Lecture 3 - Population

Population was almost constant for most part of the world history

Forces limiting population growth:

1. The scarcity of natural resources (i.e. land), a “positive check” (The scarcity of natural resources, such as food and land, is considered a positive check in Malthusian terms because it leads to conditions that increase mortality. When resources are insufficient to support the growing population, famine and malnutrition can occur, acting as natural checks on population growth.)

2. The deliberate reduction of fertility to prevent poverty, a “preventive check” (By limiting the number of children born, individuals or societies aim to ensure that population growth aligns with the availability of resources, preventing the onset of poverty and resource scarcity.)

In contrast, living standards are positively correlated with population.? In Malthus, they tend to be negatively correlated.

Negative relation between population and real wage -> Country locked in Malthusian Trap

Law of diminishing average product of labor: If we hold one input fixed (land) and expand the other input (labor), the average output per worker is going to fall

Key ideas of the Malthus model:

1. By the law of diminishing average product of labour, as more people work on the land, their income will inevitably fall

2. At the same time, if living standards decrease, population reduces (here is a negative growth rate of the population)

In equilibrium:

1. Population and income will stay constant

2. Living standards will be forced down to subsistence level

Underlying question: What could increase people’s living standards?

-> Moral restraint

New technology, e.g. introduction of irrigation or new crop

-> Rise in the quantity of food that can be grown on a given amount of land

-> We can have more population and remain at the same level of income per capita

-Model predicts a self-correcting response to new technology

-In the long run, an increase in productivity will result in increased population but not increased wages

Malthusian Trap:

Negative relation between population and real wage -> Country locked in Malthusian Trap

The Malthusian trap is a concept that describes a situation where population growth tends to outpace the growth of resources, leading to persistent poverty and hardship

Conditions to stay in the Malthusian Trap:

1. Diminishing average product of labor

2. Rising population in response to increases in wages

End of the 18th century somethign changed:

-> New innovations increased productivity

The Industrial revolution introduced improvements in technology which offset the diminishing average product of labor (With these technologies, even as more people joined the workforce, the overall productivity per person didn't decrease as much. The technology helped to offset or counteract the natural decline in average productivity as the number of workers increased.)

-> Britain was then able to escape the Malthusian trap

Since 1820: Both population and income per capita were rising!

Late 19th: As the growth of income accelerated, population growth began to fall

Future projections: Negative population growth

Negative correlation between output per capita and population growth across countries over the last decades

Solow Model with population growth:

Change in capital from today to next period is:

1. Take Logs

1. Take derivatives

1. Multiplying both sides by k

Capital accumulation equation:

Capital accumulation equation:

Interpret n*k as capital dilution (e.g. how many people operate a machine). It has the same consequences as capital depreciation.

If the quantity of capital in the country didn’t change, then population growth would result in less capital being available for each worker: capital dilution

Lower capital per worker -> lower income per worker

Question: What happens to the steady-state income when there is an exogenous increase in productivity?

-Slope of Output Curve is steeper

-> Slope of Investment Curve is steeper

-> Steady state level changes

How does this compare with the implications of the Malthusian model?

Production function:

Steady-state condition:

kss and yss:

Suppose that two countries have the same Productivity A, investment rate s, depreciation rate delta, but different growth rate of the population n