1. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 0

2. C H A P T E R 4 The Economy in the Very Long Run: The Economics of Growth Learning objectives äUnderstand that economic growth is due to growth in inputs, and to improvements in technology. äUnderstand that capital accumulates through savings and investment. äUnderstand that the long run level of output per person depends on the savings rate and the rate of population growth. äUnderstand that the basic economic growth model predicts that standards of living in different countries will eventually converge. PowerPoint® slides prepared by Marc Prud’Homme, University of Ottawa Copyright 2005 © McGraw-Hill Ryerson Ltd.

3. Slide 2 Growth Accounting oIn Chapters 2 and 3, the general production function used was: Y = AF(K, N)(1) Growth accounting equation: oThis chapter uses the Growth accounting equation: A summary of the contributions of input growth and changes in productivity to the growth of output.  Y/Y = [(1-  ) (  N/N)] + [  (  K/K)] +  A/A (2) oTotal factor productivity: oTotal factor productivity: Rate at which productivity of input increases; also a measure of technological progress. Chapter 4: The Economy in the Very Long Run

4. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 3 Growth Accounting Chapter 4: The Economy in the Very Long Run Figure 4-1: GDP per Capita for Four Countries, 1820 - 2002

5. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 4 Human Capital BOXBOX 4-1 The higher the rate of investment (physical capital or human capital) the higher the GDP.

6. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 5 Growth Accounting Table 4-1: Accounting for Growth in Canada, 1962 and 2002 (Averages) 3.4 1993- 2002 2.8 1974- 1992 5.4 1.5 0.0 1.9 1.0 1.1 1.4 0.9 1.6 2.1 1962- 1973  Y/Y  A/A  (  K/K)(1-  ) (  N/N) Year Chapter 4: The Economy in the Very Long Run

7. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 6 The Post-1973 Productivity Slowdown BOXBOX 4-2 A measurement problem A measurement problem Oil price shocks Oil price shocks The pace of innovation slowed The pace of innovation slowed

8. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 7 Growth Theory: The Neoclassical Model oNeoclassical growth theory oNeoclassical growth theory: Focuses on capital accumulation and its link to savings decisions and the like. Y = AF(K, N) (1) Assumptions: No technological change and per capita form. Y/N = f(K/N, 1) (4) capital-labour ratio If y = Y/N is per capita output and k = K/N is the capital-labour ratio, then y = f(k) (5) oCapital-labour ratio oCapital-labour ratio: Number of machines per worker. Chapter 4: The Economy in the Very Long Run

9. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 8y* k* Growth Theory: The Neoclassical Model Per capita output Capital-labour ratio Figure 4-2: Per Capita Production Function production function The production function y = f(k) is the relationship between per capita output and the capital-labour ratio... y = f(k) y k Chapter 4: The Economy in the Very Long Run marginal product of labour diminishing marginal product of capital. … it exhibits two important characteristics: 1) As k increases, y increases, so that the marginal product of labour is positive; 2) Output rises less at high levels of k because of diminishing marginal product of capital.

10. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 9 Growth Theory: The Neoclassical Model oMarginal product of capital oMarginal product of capital: Increment of output obtained by adding one unit of capital with another factor input held constant. Assumptions: No government and no foreign trade, then y = c + I (6) c = C/N i = I/N Where c = C/N and i = I/N Assumption: per capita consumption is a function of income, then c = (1 - s)y (7) s(1 - s) s is marginal propensity to save and (1 - s) is marginal propensity to consume., I = S, In the long run, I = S, therefore propensity to consume. i = sy (8) i = s f(k) (9) Chapter 4: The Economy in the Very Long Run

11. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 10 Growth Theory: The Neoclassical Model oSteady-state equilibrium oSteady-state equilibrium: The combination of per capita GDP and the capital-labour ratio where the economy will remain at rest (i.e. where per capita economic variables are no longer changing.) Assumption: Population growth increases exogenously, then 10) n =  N/N d 10) n =  N/N, and that depreciation each year equal d, then 11)  k = i = (n + d)k 12) sy = (n + d)k 11)  k = i = (n + d)k and 12) sy = (n + d)k In equilibrium: 13) sf (k*) = (n + d)k* Chapter 4: The Economy in the Very Long Run Steady-State Equilibrium

12. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 11 Growth Theory: The Neoclassical Model Per capita output Capital-labour ratio Figure 4-3: Consumption and Investment in the Neoclassical Growth Model y Chapter 4: The Economy in the Very Long Run Savings is a constant proportion of income given by sk(k). In the long run equilibrium, savings equals investment. The remainder of income is consumption, given that we assume no government and foreign trade. y = f(k) = c = c = i = i i = sf(k)

13. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 12 Growth Theory: The Neoclassical Model steady state oFigure 4-4 studies the adjustment process that leads the economy from some initial capital-labour ratio over time to the steady state. oCritical element in the transition process: rate of saving and investment compared with the rate of depreciation and population growth. Chapter 4: The Economy in the Very Long Run The Growth Process

14. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 13 Growth Theory: The Neoclassical Model Per capita output Capital-labour ratio Figure 4-4: Steady State Output and Investment y The economy starts at k 0 … sy 0 k0k0k0k0 y0y0y0y0A B C k*k*k*k* y*D … saving (A) exceeds investment (B) to hold k constant… … k increases. The adjustment process continues until point C is reached, i.e., the Steady State where k and y are constant. (n + d)k Investment requirement y = f(k) PF sySaving

15. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 14 (n + d)k Y*Y*Y*Y* K*K*K*K*C Growth Theory: The Neoclassical Model Per capita output Capital-labour ratio Figure 4-5: Increase in Savings Rate Moves Steady State y The economy starts in steady-state equilibrium at point C where saving equals investment requirement. f(k) sy K* * y**C’ s’y An increase in the fraction of income that is saved leads to sy to s’y… …saving is higher than investment required and the capital stock per head will increase until point C’ is reached.

16. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 15 Growth Theory: The Neoclassical Model Figure 4-6: Adjustment to a New Steady State Chapter 4: The Economy in the Very Long Run

17. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 16 Growth Theory: The Neoclassical Model Figure 4-7: The Golden Rule May Not be the Steady State Per capita output Capital-labour ratio y k*k*k*k* f(k)sy (n + d)k k** s*y Steady-State The Steady-State capital stock is at k* but at this level of capital per head saving is too too high. Golden Rule The Golden Rule level of capital stock is k** where consumption per head is maximized. Golden Rule Steady State The Golden Rule may not be the Steady State. Golden Rule To attain the Golden Rule level of capital stock, the saving rate, s, would need to change to s*.

18. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 17 Growth Theory: The Neoclassical Model Figure 4-8: Exogenous Technical Change Per capita output Capital-labour ratio y (n + d)k An exogenous increase in technology causes the production function and the savings curve to rise. sy 0 A0A0A0A0 sy 2 A2A2A2A2 sy 1 A1A1A1A1 k* 0 y0y0y0y0 k* 1 y1y1y1y1 y1y1y1y1 k* 2 This results in a new steady-state point at a higher per capita output and a higher capital labour-ratio.

19. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 18 Growth Theory: The Neoclassical Model oEndogenous growth oEndogenous growth: Self-sustained growth. a oAssume a production function with a constant marginal product of capital (a) and with capital as the only factor. Y = aK(14) s oAssume the savings rate is constant and at s and that there is neither population growth nor depreciation of capital.  K = sY = saK(15)  K/K = sa oSince output is proportional to capital, the growth rate of output is  Y/Y = sa(16) Chapter 4: The Economy in the Very Long Run Endogenous Growth

20. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 19 Growth Theory: The Neoclassical Model Figure 4-9: (a) Solow Growth Model vs. (b) Endogenous Growth Chapter 4: The Economy in the Very Long Run

21. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 20 Growth Theory: The Neoclassical Model oAbsolute Convergence oAbsolute Convergence: Tendency of both the levels and growth rates of output in different countries to approach each other over time, and for their steady-state values to be the same. oConditional Convergence oConditional Convergence: Tendency of growth rates of output in different countries to approach each other over time, and for their steady-state values to be the same. Chapter 4: The Economy in the Very Long Run Convergence

22. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 21 A Nobel Laureate’s Words BOXBOX 4-4

23. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 22 Growth Theory: The Neoclassical Model Table 4-2: GDP Declines in Formerly Socialist Economies, 1989-1994 Chapter 4: The Economy in the Very Long Run

24. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 23 Growth Policy Figure 4-10: Personal and Government Savings, 1961-2002 Chapter 4: The Economy in the Very Long Run

25. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 24 Chapter Summary Neoclassical growth theory accounts for growth in output as a function of growth in inputs, particularly capital labour. Each input contributes to growth by an amount equal to its factor share times its growth rate. Long run growth can result from improvements in technology. Steady-State output per person depends positively on the savings rate and negatively on the rate of population growth. Chapter 4: The Economy in the Very Long Run

26. Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 25 The End Chapter 4: The Economy in the Very Long Run