5 Harrod’s growth model

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 = sY
0 -------(1)
I = a(Y
1–Y
0) ------(2)
AtEquilibriumI=S,
a(Y
1–Y
0) = sY
0

4. Ga≡ s/ a --------(3)
Thisequationofgrowthisatruism
Expostsavingsinperiodtisequaltoadditionto
stockofK,
S=I.
ButGaneednotbesteadygrowth.Itistherateat
whichtheeconomyisactuallygrowing.
or (Y
1–Y
0)= s = G
a= Y
Y
0
a
Y

5. 2. Warranted Rate of Growth: Gw.
•Entrepreneurstakeindependentinvestment
decisions,
•Mayormaynotbesatisfiedwiththepresent
rateofgrowth,Ga.
•TheywishforaDesiredorWarrantedRateof
growth,whichsatisfiesthem.
•Iftheyaresatisfied,theywillcontinue
investmentatthesamerateinfuture.
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
GaGw, the actual rate of growth may not
be equal to warranted rate of growth.
If GaGw= 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 Gaand Gw.

8. 1. Explosive Situation:
a)In the first case: Ga> Gw, then s/a > s/d
Assumingsissameforboth,a<d,i.e.theactualK/Ois
lessthanthedesiredK/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 increaseInvestment.
But increase in Investment, leads to Gaincrease,
Gap between Gaand Gwincreases.
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= G
L+ G
T
G
L=longtermgrowthofpopulation,
G
T=neutraltechnicalprogress(K/Oconstant)
G
Nisthemaximumrateofgrowthofthe
economy,theceilingrateofgrowth.

13. Full employment, steady growth
If G
A= G
W= G
N= Full employment, steady
gth.
= s/a = s/d = G
L= G
T
Buts,a,d,populationgrowth,technical
progressareallgivenexogenously.
Thereforethisequalitycanneverbeachieved.
Sofullemployment,steadygrowthis
impossible,accordingtoHarrod.

14. The Knife Edge
To show the instability and uniqueness of full
employment, steady growth.
G
AG
WG
N
1)G
A>G
W>G
N:Actualgrowthisabovetheceiling
growth,butthiscannotbesustainedbypopulation
andtechnicalprogress.
Labourshortagesdevelopandpreventfurther
growth.G
Afalls.
2) G
A< G
W< G
N: 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: