1 MACROECONOMICS UNDERSTANDING THE GLOBAL ECONOMY Capital Accumulation and Economic Growth 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 Labor Hours Real GDP (billions of 1996 $) An increase in the quantity of labor increases Real GDP 1500 But growth rate decreases as labor increases Decreasing marginal product

4-5 Quantity of Capital Real GDP (billions of 1996 $) An increase in the quantity of capital increases Real GDP 1500 But growth rate decreases as capital increases Decreasing marginal product

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

4-11 Decreasing Marginal Product of Capital Marginal product of capital Capital Stock Cost of Capital, r/p Marginal Product = r/p Marginal Product

4-12 Capital (billions of 1996 $) Real GDP (billions of 1996 $) $80$160 $6 $12 $15 $240 Firms will cease to add capital when marginal return is less than the marginal cost… Stop here if r > 3.75%

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 Output Savings Investment R0R0 I0I0

4-15 Capital (billions of 1996 $) Real GDP (billions of 1996 $) $80$160 $6 $12 $20 $240 Effect of TFP growth

4-16 Determination of R Interest Rate Output Savings Investment R0R0 I0I0 R1R1 I1I1

4-17 Steady State Output Investment Capital Stock Real GDP Investment (20% of GDP) C + G + X - M

4-18 Steady State Output Investment Capital Stock Real GDP Depreciation = d x Capital Stock Investment = Depreciation

4-19 Investment exceeds depreciation; capital stock must decline Output Investment Depreciation Capital Stock Real GDP K ss K High K Low

4-20 Depreciation exceeds investment; capital stock must increase Output Investment Depreciation Capital Stock Real GDP K ss K High K Low

4-21 Increase in Investment Rate Output Investment (20% of GDP) Capital Stock Real GDP Depreciation Investment (30% of GDP) K 20% K 30%

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) Capital Stock Output KsKs Steady State Investment = d x K I C Real GDP

4-25 The Golden Rule Make consumption as high as possible (ignore G and X-M for the moment) Capital Stock Output KsKs Steady State Investment = d x K I C Real GDP Maximize this

4-26 The Golden Rule Note: C is getting smaller as K increases to K 1 Capital Stock Output K0K0 Steady State Investment = d x K I C Real GDP K1K1

4-27 The Golden Rule Note: C is getting smaller as K decreases to K 2 Capital Stock Output K0K0 Steady State Investment = d x K I C Real GDP K2K2

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 Capital Stock Output KsKs Steady State Investment = d x K I C Real GDP d = MPK

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

4-33 Convergence in real GDP per capita in Europe, 1820–2010.

4-34 Investment as a share of GDP ( ) Country Investment Rate Country Investment Rate Country Investment Rate Argentina19.0Germany20.9Spain24.1 Australia24.5India23.8Sweden18.8 Brazil22.5Israel20.5U.K.17.4 Canada20.6Italy21.1U.S.18.5 Chile20.8Japan27.1Zambia15.4 China33.7Mexico19.9Low Income17.9 Congo11.3Russia20.5Middle Income24.0 Egypt22.0Singapore33.9High Income21.2 France19.9S. Africa19.0World21.7

4-35 The Demographic Transition 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

4-37 Chinese Demographic Transition

4-38 Chinese investment rate

4-39 Growth Accounting for China

4-40 Inequality in China Income inequality has risen in China

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.