Economic Growth: Malthus and Solow ECN5114

Economic Growth: Malthus and Solow ECN5114

Economic Growth • Economic growth facts • Malthusian model of economic growth • Solow growth model

Robert Lucasargued that the potential social gains from a greater understanding of business cycles are dwarfed by the gains from understanding growth. • Why? Even if business cycle could be completely eliminated- the worst events we would be able to avoid-the reduction of real GDP below trend on the order of 5% (based on post WWII US data) • If changes in economic policy could cause the growth rate of real GDP to increase by 1% per year, then GDP would be 2.7 times higher after 100 years than it would otherwise have been.

Economic growth has not been uniform across countries-there are wide disparities in standard of living among the countries of the world. • In 2000, income per capita in Mexico was 23.5% of what it was in the US • In Egypt it was 13.2% of that in the US • In Burundi-it was about 2% of the US

Large differences in rates of growth across countries • Between 1960 and 2000- the real income in per capita was growing at an average rate of 2.48% in the US. • Compared to – Madagascar (-1.07%), Nicaragua (-0.03%), Hong Kong (5.40%), Taiwan (6.68%)

U.S. Per Capita Income Growth • In the United States, growth in per capita income has not strayed (deviate) far from 2% per year (excepting the Great Depression and World War II) since 1900. • The Industrial Revolution began about 1800 in UK • But the US surpassed the UK as the world industrial leader

Natural Log of Real Per-Capita Income in the United States, 1869–2005 Great depression (1929-1939) World war II (1941-1945)

Real Per Capita Income and the Investment Rate • Across countries, real per capita income and the investment rate are positively correlated. • A country that have large fraction of output is channeled into investment – tend to have a relatively high standard of living

Real Income Per Capita vs. Investment Rate Positive correlation across countries

Real per capita income and the rate of population growth • Across countries, real per capita income and the population growth rate are negatively correlated. • Countries that high population growth rates tend to have low standards of living. Vice versa

Figure 6.3 Real Income Per Capita vs. the Population Growth Rate Negative correlation

Differences in per capita incomes increased dramatically among countries of the world between 1800 and 1950 • Gap widening between Western Europe, US, Can, Aus and NZL – as a group leader and the ROW • Between 1980 and 1950 – there was a divergence between living standards in the richest and poorest countries of the world

Standard of living would be converging across countries if income (output) per capita were converging to a common value • Poor countries (low level of per capita income) are growing at a higher rate than rich countries • If convergence in income per capita is occurring, we should observe a negative correlation between the growth rate in income per capita and the level of income per capita across countries

There is no tendency for rich countries to grow faster than poor countries, and vice-versa. • Rich countries are more alike in terms of rates of growth than are poor countries. • A variability in the real income growthrates is much smaller for rich countries than for poor countries.

Growth Rate in Per Capita Income vs. Real Income Per Capita for the Countries of the World No correlation (between 1960 -2000) , thus convergence is not detectable Level of output per capita (% to US) in 1960

Growth miracles vs growth disasters • Growth miracles: where growth in a country far exceeds the world average over an extended period →country moves rapidly up the world income distribution →eg. Japan and NIC of East Asia – South Korea, Taiwan, Singapore & Hong Kong

Growth miracles vs growth disasters • Growth disasters: where a country’s growth falls far short of the world average. →eg. Argentina: in 1900 Argentina’s average income was slightly behind those of the world’s leader →to become a major industrialized country. →BUT growth was dismal →now near the middle of the world income distribution

Eg. Sub-Saharan African : such as Chad, Ghana, and Mozambique have been extremely poor through out their histories • Unable to obtain any sustained growth in average incomes • As a result: their average income has been rising steadily.

Vast difference in standards of living over time and across countries always associated with: large difference in nutrition, literacy, infant mortality, life expectancy and other direct measures of well-being. • For instance: if real income per person in Bangladesh continues to grow at its postwar, average rate of 1.4% →it will take 200 years to reach the current US levels. • If achieve 5% growth →the process will take 100 years.

A Malthusian Model of Economic Growth

Model predicts that a technological advance will just increase population, with no long-run change in the standard of living. • Higher population , reducing the average person to subsistence level of consumption before the advance in technology • Population & consumption – could grow over time • But in the log run – there would be no increase in the std of living

Production Function Output is produced from land and labor inputs. Output (eg food) that perishable labor land

In the economy: • No investment, no saving (S=I) • Closed economy • Assume no way to store food from one period to the next period • No technology for converting food into capital • Land (L) is fixed supply • Assume each person in this economy is willing to work at any wage • Has one unit of labor to supply (for normalization) • N = population and labor input

Evolution of the population • Population growth depends on the quantity of consumption per worker • Population growth is higher; the higher is per-capita consumption. For next period/future) Consumption per worker

Population Growth Depends on Consumption per Worker in the Malthusian Model N’/N positively on consumption per worker – due to the fact that higher food consumption per worker reduces death rates through better nutrition

In equilibrium: • All goods produced are consumed • C = Y (income-expenditure identity) • Substituting C for Y

Equilibrium Condition • In equilibrium, consumption equals output produced (C=Y) • Then substitute for C

Constant return to scale property implies: xzF(L,N) = zF(xL,xN) • For any x>0 , so if x= 1/N then; zF(L,N)/N = zF(L/N, 1) • Then rewrite, multiply each side by N

This equation describes how the future population depends on current population

Determination of the Population in the Steady State A LR equilibrium Refer to current population, future population Steady state for population

Population is converged toward steady state • If N< N* ; N’>N ; population increases • Then there will be relatively large quantity of consumption per worker – imply the population growth rate is relatively large (and +) –> the population will increase N* is the long run equilibrium for population

If N> N* ; N’<N ; population increases • IF N>N*: small qty of C –- population growth relatively low (-) ; so that population will decrease

That is why population converges to a steady state • Since land is fixed: population converges to the LR equilibrium (N*) thus, aggregate consumption : C* =zF (L,N*)

Analysis of steady state in the Malthusian Model • Since economy converge to a steady state with constant population (N*) and constant aggregate consumption (C*) • Useful to analyze this steady state to determine what features of the environment affect steady state variables.

The per-worker production function From Y/N = zF(L/N, 1) Denote : y = Y/N (output per worker) l = L/N (land per worker) C=C/N (consumption per worker) Thus we have:

Equilibrium condition in per-worker form Per worker production : describe the qty of output per worker y that can be produced for each qty of land per worker, l When c = y

Rewrite: • Population growth is increasing in consumption per worker, c

The Per-Worker Production Function Describe the relationship between output per worker and land per worker in the Malthusian model , assuming CRS

Determination of the Steady State in the Malthusian Model • In steady state: N’=N=N* , also N’/N = 1 • N* determine l* In the model: Land is fixed; we can determine steady state at N*=L/l*

In the model, take standard living as given by c* (steady state consumption per worker) • Therefore, LR std of living is determined entirely by the function of g (captured the effect of the standard of living on population growth) • Not any element in panel a • Even the improvement in the production technology or increase in the qty of land – have no effect on the LR std of living.

Eg. The Effect of an Increase in z (improvement in agric. Techniques) in the Malthusian Model • If z increases, this shifts up the per-worker production function. • In the long run, the population increases to the point where per capita consumption returns to its initial level. • No effect on steady state c* in (b) • Qty land per worker falls, imply that steady state population increases from N1* to N2* • There is no long-run change in living standards.

Adjustment to the Steady State in the Malthusian Model When z Increases • Economy does not move to the new steady state instantaneously – it will take time for the population and consumption to adjust • The economy at steady state before time T (where there is an increase in z) • No effect on current population at time T; but increase output, consumption and consumption per worker • However, because c has increased, there is an increase in population growth • As population grows after period T, consumption per worker decrease (give L is fixed) until consumption per worker converges to c* (initial level) • Population converges to its new higher level N2*

Population Control in the Malthusian Model • How society is better off in a Malthusian world? • Proposed –mandated population control –like what happen in china (only one child) • That give the effect of reducing the rate of population growth for each level of consumption per worker • Population control alters the relationship between population growth and per-capita consumption. • In the long run, per capita consumption increases, and living standards rise.

Population Control in the Malthusian Model • Population control policy shift the function g1 to g2. • In the steady state, consumption per worker increases and land per worker decreases (as population falls) : l1* to l2* ; thus N1* to N2*

How Useful is the Malthusian Model • Model provides a good explanation for pre-1800 growth facts in the world – - population grew over time ; as did aggregate production but no significant improvement in the average std of livings. • After 1800: sustained growth in std of living –without any significant government population control • The richest countries – experienced large dropped in birth rates • Advances in health care – increased life expectancy in the richest cty. • Malthus was wrong- concerning the ability of economies to produce LR improvements in the standard of living and the effect of the std of living on population growth • Malthus did not predict the effects of technological advances on fertility. • Malthus did not understand the role of capital accumulation in growth.

Why was Malthus wrong? 1.He did not allow for the effect of increase in the capital stock on production • land is limited supply to the size of capital stock • having more capital implies there is more productive capacity to produce additional capital • Capital can reproduce itself • The Solow model – allow us to explore the role of capital accumulation in growth

Why was Malthus wrong? 2. Malthus did not account for all of the effect of economic forces on population growth • Higher standard of living reduces death rates through better nutrition and health care • Also proved to be a reduction in birth rates • The opportunity cost of raising a large family becomes large in the face of high market wages, and more time is spent working in the market rather than raising children at home.

Summary about Malthus • Malthus argued that as wages increase within an economy, the birth-rate increases while the death-rate decreases. • high incomes: allowed people to have sufficient means to raise their children, thus resulting in greater desire to have more children which increases the population. • high incomes: allowed people to afford proper medication to fight off potentially harmful diseases, thus decreasing the death-rate. • As a result, wage-increases caused population to grow as the birth-rate increases and the death-rate decreases.

as the supply of labor increases with the increased population-growth at a constant labor demand, • the wages earned would decrease eventually to subsistence, where the birth-rate equals the death-rate, resulting in no growth in population. • However, the world generally has experienced quite a different result than the one Malthus predicted. During the late 19th and early 20th century, the population (and wages) increased as theindustrial revolutiongathered pace. • However, birth rates in highly-developed nations have dropped to bare replacement-levels, such that many Western nations like the US and Canada only grow due to immigration, and Japan faces a declining population when the post-World War II generation dies off.

Solow Growth Model • Robert Merton "Bob" Solow (born August 23, 1924) is an Americaneconomist particularly known for his work on the theory of economic growth • Academic advisor: wassiliy leontif • Notable student: Joseph stiglitz

Economic Growth: Malthus and Solow ECN5114