The Robinson Model

CHAPTER

37 Joan R obinson’  obinson’ s Model of    Ca pital pital Accum ula  ula tion  tion 

THE ROBINSON MODEL

Mrs Joan Robinson in her book “The Accumulation of Capital” builds a simple model of economic growth based on the ‘capitalist rules of the game.’ But “it is not so much concerned with an automatic convergence to a moving equilibrium in a capitalist economy, as with studying the  properties  propert ies 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   f ) There are only two classes, the workers and the entrepreneurs between whom the national income is distributed. ( g)  g) Workers save nothing and spend their wage income on consumption. (h) Entrepreneurs consume nothing but save and invest their entire income from profits for capital formation. “If they have no profits the entrepreneurs cannot accumulate and if they do

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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 model 1 is the sum of the total wage bill plus total profits which may be shown as Y =wN+pK  where Y  is the net national income, w the real wage rate, N  N the the number of workers employed, p employed,  p the profit rate and K  K the the amount of capital. Here Y  is a function of N  N and and K. Since the profit rate is crucial in the theory of capital accumulation, it can be shown as  p =

Y − wN  K 

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

Y   p =  N 

−w

K 

 N 

l−w

θ Thus the profit rate is the ratio of labour productivity minus the total real wage rate to the amount of capital utilized per unit of labour. In other words, the profit rate ( p ( p)) depends on income (Y ) , , labour productivity (l (l) , , the real wage rate (w ( w) and the capital-labour ratio (θ). On the expenditure side, net national income ( Y ) equals consumption expenditure (C ( C) plus investment expenditure (I  ( I ) , , Y  = C+I  Since Joan Robinson assumes zero saving out of wages but attributes saving to entrepreneurs, profits are meant for investment only, we have S = I  This saving-investment relation may be shown as: S = pK  = pK  and I ==∆K  I  [∆K  K is is increase in real capital]  pK = ∆K  [ S = I ]

or

p=

∆K 

=

l−w

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

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

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268

The Economics of Development and Planning  

The Golden Age. Besides the growth rate of capital (∆K/K), another factor which determines the growth rate of an economy is the growth rate of population (∆N/N ). ). When the growth rate of population equals the growth rate of capital i.e., ∆N/N = ∆K/K, the economy is in full employment equilibrium. Joan Robinson characterises it as “a golden age” to describe smooth, steady growth with full employment. “When technical progress is neutral and proceeding steadily, without any change in the time pattern of production, the competitive mechanism working freely, population growing at a steady rate and accumulation going on fast enough to supply productive capacity for all available labour, the rate of profit tends to be constant and the level of real wages to rise with output per man. There are then no internal contradictions in the system. Total annual output and the stock of capital then grow together at a constant proportionate rate compounded at the rate of increase of the labour la bour force and the rate of increase of output per man. We may describe the conditions as a golden a  golden age.” 2    t The golden age is explained in Fig. 1.   u   p    t Capital-labour ratioK/N  ratio K/N or or θ is measured   u    O along the horizontal axis and per capita T    a    t    i output on the vertical axis. The growth G   p  A P   a rate of labour force is taken to the left of    C   r O along the horizontal axis. The curve   e    P OP shows the production function. α W   E  Every point on this curve shows the ratio of capital to labour. In order to find out the capital-labour ratio and the wageβ profit relation, we draw a tangent NT  which touches the production function O K  Growth Rate  N  OP at point G and cuts the vertical axis Capital-Labour Ratio of Labour at W . Point G shows the capital-labour Fig. 1 ratio for the golden age which is measured by OK. Per capita output is OA , out of this OW  OW is is paid as wages and WA or EG is the surplus which is the rate of profit on capital. This figure also proves that the growth rate of capital (∆K/K ) equals the growth rate of labour (∆N/N ). EG/EW reflects EG/EW  reflects ∆K/K  K/K and and OW/ON  OW/ON reflects reflects ∆N/N. Thus  EG  EW 

=

OW  ON 

[ tan α = tan β]

In case the economy diverges from the path of “golden age”, certain forces may tend to bring  back the the equilibrium equilibrium positio position. n. If the the rate of population population growth is higher higher than than the rate of capital growth, i.e ∆N/N>∆K/K, it will lead to progressive underemployment. In such a situation, the surplus of labour will lead to a fall in money wages and if the price level remains constant, to a fall in real wages. As a result, the profit rate would tend to rise and increase the growth rate of capital to the population level. The equilibrating mechanism would not work if real wages fail to fall either due to the rigidity of money wages or because the price level falls in the same proportion as money wages. The golden age equilibrium will not be restored and progressive underemployment will continue. 2. J.Robinson, The Accumulation of Capital, p. 99.

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 Joan Robinson’s Robinson’s Model of Capital Accumulation 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 a change in the capital-labour ratio or in labour productivity and by shifting the whole production function 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 is  being realized. realized. The The potential potential growth ratio ratio “represents “represents the the highest highest rate of capital accumulati accumulation on that can be permanently maintained at a constant rate of profit.” This potential growth ratio is approximately equal to the proportionate rate of labour force plus force  plus the proportionate rate of growth of output per head. The conditions of a golden age require the growth ratio to be steady as frequent changes in the growth ratio disturb the tranquillity of a golden age. But this tranquillity may not be possible even when the growth ratio is stable. A rise in the total stock of capital is likely to slacken the urge to accumulate so that a state of stagnation starts and the economy goes off the path of the golden age. The golden age is not an ideal. A new growth ratio makes a new golden age possible. An increase in growth ratio necessitates a rise in the proportion of productive capacity and a fall in consumption. Contrariwise, a fall in the growth ratio leads either to unemployment or to increased consumption. A static state is, however, a special case of a golden age, where the growth ratio is zero, the profit rate is also zero and wages absorb the entire net output of industry. Joan Robinson calls this the state of economic bliss, since consumption is at the maximum level which can be permanently maintained in the given technical conditions.3 So far as technical progress is concerned, it is neutral in the sense “that the value of capital in terms of wage units per man man employed does not alter appreciably when accumulation is going on at such a pace as to keep the rate of profit constant.” But the rate of technical progress depends upon demand and supply of labour. When firms fail to take advantage of the profitable markets expanding around them, they try to adopt labour-saving devices. This is because the rate of technical progress is defined as the rise in output per head, assuming zero growth rate of population. However, technical progress continues even when there is massive unemployment.  Joan Robins Robinson on points points out that that the the growth growth of knowle knowledge dge may lead to ‘autonom ‘autonomous ous innov innovations ations,’ ,’ 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 may fall short of the possible rate of growth due to competitive and    i    t    f   o autonomous innovations.   r    P The desired growth rate is the rate of accumulation which makes    f   o the firms satisfied with the situation in which they find   e    t   a themselves. The desired growth rate is determined by the rate of    R profit caused by the rate of accumulation, and the rate of accumulation induced by that rate of profit. Robinson uses Fig. 2 to explain it. The curve A curve A represents the expected rate of profit Rate of Accumulation as a function of the rate of accumulation. The curve I  I represents represents the rate of accumulation as a function of the rate of profit. In a Fig. 2 situation to the right of the point D , the expec expected ted rate rate of profit is less than the rate of accumulation. accumulat ion. Any further investment is not 3. In the Harrodian terminology, it is a state in which the natural , , the actual and the warranted rates of growth are all equal.

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270

The Economics of Development and Planning  

likely to be profitable and the rate of accumulation will fall. Between the points S and D , the rate of accumulation is less than the expected rate of profit. Therefore, there will be tendency to increase investments investments and the rate of accumulation will rise ri se to point D. Thus the point D represents the desired growth rate. On the other hand, the possible the possible growth rate depends upon the physical conditions resulting from the growth of population and technical knowledge. When the desired growth rate equals the possible growth rate at near full employment, the economy is in a golden age. The real wage rate is rising with increasing output per head due to technical progress. But the rate of profit on capital remains constant. And techniques of production appropriate to the rate of profit are chosen. This is the golden age which Joan Robinson visualises. A CRITICAL APPRAISAL

Mrs Robinson’s Robinson’s model is an elaboration of Harrod’s growth model. The possible growth rate is Harrod’s natural growth rate. In the golden age, the actual (G ( G) and the natural growth (Gn (Gn)) rates are equal to each other and the warranted growth rate (Gw (Gw)) confirms to them. Both postulate neutral technical conditions and a constant saving ratio. However, Joan Robinson’s theory of capital accumulation accumulat ion depends on the profit-wage relation and on labour productivity. Harrod’s Harrod’s theory on the contrary depends on saving-income ratio and on capital productivity productiv ity.. The former stresses 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 contribution to post-Keynesian growth economics seems to be that she has integrated classical value and distribution 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 be regarded as objects of practical policy as they might been regarded in a completely planned economy.” 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 the capitalist rules of the game. Her model of laissez-faire growth demonstrates how precarious and insecure it is to entrust to private profit-makers the paramount task of achieving the stable growth of an economy consistent with the needs of a growing population and the possibility of advancing technology.” 2. Joan Robinson’s model is based on the assumption of a closed economy. But this is an unrealistic assumption because capitalist countries are open rather than closed economies in which 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 as one of the determinants of economic growth cannot be neglected in any model. The development of 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 economy moves on the path to progress, investment has to be increased continuously which tends to 4. K.Kurihara K.Kurihara,, op.cit. , , p. 80.

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 Joan Robinson’s Robinson’s Model of Capital Accumulation Accumulation

271

raise the demand for factors but their supply cannot be increased to match the demand. This leads 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 produce a given output. This is an unrealistic assumption because in a dynamic economy there are no fixed coefficients of production. Rather, substitutability between capital and labour takes place through time, the degree of substitutability being dependent upon the nature of technological changes. ITS APPLICABILITY TO UNDERDEVELOPED COUNTRIES

Robinson’s model has the following merits for underdeveloped countries. 1. Joan Robinson, in her theory t heory,, studies the problem of population popul ation and its effect on the t he rate of capital accumulation. There is a “golden age” which any country can achieve through planned economic development. 2. An underdeveloped economy faces the problem of the rate of population growth being faster than that of capital growth, i.e., ∆N/N>∆K/K, as posed by Joan Robinson. It reveals the tendency of progressive underemployment in such economies. 3. The “potential growth ratio” is crucial to Robinson’ Robinson’ss theory of economic growth. The golden age depends on the growth ratio. The task of planning becomes easier if the potential growth ratio of an economy is calculated for the planning period on the basis of the growth rate ra te of labour force and of output per head. 4. In an underdeveloped economy, the rate of capital accumulation is always less than its potential 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 of the growth ratio rati o for the economy economy.. An underdeveloped country cannot, however, match the two  by following the capitalist rules of the game. On the contrary contrary,, it devolve devolvess on the planning authority to take the initiative in controlling and regulating not only private investment but also public investment in such economies. However, it is not possible to use the concept of the ‘golden age’ in solving the problems of underdevelopment, for the unchanging continuity required for the golden age is not present in a developing economy.