Econ 171 -- Atanu Dey -- Lecture 5 1

Economic Growth ModelsHarrod –Domar Growth Model

Solow Growth ModelEndogenous Growth Model

Econ 171 -- Atanu Dey -- Lecture 5 2

Thinking About DevelopmentRates 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

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)

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?

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.

Econ 171 -- Atanu Dey -- Lecture 5 6

Harrod-Domar Growth ModelDeveloped independently by Sir Roy Harrod

in 1939 and Evsey Domar in 1946Explains growth  in terms of the level of

saving and productivity of capitalProduction = Consumption goods + Capital

goods Investment Capital formationSaving means delaying present consumptionGrowth depends on investing savings in

increasing capital stock

Econ 171 -- Atanu Dey -- Lecture 5 7

Macroeconomic FlowFirms and householdsFirms produce stuffFirms pay wages, profits and rents to

householdsHouseholds consume stuff Consumption expenditure is income for firmsHouseholds saveSavings are investments for firmsCircular flow of production, consumption,

saving, and investment

Econ 171 -- Atanu Dey -- Lecture 5 8

VariablesY represents income

same as output or productionK represents capital stock

δ depreciation rate of the capital stock S is savings s is the savings rate, and I is investment C is consumptionThe Harrod-Domar model makes the

following a priori assumptions:

Econ 171 -- Atanu Dey -- Lecture 5 9

AssumptionsOutput (or income) is consumption plus

savingsY(t) = C(t) + S(t)

The product of the savings rate and output equals saving, which equals investmentsY = S = I

The change in the capital stock equals investment less the depreciation of the capital stockK(t+1) = (1 – δ)K(t) + I(t)

Econ 171 -- Atanu Dey -- Lecture 5 10

Harrod-Domar EquationSavings 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 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 12

Adding population growthPopulation 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 13

What it meanss/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 + δInterpretation:

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 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 θ are considered exogenousWhat if saving rate is a function of per capita

income?Poor people cannot save at the same rate as

those who are richDistribution of income – and not just per capita

income – affects the saving rateTherefore saving rate may rise with rising

incomes

Econ 171 -- Atanu Dey -- Lecture 5 15

Population growth ratePopulation growth rate declines as incomes

go upWhy?n is endogenousThe 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