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

Harrod-Domar Modelintroduction

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 modelDynamic extension of the Keynesian analysis of static equilibriumIt 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 phenomenaStatic analysis, 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:• Current growth rate (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

• Guaranteed 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

Harrod-Domar Model Current rate of growth (Harrod)

g = s / c = (Y / Y) / (I / Y) = Y / Y

s is the propensity to savec: incremental capital-output ratio, ie K /

Y = I / Y, provided that S = ISo, since S = I, the rate of increase of the

product: g = (S / Y) / (I / Y) = Y / Y

Harrod-Domar Model warranted rate of growth (Harrod)

(gw) = Y / Y = s / crAccording 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 = gwFor dynamic equilibrium, the product should grow at this rate, that consumer spending

must equal the value of productionBut, 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

In short, away from equilibrium, rather than narrow, resulting oscillations of increasing

Harrod-Domar Model 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?


• D. introduces the natural rate of growth• Y = L (Y / L)• Two components, both exogenous1. 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


• 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


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’sgw <gn, overwork, inflation (g grows more than necessary to match savings for labor),

unemployment and lack of capital investmentTypical of developing countriesexample: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


Adjustments between gw and gn in the event that gn> gw g

gn

gw

0

S/Y

I/Y

S/Y,I/Y

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 gwadopt expansionary monetary or fiscal policies to move S / Y to the right or even stimulate labor-intensive techniques, so as to raise gw gn

1/cr

Harrod-Domar Model 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

Harrod-Domar Model 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

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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