Lecture 14 Malthusian Model

Economics Growth Solow model explains all growth facts for industrialized countries Why are many poor countries not growing? Why did all countries stagnate before 1800?

The Malthus Model 1798:"Essay on Population" Explains stagnation as resulting from limited supply of land and population growth

Outline Production function uses land and labor People decide on number of children Population growth offsets productivity growth

Differences to Solow Model Solow model does not consider land as an input Solow model takes population growth as constant

Structure of the Model Consumers work on their own farm (no firms in the model) and decide to consumption and fertility Each consumer owns an equal share of land Law of motion for population is determined by fertility decisions

The Consumer Consumer cares about consumption and number of children Consumer works one unit of time, owns equal share of land, and keeps farm output Each child eats units of consumption

The Maximization Problem Consumer takes income as given and chooses and

The Solution Plugging in the constraint: First-order condition:

Result Number of children depends positively on farm income The richer the consumer is, the more children she will have

Land and Population Total amount of land X is fixed; for simplicity, assume X=1 Population size is denoted by Amount of land per person:

The Farm Farm technology is Cobb-Douglas in labor and land (z is productivity): One unit of labor is supplied ( ) and land per person is

The Law of Motion for Population Population tomorrow is population today times children per person: Plugging in actual

Convergence in Population

Computing the Steady State Find steady-state population : Find steady-state income : Income is independent of z!

The Malthusian Mechanism Fertility in the steady state: Income adjusts such that each person has one child (zero population growth) Therefore income adjusts to the same level regardless of productivity

Explanation for the Result When income in high, people have many children and population growth is high High population growth lowers income until each parent has just one child

What Happens if Productivity Increases? Increase in z will lead to higher income and higher population growth Higher population growth pushes incomes down Ultimately, a new steady state is reached with higher population, but same income per person

A jump in productivity

Long-Run Predictions Income per capita will be roughly constant over time Increase in productivity will increase world population without raising living standards Inventive countries and regions will have higher population growth

Why is the Solow Model Different? The Solow model does not have endogenous fertility-population growth assumed to be constant The Solow technology does not use land-population increases do not lower income per capital

Why Do We Use Both Models? The Malthus model is an accurate description of the world until 1800 --Agriculture and land were important --Income and fertility were positively related The Solow model is an accurate description of industrialized countries --Agriculture is small sector today --Fertility no longer closely related to income

How Did We Get From Malthus to Solow? Two promising approaches: --Technological change replaced land-based technology by capital-based technology --People started to invest in human capital instead of having many children

Technological Changes and Growth Industrialization replaced land-based technology by capital-based technology Since the importance of land diminishes, returns to population size no longer decreasing Growth in income per capita is possible even as population is growing

The Malthus Model with a Constant-Returns Technology Consumer: Firm:

Results Fertility Choice: Output per person: population growth as a function of z:

Implication Productivity growth (increase in z) is not offset by population growth Income per capita increases with z, as in the Solow model However, population growth ever increasing Can get transition in theory, not in practice

The Demographic Transition The income-fertility relationship also changed In late 19th century, mortality rates and fertility rates fell steeply in England, U.S., and Germany Today richer people have fewer children All industrialized countries experienced demographic transition

The Malthus Model with Fixed Fertility Exogenous limit on fertility: Decreasing-returns technology:

Results Constant population: Constant labor ( ) and land per person( ) Resulting output per person:

Implication Once again, income per capita increases with z, as in the Solow model However, share of land stays constant In data, share of land in output declining over time True explanation is probably a combination

Why Did Fertility Fall? Increased cost of children (education, no more child labor) Low mortality Social security Increased female labor-force participation

The Current Situation in Developing Countries Many developing countries are still in between Malthus and Solow Agriculture plays a more important role Less education, less social security, less female labor force participation, and more child labor result in higher fertility and population growth

Income per Worker vs. Population Growth

Income per Capita vs. Share of Agriculture

Additional Problems in Developing Countries Lack of protection of property rights Inefficient government and corruption Wars and civil conflict Tropical diseases and AIDS Lack of human capital

Economics for the 21th Century What are the prospects for world economy in the next 100 years? Key questions: --Are there reasons why growth might stop in developed countries? --Will developing countries start to be more like industrialized countries?

Educated Guesses No reason why Solow model should cease to work-continued growth in rich countries is likely Fertility is falling fast, and the role of agriculture is declining-more developing countries should start to grow Expect convergence around the world

Birth Rates in a Few Developing Countries