1. Macroeconomics Chapter 5
Conditional Convergence and Long-Run Economic Growth
Macroeconomics Chapter 5

2. Conditional Convergence in Practice
Growth rate of capital per worker, ∆k/k:
∆k/k= ϕ[ k(0) , k*]
(−) (+)
y= A· f(k)
Growth rate of real GDP per worker is a function of initial and steady-state real GDP per worker
∆ y/y= ϕ[ y(0) , y*]
(−) (+)
Macroeconomics Chapter 5

3. Conditional Convergence in Practice
Macroeconomics Chapter 5

4. Conditional Convergence in Practice
Variables that influence y* that are held constant.
A measure of the saving rate
The fertility rate
Subjective measures of maintenance of the rule of law and democracy
The size of government
The extent of international openness, measured by the volume of exports and imports
Changes in the terms of trade
Measures of investment in education and health
The average rate of inflation
Macroeconomics Chapter 5

5. Conditional Convergence in Practice
Japan and Germany after 2nd world war.
East Asia countries
African Countries
Macroeconomics Chapter 5

6. Long-Run Economic Growth
Solow model, the growth rate of capital per worker, k, is given by
∆k/k= s· (y/k) − sδ − n
Macroeconomics Chapter 5

7. Long-Run Economic Growth
A case in which capital broadly defined to include human and infrastructure capital is the only factor input to production.
AK model
y= Ak
Macroeconomics Chapter 5

8. Long-Run Economic Growth
k – capital per worker
y/k= A
∆k/k= sA− sδ − n
Macroeconomics Chapter 5

9. Long-Run Economic Growth
Macroeconomics Chapter 5

10. Long-Run Economic Growth
Conclusions
The long-run growth rate of capital per worker, ∆k/k, is greater than zero and equal to sA− sδ − n
Growth rates of capital and real GDP per worker, ∆k/k and ∆y/y, do not change as capital and real GDP per worker, k and y, rise.
poor economies with low k and y do not tend to grow faster than rich economies
Macroeconomics Chapter 5

11. Long-Run Economic Growth
The regular process of improvement in technology is called technological progress.
exogenous technological progress - the improvements in technology were not explained within the model.
∆A/A= g
Macroeconomics Chapter 5

12. Long-Run Economic Growth
Exogenous Technological Progress
∆Y/Y= ∆A/A+α·(∆K/K)+(1−α)·(∆L/ L)
Using ∆A/A= g and and ∆L/L = n
∆Y/Y= g+ α·(∆K/ K) + (1−α) · n
∆y/y= ∆Y/Y− ∆L/L = ∆Y/Y− n
Macroeconomics Chapter 5

13. Long-Run Economic Growth
Exogenous Technological Progress
∆y/y= g+α·(∆K/K)+(1−α)·n − n
= g+α·(∆K/K − n)
∆ k/k= ∆ K/K − ∆L/L = ∆K/K − n
∆y/y= g+α·(∆k/k)
Macroeconomics Chapter 5

14. Long-Run Economic Growth
Exogenous Technological Progress
∆k/k - in the Solow model
∆k/k= sA·f(k)/k− sδ − n
Growth rate of real GDP per worker with technical progress
∆y/y= g+α·[ sA· f(k)/k− sδ−n]
Macroeconomics Chapter 5

15. Long-Run Economic Growth
Steady state: all variables grow at constant rates.
∆k/k is constant
∆k/k= s(y/k)− sδ − n
y/k is constant
Macroeconomics Chapter 5

16. Long-Run Economic Growth
Exogenous Technological Progress
(∆y/y)* = (∆k/k)*
(∆y/y)* = g+ α·(∆k/k)*
(∆y/y)* = g+ α·(∆y/y)*
(∆y/y)* − α·(∆y/y)* = g
(1−α)·(∆y/y)* = g
Macroeconomics Chapter 5

17. Long-Run Economic Growth
Exogenous Technological Progress
Steady-state growth rate with technological progress
(∆y/y) * = g/(1 − α)
Since 0 < α < 1 the steady-state growth rate of real GDP per worker, (∆y/y)∗, is greater than the rate of technological progress, g.
Macroeconomics Chapter 5

18. Long-Run Economic Growth
Exogenous Technological Progress
(∆k/k)* = (∆y/y)*
(∆k/k)* = g/(1−α)
Exogenous technological progress at the rate ∆A/A= g leads to long-term growth in real GDP and capital per worker, k and y, at the rate g/(1−α)
Macroeconomics Chapter 5

19. Long-Run Economic Growth
Exogenous Technological Progress
∆k/k= s·(y/k) − sδ − n
(∆k/k)* = g/(1 − α)
g/(1−α) = s·(y/ k)* − sδ − n
s·[(y/k)*−δ] = n+g/(1−α)
(y/k)*= δ+(1/s)·[n+g/(1−α)]
For Cobb-Douglas function
Macroeconomics Chapter 5

20. Long-Run Economic Growth
Macroeconomics Chapter 5

21. Long-Run Economic Growth
Macroeconomics Chapter 5

22. Long-Run Economic Growth
Macroeconomics Chapter 5

23. Endogenous Growth Theory
Extend the model to explain why technological progress occurs.
Most endogenous growth models focus on investments in research and development (R&D)
Macroeconomics Chapter 5

24. Endogenous Growth Theory
The essential feature of knowledge or technology:
non-rival good
not diminishing with the rise of A.
Macroeconomics Chapter 5

25. Macroeconomics Chapter 5
The basic R&D model
Assumptions
The labor force is the single production factor
Generalized Cobb-Douglas function without capital
3. The fraction of the labor force is exogenous
Macroeconomics Chapter 5

26. Macroeconomics Chapter 5
The basic R&D model
The evolution function of labor
where
The evolution function of knowledge
Macroeconomics Chapter 5

27. Macroeconomics Chapter 5
The basic R&D model
The dynamic of knowledge accumulation
Macroeconomics Chapter 5

28. Macroeconomics Chapter 5
The basic R&D model
Interpretation:
endogenous long run growth rate
positive link with population growth
Macroeconomics Chapter 5

29. Diffusion of Technology
The Diffusion of Technology
The imitation and adaptation of one country’s technology by another country.
The rate of technological diffusion to a developing country is high when the country trades a lot with rich countries, has high education levels, and has well functioning legal and political systems.
Macroeconomics Chapter 5