Harrod-Domar Growth Model

1. Harrod-Domar Growth Model

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3. Lord Harrod and Mr. Domar Keynesian based models Saving rates Capital/Output ratio or Capital Productivity Capital stock GDP Personal Consumption Gross Savings Gross Investment Net Investment, or Capital Accumulation Depreciation Dynamic models Topics for today In growth models, we will encounter the following terms:

4. What is a Keynesian Growth Model? • Keynes’ model and Keynesian models were developed to explains business cycles • A short run phenomena • As such they attribute a major role to aggregate expenditures (demand side) • Regarding the supply side, they assume that there is unemployment: production responds fast to increases in aggregate demand because capital and labor is unemployed.

5. Aggregate Demand, AD AD = C + I + G + X-M C, Consumption expenditures I, Investment expenditures G, Government expenditures X-M, Foreigners’ Expenditures Aggregate Supply AS < ASfe Aggregate Supply, at full employment Macroeconomic Equilibrium AS = AD Or S = I

6. A Keynesian Model • A Keynesian growth model takes a long run perspective. • Aggregate demand (or savings=investment) still is important, but • It also includes the aggregate supply • Investment has two impacts: • On expenditures (in the short run) • On capital stock (in the long run)

7. Trends and business cycles Trend One business cycle Real GDP Years

8. Main Propositions • Economic growth can be accelerated by • changing the saving rate • improving technology. • Saving rates and technology can be changed • government interventions without consideration to prices

9. Harrod-Domar Growth Model A Flow chart model Saving Rate Depreciation Rate Ig S s d C GDP D v= K/Y or a=Y/K In Capital/Output Ratio or Productivity Capital Production function

10. Factors Explaining the growth rateAccording to Harrod-Domar model s a d Saving rate + Rate of Economic Growth + g Capital productivity _ Capital depreciation Explained variableExplanatory Variables

11. Arithmetic specificationWithout Depreciation If we know output Y, and we know s, which is the saving rate, then we know total savings S. If we know total savings S, we know how much we can invest (I) in new capital (dK) s=dS/dY If we know the initial capital stock K; and we know a, (how much output increases when capital increases 1 unit) then we know what will total output Y be. S=Y.s Y=K.a dY I If we know dK and a, we know growth of output dY a=dY/dK dK K

12. Numerical specificationWithout Depreciation If we know output Y=1 and we know the saving rate s=.10, then we know total savings S=.10 Or … dY = s.a By approximation: dY/Y=s.a/Y g=s.a Since Y=1 If we know total savings S=.10 we know that we can invest I=.10 in new capital (dK=.10) s=.10 S=.10 If we know the initial capital stock K=5; and we know its productivity a=.20 then we know total output Y=1 dY=.02=2% Y=1 .10 a=.20 If we know dK=.10 and a=.20, we know growth of output dY=0.02=2% K=5 dK=.10

13. Economic growth formula • According to Harrod-Domar the rate of economic growth • is defined by the formula: • g = s.a – d • that is, if s=10% and a=0.20 and d =1%, then • g=0.10*0.20 - 0.01 = 0.02 -0.01 = 0.01 = 1% • What happens if the rate of saving (s) increases to 20% ? • What happens if the productivity of capital (a) increases to 0.40? • What happens if the depreciation (d) rate is 2% ?

14. . Mathematical derivation of Harrod-Domar model Conventional Keynes’ Model Specification Saving function (demand side) S = s.Y where s is the average propensity to save or average saving rate. In the conventional short run Keynesian model investment (I) is given. I = Ia In equilibrium S = I Solving the model s.Y = Ia Y = 1/s.Ia = m.Ia where m is the investment multiplier

15. In this model national GDP increases because the autonomous demand (I) increases. It is assumed that aggregate supply responds as to produce what is demanded. But, what will happen if the economy was at full employment? The only way for production to increase will be an increase in the capital stock. With more capital (and labor) the economy will produce more GDP.

16. Mathematical derivation of Harrod-Domar model (2) Keynes’ Model Expanded to Consider Growth Harrod and Domar explained how the aggregate supply expands. For them, investment has two effects, one on the aggregate demand side (businesses expend more) and another in the aggregate supply side (more investment increases capital stock and thereby businesses produce more the next period). We, therefore, need to add a production function: Y = a.K production function Where a is the productivity of capital: DY/ DK, which is constant Now we can determine how a change in capital changes income. DY = a.DK

17. Mathematical derivation of Harrod-Domar model (3) What we need to know is how capital changes. It changes by businesses, and government investment: DK = Ia We are assuming that capital doesn’t ware out, i.e. there is not depreciation. Returning to the equilibrium condition (S=I) we solve the model again for the long run case s.Y = Ia = DK, but we know that DK = DY/a, then s.Y = DY/a s.a = DY/Y Calling DY/Y = g : rate of GNP growth

18. Mathematical derivation of Harrod-Domar model IV g = s.a If we recognize that capital depreciates: g = s.a – d Where dis the depreciation rate per year. Notice that in this model the rate of growth (g) is constant. Why?

19. Harrod’s way: K = v.Y where v = 1/a g = s/v And with depreciation g = s/v - d

20. Production function To growth model K GDP Production function GDP GDP2> GDP1 Productivity rate GDP1 N K

21. Assumptions To growth model • Labor/capital proportions are fixed • Saving rate is given K GDP Production function GDP GDP2> GDP1 Productivity rate GDP1 N K S Saving function S Saving rate Income = GDP

22. Non-existence of equilibrium Y Y,S,D,I C S In D D K

23. Technology or capital/output ratio Saving rate Depreciation rate Capital accumulation Growth rate Review You should now be familiar with the following terms:

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