6. harrod-domar model · harrod-domar model simplified concepts the h-d model is the easiest way to...

GROWTH ECONOMICSand Fund-raising in international cooperation

SECS-P01, CFU 9Economics for Development

academic year 2019-20

Roberto Pasca di MaglianoFondazione Roma Sapienza-Cooperazione Internazionale

[email protected]

6. THE HARROD-DOMAR MODEL OF GROWTH

Harrod-Domar Modelintroduction

Development and growth are natural phenomenaThe modern theory of growth has been developed indipendently by twothe economists:•Roy Harrod in his article “An Essay in Dynamic Theory” (1939),•Evsey Domar in his article “Capital expansion, rate of growth andemployment” (1946)ØBoth inspired by the nascent Keynesian doctrine.They developed what was then known as the Harrod-Domar model ofgrowth as dynamic extension of the Keynesian analysis of staticequilibrium.The model explain that growth rate is influenced by the level of saving andthe capital productivity.

Meanwhile, Robert Solow was developing the neoclassical model of growth, inspired to the dominant influence of Alfred Marshall’s Principles

of Economy (1890).

Roberto Pasca di Magliano Pagina 2

Harrod-Domar Model Questions vs proposals

Questions• If the change Y => Δ I, which is the growth rate of Y ensuring equality

between planned I and S in order to garantee a balance in the long term?

• Is there any certainty ensuring the equality I = S ? Otherwise, whathappens?

• In the static keynesian model, temporary gap between I and S are compensated through the automatic adjustment garanteed bythemultiplier effect. Instead, according Harrod, if overall productivitygrowth rate do not increase enough, what happens?

ProposalsIn order to find answers to the main questions, H-D disign three rate ofgrowth:Ø Actual growth rate represents the real rate increase in a country's GDP

per yearØ Warranted growth rate: the rate of growth at which the economy does

not expand indefinitely or go into recession.Ø Natural growth rate: the growth of an economy required to maintain full

employment.


Harrod-Domar Model simplified concepts

The H-D model is the easiest way to start learning about growth in the long runMain concepts used in the model:

1. Relationship between income, saving and consumption:Y = C + S (all income is either consumed or saved) as S = I -> Y = C + IS = s*Y where s is the propensity to save than -> C = (1-s)Y

2. Capital accumulation:K t+1 = It + K t (1-d) where d -> depreciation rateThe model is based on the concept of capital-output ratio (efficiency of the production system measured in term of capital):k = Δ Kt / Δ Yt k shows the level of efficiency in term of the amount of

capital used in the production system3. Rate of growth:

g = s / k - d e.g.: if s = 2% and k = 2, the income rate of growth would be 1% (2%/2)


Harrod-Domar Model Growth Rates in synthesis

The three growth rates1. Actual rate of growth (g) (i.e. the real income change without any intervention):

g = s / k where: s -> propensity to save; k -> quantity of capital need to produce one unity of production

g is then equal to the ratio between the propensity to save and the current capital-output ratio

2. Warranted rate of growth (gw) (i.e. the growth that leaves everyone satisfied with an increase in production (no more, no less) needed to pursue better resource’s allocation, by impling a necessary increase in public investments)

gw = s / k* where: s -> propensity to save; k* -> extra quantity of capital needed

gw is then equal to the ratio between planned propensity to save and the extra capital required per unit of product

3. Natural growth rate (gn) (i.e. the rate that ensures a rate of growth that absorbs the available labor force in relation to its production capacity, Y = L (Y / L)

gn = Δ I / I


Harrod-Domar Model Actual rate of growth (Harrod)

g = s / k = (S / Y) / (Δ K / Δ Y)

where:s -> propensity to savek -> incremental capital-output ratio, i.e.: k = Δ K / Δ Y= I / Δ Y, provided that S = Ie.g., with s = 2% and k = 2, the actual rate of growth

would be = 2% / 2 = 1%

Since S = I, the rate of increase of the product couldalso be written:

g = (S / Y) / (Δ I / Δ Y)


Harrod-Domar Model Warranted rate of growth (Harrod)

gw = Δ Y / Y = S / cr = s*Y /k*KS is crucial in order to increase Y as we know that S is equal to I and thatmore I is needed to Δ K .So:

k = Δ Kr / Δ Y (capital-output ratio, ie, the amount of additional capital needed to

produce additional product units at a given interest rate and given the technological conditions)

Then, the question is which k is needed to increase Y at a faster rate? e.g., given a k = 2, Δ Y will increase four times

But, in presence of an external shock -> deviation from equilibrium could happen, i.e. deficiencies in equipment, new investments etc..

In this case the current rate grows beyond the guaranteed level (planned in the economy), then there will be a capital surplus and fall even greater

fall in the rate of growth (e.g.: actual situation in Germany)


Natural rate of growthDomar’s contribution 1 Domar introduces the natural rate of growth (gn)

gn = Δ I / Iinsuring the full employment -> Y = L (Y / L)

The gn is influenced by two components, both exogenous:– growth of the labor force (L)– growth of labor productivity (Y / L)

• A change in the level of I (planned in the economy) -> Δ demand: Δ Yd = Δ I /S• I increases if the same happens on the supply side: Δ Ys = Ip (p, capital

productivity, Δ Y / I)In order to have Δ Yd = Δ Ys, it is necessary that:

Δ I /s = Ip or Δ I / I thet is gn (the natural rate of growth) (i.e. I has to grow at a rate such that it matches the propensity to save

and the productivity of capital)Growth rate must ensures not only the full use of capital, but also the full employment

labor


Natural rate of growth Domar’s contribution 2

Importance of gn:•Defining a rate of growth of production capacity which ensures the long-term equilibrium between S and I in order to reach the full employment

•Fixing the upper limit of the rate of growth that would avoid an uselesscapital accumulation.

•When g -> gn:– g can continue to diverge until it reaches gn when all the labour force is

absorbed– but, g can never exceed gn as there are not enough labour force

•In the long run, the relationships between gw and gn are crucial•Full employment of capital and labor at the same time requires:

g = gw = gnensuring the so-called "golden age” that will be studied deepfully by

Cambridge’s economist Joan Robinson


Natural rate of growthDomar’s contribution 3

Deviations between gw and gn• gw > gn -> excess of capital and saving, trend to depression due to lack of labor

force (g fails to stimulate growth in the demand, i.e. the amount of saving thatmatch with job)e.g: typical aspects of the crisis of '29 and maybe of recent financial crises

• gw < gn -> overwork, increasing inflation (g grows more that is necessary to match saving), unemployment and lack of investment

e.g.: typical aspects of developing countries

Consequences• An Δ work efficiency (due to an increase in labor productivity) needs an Δ

capital accumulation (to offset rising unemployment) and an Δ saving> Δ I (to avoid inflationary pressure)

• Situations of unemployment and inflation at the same time are not a paradox, but they shows that there are opportunities to increase investment in order to increase capital accumulation (Δ K / Y), so that gw and gn can be equal in the long run


Natural rate of growthDomar’s contribution 4

Vertical axis: grow rate. Horizontal axis: savings and investment- Growth and investment are related to K / Y (k)- Propensity to save is independent from the growth

To seek for the balance, public policies have to:• 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• reduce labor supply or productivity so as to reduce gn to gw


Policy contributionsfollow-up of the H-D model 1

The H-D model contributes not only to the economic analysis but also to design

economic policy actions

eg. if a country sets a target growth-rate at the 5% and if the ratio K / Y is 3, the level of saving and investment, needed to insure taht growth-rate, hasto be setteled at the level of 15% of GDP


Theoretical debate follow-up of the H-D model 2

• The theoretical debate concerns mainly the so-called automatic adjustment -> related to the fact that labour productivity, saving and demand for K are determined independently while the model itself admits that in the long run propensity to save may vary, although it tends towards adjustment (in depression -> S may fall, in inflation -> can grow):– In depression phase (i.e. gw < gn), the profit share is reducing and this reduces

the overall propensity to save and then reduces the level of gn to gw– In inflation phase (gn > gw), profit share will increase and this increases

propensity to save and then increasing the level of gw to gn– In both cases, there are limits regarding:

• the fall in profits acceptable for businesses, • the fall in wages acceptable for workers

• An other important theoretical debate, emphasizes on the functional distribution, would have been developed at the Cambridge School (Robinson, Nicholas Kaldor, Richard Kahn, Luigi Pasinetti)


6. harrod-domar model · harrod-domar model simplified concepts the h-d model is the easiest way to...

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