Download Harrod-Domar model

POLITICAL ECONOMY OF GROWTH
SECS-P01, CFU 9
Finance and Development
academic year 2016-17
6. HARROD-DOMAR MODEL
Roberto Pasca di Magliano
Fondazione Roma Sapienza-Cooperazione Internazionale
[email protected]
Harrod-Domar Model
introduction
Unlike traditional, development and growth are natural phenomena
The modern theory of growth is manly due 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
•Inspired a vast literature, in part still in place, and many economic
policy actions
Instead, the neoclassical model of growth, which would later be
developed, derived from the dominant influence of Alfred Marshall’s
Principles of Economy (1890.
It would be developed by Solow by using the static approach, a typical
neoclasssical hypothesis
Harrod-Domar Model
Main questions for Harrod
•If the Y =>
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 /
Y=
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) =
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 /
Y) =
Y/Y
s is the propensity to save
c: incremental capital-output ratio, ie K /
Y, provided that S = I
Y=I/
So, since S = I, the rate of increase of the product:
g = (S / Y) / (I / Y) = Y / Y
Warranted rate of growth (Harrod)
(gw) =
Y / 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 / Y = I / 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 Y = cr
-Ensure that the planned S are equal to I planned, we have:
sY cr = Y
-therefore:
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 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 economist,
working independently, concluded by H., but
along different approach:
• 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
• Domar 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,
demand: Yd = I /S and I increases if the
same offering:
Ys = Ip (p, capital productivity,
Y / I)
• In order to have Yd= Ys, it is necessary that:
I /s = Ip or I / 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 aspects 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 aspects of developing countries
example:
If population (2%) and productivity L (3%) -> workforce in terms of
efficiency (5%) while
propensity saving (9%), requires a K / Y (3%):
gw = 6 (gn = 5)
Consequences: work efficiency> capital accumulation (rising
unemployment) and
saving> I (inflationary pressure)
Unemployment and inflation together is not a paradox, but indicates that there
are opportunities for increased investment to grow
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: grow rate. Horizontal axis: savings and investment
- Growth and investment are related to K / Y (iand cr)
- Propensity to save is independent from the growth
To seek for the balance the policies have to:
• reduce labor supply or productivity so as to reduce gn to 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
• Concerning 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