Chapter 6

SUSTAINABILITY

A Malthusian perspective

Demography 1Demography 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.

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 2Demography 2

Demography 3Demography 3

Demography 4Demography 4

Malthus 1Malthus 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 2Malthus 2

Why? Malthusian equilibrium1. 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 3Malthus 3

Malthus 4Malthus 4

Figure 2: Long Run Equilibrium in the Malthusian Economy

After MalthusAfter Malthus

● Then what?● Then what?

Demography 5Demography 5

Demography 5Demography 5

Karl Marx’s AnswerKarl 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 ModelSolow’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 ModelNeo-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 toSubsistance, r goes to 0

Romer’s ModelRomer’s Model

This is a production function that endogenizestechnological advancement as an explanatory variable, which leads to a surprising observation: technological advancement is a public good: non-excludability and non-exhaustibility implythat 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 youincrease workforce size.

Romer’s ModelRomer’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.