JOAN ROBINSON’S GROWTH MODEL

Prof. Prabha Panth,

Osmania University,

Hyderabad

Joan Robinson (JR)• Joan Robinson, a student of J. M. Keynes, rejected Neo

classical models and assumptions. She made an immense contribution to the Theory of Capital and its valuation.

• She eschewed the concepts of:

– Malleable and homogeneous capital as depicted in Neo Classical production functions.

– She argued that Physical Capital is specific in form and function (durable and heterogeneous), and takes time to be produced.

– Capital-Labour ratios are constant for a given technique, at a given time; capital and labour are not substitutes, but complementary inputs in production.

– Production takes place in Historical time, not logical time.

– Hence it is not possible to move up and down the production function, as argued by Neo Classical Theory.

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Neo classical theory assumes that rate of interest is the price of capital. JR showed (as also Sraffa, Neumann, and others) that this is not so, for the value of capital includes:

• (Wages + Value of capital used in production) × rate of interest.

• Unless the rate of interest is known, the value of capital cannot be estimated.

• And unless the value of capital is known, the rate of interest cannot be estimated (since capital is an input). Thus, the value of capital and the rate of interest are determined simultaneously.

• Further, the productivity of capital also affects its value. The more the output, the more the value of capital.

• Physical capital is not malleable, so the MP of capital cannot be determined. So MPK r.

• In the Neo-classical production function , if capital is expressed in physical terms, then it is not possible to ascertain its MP, since physical capital is not divisible. (MPK = Q/K)

• If expressed in value terms, then MP of K cannot be determined without knowing the rate of interest.

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At the same time, the value of capital is affected by distribution (i.e. Wage rate and rate of interest).

In Value terms:

wL + rK = Q

rK = Q – wL

And K = (Q-wL)/r

Thus the value of K includes the value of Output, the total wage bill, and the rate of interest.

But Neo-classical theory takes value of capital to be only r!

When w increases, r falls. Unless the rise in w is exactly compensated by fall in r, the value of capital will not remain constant.

(Joan Robinson called this the Wicksell Effect.)

Hence any change in distribution, can affect the value of capital also, and the position of the technique on the production function. (See J.R.’s article: “The Production function and the Theory of Capital”, Review of Economic studies, 1953).

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Joan Robinson’s Model

• She extended Harrod’s and Domar’s models of growth.

• She took the following aspects into account:

− Investment leads to Savings,

– Role of heterogeneous, durable capital, and problems of valuing capital,

– Importance of capital accumulation and its impact on the economy.

– Technical progress and its impacts.

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What are the conditions that lead to full capacity, full employment, steady growth in a capitalist system?– Economic conditions differ across countries.

– So it is not possible to apply the same growth model to all countries.

– Or at all times,

– Different economic situations require different types of models.

– She therefore built several models of growth for different economies depending on their economic conditions .

OBJECTIVE of JR’s MODEL

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Golden and Platinum Ages• Free Enterprise, free market economy,

• Driving force behind growth is entrepreneurs’ urge to invest, determined by expectations of profit on Investment.

• The different Golden and Platinum Ages are different growth paths that apply to different economies with different characteristics.

– Golden Age Models: Economies which start with equilibrium proportions of capital stock of an economy. (She calls Golden Age a myth).

– Platinum Age Models: Economies where the stock of capital is not in proper proportions to the rate of growth that is desired by entrepreneurs, in a free market economy.

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Assumptions:

1. Free enterprise economy, no government interference.

2. Closed economy,

3. Three classes – entrepreneurs, workers, rentiers.

4. Capital is fixed, durable and heterogeneous, no substitution between K and L.

5. Neutral technical progress,

6. Tranquillity conditions: entrepreneurs assume that present conditions will continue in future,

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The Determinants of Equilibrium

According to JR, seven conditions, all independent, are required to determine the equilibrium level of output:

1. Technical conditions: a) Number and quality of labour force and its growth rate. b) Technical knowledge and technical progress. c) Supply of natural resources. This gives the natural rate of growth = GN = GL + GT.

2. Thriftiness conditions: s = S/Y, determined by distribution. Entrepreneurs and rentiers save, mps= se. Labour, whose w = subsistence, does not save.

3. Market: Need not be PC. Monopoly makes Pr/Y independent, raises “animal spirits” (urge to Invest).

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4. Wage bargain: Money wages constant, except when:

– (a) capital or plants are available for Investment, but labour is not,

– (b) The rate of Investment calls for a lower real wage, not acceptable to labour, (Inflation barrier wage). Rate of Accumulation , wage rate

5. Finance: Financial institutions developed to offer finance for investment. But rate of interest and Monetary Policy play only a small role in price stability.

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6. Investment Policy: firms alone make Investment decisions, based on “animal spirits” i.e. urge to grow in managerial economies.

7. Stock of Capital: If entrepreneurs are satisfied, then capital stock composition will not change. Employment remains constant. Expectations are fulfilled and entrepreneurs do not revise their investment.– JR states that to be in steady growth, the economy should

have a history of steady growth. Not possible for an economy to shift from unsteady to steady growth!

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Rate of accumulation:

K = I ------ (1)

K K

Savings Coefficient

S = se.Pr ------ (2)

Y Y

As all profits are invested, we can rewrite (2) as:

S = I = se. Pr

K K K

Or Pr = 1 . I Following Kaldor

K se K

Since Pr/K = r, and I/K = gk.

So r = 1. gk

seIf se = 1, then r = g.19-Nov-14 12

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• What is the driving force for investment in capitalist economies? According to JR, it is the desire of the capitalists to accumulate or gd, governed by the expected rate of profit re.

gd = f(re) ----------------- (1) re Investment gd

• But when taking the actual rate of Accumulation that is going on in the economy at any moment, the causation between g and r is reversed :

re = f(ga) ------------------ (2)

• For, at any moment of time, the level of profits gets determined by the given rate of Accumulation (ga).

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The Model

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• Entrepreneur's expectations about the future, or the expected rate of profit re is determined by actual rate of growth ga. Thus:

ga profits expectations expected rate of profit re

• So there is a two-way or double-sided relationship between the rate of Accumulation and the rate of profit on Investment.

• At any moment of time the actual rate of Accumulation ga

going on in the economy, leads to an expected rate of profit on Investment re,

• This re in turn generates a desired rate of Accumulation gd.

ga re gd

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Two way relationship:

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• In JR’s model, steady or equilibrium growth takes place when ga = gd that is actual rate of growth = expected rate of growth, so that entrepreneurs do not change their investments.

• However the two may not always coincide, so she analyses the consequences of ga gd

• This can be shown diagrammatically.

In Figure 1:

1) The desired rate of accumulation gd, is a function of expected rate of profit re, gd = f(re). It is a concave function, shown by II.

2) The actual rate of profit is a function of the actual rate of accumulation going on, r = g/se. This is a straight line relationship, shown by AA, for given se, as g increases, r also increases at a constant rate.

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Fig 1. JR’s Growth Model

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0

Rate of

accumulation

g1g2

Rate

of

pro

fit

A

A

r1

I

S

D

E

F

I

Equilibrium : at S and D, with A = I.

• D is a stable equilibrium.

At E, actual g1 > desired growth g2.

But expected rate of profit = r1, with

growth rate g1. From the I-I curve,

desired gth rate for r1 is g2, and g2 <

g1. As desired rate is less than

actual rate, the rate of Accumulation

would fall, and return to original

steady growth, D.

But S is unstable, to the left of S, g

is so low, it fails to generate re, which

would sustain it and falls further.

To the right of S, at F, g accelerates

to D.

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• However, she feels that even D may not be achieved, because only an economy in steady growth, can continue in steady growth.

• The two curves may not even intersect, as seen in Figure 2.

• Thus steady, full employment, full capacity growth – the Golden Age – is a myth and may not occur in reality.

• There are too many factors which cause growth to fluctuate, such as entrepreneurs’ expectations, existing stock of capital, rentiers’ and capitalists’ savings, etc.

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Figure 2

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