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Ohio Wesleyan University Goran Skosples 7. Long-Run Growth. Objectives. Why growth matters? Learn the closed economy Solow model See how a country’s standard of living depends on its saving and population growth rates Importance of productivity growth Policies to promote growth.
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Objectives • Why growth matters? • Learn the closed economy Solow model • See how a country’s standard of living depends on its saving and population growth rates • Importance of productivity growth • Policies to promote growth
Question Shall we play a game? • Life expectancy is less than 50 years • 1 out every 10 infants dies before the age of one • More than 90% of households have no electricity, refrigerator, telephone, or car • Fewer than 10% of adults have completed high school. • What country is it?
Why growth matters …for poor countries • Data on infant mortality rates: • 20% in the poorest 1/5 of all countries • 0.4% in the richest 1/5 • In Bangladesh, about 80% of people live on less than $2/day. • One-fourth of the poorest countries have had famines during the past 3 decades. • Poverty is associated with oppression of women and minorities. Economic growth raises living standards and reduces poverty….
annual growth rate of income per capita percentage increase in standard of living after… Why growth matters …for rich countries • Anything that effects the long-run rate of economic growth – even by a tiny amount – will have huge effects on living standards in the long run. …25 years …100 years …50 years 169.2% 2.0% 64.0% 624.5% 2.5% 85.4% 243.7% 1,081.4%
The lessons of growth theory …can make a positive difference in the lives of hundreds of millions of people. These lessons help us • understand why poor countries are poor • design policies that can help them grow • learn how our own growth rate is affected by shocks and our government’s policies
Sources of Economic Growth • Given what you have learned so far, what causes differences in incomes? Y = A K L1- 1. 2. 3.
The Solow Model • due to Robert Solow,won Nobel Prize for contributions to the study of economic growth • a major paradigm: • widely used in policy making • benchmark against which most recent growth theories are compared • looks at the determinants of economic growth and the standard of living in the long run
How Solow model is different from Chapter 3’s model • K is no longer fixed:investment causes it to grow, depreciation causes it to shrink. • L is no longer fixed:population growth causes it to grow. • The consumption function is simpler. • No G or T(only to simplify presentation; we can still do fiscal policy experiments) • Cosmetic differences.
The production function • In aggregate terms: Y = F (K, L ) • Define: _______ = ______________ _______ = ______________ • Assume constant returns to scale • Divide through by L:
Output per worker, y f(k) MPK 1 Capital per worker, k The production function Note: this production function exhibits ___________MPK.
The national income identity (remember, no G ) • Y = _______ • In “per worker” terms: y = _____ , where c = _____ and i =_____ • s = the saving rate (an exogenous parameter) Note: s is the only lowercase variable that is not equal to its uppercase version divided by L • Consumption function: (per worker) The consumption function
Saving and investment • saving (per worker) = = = • National income identity is Rearrange to get: (investment = saving, like in chap. 3!) • Using the results above, i =
Output per worker, y f(k) sf(k) Capital per worker, k k1 Output, consumption, and investment
Population Growth • Assume that the population--and labor force-- grow at rate n. (n is exogenous) • EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year ( ________ ). • Then L = so L = in year 2. n L
Capital accumulation The basic idea: _________ increases the capital stock, ___________ and_______ reduces it. Change in capital stock = investment – depreciation – dilution k Since _________ , this becomes: k = sf(k)– (+n )k The equation of motion for k
Break-even investment • ( + n)k = , the amount of investment necessary to keep ___ constant. • Break-even investment includes: • ____ to replace capital as it wears out • ____ to equip new workers with capital(otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers)
Break-even investment, (+n)k Capital per worker, k Break-even investment • δ= the rate of depreciation • n = population growth rate
The steady state k = sf(k)– (+n)k If investment is just enough to cover depreciation (sf(k)– (+n)k ) then capital per worker will remain ________: k = ____. This constant value, denoted k*, is called the _______ ______________________.
Investment and depreciation (+n)k sf(k) Capital per worker, k The steady state
Investment and depreciation (+n)k sf(k) k1 k* Capital per worker, k Moving toward the steady state k = sf(k) (+n)k
Investment and depreciation (+n)k s1 f(k) k An increase in the saving rate An increase in the saving rate ______ investment… …causing k to ____________________________:
Prediction: • Higher s _______ k*. • And since y = _____ , ______ k* _______ y* . • Thus, the Solow model predicts that countries with higher rates of saving and investment will have _________ levels of capital and income per worker in the long run.
International Evidence on Investment Rates and Income per Person
sf(k) The impact of population growth Investment, break-even investment (+n1)k An increase in n causes an _______ in break-even investment, leading to a ____ steady-state level of k. k1* Capital per worker, k
Prediction: • Higher n _______ k*. • And since y = , _______ k* _______ y* . • Thus, the Solow model predicts that countries with higher population growth rates will have _________ levels of capital and income per worker in the long run. f(k)
International Evidence on Population Growth and Income per Person Income per person in 2000 (log scale)
The impact of population growth Determine what happens to each variable when population growth is 0 and when it is n? Fill in whether at the steady-state the variable is constant or whether it grows or declines and at which rate:
Output and Investment (+n)k s1 f(k) f1(k) k Productivity Growth Productivity growth _______ investment which leads to a _____ steady-state level of income per capita
Implications of the Solow Model • Countries below the steady-state level of capital per worker will _____ and countries above the steady-state level of capital per worker will _____ • The further below its steady-state level of capital per worker a country is, the _______ it will grow • After a war or a natural disaster, a country will grow _______ • Capital should flow from rich to poor countries • Why? • Is that happening?
Implications of the Solow Model • What can cause growth in the Solow model? • However, in a new steady-state: • Can the above sources of growth continuously rise? • In the long run, the rate of ______________ _____________ is the dominant factor determining how quickly living standards rise
Examples of technological progress • From 1950 to 2000, U.S. farm sector productivity nearly tripled. • The real price of computer power has fallen an average of 30% per year over the past three decades. • Percentage of U.S. households with ≥1 computers: 8% in 1984, 62% in 2003 • 2000: 361m Internet users, 740m cell phone users 2011: 2.4b Internet users, 5.9b cell phone users • 2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of Entourage. 2009: iPod capacity = 120gb, 30,000 songs. Can play episodes of Entourage.
Total Factor Productivity • Differences in income per capita: y = Ak • Both capital per worker (k) and total factor productivity (A) explain differences in incomes per capita around the world • Richer countries have both more capital per worker and higher total factor productivity • capital per worker explains about ____ of the difference in incomes per capita • TFP explain about ____ of the difference in incomes per capita
Measures of Living Standards • Is GDP per capita a good measure of the living standards? • What are some other measures?
Summary • The Solow growth model shows that, in the long run, a country’s standard of living depends • positively on its saving rate. • negatively on its population growth rate. • positively on total factor productivity • An increase in the saving rate leads to • higher output in the long run • faster growth temporarily • but not faster steady state growth.
Summary • In the long run, only a continuous increase in productivity growth can lead to sustained increase in the standard of living • Both capital per worker and total factor productivity explain income differences around the world
