The Harrod-Domar
Model
Growth Economics
Roberto Pasca di Magliano
2015/2016
Harrod-Domar Model
introduction
We owe the modern theory of growth to the economist Roy Harrod
with his article An Essay in Dynamic Theory (1939), inspired by the
nascent Keynesian doctrine
He developed what was then known as the Harrod-Domar model
Dynamic extension of the Keynesian analysis of static equilibrium
It has inspired a vast literature, in part still in place, and many
economic policy actions
Instead, the neoclassical model of growth, which will later be
developed, derived from the dominant influence of Alfred Marshall’s
Principles of Economy (1890) and was developed by Solow (later)
Unlike traditional, development and growth are natural phenomena
Static analysis, a typical neoclasssical hypothesis
Harrod-Domar Model Main questions for Harrod
•If the D Y => D I, which is the growth rate of Y which
ensures equality between planning I and S, so as to
ensure an increase in balance in the long term?
•Is there any guarantee that prevail growth rate necessary
to ensure such equality? Otherwise, what happens?
•In the static model of Keynes, if different from S I,
triggered by automatic adjustment multiplier. Instead, for
H., if overall productivity growth rate is not enough, what
happens?
Harrod-Domar Model Growth Rates
• To answer the question -> three growth rates:
• Actual rate of growth (g):
– what occurs concretely :
– g = s / c = (Y / Y) / I / D Y = D Y / Y
– equal to the ratio between the propensity to save and the current
capital-output ratio
• Warranted rate of growth (gw):
• one that leaves everyone satisfied with the necessary increase in
production (no more, no less), the necessary I:
– (gw) = D Y / Y = s / cr
– equal to the ratio between planned and propensity to consume the
extra capital required per unit of product
• Natural growth rate (gn):
– Y = L (Y / L)
– one that ensures growth that absorbs the available labor force in
relation to its production capacity
Actual rate of growth (Harrod)
g = s / c = (Y / Y) / (I / D Y) = D Y / Y
s is the propensity to save
c: incremental capital-output ratio, ie D K / D Y = I /
D Y, provided that S = I
So, since S = I, the rate of increase of the product:
g = (S / Y) / (I / D Y) = D Y / Y
Warranted rate of growth (Harrod)
(gw) = DY / Y = s / cr
According to the static model of K:
-S = sY (propensity to save)
-The application is given by the principle of acceleration, second coefficient cr:
cr = Kr D / D Y = I /D Y
-ie, the amount of additional capital or I needed to produce additional product units at a given interest rate and given the technological conditions
-The question, then:
I D Y = cr
-Ensure that the planned S are equal to I planned, we have:
sY cr = D Y
-therefore:
D Y / Y = s / cr = gw
For dynamic equilibrium, the product should grow at this rate, that consumer spending
must equal the value of production
But, if shock-> deviation from equilibrium, it may happen that c <cr namely that the I
collapse; this causes deficiencies in equipment etc.. Then manifests incentive D I, but in this case
the current rate can grow beyond the guaranteed (c> cr), then surplus capital, and fall even
greater growth rate
Natural rate of growth
(Domar’s contribution)
• Evesey Domar, an american, working independently, concluded by H.,
but in a different way
• I have a two-edged sword:
• increase demand via the multiplier
• increase supply via effects on capacity expansion
• So, what rate of growth because I offer growth = growth in demand
and you have full employment?
Natural rate of growth
(Domar’s contribution)
• D. introduces the natural rate of growth
• Y = L (Y / L)
• Two components, both exogenous
1. growth of the labor force (L)
2. growth of labor productivity (Y / L)
• A change in the level of I, D demand: DYd = D I /S and I increases if
the same offering: D Ys = Ip (p, capital productivity, D Y / I)
• In order to have DYd=D Ys, it is necessary that:
DI /s = Ip or DI / I = sp
• I.e. I has to grow at a rate such that it matches the propensity to save
and the productivity of capital
• The natural rate of growth is sp (equal 1/cr equilibrium Harrod)
• But, even if the growth ensures full utilization of capital, it is said also
to have full employment labor, which depends on the gn
Natural rate of growth (Domar’s contribution)
• Role of the Harrod model:
1.Defines the rate of growth of production capacity that
ensures the long-term equilibrium between S and I in order
to have full employment
2.Fixing the upper limit of the current rate of growth that
would lead to a useless accumulation .
• If g> gw,
-g can continue to diverge until it reaches gn when all the
work is absorbed
-it can never exceed gn because not enough work
• In the long run, the relationship between gw and gn is
crucial
• Full employment of capital and labor requires:
g = gw = gn
• That is the famous "golden age" recovery of Cambridge’s
economist Joan Robinson
Natural rate of growth
(Domar’s contribution)
Deviations between gw and gn
gw> gn, excess capital and savings, tendency to depression due to lack of
work (g fails to stimulate growth in demand The amount of savings that
match with job)
Typical of the crisis of '29 and maybe of today’s
gw <gn, overwork, inflation (g grows more than necessary to match savings
for labor), unemployment and lack of capital investment
Typical of developing countries
example:
IfD population (2%) and productivity D L (3%) -> D workforce in terms of
efficiency (5%) while D propensity saving (9%), requires aD K / Y (3%):
gw = 6 (gn = 5)
Consequences:D work efficiency> Dcapital accumulation (rising
unemployment) and D saving> D I (inflationary pressure)
Unemployment and inflation together is not a paradox, but indicates that
there are opportunities for increased investment to grow D K / Y up to 4, so
that gw and gn can equalize in the long run
•
Natural rate of growth
(Domar’s contribution)
Vertical axis: growth. Horizontal axis: savings and investment
Growth and investment are related to K / Y (ie cr)
Propensity to save is independent from the growth
To seek to balance the policies are:
reduce labor supply or productivity so as to reduce gn gw
adopt expansionary monetary or fiscal policies to move S / Y to the right
or even stimulate labor-intensive techniques, so as to raise gw gn
Policy contributions
• Not only interpretation but indications of policy
• Eg. if country sets target growth of 5% and if the ratio K / Y is 3,
the need for savings and investment is 15% of GDP
Theoretical debate
• Of automatic adjustment related to the fact that L, L productivity,
savings and demand for K are determined independently and
HD themselves admit that in the long run propensity savings
may vary, although it tends towards adjustment (in depression ->
S may fall, in inflation -> grow)
• Cambridge School (Robinson, Nicholas Kaldor, Richard Kahn,
Luigi Pasinetti) -> emphasis on the functional distribution
• In depression (gw> gn), share profits on wages is reduced,
profits from savings> savings from wages, and this reduces the
overall propensity to save and reduces to gn gw
• In inflation (gn> gw), share of profits increases wages which
deepens and increases propensity S gw to gn
• In both cases, there are limits: the fall in profits acceptable for
businesses, the fall in wages acceptable for workers