Economic Growth: Capital Accumulation and Population Growth
Economic Growth: Capital Accumulation and Population Growth -
Material standards of living have improved substantially over time for most families in most countries
-
Advance comes from rising incomes; allows people to consume more goods and services
-
Differences income come from difference in capital, labour and technology
-
Solow growth model: shows how saving, population growth and technological progress affect levels of an economy’s output and growth
Accumulation of Capital -
Model shows how growth in capital stock, labour force and advances in technology affect nation’s total output of goods and services
Supply and Demand for Goods -
-
Supply of goods is based on production function; output depends on capital stock and labour force o
Model assumes constant returns to scale; helps analyze all quantities in the economy relative to the size of the labour force
o
Size of the economy (measured by # of workers) does not affect relationship between output and capital per worker
o
For Marginal product of capital; as amount of capital increases, production function becomes flatter; production function exhibits diminishing marginal product of capital
o
Slope of production function is MPK
Demand for goods comes from consumption and investment o
Output per worker = consumption per worker + investment per worker
o
Y=c+i
o
Solow model: assumes that each year people save some of their income and consume a fraction
o
Rate of saving is fraction of output devoted to investment
-
Saving rate determines allocation of output between consumption and investment
-
Production function determines how much output an economy produces 1
Growth in Capital Stock and Steak State -
Investment and depreciation influence capital stock
-
Investment: expenditure on new plant and equipment; causes capital stock to rise
-
Depreciation: wearing out old capital; causes capital stock to fall; proportional to capital stock
-
Higher the capital stock, the greater the amounts of output, investment and depreciation
-
At K*, amount of investment must equal amount of deprecation
-
Steady state level of capital: capital stock and output are steady over time o
Economy at the steady state will stay there
o
N economy not at the steady state will go there
o
It represents the long run equilibrium of the economy
-
If investment exceeds depreciation; capital stock will rise along with output until it approaches steady state
-
If investment is less than depreciation; capital wearing out faster than being replaced; capital stock will fall and approach steady state level
Miracle of Japanese and German Growth – Case Analysis -
In 1945 economies of Japan and Germany were in shambles; WWII destroyed much capital stock
-
Output grew, because at lower capital stock, more capital is added by investment than removed by depreciation
-
High growth continues until economy approaches former steady state
How Saving Affects Growth -
Both Japan and Germany save and invest a higher fraction of their output than other countries
2
-
Increase in saving rate: amount of investment for any given capital stock is higher; investment exceeds depreciation; capital stock rises until economy reaches new steady state; results in more capital and output o
Government budget deficit can reduce national savings and crowd out investment
o
Reduced savings lower capital stock and national income
o
Higher savings = faster growth until economy reaches new steady state
-
Growth effect: policies that alter the steady state growth rate of income per person
-
Level effect: only the level of income per person is influenced by saving rate in steady state; not by its growth rate
Saving and Investment Around the World – Case Analysis -
If a nation devotes large fraction of income to saving and investment, it will have steady state capital stock and high level of income
-
Saving and investment tend to be low in countries with frequent wars, revolutions and coups, poor political institutions, high corruption
-
High levels of income somehow foster high rates of saving and investment
Golden Rule Level of Capital -
Saving rate of 100%; largest possible capital stock and largest possible income
-
If all income is saved and none is consumed, it is no good
Comparing Steady States -
Policymakers would want to have a steady state with the highest level of consumption
-
Golden Rule Level of Capital: steady state value of “k” that maximizes consumption o
Denoted kgold
3
-
o
Steady state consumption is what is left of steady state output after paying for steady state depreciation
o
More capital = more output = more output must be used to replace worn out capital
At golden rule level of capital MPK = depreciation rate o
If saving rate is higher than the rate set to produce GRLOC, capital stock will be too high
o
If saving rate is lower, steady state capital stock will be too low
Transition to Golden Rule Steady State -
Economy might begin with more capital than in Golden rule steady state, or with less Starting With Too Much Capital
-
Policymaker should pursue policies aimed at reducing rate of saving to reduce capital stock
-
Reduction in saving rate cases increase in consumption and decrease in investment
-
Investment will be less than depreciation; capital stock will fall, lead to reduction in output, consumption and investment
-
Consumption will be higher in the new steady state Starting With Too Little Capital
-
Policy maker must raise saving rate to reach golden rule
-
Increase in saving causes fall in consumption and rise I investment
-
Higher investment causes capital stock to rise; output, consumption and investment increase; approach new steady state level
-
Increase in savings leads to higher consumption in the future but initial reduction in consumption
-
If economy below golden rule, it requires raising investment and lowering consumption for current generations
Population Growth Steady State With Population Growth
4
-
Break even investment: amount of investment necessary to keep capital stock per worker constant
-
Nk: amount of investment necessary to provide new workers with capital
-
Population growth reduces accumulation of capital per worker; alike depreciation
-
Population growth reduces “k” by spreading capital stock more thinly among larger population of workers
-
If investment is greater than break even investment “k” rises
-
In steady state, positive effect on investment on capital stock per worker exactly balances negative effect of depreciation and pop. growth o
Investment will help replace depreciated capital and rest provide new workers with steady state amount of capital
Effects of Population Growth -
Population growth brings us closer to explaining sustained economic growth in total output
-
Population growth explains why some countries are rich and others poor
-
o
Increase in rate of population reduces steady state level of capital per worker; level of output per worker decreases
o
Countries with higher population growth have lower levels of GDP per person
Population growth affects criterion for determining golden rule level of capital o
MPK net of deprecation = rate of population growth
Population Growth Around the World -
Solow model; nation with high rate of pop growth will have low steady state capital stock per worker = low level of income per worker
-
Harder to maintain high level of capital per worker when number of workers is growing quickly
Alternative Perspectives on Population Growth
5
Malthusian Model -
Malthus argued that ever increasing population would continually strain society’s ability to provide for itself
-
Believed attempts by charities or government to alleviate poverty were counterproductive; only allowed the poor to have more kids
-
Populations have increased but so have living standards; due to agricultural and tech advances
-
Link between passion and population growth broken by modern birth control
Kremerian Model -
Kremer suggested that world population growth is key driver of advancing economic prosperity
-
The more people, the more scientist, inventors, engineers to contribute to innovation
-
Having more people induces more technological progress
-
If tech progress Is more rapid when there are more people to discover things, then more populous regions should have experienced more rapid growth
6
Material standards of living have improved substantially over time for most families in most countries
-
Advance comes from rising incomes; allows people to consume more goods and services
-
Differences income come from difference in capital, labour and technology
-
Solow growth model: shows how saving, population growth and technological progress affect levels of an economy’s output and growth
Accumulation of Capital -
Model shows how growth in capital stock, labour force and advances in technology affect nation’s total output of goods and services
Supply and Demand for Goods -
-
Supply of goods is based on production function; output depends on capital stock and labour force o
Model assumes constant returns to scale; helps analyze all quantities in the economy relative to the size of the labour force
o
Size of the economy (measured by # of workers) does not affect relationship between output and capital per worker
o
For Marginal product of capital; as amount of capital increases, production function becomes flatter; production function exhibits diminishing marginal product of capital
o
Slope of production function is MPK
Demand for goods comes from consumption and investment o
Output per worker = consumption per worker + investment per worker
o
Y=c+i
o
Solow model: assumes that each year people save some of their income and consume a fraction
o
Rate of saving is fraction of output devoted to investment
-
Saving rate determines allocation of output between consumption and investment
-
Production function determines how much output an economy produces 1
Growth in Capital Stock and Steak State -
Investment and depreciation influence capital stock
-
Investment: expenditure on new plant and equipment; causes capital stock to rise
-
Depreciation: wearing out old capital; causes capital stock to fall; proportional to capital stock
-
Higher the capital stock, the greater the amounts of output, investment and depreciation
-
At K*, amount of investment must equal amount of deprecation
-
Steady state level of capital: capital stock and output are steady over time o
Economy at the steady state will stay there
o
N economy not at the steady state will go there
o
It represents the long run equilibrium of the economy
-
If investment exceeds depreciation; capital stock will rise along with output until it approaches steady state
-
If investment is less than depreciation; capital wearing out faster than being replaced; capital stock will fall and approach steady state level
Miracle of Japanese and German Growth – Case Analysis -
In 1945 economies of Japan and Germany were in shambles; WWII destroyed much capital stock
-
Output grew, because at lower capital stock, more capital is added by investment than removed by depreciation
-
High growth continues until economy approaches former steady state
How Saving Affects Growth -
Both Japan and Germany save and invest a higher fraction of their output than other countries
2
-
Increase in saving rate: amount of investment for any given capital stock is higher; investment exceeds depreciation; capital stock rises until economy reaches new steady state; results in more capital and output o
Government budget deficit can reduce national savings and crowd out investment
o
Reduced savings lower capital stock and national income
o
Higher savings = faster growth until economy reaches new steady state
-
Growth effect: policies that alter the steady state growth rate of income per person
-
Level effect: only the level of income per person is influenced by saving rate in steady state; not by its growth rate
Saving and Investment Around the World – Case Analysis -
If a nation devotes large fraction of income to saving and investment, it will have steady state capital stock and high level of income
-
Saving and investment tend to be low in countries with frequent wars, revolutions and coups, poor political institutions, high corruption
-
High levels of income somehow foster high rates of saving and investment
Golden Rule Level of Capital -
Saving rate of 100%; largest possible capital stock and largest possible income
-
If all income is saved and none is consumed, it is no good
Comparing Steady States -
Policymakers would want to have a steady state with the highest level of consumption
-
Golden Rule Level of Capital: steady state value of “k” that maximizes consumption o
Denoted kgold
3
-
o
Steady state consumption is what is left of steady state output after paying for steady state depreciation
o
More capital = more output = more output must be used to replace worn out capital
At golden rule level of capital MPK = depreciation rate o
If saving rate is higher than the rate set to produce GRLOC, capital stock will be too high
o
If saving rate is lower, steady state capital stock will be too low
Transition to Golden Rule Steady State -
Economy might begin with more capital than in Golden rule steady state, or with less Starting With Too Much Capital
-
Policymaker should pursue policies aimed at reducing rate of saving to reduce capital stock
-
Reduction in saving rate cases increase in consumption and decrease in investment
-
Investment will be less than depreciation; capital stock will fall, lead to reduction in output, consumption and investment
-
Consumption will be higher in the new steady state Starting With Too Little Capital
-
Policy maker must raise saving rate to reach golden rule
-
Increase in saving causes fall in consumption and rise I investment
-
Higher investment causes capital stock to rise; output, consumption and investment increase; approach new steady state level
-
Increase in savings leads to higher consumption in the future but initial reduction in consumption
-
If economy below golden rule, it requires raising investment and lowering consumption for current generations
Population Growth Steady State With Population Growth
4
-
Break even investment: amount of investment necessary to keep capital stock per worker constant
-
Nk: amount of investment necessary to provide new workers with capital
-
Population growth reduces accumulation of capital per worker; alike depreciation
-
Population growth reduces “k” by spreading capital stock more thinly among larger population of workers
-
If investment is greater than break even investment “k” rises
-
In steady state, positive effect on investment on capital stock per worker exactly balances negative effect of depreciation and pop. growth o
Investment will help replace depreciated capital and rest provide new workers with steady state amount of capital
Effects of Population Growth -
Population growth brings us closer to explaining sustained economic growth in total output
-
Population growth explains why some countries are rich and others poor
-
o
Increase in rate of population reduces steady state level of capital per worker; level of output per worker decreases
o
Countries with higher population growth have lower levels of GDP per person
Population growth affects criterion for determining golden rule level of capital o
MPK net of deprecation = rate of population growth
Population Growth Around the World -
Solow model; nation with high rate of pop growth will have low steady state capital stock per worker = low level of income per worker
-
Harder to maintain high level of capital per worker when number of workers is growing quickly
Alternative Perspectives on Population Growth
5
Malthusian Model -
Malthus argued that ever increasing population would continually strain society’s ability to provide for itself
-
Believed attempts by charities or government to alleviate poverty were counterproductive; only allowed the poor to have more kids
-
Populations have increased but so have living standards; due to agricultural and tech advances
-
Link between passion and population growth broken by modern birth control
Kremerian Model -
Kremer suggested that world population growth is key driver of advancing economic prosperity
-
The more people, the more scientist, inventors, engineers to contribute to innovation
-
Having more people induces more technological progress
-
If tech progress Is more rapid when there are more people to discover things, then more populous regions should have experienced more rapid growth
6
