Joan Robinson developed growth models that rejected many neoclassical assumptions. Her models considered capital as durable and heterogeneous, not easily substitutable for labor. She argued the value of capital depends on distribution and cannot be estimated without knowing interest rates. Robinson built multiple models to analyze growth under different economic conditions. Her key model showed the relationship between the actual and desired rates of accumulation and profit. Steady growth required these rates to be equal, but various factors could cause them to diverge, making sustained steady growth difficult to achieve.

1. JOAN ROBINSON’S
GROWTH MODEL
Prof. Prabha Panth,
Osmania University,
Hyderabad

2. 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.
19-Nov-14
2
Prabha Panth

3. 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.
3
19-Nov-14 Prabha Panth

4. 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).
19-Nov-14 4
Prabha Panth

5. 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.
19-Nov-14 5
Prabha Panth

6. OBJECTIVE of JR’s MODEL
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 .
19-Nov-14 Prabha Panth
6

7. 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.
19-Nov-14
7
Prabha Panth

8. 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,
19-Nov-14 8
Prabha Panth

9. 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).
Prabha Panth
19-Nov-14 9

10. 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.
Prabha Panth
19-Nov-14 10

11. 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!
19-Nov-14
11
Prabha Panth

12. 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
19-Nov-14 If se = 1, then r = g. 12
se
Prabha Panth

13. The Model
• 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).
19-Nov-14 13
Prabha Panth

14. Two way relationship:
• 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
19-Nov-14 14
Prabha Panth

15. • 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.
19-Nov-14 15
Prabha Panth

16. Fig 1. JR’s Growth Model
r1
Rate of profit
0
S
F
Rate of
accumulation
D
E
g2 g1
A
I
A
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.
19-Nov-14 16
Prabha Panth

17. • 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.
Figure 2
19-Nov-14 17
Prabha Panth