1. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-1 CHAPTER 4 The Theory of Economic Growth

2. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-2 Questions What are the principal determinants of long-run economic growth? What equilibrium condition is useful in analyzing long-run growth? How quickly does an economy head for its steady-state growth path?

3. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-3 Questions What effect does faster population growth have on long-run growth? What effect does a higher savings rate have on long-run growth?

4. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-4 Long-Run Economic Growth... is the most important aspect of how the economy performs can be accelerated by good economic policies can be retarded by bad economic policies

5. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-5 Long-Run Economic Growth Policies and initial conditions affect growth through two channels –their impact on the level of technology multiplies the efficiency of labor –their impact on the capital intensity of the economy the stock of machines, equipment, and buildings that the average worker has at his or her disposal

6. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-6 Technology leads to a higher efficiency of labor –skills and education of the labor force –ability of the labor force to handle modern machines –the efficiency with which the economy’s businesses and markets function Economists are good at analyzing the consequences of better technology –have less to say about the sources

7. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-7 Capital Intensity There is a direct relationship between capital-intensity and productivity Two principal determinants –investment effort the share of total production saved and invested in order to increase the capital stock –investment requirements how much of new investment is used to equip new workers with the standard level of capital or to replace worn-out or obsolete capital

8. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-8 Standard Growth Model Also called the Solow model Steady-state balanced-growth equilibrium –the capital intensity of the economy is stable –the economy’s capital stock and level of real GDP are growing at the same rate –the economy’s capital-output ratio is constant

9. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-9 Standard Growth Model First component is the production function –tells us how the productive resources of the economy can be used to produce and determine the level of output Cobb-Douglas production function

10. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-10 Standard Growth Model Parameters of the model –E is the efficiency of labor a higher level of E means that more output per worker can be produced for each possible value of the capital stock per worker – measures how fast diminishing marginal returns to investment set in

11. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-11 Standard Growth Model 0<<1 –a level of  near zero means that the extra amount of output made possible by each additional unit of capital declines very quickly as the capital stock increases

12. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-12 Figure 4.1 - The Cobb-Douglas Production Function for Parameter  Near Zero

13. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-13 Standard Growth Model 0<<1 –a level of  near one means that the next additional unit of capital makes possible almost as large an increase in output as the last unit of capital –a level of  equal to one means that changes in output are proportional to changes in capital

14. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-14 Figure 4.2 - The Cobb-Douglas Production Function for Parameter  Near 1

15. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-15 Figure 4.3 - The Cobb-Douglas Production Function is Flexible

16. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-16 Standard Growth Model Growth in labor force (L) –assume that L is growing at a constant rate (n) –if this year’s labor force is equal to 10 million and the growth rate is 2% per year, next year’s labor force will be

17. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-17 Figure 4.4 - Constant Proportional Labor-Force Growth (at Rate n = 2 Percent per Year)

18. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-18 Standard Growth Model Growth in the efficiency of labor (E) –assume that E is growing at a constant proportional rate (g) –if this year’s efficiency of labor is $10,000 and the growth rate is 1.5% per year, next year’s efficiency of labor will be

19. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-19 Figure 4.5 - Constant Proportional Growth in the Efficiency of Labor (at Rate g = 1.5 Percent per Year)

20. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-20 Standard Growth Model Saving and investment –assume that a constant share of real GDP is saved and invested each year (s) –capital stock does not grow by full amount of gross investment  represents the fraction of the capital stock that wears out or is scrapped each year

21. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-21 Figure 4.6 - Changes in the Capital Stock

22. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-22 Standard Growth Model An example of capital accumulation –current real GDP = $8 trillion –current capital stock = $24 trillion –savings rate = 20% –depreciation rate = 4%

23. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-23 Figure 4.7 - Additions to and Subtractions from the Capital Stock

24. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-24 Summary of Standard Growth Model Three assumptions –labor force grows at proportional rate n –efficiency of labor grows at proportional rate g –there is a constant proportion of real GDP saved and invested each year (s) The capital stock changes over time due to investment and depreciation Cobb-Douglas production function

25. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-25 Equilibrium in Standard Growth Model Key economic variables in the growth model are never constant Equilibrium occurs when the variables are growing together at the same proportional rate Steady-state balanced growth –occurs when the capital-output ratio is constant over time

26. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-26 Three Mathematical Rules The proportional growth rate of a product (PQ) is the sum of the proportional growth rates of each P and Q The proportional growth rate of a quotient (E/Q) is the difference of the proportional growth rates of the dividend (E) and the divisor (Q)

27. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-27 Three Mathematical Rules The proportional growth rate of a quantity raised to an exponent (Q y ) is equal to the exponent (y) times the growth rates of the quantity (Q)

28. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-28 Growth of Capital per Worker The proportional growth rate of capital per worker [g(k t )] is Since this is a growth rate of a quotient, it will be equal to the growth rate of capital minus the growth rate of labor (n)

29. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-29 Figure 4.8 - Calculating the Proportional Growth Rate of the Capital-per-Worker Ratio

30. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-30 Growth of Capital per Worker The growth rate of capital stock is Next year’s capital stock is Making the substitution, we get

31. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-31 Growth of Capital per Worker The proportional growth rate of capital per worker is Let  represent the capital-output ratio (K/Y)

32. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-32 Growth of Capital per Worker All else equal, the rate of growth of capital per worker will be lower –the higher the rate of labor force growth (n) –the higher the rate of depreciation () –the lower the rate of saving (s) –the higher the capital-output ratio ()

33. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-33 Figure 4.9 - Capital-per-Worker Growth as a Function of the Capital-Output Ratio

34. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-34 Growth of Output per Worker With the Cobb-Douglas production function, output per worker is The growth rate of output per worker [g(y t )] will be

35. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-35 Figure 4.10 - Calculating the Growth Rate of Output per Worker

36. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-36 Growth of Output per Worker Since g(k t ) is equal to [(s/ t )--n], we can substitute and simplify to get

37. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-37 Growth of Capital-Output Ratio Equilibrium occurs when the capital- output ratio (=K/Y) is constant The growth rate of the capital-output ratio [g( t )] is equal to the difference in the growth rate of capital [g(k t )] and the growth rate of output [g(y t )]

38. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-38 Growth of Capital-Output Ratio We can make substitutions for [g(k t )] and [g(y t )] and simplify to get

39. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-39 Growth of Capital-Output Ratio The growth rate of the capital-output ratio depends on the balance between –investment requirements (n+g+) –investment effort (s) All else equal, a higher investment requirement will mean a lower growth rate of the capital-output ratio

40. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-40 Figure 4.11 - Growth of the Capital-Output Ratio

41. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-41 Steady-State Growth Equilibrium occurs when the capital-output ratio is constant If  t >[s/(n+g+)] –the capital-output ratio will be shrinking If  t <[s/(n+g+)] –the capital-output ratio will be growing

42. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-42 Figure 4.12 - Growth of the Capital-Output Ratio as a Function of the Level of the Capital-Output Ratio

43. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-43 Steady-State Growth Equilibrium If  t =[s/(n+g+)] –the growth rate of the capital-output ratio will be zero –the capital-output ratio will be stable (neither shrinking nor growing) *=[s/(n+g+)] is the equilibrium level of the capital-output ratio

44. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-44 Figure 4.13 - Convergence of the Capital- Output Ratio to Its Steady-State Value

45. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-45 Steady-State Growth Equilibrium When the capital-output ratio ( t ) is at its steady state value (*) –output per worker [g(y t )] is growing at proportional rate g –capital stock per worker is growing at the same proportional rate g –the economy wide capital stock is growing at the proportional rate n+g –real GDP is also growing at proportional rate n+g

46. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-46 Steady-State Growth Path When the capital-output ratio is at its equilibrium value (*), the economy is on its steady-state growth path From Chapter 3, we know that as long as we are on the steady-state growth path

47. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-47 Figure 4.14 - Calculating Steady-State Output per Worker along the Steady-State Growth Path

48. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-48 Steady-State Growth Path An increase in the capital-output ratio increases the capital stock directly and indirectly –extra output generated by new capital is source for additional saving and investment This leads to a multiplier effect of anything that raises *

49. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-49 Figure 4.16 - The Growth Multiplier: The Effect of Increasing the Capital-Output Ratio on the Steady-State Output per Worker

50. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-50 Steady-State Growth Path Let the growth multiplier () equal [/1- ] Output per worker along the steady- state growth path will be

51. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-51 Steady-State Growth Path To calculate output per worker when the economy is on its steady-state growth path –calculate the steady-state capital-output ratio [*=s/(n+g+)] –amplify the steady-state capital-output ratio (*) by the growth multiplier [=/(1- )] –multiply by the current value of the efficiency of labor (E t )

52. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-52 Figure 4.15 - Output per Worker on the Steady-State Growth Path

53. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-53 Reaching the Steady-State Growth Path How long does it take for the capital- output ratio to adjust to its steady- state value (*)? –an economy that is not on its steady- state growth path will close a fraction [(1- )(n+g+)] of the gap between the steady state value (*) and its current value ( t ) in a year

54. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-54 Figure 4.17 - West German Convergence to Its Steady-State Growth Path

55. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-55 Labor Force Growth The faster the growth of the labor force, the lower will be the economy’s steady-state capital-output ratio –the larger the share of current investment that must go to equip new workers with the capital they need A sudden, permanent increase in labor force growth will lower output per worker on the steady-state growth path

56. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-56 Figure 4.18 - Labor Force Growth and GDP-per-Worker Levels

57. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-57 Figure 4.19 - Effects of a Rise in Population Growth on the Economy’s Growth Path

58. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-58 Increases in the Depreciation Rate The higher the depreciation rate, the lower will be the economy’s steady- state capital-output ratio –existing capital stock wears out and must be replaced more quickly An increase in the depreciation rate will lower output per worker on the steady-state growth path

59. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-59 Productivity Growth The faster the growth rate of productivity, the lower will be the economy’s steady-state capital-output ratio –past investment will be small relative to current output An increase in productivity growth will raise output per worker along the steady-state growth path

60. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-60 Increases in the Saving Rate The higher the share of real GDP devoted to saving and investment, the higher will be the economy’s steady- state capital-output ratio –more investment increases the amount of new capital A higher saving rate also increases output per worker along the steady- state growth path

61. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-61 Figure 4.20 - National Investment Shares and GDP-per-Worker Levels

62. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-62 Chapter Summary One principal force driving long-run growth in output per worker is the set of improvements in the efficiency of labor springing from technological progress

63. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-63 Chapter Summary A second principal force driving long- run growth in output per worker are the increases in the capital stock which the average worker has at his or her disposal and which further multiplies productivity

64. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-64 Chapter Summary An economy undergoing long-run growth converges toward and settles onto an equilibrium steady-state growth path, in which the economy’s capital-output ratio is constant

65. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 4-65 Chapter Summary The steady-state level of the capital- output ratio is equal to the economy’s saving rate divided by the sum of its labor force growth rate, labor efficiency growth rate, and depreciation rate