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Lecture 11: Malthusian Model of Economic Growth Nicolas Roys University of Wisconsin Madison Econ 302 - Spring 2015 Topics of today’s class Last Lecture: I Introduction to Economic Growth Today: I Malthusian Model of Economic Growth Economic Growth over the very long run Malthus Thomas Malthus: An essay on the Principle of Population (1798) I population growth has a negative impact on standards of living because increases in population dilute any gains in productivity I He predicts that a technological advance will only increase population, with no long-run change in the standard of living I He argues in favor of population control or “forced family planning” Proximate and Ultimate Causes of Growth The Modern Growth Regime Major Puzzles althusian Adjustments of Income and of Population: 1250ñ1750 Malthusian Adjustments IncomeEngland, and Population: England, 1250-1750 Oded Galor Growth and Comparative Development - An Overview Production Function Production Function: Y 1 2 = zL 3 N 3 I L: Fixed Quantity of land I C = Y : food Production Function Production function: Y Y N y 1 2 = zL 3 N 3 ✓ ◆1 L 3 = z N 1 = zl 3 where I y : output per worker I l : land per worker Since consumption equals output, consumption per worker c is: 1 c = zl 3 Dynamic Model I before: static model I now: dynamic model I no-investment: there is no way to store food from one period to the other Population Evolution Population Growth: N0 =g N where g is increasing. ✓ ◆ C N 1. Birth rate increases with consumption per capita I I people will have more children by choice, as they are better able to provide for children better nutrition increases fertility 2. death rate decreases with consumption per capita I decreases infant mortality I population more healthy, increasing the average lifespan Population growth is higher the higher is per-capita consumption. Population Growth and Consumption per Worker Equilibrium Evolution of the Population N0 =g N or N0 = g ✓ ◆1 ! L 3 z N ✓ ◆1 ! L 3 z N N Steady State Population The steady state is the long-run outcome of the economy N ⇤ so that ✓ ◆1 ! L 3 N⇤ = g z N⇤ N⇤ I N > N ⇤ : population decreases I N < N ⇤ : population increases Steady State Population A Steady Sate Condition Population growth is increasing in consumption per worker c: N0 = g (c) N At the steady state: then, 1 = g (c ⇤ ) 1 2 C ⇤ = zL 3 (N ⇤ ) 3 standards of living in the long run are entirely determined by the function g . Determination of the Steady State in the Malthusian Model An Increase in TFP If z increases, this shifts up the per-worker production function - An Increase in TFP An Increase in TFP An Increase in TFP Immediate Effect of an Increase in TFP I increase in the productivity of labor I and so an increase in consumption per capita But increase in consumption per capita leads to: I an increase in population size I an decrease in the productivity of labor (decreasing marginal return to labor) In the long-run: I consumption per worker is unchanged I population increases Pessimistic View: improvements in technology do not improve standard of living in the long run Population Control Population control alters the relationship between population growth and per-capita consumption Example ”one child” policy in China Population Control Population Control In the long-run: I Population decreases I Consumption per worker increases Everyone is better off in the long run! What is missing in the Malthusian Model? I Model succesful at explaining before GDP per capita and Population before the Industrial Revolution BUT large growth in GDP per capita since the industrial revolution: 1. Capital Accumulation 2. Demographic Transition: both birth and death rates dropped and population growth eventually started to slow. 2.1 As wages rise, the opportunity cost of raising children increases (especially for women), and large families become less attractive. 2.2 What is more, as the link between education and economic success grows stronger, parents invest ever more in their children