1. Ohio Wesleyan University Goran Skosples 7. Long-Run Growth

2. 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

3. Key Concepts Solow growth model Steady state Break-even investment
Rule of 70
Depreciation
Dilution
Productivity
Sustainable growth rate
Capital flows
Foreign Direct Investment (FDI)

4. Question Shall we play a game? What country is it?
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?

5. 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….

6. Income and poverty in the world selected countries, 2000

7. 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.
percentage increase in standard of living after…
annual growth rate of income per capita
…25 years
…50 years
…100 years
2.0%
64.0%
169.2%
624.5%
2.5%
85.4%
243.7%
1,081.4%

8. 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

9. Int’l Differences in the Standard of Living
GDP
Country
per capita
Qatar
$179,000
France
$33,100
Singapore
$62,100
Israel
$29,800
Norway
$54,600
Argentina
$14,700
United States
$47,200
Brazil
$10,800
Hong Kong
$45,900
China
$7,600
Australia
$41,000
India
$3,500
Netherlands
$40,300
Nigeria
$2,500
Canada
$39,400
Ghana
Sweden
$39,100
Bangladesh
$1,700
Germany
$35,700
Somalia
$600
United Kingdom
$34,800
Zimbabwe
$500
Japan
$34,000
Congo, DR
$300
data is in PPP

10. Historical GDP per capita

11. US GDP per capita

12. Growth of US GDP per capita

13. Sources of Economic Growth
Given what you have learned so far, what causes differences in incomes?
Y = A K L1-  1. 2. 3.

14. 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

15. 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.

16. The production function
In aggregate terms: Y = F (K, L )
Define: _______ = ______________
_______ = ______________
Assume constant returns to scale
Divide through by L:

17. The production function
Output per worker, y
Capital per worker, k
f(k) 1
MPK
Note: this production function exhibits ___________MPK.

18. 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

19. Saving and investment saving (per worker) = =
National income identity is
Rearrange to get: (investment = saving, like in chap. 3!)
Using the results above, i =

20. Output, consumption, and investment
Output per worker, y
Capital per worker, k
f(k) k1
sf(k)

21. 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

22. The equation of motion for k
Capital accumulation
The basic idea: _________ increases the capital stock, ___________ and_______ reduces it.
Change in
capital stock = investment – depreciation – dilution k
Since _________ , this becomes:
k = s f(k) – (+n )k
The equation of motion for k

23. 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)

24. Break-even investment
δ = the rate of depreciation
n = population growth rate
Break-even investment, (+n)k
Capital per worker, k

25. k = s f(k) – (+n)k The steady state
If investment is just enough to cover depreciation (s f(k) – (+n)k ) then capital per worker will remain ________:
k = ____.
This constant value, denoted k*, is called the _______ ______________________.

26. Investment and depreciation
The steady state
Investment and depreciation
Capital per worker, k
(+n)k
sf(k)

27. Moving toward the steady state
k = sf(k)  (+n)k
Investment and depreciation
Capital per worker, k
(+n)k
sf(k) k* k1

28. An increase in the saving rate
An increase in the saving rate ______ investment …
…causing k to ____________________________:
Investment and depreciation k
(+n)k
s1 f(k)

29. 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.

30. International Evidence on Investment Rates and Income per Person

31. The impact of population growth
Investment, break-even investment
( +n1) k
An increase in n causes an _______ in break-even investment,
sf(k)
leading to a ____ steady-state level of k.
k1*
Capital per worker, k

32. 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)

33. International Evidence on Population Growth and Income per Person
Income per person in 2000 (log scale)

34. 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:
Population growth = 0
Population growth = n L: K: Y: k: y:

35. Productivity Growth
Output and Investment k
(+n)k
f1(k)
Productivity growth _______ investment which leads to a _____ steady-state level of income per capita
s1 f(k)

36. 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?

37. Growth Rates in the OECD

38. Growth Rates Around the World

39. 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

40. 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 : 2.4b Internet users, 5.9b cell phone users
2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of Entourage : iPod capacity = 120gb, 30,000 songs. Can play episodes of Entourage.

41. 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

42. The US and China

43. Policies to Raise Living Standards

44. Measures of Living Standards
Is GDP per capita a good measure of the living standards?
What are some other measures?

45. Happiness and GDP per capita

46. 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.
Before leaving this chapter, you should emphasize that we have not yet answered an important question: What causes the kind of sustained growth in living standards that we’ve experienced in the U.S. and elsewhere over the very long run? The Solow model as described in Chapter 7 has a steady state in which income per capita remains constant.
Chapter 8 addresses this issue by introducing technological progress into the Solow model.

47. 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