Post Keynesian theory of growth. Meaning of steady growth, instability problem, knife edge problem

1. HARROD’S GROWTH
MODEL
LECTURE 6

2. OBJECTIVES
To determine:
 What are the conditions necessary for
Steady Growth?
 Is there stability of Steady Growth?
Assumptions:
 Post Keynesian model, S/Y = S/ Y = s
 I = ( Y), I is Induced investment, function of
increase in Y.
 Keynesian causation, I = S
 Capital is durable and produces C goods,

3. 5) = incremental K/O ratio, constant, given the
technology. I = ( Y), or = I/ Y = K/ Y,
6) No capital depreciation, I = K,
7) Aggregate analysis, Y, C, S, and I in aggregate,
8) Growth of labour is given exogenously
I) The Actual Rate of Growth (Ga)
The economy has some rate of growth = Ga,
But this rate may not be steady growth,
S = sY0 ------- (1)
I = a(Y1 – Y0) ------ (2)
At Equilibrium I = S,
a(Y1 – Y0) = sY0

4. Ga ≡ s/ a -------- (3)
This equation of growth is a truism
Ex post savings in period t is equal to addition to
stock of K,
S = I.
But Ga need not be steady growth. It is the rate at
which the economy is actually growing.
or (Y1 – Y0) = s = Ga = Y
Y0
a Y

5. 2. Warranted Rate of Growth: Gw.
• Entrepreneurs take independent investment
decisions,
• May or may not be satisfied with the present
rate of growth, Ga.
• They wish for a Desired or Warranted Rate of
growth, which satisfies them.
• If they are satisfied, they will continue
investment at the same rate in future.
Warranted rate of growth Gw = s/ d
Where d is the desired K/O ratio

6. Features of Gw:
1) Rigidly given only one d can achieve steady
growth.
2) Equality of I and S: the ex ante S should be
exactly equal to the ex post I.
Gw
I Y = C , S

7. Instability
 Ga Gw, the actual rate of growth may not
be equal to warranted rate of growth.
 If Ga Gw = instability, and they can never
become equal. Instability continues.
 If Ga = Gw, then there is steady growth, but
this is difficult to achieve.
 Instability occurs because entrepreneurs do
not properly understand the signals in the
economy.
 Harrod explains how entrepreneurs react to
the inequality of Ga and Gw.

8. 1. Explosive Situation:
a) In the first case: Ga > Gw, then s/ a > s/ d
Assuming s is same for both, a < d , i.e. the actual K/O is
less than the desired K/O.
Example:
• Ga = 5% > s = 10%,
s/ a = 10/2 = 5%
• Gw = 2.5%, s = 10%.
s/ d = 10/4 = 2.5%
Entrepreneurs want K/O to be 4, but actually it is 2. So to
increase K/O they increase Investment.
But increase in Investment, leads to Ga increase,
Gap between Ga and Gw increases.
This leads to a BOOM or Inflationary situation.

9. 2. Contraction:
 If Ga < Gw, then a > d, given s.
 E.g. If Ga = 2%, s = 10%, then a = 5.
 Gw = 5%, then d= 2, i.e. a > d
 Entrepreneurs think they have over invested,
and reduce their investment.
 When investment falls, actual rate of growth
falls.
 This leads to recession and unemployment.

10. Instability
Gth %
Time
Gw =
Steady
growth
Ga
Expansion
Ga
Contraction
0

11. Conundrum
 Thus when entrepreneurs think they are producing
more they are actually producing less. Gw > Ga,
 When they are think they are producing less, they
are producing more. Gw < Ga.
 Therefore Harrod concludes that because of wrong
reasoning by entrepreneurs, it is not possible to
achieve Steady Growth.
 Thus growth in a capitalist economy is basically
unstable.
 No self correcting mechanism to achieve steady
growth, as s, and I are rigidly given.

12. Natural Rate of Growth (Gn)
 Will there be full employment also with steady
growth?
 Will there be full utilisation of productive
capacity?
Gn = GL + GT
 GL= long term growth of population,
 GT = neutral technical progress (K/O constant)
 GN is the maximum rate of growth of the
economy, the ceiling rate of growth.

13. Full employment, steady growth
If GA = GW = GN = Full employment, steady
gth.
= s/ a = s/ d = GL = GT
But s, a, d, population growth, technical
progress are all given exogenously.
Therefore this equality can never be achieved.
So full employment, steady growth is
impossible, according to Harrod.

14. The Knife Edge
To show the instability and uniqueness of full
employment, steady growth.
GA GW GN
1) GA > GW > GN : Actual growth is above the ceiling
growth, but this cannot be sustained by population
and technical progress.
Labour shortages develop and prevent further
growth. GA falls.
2) GA < GW < GN : deflationary conditions, with rising
unemployment.

15. • s and rigidity is unreasonable, can change.
• Does not show how steady growth is
achieved, only deviations from it.
• Entrepreneurs are myopic, and do not learn
from their mistakes.
• No policy prescriptions
• No role of autonomous investment, main
Keynesian principle.
CRITICISM: