Download Lecture 11: Malthusian Model of Economic Growth

Lecture 11: Malthusian Model of Economic
Growth
Nicolas Roys
University of Wisconsin Madison
Econ 302 - Spring 2015
Topics of today’s class
Last Lecture:
I
Introduction to Economic Growth
Today:
I
Malthusian Model of Economic Growth
Economic Growth over the very long run
Malthus
Thomas Malthus: An essay on the Principle of Population (1798)
I
population growth has a negative impact on standards of living
because increases in population dilute any gains in productivity
I
He predicts that a technological advance will only increase
population, with no long-run change in the standard of living
I
He argues in favor of population control or “forced family
planning”
Proximate and Ultimate Causes of Growth
The Modern Growth Regime
Major Puzzles
althusian
Adjustments
of Income and of
Population:
1250ñ1750
Malthusian
Adjustments
IncomeEngland,
and Population:
England, 1250-1750
Oded Galor
Growth and Comparative Development - An Overview
Production Function
Production Function:
Y
1
2
= zL 3 N 3
I
L: Fixed Quantity of land
I
C = Y : food
Production Function
Production function:
Y
Y
N
y
1
2
= zL 3 N 3
✓ ◆1
L 3
= z
N
1
= zl 3
where
I
y : output per worker
I
l : land per worker
Since consumption equals output, consumption per worker c is:
1
c = zl 3
Dynamic Model
I
before: static model
I
now: dynamic model
I
no-investment: there is no way to store food from one period
to the other
Population Evolution
Population Growth:
N0
=g
N
where g is increasing.
✓ ◆
C
N
1. Birth rate increases with consumption per capita
I
I
people will have more children by choice, as they are better
able to provide for children
better nutrition increases fertility
2. death rate decreases with consumption per capita
I
decreases infant mortality
I
population more healthy, increasing the average lifespan
Population growth is higher the higher is per-capita consumption.
Population Growth and Consumption per Worker
Equilibrium Evolution of the Population
N0
=g
N
or
N0 = g
✓ ◆1 !
L 3
z
N
✓ ◆1 !
L 3
z
N
N
Steady State Population
The steady state is the long-run outcome of the economy N ⇤ so
that
✓ ◆1 !
L 3
N⇤ = g z
N⇤
N⇤
I
N > N ⇤ : population decreases
I
N < N ⇤ : population increases
Steady State Population
A Steady Sate Condition
Population growth is increasing in consumption per worker c:
N0
= g (c)
N
At the steady state:
then,
1 = g (c ⇤ )
1
2
C ⇤ = zL 3 (N ⇤ ) 3
standards of living in the long run are entirely determined by the
function g .
Determination of the Steady State in the Malthusian Model
An Increase in TFP
If z increases, this shifts up the per-worker production function
-
An Increase
in TFP
An Increase
in TFP
An Increase in TFP
Immediate Effect of an Increase in TFP
I
increase in the productivity of labor
I
and so an increase in consumption per capita
But increase in consumption per capita leads to:
I
an increase in population size
I
an decrease in the productivity of labor (decreasing marginal
return to labor)
In the long-run:
I
consumption per worker is unchanged
I
population increases
Pessimistic View: improvements in technology do not
improve standard of living in the long run
Population Control
Population control alters the relationship between population
growth and per-capita consumption
Example
”one child” policy in China
Population Control
Population Control
In the long-run:
I
Population decreases
I
Consumption per worker increases
Everyone is better off in the long run!
What is missing in the Malthusian Model?
I
Model succesful at explaining before GDP per capita and
Population before the Industrial Revolution
BUT large growth in GDP per capita since the industrial revolution:
1. Capital Accumulation
2. Demographic Transition: both birth and death rates dropped
and population growth eventually started to slow.
2.1 As wages rise, the opportunity cost of raising children increases
(especially for women), and large families become less
attractive.
2.2 What is more, as the link between education and economic
success grows stronger, parents invest ever more in their
children