POLITICAL ECONOMY OF GROWTH SECS-P01, CFU 9 Finance and Development academic year 2016-17

1. POLITICAL ECONOMY OF GROWTHSECS-P01, CFU 9Finance and Developmentacademic year 2016-17 6. HARROD-DOMAR MODEL Roberto Pasca di Magliano Fondazione Roma Sapienza-Cooperazione Internazionale roberto.pasca@uniroma1.it

2. Harrod-Domar Modelintroduction 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

3. Harrod-Domar Model Main questions for Harrod • If the  Y =>  I, whichis the growth rate of Y whichensuresequalitybetween planning I and S, so as to ensure an increase in balance in the long term? • Isthereanyguaranteethatprevailgrowth rate necessary to ensuresuchequality? Otherwise, whathappens? • In the static model of Keynes, ifdifferent from S I, triggered by automaticadjustmentmultiplier. Instead, for H., ifoverallproductivitygrowth rate isnotenough, whathappens?

4. Harrod-Domar Model Growth Rates • To answer the question -> threegrowthrates: • Actual rate of growth (g): • whatoccursconcretely : • 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): • onethatleaveseveryonesatisfied with the necessaryincrease in production (no more, no less), the necessary I: • (gw) =  Y / Y = s / cr • equal to the ratio betweenplanned and propensity to consume the extra capital required per unit of product • Natural growth rate (gn): • Y = L (Y / L) • onethatensuresgrowththatabsorbs the availablelabor force in relation to its production capacity

5. 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 = I /  Y, provided that S = I So, since S = I, the rate of increase of the product: g = (S / Y) / (I /  Y) =  Y / Y

6. 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

7. Natural rate of growth(Domar’s contribution) • EveseyDomar, an american economist, workingindependently, concluded by H., butalongdifferentapproach: • increasedemand via the multiplier • increasesupply via effects on capacityexpansion • So, what rate of growthbecause I offergrowth = growth in demand and youhave full employment?

8. Natural rate of growthDomar’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

9. Natural rate of growth (Domar’s contribution) • Role of the Harrod model: • Defines the rate of growth of production capacity that ensures the long-term equilibrium between S and I in order to have full 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 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

10. 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

11. Natural rate of growth(Domar’s contribution) • Vertical axis: grow rate. Horizontalaxis: savings and investment • - Growth and investment are related to K / Y (iandcr) • - Propensity to saveisindependent from the growth • To seek for the balance the policieshave to: • reduce laborsupply or productivity so as to reduce gn to gw • adoptexpansionarymonetary or fiscal policies to moveS / Y to the right or evenstimulatelabor-intensive techniques, so as to raisegwgn

12. Policy contributions • Notonlyinterpretationbutindications of policy • Eg. if country sets target growth of 5% and if the ratio K / Y is 3, the need for savings and investmentis 15% of GDP

13. 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