1. Lecture 14
Malthusian Model

2. 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?

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

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

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

6. 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

7. 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

8. The Maximization Problem
Consumer takes income as given and chooses and

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

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

11. 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:

12. 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

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

14. Convergence in Population

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

16. 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

17. 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

18. 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

19. A jump in productivity

20. 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

21. 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

22. 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

23. 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

24. 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

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

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

27. 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

28. 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

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

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

31. 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

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

33. 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

34. Income per Worker vs. Population Growth

35. Income per Capita vs. Share of Agriculture

36. 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

37. 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?

38. 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

39. Birth Rates in a Few Developing Countries