1. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 1 of 39 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. Saving, Capital Accumulation, and Output

2. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 2 of 39 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, in turn, the amount of capital accumulated over time. 11-1 Interactions between Output and Capital

3. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 3 of 39 Capital, Output, and Saving/Investment Figure 11 - 1 11-1 Interactions between Output and Capital

4. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 4 of 39 Under constant returns to scale, we can write the relation between output and capital per worker as follows: The Effects of Capital on Output 11-1 Interactions between Output and Capital

5. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 5 of 39 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. The Effects of Capital on Output 11-1 Interactions between Output and Capital

6. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 6 of 39 With these two assumptions, our first relation between output and capital per worker, from the production side, can be written as In words, higher capital per worker leads to higher output per worker. The Effects of Capital on Output 11-1 Interactions between Output and Capital

7. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 7 of 39 To derive the second relation, between output and capital accumulation, we proceed in two steps: 1.We derive the relation between output and investment. 2.We derive the relation between investment and capital accumulation. The Effects of Output on Capital Accumulation 11-1 Interactions between Output and Capital

8. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 8 of 39 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: The Effects of Output on Capital Accumulation Output and Investment 11-1 Interactions between Output and Capital

9. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 9 of 39 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: The Effects of Output on Capital Accumulation Investment and Capital Accumulation 11-1 Interactions between Output and Capital

10. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 10 of 39 The Effects of Output on Capital Accumulation 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: 11-1 Interactions between Output and Capital

11. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 11 of 39 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.  Second relation: Output determines capital accumulation 11-2 The Implications of Alternative Saving Rates

12. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 12 of 39 Change in capital from year t to year t + 1 _ Depreciation during year t _ = Investment during year t = Dynamics of Capital and Output 11-2 The Implications of Alternative Saving Rates From our main relations above, we express output per worker (Y t /N) in terms of capital per worker to derive the equation below:

13. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 13 of 39 This relation describes what happens to capital per worker. The change in capital per worker from this year to next year depends on the difference between two terms:  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. 11-2 The Implications of Alternative Saving Rates Dynamics of Capital and Output Change in capital from year t to year t + 1 _ Depreciation during year t _ = Investment during year t =

14. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 14 of 39 11-2 The Implications of Alternative Saving Rates 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.

15. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 15 of 39 11-2 The Implications of Alternative Saving Rates 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.

16. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 16 of 39 11-2 The Implications of Alternative Saving Rates Dynamics of Capital and Output 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. Capital and Output Dynamics Figure 11 - 2

17. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 17 of 39 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: 11-2 The Implications of Alternative Saving Rates Steady-State Capital and Output

18. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 18 of 39 Capital Accumulation and Growth in France in the Aftermath of World War II Table 1Proportion of the French Capital Stock Destroyed by the End of World War II RailwaysTracks6%RiversWaterways86% Stations38%Canal Locks11% Engines21%Barges80% Hardware60%Buildings(numbers) RoadsCars31%Dwellings1,229,000 Trucks40%Industrial246,000 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.

19. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 19 of 39 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. 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. 3.An increase in the saving rate will lead to higher growth of output per worker for some time, but not forever. 11-2 The Implications of Alternative Saving Rates The Saving Rate and Output

20. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 20 of 39 11-2 The Implications of Alternative Saving Rates The Saving Rate and Output A country with a higher saving rate achieves a higher steady- state level of output per worker. The Effects of Different Saving Rates Figure 11 - 3

21. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 21 of 39 11-2 The Implications of Alternative Saving Rates The Saving Rate and Output An increase in the saving rate leads to a period of higher growth until output reaches its new, higher steady-state level. The Effects of an Increase in the Saving Rate on Output per Worker Figure 11 - 4

22. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 22 of 39 11-2 The Implications of Alternative Saving Rates The Saving Rate and Output An increase in the saving rate leads to a period of higher growth until output reaches a new, higher path. The Effects of an Increase in the Saving Rate on Output per Worker in an Economy with Technological Progress Figure 11 - 5

23. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 23 of 39 11-2 The Implications of Alternative Saving Rates The Saving Rate and Consumption An increase in the saving rate always leads to an increase in the level of output per worker. But output is not the same as consumption. To see why, consider what happens for two extreme values of the saving rate:  An economy in which the saving rate is (and has always been) 0 is an economy in which capital is equal to zero. In this case, output is also equal to zero, and so is consumption. A saving rate equal to zero implies zero consumption in the long run.  Now consider an economy in which the saving rate is equal to one: People save all their income. The level of capital, and thus output, in this economy will be very high. But because people save all their income, consumption is equal to zero. A saving rate equal to one also implies zero consumption in the long run.

24. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 24 of 39 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. 11-2 The Implications of Alternative Saving Rates The Saving Rate and Consumption

25. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 25 of 39 11-2 The Implications of Alternative Saving Rates The Saving Rate and Consumption An increase in the saving rate leads to an increase and then to a decrease in steady-state consumption per worker. The Effects of the Saving Rate on Steady- State Consumption per Worker Figure 11 - 6

26. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 26 of 39 Social Security, Saving, and Capital Accumulation in the United States  One way to run a social security system 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.  Another 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. In anticipation of demographic changes, the Social Security tax rate has seen increases, and contributions are now larger than benefits, leading to the accumulation of a Social Security trust fund.

27. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 27 of 39 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 Getting a Sense of Magnitudes

28. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 28 of 39 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. 11-3 Getting a Sense of Magnitudes The Effects of the Saving Rate on Steady-State Output

29. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 29 of 39 11-3 Getting a Sense of Magnitudes The Dynamic Effects of an Increase in the Saving Rate 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. The Dynamic Effects of an Increase in the Saving Rate from 10% to 20% on the Level and the Growth Rate of Output per Worker Figure 11 - 7

30. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 30 of 39 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 Table 11-1 in the next slide. 11-3 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule

31. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 31 of 39 Table 11-1 The Saving Rate and the Steady-state Levels of Capital, Output, and Consumption per Worker 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 11-3 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule

32. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 32 of 39 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 Physical versus Human Capital

33. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 33 of 39 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. 11-4 Physical versus Human Capital Extending the Production Function

34. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 34 of 39 A measure of human capital 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: 11-4 Physical versus Human Capital Extending the Production Function

35. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 35 of 39 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. 11-4 Physical versus Human Capital Human Capital, Physical Capital, and Output

36. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 36 of 39 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. 11-4 Physical versus Human Capital Human Capital, Physical Capital, and Output

37. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 37 of 39 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.  Output per worker depends on the level of both physical capital per worker and human capital per worker.  Is technological progress unrelated to the level of human capital in the economy? Can’t a better-educated labor force lead to a higher rate of technological progress? These questions take us to the topic of the next chapter: the sources and the effects of technological progress. 11-4 Physical versus Human Capital Endogenous Growth

38. Chapter 11: Saving, Capital Accumulation, and Output Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 38 of 39 Key Terms  saving rate  steady state  golden-rule level of capital  fully funded system  pay-as-you-go system  trust fund  human capital  models of endogenous growth