GROWTH ECONOMICS and Fund-raising in international cooperation SECS-P01, CFU 9 Economics for Development academic year 2018-19 6. THE HARROD-DOMAR MODEL OF GROWTH Roberto Pasca di Magliano Fondazione Roma Sapienza-Cooperazione Internazionale roberto.pasca@uniroma1.it

Harrod-Domar Model introduction Development and growth are natural phenomena The modern theory of growth has been developed indipendently by two the economists: Roy Harrod in his article “An Essay in Dynamic Theory” (1939), Evsey Domar in his article “Capital expansion, rate of growth and employment” (1946) Both inspired by the nascent Keynesian doctrine. They developed what was then known as the Harrod-Domar model of growth as dynamic extension of the Keynesian analysis of static equilibrium. The model explain that growth rate is influenced by the level of saving and the 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

Harrod-Domar Model Main questions If the var. Y => Δ I, which is the growth rate of Y ensuring equality between planned I and S to garantee a balance in the long term? Is there any certainty prevailing growth rate needs to ensure such equality? Otherwise, what happens? In the static keynesian model, temporary gap between I and S are compensated through the automatic adjustment garanteed by multiplier. Instead, according Harrod, if overall productivity growth rate do not increase enough, what happens? Answers Actual growth rate represents the real rate increase in a country's GDP per year Warranted growth rate: the rate of growth at which the economy does not expand indefinitely or go into recession. Natural growth rate: the growth of an economy required to maintain full employment. Roberto Pasca di Magliano

Harrod-Domar Model simplified concepts The H-D model is the easiest way to start learning about growth in the long run Main concepts used in the model: 1. Relationship between income, saving and consumption: Y = C + S (all income is either consumed or saved) S = s*Y , than -> C = (1-s)Y as S = I -> Y = C + I 2. Capital accumulation: K t+1 = It + K(1-d) where d -> depreciation The model use the concept of capital-output ratio (efficiency of the production system measured in term of capital): cr = Kt / Yt This to show that an economy can produce a lot of output with a small amount of capital (and viceversa). 3. Rate of growth: g = s / cr - d Roberto Pasca di Magliano

Harrod-Domar Model Growth Rates in synthesis The three growth rates Actual rate of growth (g) (i.e. the real income change without any intervention): g = s / c where: s -> propensity to save; c -> quantity of capital need toproduce one unity of production g is then equal to the ratio between the propensity to save and the current capital- output ratio 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 ininvestments) gw = s / cr where: s -> propensity to save; cr -> 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 Natural growth rate (gn) (i.e. one that ensures growth that absorbs the available labor force in relation to its production capacity) as: Y = L (Y / L) Roberto Pasca di Magliano

Harrod-Domar Model Actual rate of growth (Harrod) g = s / c = (S / Y) / (Δ K / Δ Y) where: s -> propensity to save c -> incremental capital-output ratio, i.e.: c = Δ K / Δ Y = I / Δ Y, provided that S = I So, since S = I, the rate of increase of the product is: g = (S / Y) / (I / Δ Y) For example, with s = 2% and c = 2, the actual rate of growth would be = 2% / 2 = 1% Roberto Pasca di Magliano

Harrod-Domar Model Warranted rate of growth (Harrod) gw = Δ Y / Y = S / cr = s*Y /k*K S is crucial in order to increase Y as we know that S is equal to I and that I is needed to Δ K . So: cr = 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 cr is needed to increase Y at a faster rate? For example, given a cr = 2, Δ Y will increase four times But, in presence of an external shock -> deviation from equilibrium could happen, i.e. deficiencies in equipment etc.. In this case the current rate can growth beyond the guaranteed (c> cr), then surplus capital, and fall even greater growth rate. Roberto Pasca di Magliano

Natural rate of growth Domar’s contribution Domar introduces the natural rate of growth (gn) Y = L (Y / L) Two components, both exogenous: growth of the labor force (L) growth of labor productivity (Y / L) A change in the level of I -> Δ demand: Δ Yd = Δ I /S I increases if the same happens on supply: 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 = sp (natural rate of growth) (i.e. I It 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 utilization of capital, but also the full employment labor. Roberto Pasca di Magliano

Natural rate of growth (Domar’s contribution) Importance of the model: Defining the rate of growth of production capacity that ensures the long-term equilibrium between S and I in order to reachifull employment 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 labour force is absorbed but, g can never exceed gn as there are not enough labour force In the long run, the relationship between gw and gn is crucial Full employment of capital and labor requires: g = gw = gn and the ennsuring the famous "golden age” studied by Cambridge’s economist Joan Robinson Roberto Pasca di Magliano

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, i.e. the amount of savings that match with job) Typical aspects of the crisis of '29 and maybe of recent financial crises gw < gn -> overwork, inflation (g grows more that is necessary to match savings for labor), unemployment and lack of capital investment Typical aspects of developing countries example: If Δ population (2%) and productivity Δ L (3%) -> Δ workforce in terms of efficiency (5%) while Δ propensity saving (9%), requires a Δ K / Y (3%): gw = 6 (gn = 5) Consequences: Δ work efficiency> Δ capital accumulation (rising unemployment) and Δ saving> Δ I (inflationary pressure) Unemployment and inflation together is not a paradox, but it indicates that there are opportunities to increase investment in order to increase capital (Δ K / Y) up to 4, so that gw and gn can be equal in the long run Roberto Pasca di Magliano

Natural rate of growth (Domar’s contribution) Vertical axis: grow rate. Horizontal axis: savings and investment - Growth and investment are related to K / Y (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 Roberto Pasca di Magliano

Policy contributions following the H-D model Not only analysis but elements to design economic policy actions eg. if country sets target growth rate of 5% and if the ratio K / Y is 3, the needed level of saving and investment has to be 15% of GDP Roberto Pasca di Magliano

Theoretical debate following the H-D model Concerning automatic adjustment related to the fact that labour productivity, savings and demand for K are determined independently while the model itself admits that in the long run propensity savings may vary, although it tends towards adjustment (in depression -> S may fall, in inflation -> can grow) In depression (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 (gn > gw), profit share will increase and this increases propensity to save and then increaasing the level of gw to gn In both cases, there are limits: the fall in profits acceptable for businesses, the fall in wages acceptable for workers Cambridge School (Robinson, Nicholas Kaldor, Richard Kahn, Luigi Pasinetti) -> emphasizes on the functional distribution Roberto Pasca di Magliano