plus a notional or actual profit charge. (This is why it is necessary to postulate a steadily-developing economy, in which the rate of profit is constant, to obtain an unambiguous measure of the stock of capital.) But in what follows, we shall assume that the value of capital is equal to its wages cost, since the profit component has no great bearing on the process of growth as such.

(d)As congealed labour time, that is, in terms of the quantity of labour devoted to building it up. Following Mrs. Robinson, we may call capital measured in this way, real capital, and the ratio between real capital and the employment which it offers, the real- capital-ratio.

Growth models are properly concerned with the growth of output and not the desirability of it, and give little consideration to the maximization principle which is the basis of economic theory. But in any meaningful sense, it is misleading to consider only the growth of output per head, since it is consumption per head which determines the “worthwhile-ness” of any process of development. The ultimate solution to the Economic Problem (which is surely the purpose of growth) is for each individual to have scaled the Hill of Pleasure and attained the peak of Economic Bliss (not to be confused with the Beatitude, which raises problems of a very different order). So growth theorists should in the first instance be prepared to save something about the consequences of the distribution of total output between consumption and investment. As Professor Swan has pointed out, “higher output per head would be of no advantage i f (by reason of the higher S) consumption per head were permanently lowered”.lO Oddly enough, this problem has received scant attention in the literature. P. C. Mahalanobis has examined a two-sector model which analyses the consequences of a planning decision concerning the allocation of investment resources between the investment-goods industries and the consumption- goods industries.11 The model is designed to show the consequences of alternative possibilities, but no optimizing solution is considered. The most celebrated attempt to do so is Ramsey’s model for determining the allocation of product between consumption and investment which will maximize the total utility of consumption over time.12 Richard Stone has shown that

9 T. W. Swan, “Economic Growth and Capital Accumuhtion”. Economic Record, Novem-

10T. W. Swan, “Of Golden Ages and Production Functions”. Paper delivered to the

11 P. C. Mahalanobis, “Some Observations on the Process of Growth of National Income”,

laF. P. Ramsay, “A Mathematical Theory of Saving”, Economic Journal, 1928.

ber 1956.

Round Table on Economic Development, Garnagon, April 1960.

Sankhya, Vol. 12, 1955.


on very simple assumptions the results of this optimizing model tend to those which follow from the assumption of constant savings and capital coefficients.13 The model does however give an account of the way in which the system reaches its ultimate state, and is important because it points the way to a rational solution of the planning problem, and does take into account the welfare consideration of the satisfaction of consumers’ wants.

I1 The basic ingredient of all growth models is the Keynesian proposition

that the equilibrium level of output in any period is determined by the interaction between the propensity to save and the inducement to invest. Pepper this with the fact that investment is an addition to capital, add a production function to taste, and a Growth Model is ready to be served. The recipe is summarized in the following propositions:

S = s Y = I dK I =- dt

y = f(K,N) Here N is taken to be the available labour force, and the full employ-

ment of both labour and capital is assumed. The rate of growth in output is thus determined by the rate of capital accumulation, the rate of growth in the labour force, and the state of technical knowledge described in the production function. Growth theory can be said to consist of elaborations of, quarrels with, and departures from this basic model.

It may be helpful to begin with a brief rksumC of the dynamic analysis introduced by Harrod,l4 since it is true of modern growth theory that “in the beginning there was Harrod”, and the terms he introduced have become part of the standard terminology in the subject. Essentially, the analysis consists of substituting the Acceleration Principle for the Investment- demand schedule in Keynes’s General Theory. Its validity is consistent with rival causal theories of growth, and different interpretations can be given to it, but the following exposition seems to be that which is most consistent with Harrod‘s own views.

The model can be summarized in the following proposition. First, saving is a constant proportion of income, and, for any level of income identically equal in value to investment.

S = s Y = I

Here investment includes stocks of consumption goods. Harrod ex- pressly makes no distinction between capital goods and consumption goods;

18 R. Stone, “Three Models of Economic Growth” (University of Cambridge, Department

14R. F. Harrod, Towards a Dynamic Economics (London, Macmillan & Co., 1948). of Applied Economics, 1963, Reprint Series No. 194).


investment is a net addition to capital, but “need not consist exclusively or even mostly of capital goods. I t is merely the accretion during the period of all goods”.

Secondly, a relation exists between the growth of output, and the addi- tional capital required to sustain that growth.

dY I , = v, - d t

v, is thus a marginal concept; “it is the new capital required to sustain the output which will satisfy the demands for consumption arising out of consumers’ marginal addition to income”. For v, to remain constant, it is necessary that the rate of interest remain constant (so that there is no Vulgar technical progress) and that technical progress Proper be neutral, in the sense that the productivity of men making machines increases at the same rate as the productivity of men minding machines. (There is no “bias” in technical progress.)l“

It is also important to remember that v, is not a technical but a value coefficient, since saving, investment and output are all measured in the same units. Hence, as we have seen, its value depends both upon the price of capital, and its productive capacity. In our previous notation, v, = ( p / q ) .

Thirdly, the actual rate of growth in output between any two periods of time is given by g = ( l / Y ) ( d Y / d t ) , and is determined by “the collective trials and errors of vast numbers of people”.

Fourthly, if I, = I, then SY = v,. ( d Y / d t ) , and g = (slur). This represents the rate of growth in output for which the productive

capacity generated by new investment is just sufficient to satisfy the antici- pated increase in demand for output on which the investment is based (so that entrepreneurs’ expected rate of profit is realized). This rate of growth (which is designated by g,) Harrod calls the warranted rate of growth; it is the rate of growth in output which is “warranted” by the thriftness of the economy, as defined by the savings coefficient. Hence g, = (s/v,).

But if g > g,, it follows that I, > I, so that demand is greater than expected, and output will be increased. The converse is true if g < g,. Hence the warranted rate of growth represents an unstable line of advance, since if the actual rate does not equal the warranted rate, there is no tendency for it to be adapted towards it, but on the contrary, a tendency for it to be adapted still further away.

In view of the immediate publication of a number of articles which purported to overcome the problem of the apparently “knife-edge’’ equili-

14aFrom the identity$=$’f5 is follows that if output per man is increasing, while

is constant, then -and - must increase at the same rate, that is, the value of capital Y K N N

per man must increase at the same rate as productivity is increasing.


brium represented by the warranted rate of growth, it is worthwhile noting Harrod’s emphasis of the point that “this kind of instability has nothing to do with the effect of lags, and strikes me as more fundamental”.

Fifthly, the maximum rate at which the economy can develop (the “natural” rate of growth) is determined by the “fundamental conditions” of the increases in the available workforce and its productivity.

If n = rate of growth in the labour force and r = rate of increase of output per man, then the natural rate of growth is given by g,,= n + r.

Sixthly, g, is thus the rate of growth of output which ensures full employment of capital, g,, the rate which ensures full employment of the labour force. So to create the possibility of growth with full employment of both labour and capital, it is necessary that g, = g,,; and for this possibility to be realized, i t is necessary that, either through social action or through entrepreneurial energy, g = g, = g,,. In this case, the economy may be said to be experiencing what Mrs. Robinson has called a Golden Age (to indicate “that it represents a mythical state of affairs not likely to obtain in any actual economy”). The Golden Age is the dynamic counter- part of the Stationary State of classical theory,lO and is designed to serve the same purpose-though it requires more specialized assumptions than the latter, as Professor Swan has pointed out.

Inequality between the natural and warranted rates of growth is a purely conceptual problem, and cannot define the actual state of the economy, which depends upon the relationship between g, g,, and g,,. Suppose for instance that the natural rate of growth exceeds the warranted rate. This means that, with a given u,, the savings coefficient is too small to admit of a rate of growth of output sufficient to create employment for the expanding labour force, without creating a shortage of capacity. Paradoxically enough, the solution to this problem is to reduce the relative demand for consumption goods (by increasing s) and so increase the proportion of output devoted to investment. (This has relevance to the problem posed by Mahalanobis.) This is true regardless of the economic situation involved. Harrod, for instance, considers that in these circumstances the actual rate of growth will be above the warranted rate, and an inflationary situation will develop. Mrs. Robinson, however, tends to identify the actual rate of growth with the warranted rate, so that the above situation leads to a state of long-run unemployment.l6 It would seem that to increase the propensity to save is a cure both for inflation and unemployment1 The difference is that in Mrs. Robinson’s case the increased saving must be accompanied by an increased desire to invest, otherwise the situation would become worse. The Keynesian moral of this story is that the growth of output depends

16Se-e Manhall’s description of a regularly progressing economy, Principles, p. 368-

1eSee The Accumulation of Capital, p. 79. though he does not allow for any form of technical progress.


fundamentally upon “animal spirits” and a strong inducement to invest. Failing this, increased saving can be a positive impediment to growth.

Changes in the warranted rate of growth can of course be achieved by changing v, as well as by changing s. This is particularly relevant to the situation in which the warranted rate of growth exceeds the natural rate. If v, is increased, so decreasing g,, then in the period of transition g,, will be increased, since an increasing value of v, means an increase in the degree of mechanization (assuming the price of capital to be constant), and so an increase in output per head due to technical progress of the Vulgar kind.

Harrod’s analysis is probably more significant for the problems which it raises, and for the change in economic thinking which i t inspired, than for its practical virtues. I t does, however, provide a means of analysing situations in terms of the propensity to save, and the techniques of production employed.

J. R. Sargent’s recent analysis of the British economy, for instance, can be interpreted simply in terms of the relationship between g, g,, and g,, and of the relative significance of s and v,.l‘ The formula for the warranted rate of growth also contains the implication that, if a particular rate of growth is to be achieved, the ratio of consumption to income that can be allowed is higher, the more “capital-saving” is the type of investment made; or that, given the technique of production being implemented, the rate of growth that can be achieved depends upon the proportion of output which is devoted to investment.

In The Accumulation of Capital, Mrs. Robinson illuminates much that is obscure in Harrod‘s analysis, and provides a good deal more besides. The method adopted is to begin with the very simplest model of a growing economy, in order to examine the basic properties of the growth process, and proceed to the successive relaxation of the initial assumptions, 50 as to provide models of greater complexity. The analysis is characterized by the fact that it makes explicit distinction between the machine-minding sector (the consumption-goods sector) and the machine-making sector (the investment-goods sector).

I do not wish to spell out in detail the assumptions underlying the model.l* Basically, what is envisaged is a community consisting of two classes of persons, workers and entrepreneurs, the workers being employed by the entrepreneurs in two ways: to produce, with the aid of machines, a homogeneous consumption good, and to produce machines. There is only one type of machine known; the output of consumption goods per machine, and the numbers of men needed to make and to mind a machine are

17 J. R. Sargent, Out of Stagnation (Fabian Tract No. 343). 18 They are to be found in The Accumulation of Capii?d, Chapter 7.

12 AUSTRALIAN EOONOMIC PAPERS JUNE-DEC.

constant. I shall also assume that machines are built by unassisted labour,l9 and are infiinitely longeval (so that there is no depreciation). Production is vertically integrated; each entrepreneur supervises the construction of his own machines, and derives his profit from the sale of consumption goods.

I t is also assumed that the total output of consumption goods is con- sumed by the workers in the two sectors, who do not save. Entrepreneurs do not consume (we are treating them purely as firms), and all profits are invested in the production of machines.20 As far as the income equations Y = W + P and Y = C + S are concerned, this assumption means that W = C and P = S; and the value of investment in terms of machines is given by I* = P = S. Since all machines are alike, investment (4 and the stock of capital ( K ) can be measured unambiguously in terms of machines, and “physical capital” has a definite quantitative meaning.

The model can thus be described in the following terms: (i) C = aK; a is the output of consumption goods per machine.

(ii) Lo= bK; b is the number of men to mind a machine. Hence y = ( a / b ) = output of consumption goods per man.

(iii) LI = pZ; p is the number of men to make a machine. Hence p represents the value of a machine in terms of labour time, and the real-capital-ratio in the consumption sector is given by

B b x = -

If w = real wage in terms of consumption goods, the wages cost 19This assumption may appear particularly offensive. As Solow says, “I regret having

to do this, but it is an immense simplification, and I do not believe that any matter of principle is involved”. Expositions of Mrs. Robinson’s model involving the use of machines to make machines can be found in G. D. N. Worswick, “Mrs. Robinson on Simple Accumulation”, Oxford Economic Papers, June 1959, and K. Lancaster, “Mrs. Robinson’s Dynamics”, Economica, February 1960 (though I should quarrel severely with the interpretation of Mrs. Robinson’s model contained in these articles). But even here some assumption must be made as to whether these machines are herma- phroditic, that is, “dual-purpose” (see Adolf Lowe, “Structural Analysis of Real Capital Formation”, Capital Formation and Economic Growth, N.B.E.R.), or non-substitutable and unable to reproduce themselves (see A. K. Sen, “Capital Intensity and Development Planning”, and “Choice of Capital Intensity Further Considered”, Quarterly Journal of Economics, November 1957 and August 1959). The conclusions obtained from these models do not differ radically from those which follow from the assumption that machines are made by labour alone, and this provides a good case for invoking the principle of Occam’s Razor.

2oThe assumption is made purely for the sake of simplicity, and is extremely easy to relax. Interestingly enough, Professor Swan has shown that, on the assumption that the production function is linear and homogeneous, and the rate of profit and the real wage rate are equal to the marginal products of capital and labour respectively, consumption per head is maximized in the long run if all profits are saved (and invested) and all wages spent. See also Joan Robinson, “A Neo-Classical Theorem”, Reoiew of Economic Studies, No. 80, June 1962. Here it is shown that Professor Swan’s proposition is true, no matter who does the saving, as long as the rate of profit is equal to the rate of growth of output.


of a machine is p = pw. Total Profit is given by P = C - wL0. The assumption that all profits are invested means that

(iv) P = p I . dK dt

(v) z = - It follows from these propositions that the rate of growth of capital (and

of output) is given by a - b w y - w g w = - - - -

Pw wx Given the coefficients of production, there is perfect inverse correlation

between the rate of accumulation and the real wage; but “it would be misleading to say that one determines the other, for the relationship between them involves a long past history”. It may be that workers are so organized that they can determine the level of wages, and so determine the profit available for investment; or i t may be that entrepreneurs are powerful enough to impose upon workers the real wage compatible with the rate of investment they desire. If both workers and entrepreneurs are power- fully organized, there may arise a conflict between the desire of entrepreneurs to invest, and the refusal of workers to accept the level of wages which this rate of investment entails. Thus the level of wages which workers are prepared to accept constitutes at the upper end of the scale of possible rates of growth an “inflation barrier” to the maximum rate of growth.

The first elementary conclusion which emerges from the model is that for growth to take place, there must exist in the Consumption-sector a technical surplus above the level of output necessary for subsistence. Within this barrier i t is necessary that workers are prepared (or are forced) to accept a real wage low enough to provide an investible surplus. This is the unwelcome conclusion for countries which are “technically poor”, that “coercive power is a necessary element in the process of capital accumulation, as necessary as the margin of squeezable resources on which it operates. Someone-enclosing landlord, exploiting industrialist, financial manipu- lator, commissar or democratically trusted leader-has got to be tough. (Hence since the commissar has a long lead in toughness over the demo- cratic leader, his advantage must be neutralized by outside aid to supple- ment that margin the inadequacy of which makes toughness the supreme economic virtue.”)21

The opposite problem exists for a “technically rich” community. A large technical surplus may exist; but entrepreneurs must have the energy and the willingness to invest this surplus, i f the economy is not to fall into stagnation. (The surplus may of course be taken out in a high level of wages, or entrepreneurial consumption out of profits, in lieu of a high rate

21 The &onomist, February 13, 1960 Review of Keintead, Capital, Interest and Profits.

of growth.)


The rate of growth derived from the model corresponds to Harrod’s warranted rate of growth, since it is based on the assumption that capital is fully employed. It is easy to show that 0, - w) /wx = slur. The situations discussed by Mrs. Robinson, of scarcity and surplus of labour, and the relation between monopoly and real wages, are simply examples of inequality between g, g,, and g,. Some formal properties of the model are:

(a)The level of total output (measured in terms of consumption

(b) The distribution of income is constant. goods) is given by Y = C + I* = C 3- PI .

P a - b w W A=-=-- - I - - W a Y

and P = AC Hence Y = C + I * = (1 + A)C.

,Y - -w

(c) The rate of profit on capital is given by

*--- - gw wx (d) The savings coefficient for total income is given by

s x Y - K s=- -

Hence total saving is a function both of the level and the distribution of income.

(e) The relationship between output and the value of ca ital (which in this case is the same thing as Harrod’s “margina P capital coefficient”) is given by

K* P v‘=Y= a(l + A )

Hence 0, depends on the distribution of income, as well as upon the technical coefficients of production.

(f) Changes in the distribution of income thus cause both s and v, to change, and the distribution of income is a means of effecting changes in g,.

(g)The natural rate of growth is determined solely by the rate of growth in the available labour force. g,, = n, and sets a maximum upper limit to the rate of development.

(h) The rate of growth in the demand for labour (that is, in the labour force employed) is determined by the rate of accumulation.

1 = g, (i) If 1 =n, then the economy is in a Golden Age, exactly as it is

described by Marshall. (j) Consideration of a two-sector economy makes explicit the role

of saving and investment in the growth process. It seems to me much more meaningful, in the context of growth, to say that S = AC = PI, rather than the common tulate that S = SY = I .

(k) The fact that u,. is a value coefficient, Kend ing on the distribution of income (i.e. the wage rate) and the technical coefficients of production has an important consequence for Harrod’s problem of inequality between the natural and warranted rates of growth,


since it means that v, can be changed either by changing the cost of a given type of machine, or by changing the sort of machine being produced.

Mrs. Robinson introduces technical progress into the model with the assumption that in each period there is only one technique of production known, but that this technique becomes more efficient in each period. If technical progress is neutral, in the sense that the productivity of men minding machines rises at the same rate as the productivity of men making machines, then we have to make the simple alteration to the model that

b = boe-rt and p = &e-rt

so that the output per man rises at the same rate r in both sectors. Here we are assuming that the type of machine used does not change

(a = output per machine is constant) so that the increases in productivity are due entirely to increases in labour efficiency. This assumption is made so that we can preserve a physical measure of capital, as the stock of machines in existence; that is, we are able to measure capital in its own technical unit. The characteristics of the model are not radically altered if we assume that a different kind of machine is produced in each period (though its formulation is naturally more complex), but the whole problem of the measurement of capital is called into question, and I should prefer to avoid this question as much as possible.

Assuming that all capital is fully utilized, the rate of accumulation is again given by

a - b w g, = ~ - y - w -- PW wx

where b, p and w are initial values. If the real wage increases at the same rate as productivity, then g, is

mnstant (and so the rate of profit on capital is constant). When this condition is satisfied, the rate of technical progress has no effect at all upon the rate of development-in fact this is always true as long as wages and productivity change in unison. Changes in the rate of growth are caused by “once-and-for-all” changes in the technical coefficients, or in the distribution of income, in any given period. This seemingly *‘pro-accumulation, anti-technology” argument, however, only applies if the rate of accumulation is less than the maximum possible rate, which is now

g, = n + r.

Technical progress is a means of averting the fall in the rate of profit which is threatened by the attempt to accumulate faster than the rate of growth in the available labour force. It means that the possible rate of development is no longer limited by the rate of growth in the labour supply; in fact, if the real wage rises only as fast as productivity, it is


necessary that the rate of accumulation exceed the rate of growth of population, if the potential increase in output due to the increase in productivity is to be realized.

The growth in the demand for labour is now determined by the rate of accumulation and technical progress.

1 = g,--r The condition for a Golden Age is that 1 = n; the difference between

this model and the previous one being that the system is no longer expanding in all its parts at the same rate, since the rates of growth in output and capital are now faster than the rate of growth in population. Otherwise, the basic properties of the model remain much the same as before.

An important consideration is that the real-capital-ratio for each addition to capital is constant over time; but i t is untrue to say that the ratio between total real capital and total employment in the consumption- sector remains constant, as Mrs. Robinson seems to imply. To do this is to make the implicit assumption either that existing capital changes its nature in each successive period of time, or (which comes to the same thing) that capital has a very short life, and the whole capital stock is adjusted more or less instanteously to changing conditions. But the labour time embodied in a machine produced in period 0 is Po, while the time embodied in a machine produced in period 1 is only PI. This applies equally well to Professor Swan’s meccano sets, as to our machines of a constant type, both of which are only devices for measuring capital in its own technical unit. It illustrates the point made earlier in this paper that, while the efficiency of current labour can be increased, the labour time embodied in a piece of equipment is an immutable fact of history. Perhaps Mrs. Robinson did not realize the full implications of her statement that “it is important to observe that though both elements in this ratio (the real-capital-ratio) are expressed as quantities of labour time, they are not in pari materia; one consists of past labour time embodied in a stock of capital goods, the other is a flow per unit of time of current labour”, but it is a matter which becomes extremely important in the consideration of the measurement of the capital stock involved in the use of a production function. Under the conditions postulated, with wages rising with productivity, the overall real-capital-ratio is increasing, though at a declining rate (the increase is linear). If capital is measured in terms of machines, the overall capital- labour ratio increases at the same rate as does productivity; and the same is true if capital is valued in terms of consumption goods, since the price of a machine is constant. In these cases, the capital-labour ratio involved in each addition to capital is higher, as technical progress goes on.

These two models suffer from the severe simplifying assumption that only one technique of production is available in each period. But a given state of technical knowledge is usually taken to mean that at any time


there are a variety of techniques available for producing any given output, and entrepreneurs are faced with the economic choice of deciding which technique to use. One technique is differentiated from another by its cost, and the output per man to be obtained from its use, and the economic choice is to adopt the technique which will provide the maximum expected rate of profit on investment.

In a given state of knowledge, the efficiency of labour is improved by the use of Bigger and Better machines: machines which are Bigger in the sense that they require more men to make them, Better in the sense that the productivity of the men minding them is increased. We may thus define a technique by x, the real-capital-ratio which it entails. The larger the value of x, the more mechanized is the technique, and the higher is y, the output per man employed using that technique. The range of known techniques can therefore be summarized in the “productivity function”,

for which dyldx is positive, but decreases as x increases. Movement along this function involves technical progress of the Vulgar kind; technical progress Proper involves an upward shift in the curve.

The productivity function is not to be confused with the conditional Total Product curve (conditional, that is, upon the quantity of labour taken as given) of conventional theory. It is only on special assumptions concerning the nature of the production function Y = f(K,L) that from it we can derive a functional relationship between Y I L and K / L . Moreover, the conventional use of the production function is to determine the total quantities of the factors of production which will be employed, their prices being given; the productivity function can only be used to decide the best technique to be used, and the quantities of labour and capital actually employed are determined by other considerations.

Entrepreneurs will choose to use the technique which maximizes the rate of profit on investment, given by

Y = f ( x >

Y - W r = - wx If the real wage is given, then p is a maximum when22

dY w = y - x - dx that is, when

- dY - Y - W - WT. dx--- X

Since the slope of the straight line with w as ordinate, drawn to any point on the productivity curve, is also equal to (y - w ) / x , the geometric

23 Cf. R. Dorfman, “A Graphical Exposition of Bohm-Bawerk’s Interest Theory”, Rmim of Economic Studies, February 1959. B


solution to the problem is that the value of x which maximizes v is determined by the tangent to the curve drawn through w .

It can be seen that the higher is the wage rate, the more mechanized is the technique of production used, and the lower is the rate of profit. The significance of the availability of a range of techniques is that, with a higher wage, the rate of profit is not as low as it would be, if only one technique were known.

If we treat the productivity function simply as a blueprint of techniques from which one is chosen, then once the choice is made, the situation is the same as that described in the first simple model, in which the technique of production was fixed. The difference is that in this case the technique used is a result of economic considerations, whereas previously i t was due to the limited state of knowledge. We can then make comparisons between two economies which enjoy the same state of technical knowledge, but in which the level of real wages is different. In the economy with the higher wage, the degree of‘ mechanization is higher, and productivity is higher, but the rate of profit, and hence the rate of accumulation, are lower; these are the advantages and disadvantages of technical progress of the Vulgar kind.

Comparisons between different economies, each settled into and enjoying its own Golden Age, are an exercise in comparative dynamics. The analysis of the time-path by which an economy moves from one Golden Age to another is an infinitely more difficult problem, since the movement involves a continuous shift to more mechanized techniques as the real wage rises, and accumulation must continue in the face of a falling rate of profit. Mrs. Robinson has made several valiant attempts to cope with this problem.28 We can perhaps, as a first approximation, obtain some broad generalizations about what goes on from comparing adjacent positions of Golden Age equilibra; that is, to consider the results of getting there, rather than how we get there. Increasing the degree of mechanization enables entrepreneurs to fend off the fall in the rate of profit that is associated with using real wages, and also enables them to accumulate capital at a rate faster than the rate of growth in population. (In the transition period, the natural rate of growth is increased due to rising productivity.) Part of this accumulation is absorbed by the rising real wage; this is the influence of the “Wicksell Effect”. The distribution of‘ income between wages and profits is, as we have seen, given by A = 1 - w / y ; the profit- maximization-principle means then that

28See The Accumulation of Capital, Ch. 14; “The Real Wicksell Effect”, Economic Journal, 1958; and “AccumuIation and the Production Function”, Economic Journal, 1959.

1964 RECENT DEVELOPMENTS IN GROWTH THEORY 19 so that the distribution of income depends upon the elasticity of output per man with respect to the real-capital-ratio.

But the production of Bigger and Better machines as the process of transition continues calls into question the measurement of the total stock of capital; and this is the crux of the matter. T o avoid this problem, it is necessary to assume either that capital is a fluid factor of production, capable of changing its form and its nature, or that there is instantaneous adjustment to each new technique introduced; and this is not compatible with an analysis of the time-path followed by the economy, for to neglect the adjustment process is tantamount to applying comparative statics to a process in time.

If the existing stock of capital is taken as datum, then we may think about the model in the following way.

At any given time there is an inherited stock of machines, which determines the level of employment in the consumption-sector. If the real wage is expected to remain constant, then capital accumulation will consist of machines of the latest type, and total employment in the investment sector (which is the value of investment in terms of labour time, or “real” investment) is determined by the current real wage and the size of the investible surplus (Total Profit). Since the real-capital-ratio for this investment is determined, total employment in the investment sector determines the increase in employment in the consumption-sector which will be associated with the new machines. The output per head of these workers is determined by the technique used, so the increase in the total output of consumption goods is determined, and the whole process is repeated.

Suppose however that entrepreneurs forecast (correctly) a rise in the real wage, so that a more mechanised technique is adopted, and investment consists of Bigger and Better machines. Total employment in the investment Sector is again determined by the current real wage, with the same consequences as above. These propositions may be expressed:

(9 Y = f(x) (ii) w , = y - x -, dY where we = expected real wage

dx (iii) P = C - wLa = wLI, where w is the current real wage

dLa (iv) L I = x - dt dC dLO

(v) dt = Y dt It is necessary in this case to stipulate initial values for the level of total

Consumption, the level of employment in the Consumption-sector, the current real wage, and the expected real wage. Here the value of investment is determined by the current real wage; this is in contrast to the neo-classical


theory, in which the real wage is determined by the marginal product of labour, and the given quantity of labour.

I am not sure how (or even if it is possible) to describe the time-path of this model, but i t would seem that something of this kind must be done, as soon as we want to take account of the changing nature of capital equipment.

Professor Swan discusses the problem in his Gamagori paper; but (to my knowledge) the first person to make this point, and to insist strongly on its recognition, was W. E. G. Salter.24 T o quote directly from his Vienna paper: “Total supplies of capital in each period consist of current net investment plus capital accumulated in the past. Successive periods therefore imply total supplies of capital K1, K,, K 3 . . . .These together with available supplies of labour lead to a sequence of techniques, A, B, C . . , , implying values of total output Y1, Y,, Y 3 . . . . Strictly speaking, these values refer only to notional equilibria that would be reached if the whole economy were adjusted to these techniques. Only if the capital stock were wholly transformed in each period into the physical forms appropriate to A, B, C . . ., would the values Y,, Y2, Y 3 . . ., be achieved. In fact, however, the rate at which the capital stock may be so transformed is limited by the rate of gross investment. This year technique A* is appropriate and is reflected in the physical form of current investment; but, before a fraction of industry is equipped with A* equipment, either technical progress or capital accumulation have made technique B* appropriate; and so on with new techniques appearing before their predecessors have worked their way through the capital stock. Output, and output per head never reach their notional values, Y1, Y2, Y 3 . . ., and Yl/N1, Y 2 / N 2 , Y 3 / N 3 . . ., but fall short by an amount reflecting inability to transform the physical form of the capital stock.” Salter then proceeds to derive two basic functions:

(i) A “best-practice production function”, Y t = Ft (ntt Gt)

where y t = output of plants built at time t n, = employment associated with these plants G , = gross investment at time t.

“This function is similar in concept to an ordinary production function except that its relevance is restricted to new plants.” The model dispenses with the need to measure the existing capital stock, which is treated as a “Who’s who” of inherited capital goods, and so offers “a means of escape from the tyranny of the aggregate production function Y = f(K,N)”.

Total output (Y,) is then the sum of the outputs produced by the various

24 W. E. G. Salter, “The Production Function and the Durability of Capital”, Economic Record, 1959; and “Productivity, Growth and Accumulation as Historical Processes” (Paper delivered to the Znternational Congress on Economic Development, Vienna, 1962).


plants of different ages which make up the existing capital stock, and total employment (N,) the sum of the labour forces employed by these plants.

(ii) A “capital stock function” derived from the relationship between Y t and N,, and the form of which depends on the age of the oldest plant in existence (which in turn depends on the current real wage).

This function summarizes certain characteristics of the existing capital stock, and thus of the past economic history of the economy. The use of this function enables us to break away from “the notion of a self-contained present”, and introduce into the analysis “a new class of restraints”- historical restraints that depend on the past history of the economy.

If gross investment is a function of total output, these two relationships (together with the neo-classical assumption that the marginal product of labour is equal to the real wage) determine the characteristics of the system at any time. Setting the model in motion, however, raises difficult problems; as Salter says, “complex issues involved for a system such as this, which generates its own history, quickly become very involved”, and “clearly there is much to be done in exploring how different kinds of technical and historical restraints affect the growth path of an economy”. The real significance of Salter’s work is that it points the way to what I believe is the proper future development of growth theory, and makes brighter the “dim conception of the kind of revolution that is required in economics” first provided by Harrod’s dynamic equations.26

Everything that has been said so far can be regarded as an extension and deveIopment of Harrod’s “simple piece of arithmetic”, and an examination of its implications. Another obvious line of attack was suggested by Professor Swan% and R. M. Solow.27 This is to substitute a production function of

25 In his latest (published) model, Mr. Kaldor has abandoned the use of a total production function, and redefined his “technical progress function” so as to describe the relationship between the rate of change of gross (fixed) investment per operative and the rate of increase in labour and productivity on newly-installed equipment. (See Kaldor and Mirrlees, “A New Model of Economic Growth”, Review of Economic Studies, No. 80, June 1962.) The model is too detailed to be summarized here; but its affinity with Salter’s work is readily seen from Kaldor’s own description of it. “A ‘production function’ in the sense of a single-valued relationship between some measure of capital, X,, the labour force N t and of output Y, (all a t time t ) clearly does not exist. Every- thing depends on past history, on how the collection of equipment goods which composes K, has been built up.” Where he diflers from Salter is in that “the model is Keynesian in its operation (entrepreneurial expenditure decisions are primary; incomes, etc., are secondary) and severely non-neo-classical in that technological factors (marginal productivities or marginal substitution ratios) play no role in the deter- mination of wages and profits”. The distinguishing features of Mr. Kaldor’s approach to growth theory are his explicit rejection of neo-classical, “marginal-productivity” analyses, and the facr that his models attempt to explain “how a system could attain steady growth, and how changing investment would call forth the required changes in savings”, rather than to analyse the characteristics of steady growth.

28 T. W. Swan, “Economic Growth and Capital Accumulation”. Economic Record, 1956. 27 R. M. Solow, “A Contribution to the Theory of Economic Growth”, Quarterly Journal

of Economics, 1956.


the form Y = f(K,N) for Harrod’s “relation” between investment and the increase in income, so obtaining a model of the form described in the first paragraph of this section, that is,

S = s Y = I dK z = - dt

These models differ fundamentally from those we have so far considered, in that the supplies of the factors are determined (n =rate of growth in the labour force is taken as a datum, and k = rate of growth in the capital stock is determined by the propensity to save), and the wage-rate and the rate of profit are determined by the marginal productivities of labour and capital respectively. (As Solow points out, the rate of profit must be regarded as the annual “rental value” of a unit of capital.) As expository devices, these models have considerable value, though they depend for their operation on the assumption that the “price” of capital is constant and that capital is, like labour, measurable in its own technical unit.

In his first article, Swan assumes that the production function is of the form Y = KaNb (a and b are constant, and their sum is unity), so that the rate of growth of output is given by y = ak + bn, and shows that this will always tend towards n. In this position, the economy is in a Golden Age with y = k = n. Harrod’s natural rate of growth is equivalent to the rate of growth of output, since labour and capital are always fully employed. If y > n, then output per man is increasing, and there is technical progress of the Vulgar kind, given by r = a(k - n). This is the result of increasing v,.. The significance of the savings coefficient in the model is that it determines the equilibrium value for v,., which is s l y =s/n. If Proper technical progress is shifting the production function upwards at an annual rate m (in which case the rate of growth of output per man is y - n = r + m, that is, the sum of Vulgar technical progress and technical progress Proper), then y = ak + b n 3- m, and the equilibrium value for y is y = n + m/b-which is again independent of s.

The limitation of the production function employed in this model is that the elasticity of substitution between labour and capital is unity. J. D. Pitchford has examined the implications of a production function which allows the elasticity of substitution to take any value between zero and infinity, and shown that in this case a variety of growth paths are possible, depending on the elasticity of substitution.28 In his Gamagori paper, Professor Swan postulates a production function which is linear and homogeneous, and for which the production elasticities a and b sum to unity, but are not necessarily constant. The purpose of this model is to 28 J. D. Pitchford, “Growth and the Elasticity of Factor Substitution”, Economic Record,

y = f(K,N)

1960.

1964 RECENT DEVELOPMENTS IN GROWTH THEORY 23 explore the properties and uses of Golden Age equilibria, to determine their value as “a device for sorting out our ideas”. The conclusions reached about the apparent generality of assumptions made by model-builders such as Kaldor and Champernowne, are helpfully iconoclastic, and it is shown that the Golden Age is not a straightforward generalization of the Station- ary State, but requires more specialized assumptions.

Since increasing productivity is the mainspring of growth, it is pertinent to ask the question, “What makes productivity increase?” Dr. Coombs has listed some of the factors which can be expected to influence the rate of technical progress.20 In this paper, two sorts of technical progress have been distinguished: one of the Vulgar kind, which is due to rising real wages caused by a shortage of labour, the other of a Proper kind, which has been taken as a datum, and comes about through the mere accumulation and application of knowledge. There are thus two factors causing productivity to increase, the pressure of rising wages, and inventiveness per se. This latter is a force making for increased productivity even when there is a surplus of available labour. But the application of new ideas is obviously very much a matter of social and economic climate; as Kaldor says, “Tech- nical invention and population growth. . .are not like the weather or the movement of the seasons, that go on quite independently of human action, but are very much the outcome of social processes.. .. Though new ideas, looked at in isolation, are the spontaneous product of the working of the human brain, the kind of ideas that come forth, and their frequency, is very much a matter of environment.” It is obvious that there is a strong con- nection between the urge to accumulate, and the impetus to introduce labour-saving techniques of production; which leads us to the sort of conclusion so often arrived at in economics, that the desire to grow will of itself stimulate the process of growth. (Underdeveloped countries are limited not so much by a paucity of technical knowledge, which they can obtain from the developed economies, as by a shortage of capital.) Tech- nical progress is a means of warding off the fall in the rate of profit threatened by rising real wages. Technical progress Proper enables this threat to be averted completely, but Vulgar Technical Progress only permits the blow to be softened.

The division of production into a consumption-sector and an investment- sector is one way of “disaggregating” the economy; but another critical division (particularly in the early stages of development) is that between agriculture and industry. The growth of industrial production necessarily presupposes the growth of agricultural production. Increasing productivity of workers engaged in agriculture is a prior condition for industrial

29H. C. Coombs, “Some Ingredients for Growth”. Shann Memorial Lecture, 1963 (published by the University of Western Australian Press).

24 AUSTRALIAN ECONOMIC PAPERS JUNE-DEC., 1964

development, since the inability to supply food for a growing industrial population may severely inhibit the growth of the manufacturing sector.30 “Civilization is the result of agriculture plus coercion.”31 A more complete description of the growth process could thus be obtained from a four-sector model: a differentiation of the agricultural and industrial sectors, and within each, the division between the consumption and investment sectors.

CIONCLUSION It was at the outset of contemporary growth theory that Harrod re-

marked that the proper development of dynamic theory “should involve a considerable rewriting of economics”. Certainly this has not as yet been done, though I think some progress has been made. The argument and controversy which has developed about growth models has served to clarify in some measure the sort of economic theory which is appropriate for true dynamic economics. As Professor Swan has said of Trade Cycle theory, “each hopeless effort adds its quota to knowledge and understanding of some of the forces operating in the economic organism and its cells”. I t would seem that the main casualty in the process may well be the conventional production function (and perhaps marginal productivity theory, if Mr. Kaldor has his way); these concepts are appropriate to the theory of the individual firm, but cannot be carried straight over to a theory about the economy as a whole. Harrod also remarked that he was convinced that “economic theory will only make good progress to the extent that it can transform itself into econometrics”; and it could well be that growth theory is now in need of a rest-pause, while i t digests what it has, and begins to develop empirical foundations. To come back to Professor Swan (and substituting “economic growth” for “trade cycle”): “Is it not time to turn from alchemy to chemistry-to forget the glittering prize of achieving the theory of economic growth, and concentrate upon a systematic and pedestrian attempt to discover how the economy works and grows in its parts and as a whole?”

80 See N. Kaldor, “Characteristics of Economic Development”, Asian Studies, Vol. I,

3lRemark made by Professor K. Boulding, at a seminar in Melbourne, January 1964. November 1956.

recent developments in the theory of economic growth

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