Chapter 6
SUSTAINABILITY
A Malthusian
perspective
Demography 1
Rate of population change = Birth rate - death rate
Birth rate is a function of fertility
In a stable population the birth rate equals the death rate by definition,
so life expectancy can be equivalently calculated as the inverse of
the birth rate.
For example, a birthrate of 50 per thousand of population implies a life
expectancy of 20 at birth.
Demography 2
Demography 3
Demography 4
Malthus 1
What is the fundamental logic of the
“natural” economy?
Births per year per hundred people in a population =
Deaths per year per hundred people in a population
Birth rate = Death rate
Malthus 2
Why? Malthusian equilibrium
1. The BIRTH RATE is a socially determined
constant, independent of material living standards.
2. The DEATH RATE declines as living standards
increase.
3. MATERIAL LIVING STANDARDS decline as
population increases.
Malthus 3
Malthus 4
Figure 2:
Long Run Equilibrium
in the Malthusian Economy
After Malthus
● Then what?
Demography 5
Demography 5
Karl Marx’s Answer
What is the fundamental logic of
the “capitalist” economy?
Capital accumulation (the law and the prophets)
and the magic of compound interest permit
unlimited growth in material standard of living
The only limit is the rate of savings
Solow’s Growth Model
Start with a Production Function = a mathematical
representation of the process through which capital and
labor are combined to produce goods and services
y = ƒ(k), y = r, sy = nk, r = n
What you find is that, beyond a certain point you cannot
increase the material standard of living per unit of labor
input by adding more capital.
The implication is that once the optimal labor capital
combination (k*) has been reached an economy can grow
no faster that the rate at which the labor force expands
(n), except by reducing consumption.
Neo-Malthusian Model
In the real world, where resources can and
throughout history have been depleted,
this implies that output per worker must fall,
ultimately to below subsistence levels.
Since n = B-D, as this goes to
Subsistance, r goes to 0
Romer’s Model
This is a production function that endogenizes
technological advancement as an explanatory
variable, which leads to a surprising observation:
technological advancement is a public good:
non-excludability and non-exhaustibility imply
that even if the rate of technological innovation
is a direct or linear function of the size of the
population and, thereby, the workforce, its
payoff increases at an increasing rate when you
increase workforce size.
Romer’s Model
For example, if every unit of the workforce invents
Something that makes work ten percent more productive
and you have one workforce unit, productivity is increased
ten percent. If you have two units, you can produce 21
percent more stuff; ten units, 160 percent; and 100 units,
1,378,000 percent.