MacroEcon 2020 Data Attached

– The amount of capital determines the amount of output – The amount of output being produced determines the amount of saving, which in turn determines the amount of capital being accumulated over time Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -5 11 - 1 Interactions between Output and Capital Figure 11 -1 Capital, Output, and Saving/Investment Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -6 11 - 1 Interactions between Output and Capital • Recall Chapter 10: or • Assume that N is constant, and there is no technological progress, so f does not change over time: • Higher capital per worker leads to higher output per worker. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -7 11 - 1 Interactions between Output and Capital • Assume:

– The economy is closed: I = S + (T − G ) – Public saving (T − G ) is 0: I = S – Private saving is proportional to income: S = sY • So the relation between output and investment: I t = sY t • Investment is proportional to output. • The higher (lower) output is, the higher (lower) is saving and so the higher (lower) is investment. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -8 11 - 1 Interactions between Output and Capital • The evolution of the capital stock is: • Replace investment by the above expression and divide both sides by N : or • The change in the capital stock per worker is equal to saving per worker minus depreciation. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -9 11 - 2 The Implications of Alternative Saving Rates • Combining equations (11.1) and (11.2): • If investment per worker exceeds (is less than) depreciation per worker, the change in capital per worker is positive (negative). Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -10 11 - 2 The Implications of Alternative Saving Rates Figure 11 -2 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. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -11 11 - 2 The Implications of Alternative Saving Rates • The state in which output per worker and capital per worker are no longer changing is called the steady state of the economy. • The steady - state value of capital per worker is such that the amount of saving per worker is sufficient to cover depreciation of the capital stock per worker. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -12 Focus: Capital Accumulation and Growth in France in the Aftermath of World War II Table 1 Proportion of the French Capital Stock Destroyed by the End of World War II • France suffered heavy losses in capital when World War II ended in 1945. • The growth model predicts that France would experience high capital accumulation and output growth for some time. • From 1946 to 1950, French real GDP indeed grew at 9.6% per year. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -13 11 - 2 The Implications of Alternative Saving Rates • The saving rate has no effect on the long - run growth rate of output per worker, which is equal to zero. • The saving rate determines the level of output per worker in the long run. • An increase in the saving rate will lead to higher growth of output per worker for some time, but not forever. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -14 11 - 2 The Implications of Alternative Saving Rates Figure 11 -3 The Effects of Different Saving Rates A country with a higher saving rate achieves a higher steady -state level of output per worker. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -15 11 - 2 The Implications of Alternative Saving Rates Figure 11 -4 The Effects of an Increase in the Saving Rate on Output per Worker in an Economy Without Technological Progress An increase in the saving rate leads to a period of higher growth until output reaches its new higher steady -state level. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -16 11 - 2 The Implications of Alternative Saving Rates Figure 11 -5 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 its new higher steady -state level. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -17 11 - 2 The Implications of Alternative Saving Rates • What matters to people is not how many is produced, but how much they consume. • Governments can affect the saving rate by:

– changing public saving (budget surplus) – using taxes to affect private saving • Golden - rule level of capital: The level of capital associated with the saving rate that yields the highest level of consumption in steady state. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -18 11 - 2 The Implications of Alternative Saving Rates Figure 11 -6 The Effects of the Saving Rate on Steady -State Consumption per Worker An increase in the saving rate leads to an increase, then to a decrease in steady -state consumption per worker. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -19 11 - 2 The Implications of Alternative Saving Rates • For a saving rate between zero and the golden - rule level, a higher saving rate leads to higher capital per worker, higher output per worker and higher consumption per worker. • For a saving rate greater than the golden - rule level, a higher saving rate still leads to higher capital per worker and output per worker, but lower consumption per worker . • An increase in the saving rate leads to lower consumption for some time but higher consumption later. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -20 11 - 3 Getting a Sense of Magnitudes • Assume the production function f: • so that equation (11.3) becomes: • which describes the evolution of capital over time. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -21 FOCUS: Social Security, Saving, and Capital Accumulation in the United States • Social Security, introduced in 1935, has led to a lower U.S. saving rate and thus lower capital accumulation and lower output per person in the long run. • Social Security is a pay - as - you - can system that taxes workers and redistributes the tax contributions as benefits to current retirees, resulting in lower private saving as workers anticipate receiving benefits when they retire. • An alternative is a fully - funded system that pays back the principal plus interest to the workers when they retire , resulting in lower private saving but higher public saving as the System invests their contributions in financial assets. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -22 11 - 3 Getting a Sense of Magnitudes • Equation (11.7) implies that capital per worker in the steady state ( K * /N ) becomes: • Combining equations (11.6) and (11.8) gives the steady state output per worker: • In the long run, output per worker doubles when the saving rate doubles. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -23 11 - 3 Getting a Sense of Magnitudes Figure 11 -7(a) 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 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. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -24 11 - 3 Getting a Sense of Magnitudes Figure 11 -7(b) 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 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. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -25 11 - 3 Getting a Sense of Magnitudes • In the steady state, consumption per worker is: • Given equations (11.8) and (11.9), the steady - state consumption per worker is: • Table 11 - 1 gives the steady - state values of capital per worker, output per worker and consumption per worker for different saving rates (given δ =10%) Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -26 11 - 3 Getting a Sense of Magnitudes Table 11 -1 The Saving Rate and the Steady -State Levels of Capital, Output, and Consumption per Worker Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -27 11 - 4 Physical versus Human Capital • Human capital ( H ): The set of skills of the workers in the economy built through education and on - the - job training. • The production function with human capital: • As for physical capital ( K ) accumulation, countries that save more or spend more on education can achieve higher steady - state levels of output per worker. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -28 11 - 4 Physical versus Human Capital • Models of endogenous growth: Steady - state growth in output per worker depends on variables such as the saving rate and the rate of spending on education, even without technological progress. • However, the current consensus is that given the rate of technological progress, higher rates of saving or spending on education do not lead to a permanently higher growth rate. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -29 APPENDIX: The Cobb - Douglas Production Function and the Steady State • The Cobb -Douglas production function: which gives a good description of the relation between output, physical capital, and labor in the United States from 1899 to 1922. • In steady state, saving per worker must be equal to depreciation per worker, implying that: s (K */N )α = δ (K */N ) where K * is the steady -state level of capital. Copyright © 2017 Pearson Education, Inc. All rights reserved. 11 -30 APPENDIX: The Cobb - Douglas Production Function and the Steady State • The preceding expression can be rewritten as: s = δ (K */N ) 1-α • The steady -state level of capital per worker becomes: (K */N ) = (s/ δ ) α/(1 -α) • If α = 0.5, then: K */N = s/ δ which implies that a doubling of the saving rate leads to a doubling in steady -state output per worker.