HarrodDomar Growth Model

1
Harrod-Domar Growth Model

• Professor Carlos A. Benito
• Department of Economics
• Sonoma State University

ECON 403
2
Topics for today
In growth models, we will encounter the
following terms

• 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

3
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.

4

• 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 lt ASfe
• Aggregate Supply, at full employment
• Macroeconomic Equilibrium
• AS AD
• Or
• S I

5
A Keynesian Model

• A Keynesian growth model takes a long run
  perspective.
• Aggregate demand (or savingsinvestment) 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)

6
Trends and business cycles
Trend
One business cycle
Real GDP
Years
7
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

8
Harrod-Domar Growth Model A Flow chart model
Saving Rate
Depreciation Rate
s
S
Ig
d
C
GDP
D
v K/Y or aY/K
In
Capital/Output Ratio or Productivity
Capital
Production function
9
Factors Explaining the growth rateAccording to
Harrod-Domar model
s a d
Saving rate

Rate of Economic Growth

g
Capital productivity
_
Capital depreciation
Explained variable
Explanatory Variables
10
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)
sdS/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.
SY.s
YK.a
dY
I
If we know dK and a, we know growth of output dY
adY/dK
dK
K
11
Numerical specificationWithout Depreciation
If we know output Y1 and we know the saving rate
s.10, then we know total savings S.10
Or dY s.a By approximation
dY/Ys.a/Y gs.a Since Y1
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 K5 and we
know its productivity a.20 then we know total
output Y1
dY.022
Y1
.10
a.20
dK.10
If we know dK.10 and a.20, we know growth of
output dY0.022
K5
12
Economic growth formula
According to Harrod-Domar the rate of economic
growth is defined by the formula g s.a
d that is, if s10 and a0.20 and d 1,
then g0.100.20 - 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 ?
13
.
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
14

• 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.

15
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
16
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
doesnt ware out, i.e. there is not
depreciation. Returning to the equilibrium
condition (SI) 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
17
Mathematical derivation of Harrod-Domar model IV
g s.a
If we recognize that capital depreciates g
s.a d Where d is the depreciation rate per
year.
Notice that in this model the rate of growth (g)
is constant. Why?
18

• Harrods way
• K v.Y where v 1/a
• g s/v
• And with depreciation
• g s/v - d

19
Production function
To growth model
K
Production function
GDP
GDP
GDP2gt GDP1
Productivity rate
GDP1
N
K
20
Assumptions
To growth model

• Labor/capital proportions are fixed
• Saving rate is given

K
Production function
GDP
GDP
GDP2gt GDP1
Productivity rate
GDP1
N
K
S
Saving function
S
Saving rate
Income GDP
21
Non-existence of equilibrium
Y
Y,S,D,I
C
S
In
D
D
K
22
Review
You should now be familiar with the following
terms

• Technology or capital/output ratio
• Saving rate

• Depreciation rate
• Capital accumulation
• Growth rate

23
(No Transcript)