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Malthusian Model of Economic Growth

This lecture explores the Malthusian model of economic growth, which explains the stagnation and limited growth in pre-1800 countries due to land limitations and population growth. It compares this model to the Solow model to understand the differences and why both are used. It also discusses the transition from Malthusian to Solow model and technological changes that led to growth.

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Malthusian Model of Economic Growth

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  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 • 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

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