Macro 8

2. Macroeconomics
Lecture 8
Growth Models
Chapter 8

3. Questions?

4. Exam 2
Chapters 8-12

5. Chapter 8
Growth Models

6. 2.2% 10%
32 years 7 years

7. Growth
Catching Up
Cutting Edge

8. Catching Up
adopt
imitate

9. Cutting Edge
new ideas
new inventions
new innovations

10. Model
Simplify
Assumptions

11. Robert
Solow
Nobel
Prize
1987

12. Solow Model
Output is a function of
ideas, capital, education and
labor.

13. Y = Output
A = Ideas
K = Capital
e = education
L = Labor
Y = F(A, K, eL)
Solow Model

14. Y = F(A, K, eL)
Simplify to analyze
Assume A , e and L don’t change
don’t change = hold constant
Y = F(K)
Solow Model

15. Y = F(K)
Output is a function of Capital
Assume that the function increases at
a decreasing rate
Diminishing Returns
Solow Model

16. Rates of Return
Constant
Diminishing
Increasing

17. Rates of Return
Constant
Increasing
Decreasing

18. Y = F(K)
function is not linear
diminishing
Y = √K
Solow Model

19. Solow Growth Model
Capital K
Y
Output
Y = √K

20. How much output do you
get out of the next
addition of capital?
Diminishing
Marginal Product of Capital

21. Can poor catch up?
Capital Per Worker
Output
Per
Worker
Big
Gain
Little
Gain
Maybe?

22. Solow Growth Model
Capital K
Y
Output
Y = √K
S = I = s√K
K
Y =F(K)
Saving
=
Investment
S = I
S = s√K
Consumption
Investment

23. Solow Growth Model
Capital K
Y
Output
Depreciation
D
Function of K
d = rate
D = dK
Stuff wears out
D = dk

24. Solow Growth Model
Capital K
Y
Output
Depreciation
D
Function of K
d = rate
D = dK
2%
5%
Slope is the rate

25. Solow Growth Model
Y = √K
S = I = s√K
D = dk
Capital K
Y
Output Steady State
D = S = I
Consumption

26. K = 100
Y = √K
s = .30 or 30%
d = .02 or 2%
Y = ?
S = ?
D = ?
Consumption = ?
Quiz

27. Solow Growth Model
Y = √K
S = I = s√K
D = dk
Capital K
Y
Output
100
10
3
2

28. Solow Growth Model
Y = √K
S = I = s√K
D = dk
Capital K
Y
Output
144
12
3.60
Consumption
8.40

29. Increase Savings
Increase Productivity
Two Ways to Grow

30. Solow Growth Model
Raise
Savings
Rate
30%
40%
Capital K
Y
Output

31. Solow Growth Model
income is a function of K
add a productivity factor to
K
A = technology
Y = √K
Y = A√K

32. Solow Growth Model
Y = A1√K
Y = A2√K
Capital K
Y
Output

33. Increase Savings Rate

34. Increase Technology

35. Solow Growth Model
Yabut….
Diminishing?
Ideas
Increasing Returns

36. Romer
Growth Model
Ideas
Paul Romer

37. Every generation has
underestimated the potential for
finding new ideas…Possibilities do
not add up.They multiply
A + B
A x B
AB

38. Economics of Ideas
Ideas
Inventions
Innovations
Increasing Returns

39. A candle loses
nothing by
lighting another
candle
- John Heller