1. CHAPTER 11 © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard Saving, Capital Accumulation, and Output Prepared by: Fernando Quijano and Yvonn Quijano

2. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard2 of 42 Saving, Capital Accumulation, and Output The effects of the saving rate - the ratio of saving to GDP – on capital and output per capita are the topics of this chapter. An increase in the saving rate would lead to higher growth for some time, and eventually to a higher standard of living in the United States.

3. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard3 of 42 Interactions Between Output and Capital At the center of the determination of output in the long run are two relations between output and capital:  The amount of capital determines the amount of output being produced.  The amount of output determines the amount of saving and investment, and so the amount of capital being accumulated. 11-1

4. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard4 of 42 Interactions Between Output and Capital Capital, Output, and Saving/Investment Figure 11 - 1

5. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard5 of 42 The Effects of Capital on Output Under constant returns to scale, we can write the relation between output and capital per worker as follows: In words: Higher capital per worker leads to higher output per worker.

6. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard6 of 42 The Effects of Capital on Output Since the focus here is on the role of capital accumulation, we make the following assumptions:  The size of the population, the participation rate, and the unemployment rate are all constant.  There is no technological progress.

7. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard7 of 42 The Effects of Capital on Output Under these assumptions, the first important relation we want to express is between output and capital per worker: In words, higher capital per worker leads to higher output per worker.

8. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard8 of 42 The Effects of Output on Capital Accumulation We proceed in two steps: First, we derive the relation between output and investment. Then, we derive the relation between investment and capital accumulation.

9. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard9 of 42 Output and Investment We make three assumptions to derive the relation between output and investment:  We assume the economy is closed.  We assume public saving, T – G, is equal to zero.  We assume that private saving is proportional to income, so Combining these two relations gives:

10. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard10 of 42 Investment and Capital Accumulation The evolution of the capital stock is given by:  denotes the rate of depreciation. Combining the relation from output to investment,, and the relation from investment to capital accumulation, we obtain the second important relation we want to express, from output to capital accumulation:

11. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard11 of 42 Investment and Capital Accumulation Rearranging terms in the equation above, we can articulate the change in capital per worker over time: In words, the change in the capital stock per worker (left side) is equal to saving per worker minus depreciation (right side). Output and Capital per Worker:

12. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard12 of 42 Implications of Alternative Saving Rates Our two main relations are: Combining the two relations, we can study the behavior of output and capital over time.  First relation: Capital determines output. Output determines capital accumulation  Second relation: Output determines capital accumulation 11-2

13. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard13 of 42 Dynamics of Capital and Output From our main relations above, we express output per worker (Y/N) in terms of capital per worker to derive the equation below: change in capital from year t to year t+1  investment during year t  depreciation during year t

14. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard14 of 42 Dynamics of Capital and Output If investment per worker exceeds depreciation per worker, the change in capital per worker is positive: Capital per worker increases. If investment per worker is less than depreciation per worker, the change in capital per worker is negative: Capital per worker decreases. change in capital from year t to year t+1  investment during year t  depreciation during year t

15. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard15 of 42 Dynamics of Capital and Output Capital and Output Dynamics When capital and output are low, investment exceeds depreciation, and capital increases. When capital and output are high, investment is less than depreciation and capital decreases. Figure 11 - 2

16. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard16 of 42 Dynamics of Capital and Output At K 0/N, capital per worker is low, investment exceeds depreciation, thus, capital per worker and output per worker tend to increase over time.

17. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard17 of 42 Dynamics of Capital and Output At K*/N, output per worker and capital per worker remain constant at their long-run equilibrium levels.  Investment per worker increases with capital per worker, but by less and less as capital per worker increases.  Depreciation per worker increases in proportion to capital per worker.

18. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard18 of 42 Steady-State Capital and Output The state in which output per worker and capital per worker are no longer changing is called the steady state of the economy. In steady state, the left side of the equation above equals zero, then: Given the steady state of capital per worker (K*/N), the steady-state value of output per worker (Y*/N), is given by the production function:

19. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard19 of 42 The Saving Rate and Output Three observations about the effects of the saving rate on the growth rate of output per worker are: 1.The saving rate has no effect on the long run growth rate of output per worker, which is equal to zero.

20. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard20 of 42 The Saving Rate and Output 2. Nonetheless, the saving rate determines the level of output per worker in the long run. Other things equal, countries with a higher saving rate will achieve higher output per worker in the long run. Three observations about the effects of the saving rate on the growth rate of output per worker are:

21. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard21 of 42 The Saving Rate and Output 3. An increase in the saving rate will lead to higher growth of output per worker for some time, but not forever. The saving rate does not affect the long-run growth rate of output per worker. After a higher saving rate, growth will end once the economy reaches its new steady state. Three observations about the effects of the saving rate on the growth rate of output per worker are:

22. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard22 of 42 The Saving Rate and Output The Effects of Different Saving Rates A country with a higher saving rate achieves a higher steady-state level of output per worker. Figure 11 - 3

23. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard23 of 42 The Saving Rate and Output The Effects of an Increase in the Saving Rate on Output per Worker An increase in the saving rate leads to a period of higher growth until output reaches its new higher steady-state level. Figure 11 - 4

24. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard24 of 42 Capital Accumulation and Growth in France in the Aftermath of WWII Table 1 Proportion of the French Capital Stock Destroyed by the End of World War II Railways(%)Tracks6Rivers (%)Waterways86 Stations38Canal Locks11 Engines21Barges80 Hardware60Buildings(numbers) Dwellings 1,229,000 Roads (%)Cars31 Trucks40Industrial246,000 When WWII ended in 1945, France had suffered some of the heaviest losses of all European countries. A vivid picture of the destruction of capital is provided by the numbers in Table 1.

25. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard25 of 42 The Saving Rate and Consumption The Effects of an Increase in the Saving Rate on Output per Worker in an Economy with Technological Progress An increase in the saving rate leads to a period of higher growth until output reaches a new, higher path. Figure 11 - 5

26. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard26 of 42 The Saving Rate and Consumption The level of capital associated with the value of the saving rate that yields the highest level of consumption in steady state is known as the golden-rule level of capital.

27. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard27 of 42 The Saving Rate and Consumption The Effects of the Saving Rate on Consumption per Worker in Steady State An increase in the saving rate leads to an increase, then to a decrease, in consumption per worker in steady state. Figure 11 - 6

28. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard28 of 42 The Saving Rate and Consumption For s larger than s G, increases in the saving rate still lead to higher capital and output per worker, but lower consumption per worker. For s=1, capital and output per worker are high, but all of the output is used to replace depreciation, leaving nothing for consumption.

29. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard29 of 42  One way to run a social security system is the pay- as-you-go system, where the taxes that workers pay are the benefits that current retirees receive.  Another is the fully-funded system, where workers are taxed, their contributions invested in financial assets, and when workers retire, they receive the principal plus the interest payments on their investments.  In anticipation of demographic changes, the Social Security tax rate has been increases, and contributions are now larger than benefits, leading to the accumulation of a Social Security trust fund. Social Security, Savings, and Capital Accumulation in the United States

30. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard30 of 42 Getting a Sense of the Magnitudes Assume the production function is: Output per worker is: Output per worker, as it relates to capital per worker is: Given our second relation, Then, 11-3

31. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard31 of 42 The Effects of the Saving Rate on Steady-State Output In steady state, the left side equals zero, then: Squaring both sides, Dividing by (K/N) and rearranging, Output per worker is given by: In words, the steady state capital per worker is equal to the square of the ratio of the saving rate to the depreciation rate.

32. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard32 of 42 The Effects of the Saving Rate on Steady-State Output Steady-state output per worker is equal to the ratio of the saving rate to the depreciation rate. A higher saving rate and a lower depreciation rate both lead to higher steady-state capital per worker and higher steady-state output per worker.

33. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard33 of 42 The Dynamic Effects of an Increase in the Saving Rate Dynamic Effects of an Increase in the Saving Rate from 10 to 20% on the Level and the Growth Rate of Output per Worker It takes a long time for output to adjust to its new higher level after an increase in the saving rate. Put another way, an increase in the saving rate leads to a long period of higher growth. Figure 11 - 7

34. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard34 of 42 The U.S. Saving Rate and the Golden Rule In steady state, consumption per worker is equal to output per worker minus depreciation per worker. Knowing that: then: and These equations are used to derive the Table 11-1 in the next slide.

35. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard35 of 42 The U.S. Saving Rate and the Golden Rule Table 11-1 The Saving Rate and the Steady-state Levels of Capital, Output, and Consumption per Worker (  =10%) Saving Rate, s Capital per worker, K/N Output per worker, Y/N Consumption per worker, C/N 0.0 0.11.0 0.9 0.24.02.01.6 0.39.03.02.1 0.416.04.02.4 0.525.05.02.5 0.636.06.02.4 –––– 1.0100.010.00.0

36. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard36 of 42 Physical Versus Human Capital The set of skills of the workers in the economy is called human capital. An economy with many highly skilled workers is likely to be much more productive than an economy in which most workers cannot read or write. The conclusions drawn about physical capital accumulation remain valid after the introduction of human capital in the analysis. 11-4

37. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard37 of 42 Extending the Production Function When the level of output per workers depends on both the level of physical capital per worker, K/N, and the level of human capital per worker, H/N, the production function may be written as: An increase in capital per worker or the average skill of workers leads to an increase in output per worker.

38. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard38 of 42 Extending the Production Function A measure of human may be constructed as follows: Suppose an economy has 100 workers, half of them unskilled and half of them skilled. The relative wage of skilled workers is twice that of unskilled workers. Then:

39. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard39 of 42 Human Capital, Physical Capital, and Output An increase in how much society “saves” in the form of human capital—through education and on-the-job-training—increases steady-state human capital per worker, which leads to an increase in output per worker. In the long run, output per worker depends not only on how much society saves but also how much it spends on education.

40. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard40 of 42 Human Capital, Physical Capital, and Output In the United States, spending on education comprises about 6.5% of GDP, compared to 16% investment in physical capital. This comparison:  Accounts for the fact that education is partly consumption.  Does not account for the opportunity cost of education.  Does not account for the opportunity cost of on-the- job-training.  Considers gross, not net investment. Depreciation of human capital is slower than that of physical capital.

41. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard41 of 42 Endogenous Growth A recent study has concluded that output per worker depends roughly equally on the amount of physical capital and the amount of human capital in the economy. Models that generate steady growth even without technological progress are called models of endogenous growth, where growth depends on variables such as the saving rate and the rate of spending on education.

42. Chapter 11: Saving, Capital Accumulation, and Output © 2006 Prentice Hall Business Publishing Macroeconomics, 4/e Olivier Blanchard42 of 42 Key Terms  saving rate  steady state  golden-rule level of capital  pay-as-you-go social security system  fully-funded social security system  social security trust fund  human capital  models of endogenous growth