1、Lecture 14Malthusian ModelEconomics GrowthSolow model explains all growth facts for industrialized countriesWhy are many poor countries not growing?Why did all countries stagnate before 1800?The Malthus Model1798:Essay on PopulationExplains stagnation as resulting from limited supply of land and pop

2、ulation growthOutlineProduction function uses land and laborPeople decide on number of childrenPopulation growth offsets productivity growthDifferences to Solow ModelSolow model does not consider land as an inputSolow model takes population growth as constantStructure of the ModelConsumers work on t

3、heir own farm (no firms in the model) and decide to consumption and fertilityEach consumer owns an equal share of land Law of motion for population is determined by fertility decisions The ConsumerConsumer cares about consumption and number of children Consumer works one unit of time, owns equal sha

4、re of land, and keeps farm output Each child eats units of consumption The Maximization ProblemConsumer takes e as given and chooses and The SolutionPlugging in the constraint:First-order condition:ResultNumber of children depends positively on farm eThe richer the consumer is, the more children she

5、 will haveLand and PopulationTotal amount of land X is fixed; for simplicity, assume X=1Population size is denoted by Amount of land per person: The FarmFarm 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 fo

6、r PopulationPopulation tomorrow is population today times children per person:Plugging in actual Plugging in actual Convergence in Population Computing the Steady State Find steady-state population :Find steady-state e : e is independent of z!The Malthusian MechanismFertility in the steady state: e

7、adjusts such that each person has one child (zero population growth)Therefore e adjusts to the same level regardless of productivity Explanation for the ResultWhen e in high, people have many children and population growth is highHigh population growth lowers e until each parent has just one child W

8、hat Happens if Productivity Increases?Increase in z will lead to higher e and higher population growthHigher population growth pushes es downUltimately, a new steady state is reached with higher population, but same e per person A jump in productivity Long-Run Predictions e per capita will be roughl

9、y constant over timeIncrease in productivity will increase world population without raising living standardsInventive 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

10、The Solow technology does not use land-population increases do not lower e per capitalWhy Do We Use Both Models?The Malthus model is an accurate description of the world until 1800 -Agriculture and land were important e and fertility were positively relatedThe Solow model is an accurate description

11、of industrialized countries -Agriculture is small sector today -Fertility no longer closely related to e 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

12、of having many children Technological Changes and GrowthIndustrialization replaced land-based technology by capital-based technologySince the importance of land diminishes, returns to population size no longer decreasingGrowth in e per capita is possible even as population is growing The Malthus Mod

13、el with a Constant-Returns Technology Consumer:Firm:ResultsFertility Choice:Output per person:population growth as a function of z:ImplicationProductivity growth (increase in z) is not offset by population growth e per capita increases with z, as in the Solow modelHowever, population growth ever inc

14、reasingCan get transition in theory, not in practice The Demographic TransitionThe e-fertility relationship also changedIn late 19th century, mortality rates and fertility rates fell steeply in England, U.S., and GermanyToday richer people have fewer childrenAll industrialized countries experienced

15、demographic transition The Malthus Model with Fixed FertilityExogenous limit on fertility:Decreasing-returns technology: ResultsConstant population:Constant labor ( ) and land per person( )Resulting output per person: ImplicationOnce again, e per capita increases with z, as in the Solow modelHowever

16、, share of land stays constantIn data, share of land in output declining over timeTrue explanation is probably a combination Why Did Fertility Fall?Increased cost of children (education, no more child labor)Low mortalitySocial securityIncreased female labor-force participation The Current Situation

17、in Developing CountriesMany developing countries are still in between Malthus and SolowAgriculture plays a more important roleLess education, less social security, less female labor force participation, and more child labor result in higher fertility and population growth e per Worker vs. Population

18、 Growth e per Capita vs. Share of Agriculture Additional Problems in Developing CountriesLack of protection of property rightsInefficient government and corruptionWars and civil conflictTropical diseases and AIDSLack of human capital Economics for the 21th CenturyWhat 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? Educ