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MACROECONOMICS UNDERSTANDING THE GLOBAL ECONOMY Capital Accumulation and Economic Growth 1 Copyright © 2012 John Wiley & Sons, Inc. All rights reserved. 4-2 Key Concepts Definition of Capital and Investment Decreasing Marginal Return Convergence in Rates of Growth The Steady State The Golden Rule 4-3 Growth Transitions Labor Growth Capital Growth TFP Growth 4-4 Real GDP (billions of 1996 $) Decreasing marginal product An increase in the quantity of labor But growth increases Real rate GDP decreases as labor increases 15 12 6 500 1000 1500 Labor Hours 4-5 Real GDP (billions of 1996 $) Decreasing marginal product An increase in the quantity of capital But growth increases Real rate GDP decreases as capital increases 15 12 6 500 1000 1500 Quantity of Capital 4-6 Capital (K) Total value of the machines and buildings used to produce output Capital depreciates (wears out) Assume constant rate of depreciation, d Assume depreciation is fraction of capital stock, d*K 4-7 GDP per capita versus capital stock per worker in 1990 4-8 Capital growth and GDP growth, 1965–90. 4-9 Diminishing Marginal Return Growth will be fast when level of capital is low Growth slows down as capital accumulates Eventually, firms won’t add new capital – firms only replace depreciated capital Economy reaches a Steady State 4-10 Optimal Investment Value of new capital is (Marginal Product) x (Price of Output) Suppose 6 x $2 = $12 Cost of new capital Denoted by “r” Suppose r = $12 Purchase new capital if MP x Price of output= r MP Price of Output r 4-11 Marginal product of capital Decreasing Marginal Product of Capital Marginal Product = r/p Cost of Capital, r/p Marginal Product Capital Stock 4-12 Firms will cease to add capital when marginal return is less than the marginal cost… Real GDP (billions of 1996 $) Stop here if r > 3.75% $15 $12 $6 $80 $160 $240 Capital (billions of 1996 $) 4-13 Comments on interest rates (R) What determines the interest rate? Interaction of savings and investment Effect of changes in the interest rate High interest rate economy is a low capital economy Low interest rate economy is a high capital economy 4-14 Determination of R Interest Rate Savings R0 Investment I0 Output 4-15 Real GDP (billions of 1996 $) Effect of TFP growth $20 $12 $6 $80 $160 $240 Capital (billions of 1996 $) 4-16 Determination of R Interest Rate Savings R1 R0 Investment I0 I1 Output 4-17 Steady State Real GDP Output C+G+X-M Investment Investment (20% of GDP) Capital Stock 4-18 Steady State Real GDP Investment = Depreciation Output Depreciation = d x Capital Stock Investment Capital Stock 4-19 Investment exceeds depreciation; capital stock must decline Output Real GDP Depreciation Investment KLow Kss KHigh Capital Stock 4-20 Depreciation exceeds investment; capital stock must increase Output Real GDP Depreciation Investment KLow Kss KHigh Capital Stock 4-21 Increase in Investment Rate Output Real GDP Depreciation Investment (30% of GDP) Investment (20% of GDP) K20% K30% Capital Stock 4-22 Investment Rate The higher the investment rate of a country, the greater the steady state capital stock and its output level 4-23 The Golden Rule Level of Capital Depreciation = d x Capital Stock “d” is a technological parameter NIPA 3% for structures 8% for equipment New Capital = Investment – d x K Steady State Because of diminishing returns, will reach point where increases in capital stock don’t pay off Investment = d*K 4-24 The Golden Rule Make consumption as high as possible (ignore G and X-M for the moment) Steady State Investment = d x K Real GDP Output C I Ks Capital Stock 4-25 The Golden Rule Make consumption as high as possible (ignore G and X-M for the moment) Steady State Investment = d x K Real GDP Output Maximize this C I Ks Capital Stock 4-26 The Golden Rule Note: C is getting smaller as K increases to K1 Real GDP Steady State Investment = d x K Output C I K0 K1 Capital Stock 4-27 The Golden Rule Note: C is getting smaller as K decreases to K2 Real GDP Steady State Investment = d x K Output C I K2 K0 Capital Stock 4-28 Golden Rule Capital stock is too high Output is used to maintain an overly-large capital stock Consumption is low Capital stock is too low Output is used to support consumption Capital is too low to produce sufficient output 4-29 Golden Rule Marginal Product of Capital = Rate of Depreciation Cobb – Douglas parameter (a) = Savings Rate 4-30 The Golden Rule d = MPK Steady State Investment = d x K Real GDP Output C I Ks Capital Stock 4-31 The Golden Rule What level of capital might a free market choose? Are there forces that keep a country away from the Golden Rule? 4-32 Investment & Depreciation 25% Investment/GDP Depreciation/GDP 20% 15% 10% 5% 0% Canada France Germany Italy Japan UK US 4-33 Convergence in real GDP per capita in Europe, 1820–2010. 32000 France 16000 Germany Italy UK 8000 4000 2000 1000 4-34 Investment as a share of GDP (1980-2009) Country Investment Rate Country Investment Rate Country Investment Rate Argentina 19.0 Germany 20.9 Spain 24.1 Australia 24.5 India 23.8 Sweden 18.8 Brazil 22.5 Israel 20.5 U.K. 17.4 Canada 20.6 Italy 21.1 U.S. 18.5 Chile 20.8 Japan 27.1 Zambia 15.4 China 33.7 Mexico 19.9 Low Income 17.9 Congo 11.3 Russia 20.5 Middle Income 24.0 Egypt 22.0 Singapore 33.9 High Income 21.2 France 19.9 S. Africa 19.0 World 21.7 4-35 The Demographic Transition Child dependency ratio Old Age dependency ratio Death Rate Birth Rate Stage 1 Stage 2 Stage 3 Stage 4 Falling death rates and birth rates associated with improved health can lead to a temporary fall in the overall dependency ratio. 4-36 China and Europe, GDP per capita 51200 Western Europe 25600 China GDP per capita 12800 6400 3200 1600 800 400 200 400 600 800 1000 1200 1400 1600 1800 2010 Year 4-37 Chinese Demographic Transition 90% Old age dependency ratio 80% Child dependency ratio 70% Gross domestic savings % of GDP 60% 50% 40% 30% 20% 10% 0% 4-38 Chinese investment rate 50% 40% 30% 20% 10% 0% 4-39 Growth Accounting for China 4-40 Inequality in China 0.5 0.4 0.3 0.2 National pre 2002 0.1 National 2002 and after Income inequality has risen in China 2007 2005 2003 2001 1999 1997 1995 1993 1991 1989 1987 1985 0 4-41 Regional Inequality in China 4-42 Summary Marginal Product of Capital Implications of decreasing MPK Role in determining Steady State Steady State Investment Investment = Depreciation Growth can no longer be achieved through investment Golden Rule Demographic Transition China’s Growth Miracle Copyright © 2012 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained therein.