THE ROBINSON MODEL

Mrs Joan Robinson in her book “The Accumulation of Capital” builds a simple model of economicgrowth based on the ‘capitalist rules of the game.’ But “it is not so much concerned with anautomatic convergence to a moving equilibrium in a capitalist economy, as with studying theproperties of equilibrium growth.”Assumptions. Mrs Robinson’s model is based upon the following assumptions:(a) There is a laissez-faire closed economy.(b) In such an economy capital and labour are the only productive factors.(c) In order to produce a given output, capital and labour are employed in fixed proportions.(d) There is neutral technical progress.(e) There is no shortage of labour and entrepreneurs can employ as much labour as they wish.(f) There are only two classes, the workers and the entrepreneurs between whom the nationalincome is distributed.(g) Workers save nothing and spend their wage income on consumption.(h) Entrepreneurs consume nothing but save and invest their entire income from profits forcapital formation. “If they have no profits the entrepreneurs cannot accumulate and if they do

C H A P T E RC H A P T E RC H A P T E RC H A P T E RC H A P T E R

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37

not accumulate, they have no profits.”(i) There are no changes in the price level.

THE MODEL

Given these assumptions, net national income in the Robinson model1 is the sum of the totalwage bill plus total profits which may be shown as

Y=wN+pKwhere Y is the net national income, w the real wage rate, N the number of workers employed, pthe profit rate and K the amount of capital. Here Y is a function of N and K. Since the profit rateis crucial in the theory of capital accumulation, it can be shown as

pY wN

K= −

Divided by N,

p

Y

Nw

K

N

=−

By putting Y/N = l and K/N = θ (theta), we have

pl w

=−θ

Thus the profit rate is the ratio of labour productivity minus the total real wage rate to theamount of capital utilized per unit of labour. In other words, the profit rate (p) depends onincome (Y), labour productivity (l), the real wage rate (w) and the capital-labour ratio (θ).On the expenditure side, net national income (Y) equals consumption expenditure (C) plusinvestment expenditure (I),

Y = C+ISince Joan Robinson assumes zero saving out of wages but attributes saving to entrepreneurs,profits are meant for investment only, we have

S = IThis saving-investment relation may be shown as:

S = pKand I =∆K [∆K is increase in real capital]

pK = ∆K [ Q S = I]

or pK

K

l w= =

−∆θ

The growth rate of capital (∆K/K) being equal to p (the profit rate), it depends on the ratio of thenet return on capital relative to the given stock of capital. If income remains constant and thewage rate decreases or income increases and the wage rate remains constant, the profit ratewould tend to increase. The profit rate can also increase if the capital-labour ratio falls. In thisway, the entrepreneurs maximize profits.

1. Mrs Joan Robinson builds only a “verbal” model. The credit for constructing a mathematical modelgoes to Prof. Kenneth K.Kurihara, op.cit.

268 The Economics of Development and Planning

The Golden Age. Besides the growth rate of capital (∆K/K), another factor which determinesthe growth rate of an economy is the growth rate of population (∆N/N). When the growth rateof population equals the growth rate of capital i.e., ∆N/N = ∆K/K, the economy is in fullemployment equilibrium. Joan Robinson characterises it as “a golden age” to describe smooth,steady growth with full employment. “When technical progress is neutral and proceedingsteadily, without any change in the time pattern of production, the competitive mechanismworking freely, population growing at a steady rate and accumulation going on fast enough tosupply productive capacity for all available labour, the rate of profit tends to be constant andthe level of real wages to rise with output per man. There are then no internal contradictions inthe system. Total annual output and the stock of capital then grow together at a constantproportionate rate compounded at the rate of increase of the labour force and the rate of increaseof output per man. We may describe theconditions as a golden age.” 2

The golden age is explained in Fig. 1.Capital-labour ratio K/N or θ is measuredalong the horizontal axis and per capitaoutput on the vertical axis. The growthrate of labour force is taken to the left ofO along the horizontal axis. The curveOP shows the production function.Every point on this curve shows the ratioof capital to labour. In order to find outthe capital-labour ratio and the wage-profit relation, we draw a tangent NTwhich touches the production functionOP at point G and cuts the vertical axisat W. Point G shows the capital-labourratio for the golden age which ismeasured by OK. Per capita output isOA, out of this OW is paid as wages and WA or EG is the surplus which is the rate of profit oncapital.This figure also proves that the growth rate of capital (∆K/K) equals the growth rate of labour(∆N/N). EG/EW reflects ∆K/K and OW/ON reflects ∆N/N. Thus

EG

EW

OW

ON= [ Q tan α = tan β]

In case the economy diverges from the path of “golden age”, certain forces may tend to bringback the equilibrium position. If the rate of population growth is higher than the rate of capitalgrowth, i.e ∆N/N>∆K/K, it will lead to progressive underemployment. In such a situation, thesurplus of labour will lead to a fall in money wages and if the price level remains constant, to afall in real wages. As a result, the profit rate would tend to rise and increase the growth rate ofcapital to the population level. The equilibrating mechanism would not work if real wages failto fall either due to the rigidity of money wages or because the price level falls in the sameproportion as money wages. The golden age equilibrium will not be restored and progressiveunderemployment will continue.

A GT

P

E

KON

α

β

Capital-Labour RatioGrowth Rate

of Labour

WP

er C

apita

Out

put

Fig. 1

2. J.Robinson, The Accumulation of Capital, p. 99.

Joan Robinson’s Model of Capital Accumulation 269

In the contrary case of capital growing faster than population growth, i.e., ∆K/K>∆N/N,equilibrium to the path of golden age can be brought about by technological changes such as achange in the capital-labour ratio or in labour productivity and by shifting the whole productionfunction upward so that as capital accumulates, the need for labour also increases.According to Mrs Robinson, an economy is in a golden age when the potential growh ratio isbeing realized. The potential growth ratio “represents the highest rate of capital accumulationthat can be permanently maintained at a constant rate of profit.” This potential growth ratio isapproximately equal to the proportionate rate of labour force plus the proportionate rate ofgrowth of output per head. The conditions of a golden age require the growth ratio to be steadyas frequent changes in the growth ratio disturb the tranquillity of a golden age. But thistranquillity may not be possible even when the growth ratio is stable. A rise in the total stock ofcapital is likely to slacken the urge to accumulate so that a state of stagnation starts and theeconomy goes off the path of the golden age. The golden age is not an ideal. A new growth ratiomakes a new golden age possible. An increase in growth ratio necessitates a rise in the proportionof productive capacity and a fall in consumption. Contrariwise, a fall in the growth ratio leadseither to unemployment or to increased consumption. A static state is, however, a special case ofa golden age, where the growth ratio is zero, the profit rate is also zero and wages absorb theentire net output of industry. Joan Robinson calls this the state of economic bliss, sinceconsumption is at the maximum level which can be permanently maintained in the giventechnical conditions.3So far as technical progress is concerned, it is neutral in the sense “that the value of capital interms of wage units per man employed does not alter appreciably when accumulation is goingon at such a pace as to keep the rate of profit constant.” But the rate of technical progressdepends upon demand and supply of labour. When firms fail to take advantage of the profitablemarkets expanding around them, they try to adopt labour-saving devices. This is because therate of technical progress is defined as the rise in output per head, assuming zero growth rate ofpopulation. However, technical progress continues even when there is massive unemployment.Joan Robinson points out that the growth of knowledge may lead to ‘autonomous innovations,’competition among firms may lead to ‘competitive innovations,’and the scarcity of labour may lead to ‘induced innovations.’For the purpose of the model, the desired rate of growth mayfall short of the possible rate of growth due to competitive andautonomous innovations.The desired growth rate is the rate of accumulation which makesthe firms satisfied with the situation in which they findthemselves. The desired growth rate is determined by the rate ofprofit caused by the rate of accumulation, and the rate ofaccumulation induced by that rate of profit. Robinson uses Fig.2 to explain it. The curve A represents the expected rate of profitas a function of the rate of accumulation. The curve I representsthe rate of accumulation as a function of the rate of profit. In asituation to the right of the point D, the expected rate of profit isless than the rate of accumulation. Any further investment is not

Rate of Accumulation

Rat

e of

Pro

fit

Fig. 2

3. In the Harrodian terminology, it is a state in which the natural, the actual and the warranted rates ofgrowth are all equal.

270 The Economics of Development and Planning

likely to be profitable and the rate of accumulation will fall. Between the points S and D, therate of accumulation is less than the expected rate of profit. Therefore, there will be tendency toincrease investments and the rate of accumulation will rise to point D. Thus the point D representsthe desired growth rate.On the other hand, the possible growth rate depends upon the physical conditions resulting fromthe growth of population and technical knowledge. When the desired growth rate equals thepossible growth rate at near full employment, the economy is in a golden age. The real wagerate is rising with increasing output per head due to technical progress. But the rate of profit oncapital remains constant. And techniques of production appropriate to the rate of profit arechosen. This is the golden age which Joan Robinson visualises.

A CRITICAL APPRAISAL

Mrs Robinson’s model is an elaboration of Harrod’s growth model. The possible growth rate isHarrod’s natural growth rate. In the golden age, the actual (G) and the natural growth (Gn)rates are equal to each other and the warranted growth rate (Gw) confirms to them. Both postulateneutral technical conditions and a constant saving ratio. However, Joan Robinson’s theory ofcapital accumulation depends on the profit-wage relation and on labour productivity. Harrod’stheory on the contrary depends on saving-income ratio and on capital productivity. The formerstresses the importance of labour in capital accumulation while the latter that of capital.Commenting on Mrs Robinson’s model Kurihara opines that “J. Robinson’s chief contributionto post-Keynesian growth economics seems to be that she has integrated classical value anddistribution theory and modern Keynesian saving-investment theory into one coherent system.”But it “is not capable of being modified so as to introduce fiscal-monetary policy parameters—unless labour productivity, the wage rate, the profit rate and the capital-labour ratio could beregarded as objects of practical policy as they might been regarded in a completely plannedeconomy.”4

ITS WEAKNESSES

Despite these merits, it has the following weaknesses:1. According to Kurihara, “Joan Robinson’s discussion of capital growth has the subtle effect

of discrediting the whole idea of leaving so important a problem as economic growth to thecapitalist rules of the game. Her model of laissez-faire growth demonstrates how precariousand insecure it is to entrust to private profit-makers the paramount task of achieving the stablegrowth of an economy consistent with the needs of a growing population and the possibility ofadvancing technology.”

2. Joan Robinson’s model is based on the assumption of a closed economy. But this is anunrealistic assumption because capitalist countries are open rather than closed economies inwhich foreign trade plays a crucial role in accelerating the growth rate.

3. This model assumes institutional factors as given. But the role of institutional factors asone of the determinants of economic growth cannot be neglected in any model. The developmentof an economy to a considerable extent depends on social, cultural and institutional changes.

4. This model is based on the unrealistic assumption of constant price level. When an economymoves on the path to progress, investment has to be increased continuously which tends to

4. K.Kurihara, op.cit., p. 80.

Joan Robinson’s Model of Capital Accumulation 271

raise the demand for factors but their supply cannot be increased to match the demand. Thisleads to rise in prices. Thus price rise is inevitable with growth.

5. Mrs Robinson assumes that capital and labour are employed in fixed proportions to producea given output. This is an unrealistic assumption because in a dynamic economy there are nofixed coefficients of production. Rather, substitutability between capital and labour takes placethrough time, the degree of substitutability being dependent upon the nature of technologicalchanges.

ITS APPLICABILITY TO UNDERDEVELOPED COUNTRIES

Robinson’s model has the following merits for underdeveloped countries.1. Joan Robinson, in her theory, studies the problem of population and its effect on the rate of

capital accumulation. There is a “golden age” which any country can achieve through plannedeconomic development.

2. An underdeveloped economy faces the problem of the rate of population growth beingfaster than that of capital growth, i.e., ∆N/N>∆K/K, as posed by Joan Robinson. It reveals thetendency of progressive underemployment in such economies.

3. The “potential growth ratio” is crucial to Robinson’s theory of economic growth. Thegolden age depends on the growth ratio. The task of planning becomes easier if the potentialgrowth ratio of an economy is calculated for the planning period on the basis of the growth rateof labour force and of output per head.

4. In an underdeveloped economy, the rate of capital accumulation is always less than itspotential growth ratio, that is why it is backward and possesses surplus of labour force. It,therefore, rests with the planning authority to increase the rate of accumulation to the level ofthe growth ratio for the economy. An underdeveloped country cannot, however, match the twoby following the capitalist rules of the game. On the contrary, it devolves on the planningauthority to take the initiative in controlling and regulating not only private investment butalso public investment in such economies.However, it is not possible to use the concept of the ‘golden age’ in solving the problems ofunderdevelopment, for the unchanging continuity required for the golden age is not present ina developing economy.