This document discusses the Solow growth model and economic convergence. It introduces key equations of the Solow model relating capital per worker (k), GDP per worker (y), saving rate (s), depreciation rate (δ), and population growth rate (n). It explains that economies starting at different levels of capital per worker will converge over time towards the same steady-state level as the lower starting economy grows faster initially. GDP per worker convergence follows from capital per worker convergence. Conditional and absolute convergence are defined.

1. Growth & Convergence
EC4004 Lecture 16

3. Recap

4. Recap
Convergence

5. Recap
Convergence
World Income

6. Recap
Convergence
World Income

7. Key Equations
Solow Growth Model
3

8. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
3

9. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
3

10. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
–y is real gross domestic product (real GDP)
per worker
3

11. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
–y is real gross domestic product (real GDP)
per worker
–y/k is the average product of capital
3

12. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
–y is real gross domestic product (real GDP)
per worker
–y/k is the average product of capital
–s is the saving rate
3

13. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
–y is real gross domestic product (real GDP)
per worker
–y/k is the average product of capital
–s is the saving rate
–δ is the depreciation rate
3

14. Key Equations
Solow Growth Model
∆k/k= s· (y/k) − sδ − n
–k is capital per worker
–y is real gross domestic product (real GDP)
per worker
–y/k is the average product of capital
–s is the saving rate
–δ is the depreciation rate
–n is the population growth rate.
3

15. 4

16. Production function
y = A · f (k)
Solow Growth Equation
∆k/ k= s A· f( k)/k − sδ − n
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17. k* = k*[ s, A, n, δ, L(0) ]
(+) (+) (−) (−)(0)
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18. One of the most important questions about
economic growth is whether poor countries
tend to converge or catch up to rich
countries.
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19. 7

20. Convergence and Transition Paths for Two Economies
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22. Economy 1 starts at capital per worker k(0)1 and
economy 2 starts at k(0)2, where k(0)1 is less than
k(0)2.
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23. Economy 1 starts at capital per worker k(0)1 and
economy 2 starts at k(0)2, where k(0)1 is less than
k(0)2.
The two economies have the same steady-state
capital per worker, k*, shown by the dashed blue
line.
9

24. Economy 1 starts at capital per worker k(0)1 and
economy 2 starts at k(0)2, where k(0)1 is less than
k(0)2.
The two economies have the same steady-state
capital per worker, k*, shown by the dashed blue
line.
In each economy, k rises over time toward k*.
However, k grows faster in economy 1 because
k(0)1 is less than k(0)2.
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25. Economy 1 starts at capital per worker k(0)1 and
economy 2 starts at k(0)2, where k(0)1 is less than
k(0)2.
The two economies have the same steady-state
capital per worker, k*, shown by the dashed blue
line.
In each economy, k rises over time toward k*.
However, k grows faster in economy 1 because
k(0)1 is less than k(0)2.
Therefore, k1 converges over time toward k2.
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26. 10

27. y= A· f( k) and ∆y/y= α·(k/ k)
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28. y= A· f( k) and ∆y/y= α·(k/ k)
∆k/k was higher initially in economy 1 than in
economy 2.
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29. y= A· f( k) and ∆y/y= α·(k/ k)
∆k/k was higher initially in economy 1 than in
economy 2.
Therefore, ∆y/y is also higher initially in
economy 1. Hence, economy 1’s real GDP
per worker, y, converges over time toward
economy 2’s real GDP per worker.
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30. Growth Rate vs Level of Real GDP per person
for a group of countries
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31. Growth Rate vs Level of Real GDP per person for the
OECD Countries
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32. Growth Rate vs Level of Income per Person for US
States, 1880--2000
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33. Conditional convergence:
a lower k(0) predicts a higher ∆k/k,
conditional on k∗.
Absolute convergence
the prediction that a lower k(0) raises ∆k/k
without any conditioning is called.
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34. www.gapminder.org

35. 086 399 83 06

36. Questions
An increase in the depreciation rate affects the steady-state
capital per worker the same way as an increase in the
population growth rate.
T/F?
Text to 086 399 83 06

37. World growth data reveals that
from 1960 to 2000:
a. the US and other OECD countries stagnated.
c. some countries particularly East Asian countries
grew at low or negative rates.
b. sub-Saharan African countries grew at low or
negative rates.
d. all of the above.
Text to 086 399 83 06

38. Next Time
Micro Models-> Macro Models
Read Barro Chapters 4 & 5