Economic Growth Model -- Harrod-Domar

1. Economic Growth Models Harrod –Domar Growth Model Solow Growth Model Endogenous Growth Model 1 Econ 171 -- Atanu Dey -- Lecture 5

2. Thinking About Development Rates of growth of real per-capita income are . . . diverse, even over sustained periods . . . I do not see how one can look at figures like those without seeing them as representing possibilities. . . The consequences for human welfare involved in [questions related to development] are simply staggering: Once one starts thinking about them, it is hard to think about anything else. -- Robert Lucas 2 Econ 171 -- Atanu Dey -- Lecture 5

3. Link between Human Development and Income [A] unity of interests would exist if there were rigid links between economic production (as measured by income per head) and human development (reflected by human indicators such as life expectancy or literacy, or achievements such as self-respect, not easily measured). But these two sets of indicators are not very closely related. -- Paul Streeten (1994) 3 Econ 171 -- Atanu Dey -- Lecture 5

4. Rate of Growth How long would it take for a quantity to double if it grows at a compounded rate of growth of 7 percent? . . . of 10 percent? 4 Econ 171 -- Atanu Dey -- Lecture 5

5. Rule of 70 Simple formula: Divide 70 by the rate of growth At 7 percent compounded rate of growth, the doubling time is 10 years, and vice versa. 5 Econ 171 -- Atanu Dey -- Lecture 5

6. Harrod-Domar Growth Model Developed independently by Sir Roy Harrod in 1939 and EvseyDomar in 1946 Explains growth in terms of the level of saving and productivity of capital Production = Consumption goods + Capital goods Investment  Capital formation Saving means delaying present consumption Growth depends on investing savings in increasing capital stock Econ 171 -- Atanu Dey -- Lecture 5 6

7. Macroeconomic Flow Firms and households Firms produce stuff Firms pay wages, profits and rents to households Households consume stuff Consumption expenditure is income for firms Households save Savings are investments for firms Circular flow of production, consumption, saving, and investment Econ 171 -- Atanu Dey -- Lecture 5 7

8. Variables Y represents income same as output or production K represents capital stock δ depreciation rate of the capital stock S is savings s is the savings rate, and I is investment C is consumption The Harrod-Domar model makes the following a priori assumptions: Econ 171 -- Atanu Dey -- Lecture 5 8

9. Assumptions Output (or income) is consumption plus savings Y(t) = C(t) + S(t) The product of the savings rate and output equals saving, which equals investment sY = S = I The change in the capital stock equals investment less the depreciation of the capital stock K(t+1) = (1 – δ)K(t) + I(t) Econ 171 -- Atanu Dey -- Lecture 5 9

10. Harrod-Domar Equation Savings rate is s s = S(t)/Y(t) Capital-output ratio is θ Amount of capital required to produce one unit of output θ = K(t)/Y(t) Rate of growth g g = [Y(t+1) – Y(t)]/Y(t) s/θ = g + δ – the Harrod-Domar Equation Econ 171 -- Atanu Dey -- Lecture 5 10

11. What the H-D equation means g = s/θ - δ It links growth rate g to two other rates The savings rate s and the capital-output ratio θ What’s the effect of population growth? Econ 171 -- Atanu Dey -- Lecture 5 11

12. Adding population growth Population P grows at rate n P(t+1) = P(t)(1 +n) Per capita income is y(t) y(t) = Y(t)/P(t) Per capita income growth rate is g* y(t+1) = y(t)(1 + g*) New equation s/θ = (1 + g*)(1 + n) – (1 – δ) Combines savings ability, capital productivity, depreciation, and population growth Econ 171 -- Atanu Dey -- Lecture 5 12

13. What it means s/θ = (1 + g*)(1 + n) – (1 – δ) (1 + g*)(1 + n) = 1 + g* + n + g*n But g* and n small numbers, and so g*n is negligible So s/θ ≈ g* + n + δ Interpretation: Per capita growth rate is reduced by population growth rate and by capital depreciation rate Per capita growth rate is increased by savings rate and by more efficient use of capital Econ 171 -- Atanu Dey -- Lecture 5 13

14. Are the variables exogenous? H-D models saving rate, capital-output ratio, and population growth rate as constants, and not affected by the growth of the economy s, n and θare considered exogenous What if saving rate is a function of per capita income? Poor people cannot save at the same rate as those who are rich Distribution of income – and not just per capita income – affects the saving rate Therefore saving rate may rise with rising incomes Econ 171 -- Atanu Dey -- Lecture 5 14

15. Population growth rate Population growth rate declines as incomes go up Why? n is endogenous The capital-output ratio also changes due to the law of diminishing returns to individual factors of production When capital level is low, the marginal productivity of capital is high So θ is endogenous as well Econ 171 -- Atanu Dey -- Lecture 5 15