Economic growth a unified approach, second edition

Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information Economic Growth In the second edition of this user-friendly book, Olivier de La Grandville provides a clear and original introduction to the theory of economic growth, its mechanisms and its challenges The book has been fully updated to incorporate several important new results and proofs since the irst edition In addition to a progressive treatment of dynamic optimization, readers will ind intuitive derivations of all central equations of the calculus of variations and of optimal control theory It offers a new solution to the fundamental question: How much should a nation save and invest? La Grandville shows that the optimal savings rule he suggests not only corresponds to the maximization of future welfare lows for society, but also maximizes the value of society’s activity, as well as the total remuneration of labour The rule offers a fresh alternative to dire current predictions about an ever-increasing capital–output ratio and a decrease of the labour share in national income O l i v i e r d e L a G r a n d v i l l e is Senior Professor at Frankfurt University and Visiting Professor in the Management Science and Engineering Department at Stanford University He was Professor of Economics at the University of Geneva from 1978 to 2007 and held visiting positions at the Massachusetts Institute of Technology, at École Polytechnique Fédérale de Lausanne, at the University of Neuchâtel and at the University of Western Australia He is the author of seven books on topics ranging from microeconomics to macroeconomics and inance, and his research work has been published in international journals such as the American Economic Review and Econometrica www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information Praise for Economic Growth, Second Edition ‘Olivier de La Grandville has written a sparkling, wide-ranging and provocative analysis of economic growth models The work is marked by a large number of novel speciic analytic results which will be of wide use.’ Kenneth J Arrow, Stanford University, Nobel Laureate ‘This is a very useful book It covers in extensive detail the neoclassical perspective on optimal economic growth, going beyond what is available in the current textbook expositions Especially noteworthy are the new results in Theorem 16.1 Researchers working on the topic will greatly beneit from the attention that the book pays to the analytical foundations of the approach and its numerical exploration of speciications of the main model that often not get the attention they deserve Indeed, the quantitative analysis is what makes this book especially useful for fully understanding what the standard model of capital accumulation really teaches us about economic growth.’ Pietro F Peretto, Duke University ‘What strikes in this book is that the author, when confronted with a dificult problem in economic growth, irst checks for the validity of the standard theoretical solution to such a problem, and, if he inds it wrong, offers his own solution, which turns out to be the correct one An example is the new chapter on poverty traps I repeat what I already wrote on the irst edition: this is an important book that every economist should read.’ Giancarlo Gandolfo, Accademia Nazionale dei Lincei, Rome ‘Now in a new edition, this book combines rigorous analysis with a keen attention to its practical implications This applies – for instance – to the implausibly high level of the saving rate required by standard growth theory, for which the author offers an innovative solution, and to the diagnosis provided for poverty traps, which also suggests how they can be escaped.’ Graziella Bertocchi, University of Modena and Reggio Emilia ‘Olivier de La Grandville takes the reader on a fascinating tour through neoclassical growth theory Idiosyncratic in scope and style, the tour stops at major intellectual sights In addition, the author guides us to new and important places of interest that emanate from his own research All this is accomplished in a formidable self-contained manner.’ Andreas Irmen, University of Luxembourg ‘Economists need a better understanding of the Euler and Pontryagin dynamic equations, both from an analytical and a computational point of view They also need a new, reasonable solution to the crucial problem of optimal growth They will ind both in this remarkable book by Olivier de La Grandville.’ Bjarne S Jensen, University of Southern Denmark www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information ‘With exceptional clarity, de la Grandville presents the theory of economic growth, incorporating, in this second edition, new results and raising interesting research questions Its rigorous theoretical and insightful analysis provides a foundation on which future students and academic researchers, dealing with complex issues of growth, inequality, poverty, and social welfare, are sure to build.’ Daniela Federici, University of Cassino and Southern Lazio-Italy ‘Olivier de La Grandville continues his profound research on economic growth and development in the second edition of his fascinating book His argument that a realistic model of economic growth requires competitive equilibrium warrants widespread recognition in a graduate courses Economic policy makers should heed his indings on the critical role of the elasticity of substitution between input factors for economic growh and the distribution of factor incomes.’ E Juerg Weber, University of Western Australia ‘This book is much more than an excellent textbook on growth economics: it examines some fundamental questions in the neoclassical growth theory that have thus far not been fully articulated Olivier de La Grandville’s penetrating discussion on the role of factor substitutability and the relation between positive and normative growth theories are particularly insightful I highly recommend this book for anyone interested in the theories of growth and development.’ Kazuo Mino, Doshisha University and Kyoto University ‘A remarkable and masterfully written text De La Grandville’s approach to growth theory is insightful and reveals how much more there is to learn from the workhorse neoclassical growth model The new edition incorporates substantive and original new material It is a thought provoking combination of a textbook and original essays Essential material for researchers and graduate students interested in growth and development theory.’ Miguel León-Ledesma, University of Kent ‘Olivier de La Grandville presents a sound and stimulating introduction to modern growth theory His analysis is at once rigorous and intuitive, opening new perspectives along the Solovian growth model tradition His approach to the problem of optimal growth leads to a deeper understanding of main theoretical results of current growth literature, and also uncovers some of its more serious drawbacks His solution is convincing, always leading to reasonable time paths for the economy This book should be read by all scholars interested in growth theory.’ Davide Fiaschi, University of Pisa ‘This book is a truly delightful revisiting of the theory of economic growth starting with the very essential foundations of the theory: preferences of consumers and technology in the hands of producers Olivier de La Grandville digs deeper into these foundations compared to other textbooks, and provides us with an original light on the non-trivial role of several key assumptions inherent in neoclassical growth In particular, the systematic analysis of www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information the implications strictly concave utility functions for sustainable growth and underlying competitive equilibria is a very stimulating contribution La Grandville’s determination to take the neoclassical model to the data and his incomparable intuitive use of optimal control theory are other remarkable features of this otherwise highly pedagogical and informative textbook.’ Raouf Boucekkine, University of Louvain, Center of Center of Operations Research and Econometrics, and Aix-Marseille University www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information O L I V I E R D E L A G R A N DV I L L E Economic Growth A Uniied Approach Second edition With a foreword and two contributions by Robert M Solow www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence www.cambridge.org Information on this title: www.cambridge.org/9781107115231 C Olivier de La Grandville 2017 This publication is in copyright Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 2009 Second edition 2017 Printed in the United Kingdom by Clays, St Ives plc A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Names: La Grandville, Olivier de, author | Solow, Robert M., contributor Title: Economic growth : a uniied approach / Olivier de La Grandville ; with a foreword and two contributions by Robert M Solowc Description: Second edition | Cambridge, United Kingdom : Cambridge University Press, 2016 Identiiers: LCCN 2016004780 | ISBN 9781107115231 (hardback) Subjects: LCSH: Economic development | Economics – Mathematical models | BISAC: BUSINESS & ECONOMICS / Development / Economic Development Classiication: LCC HD75 L295 2016 | DDC 338.9001 – dc23 LC record ttps://lccn.loc.gov/2016004780 ISBN 978-1-107-11523-1 Hardback ISBN 978-1-107-53560-2 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information This book is lovingly dedicated to my wife Ann, to our children Diane, Isabelle and Henri, and to their own children Ferdinand and Théodore, Eloïse, Maxime and Margaux www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information CONTENTS page xiii xv xviii Foreword by Robert M Solow Preface to the second edition Introduction to the irst edition PART I POSITIVE GROWTH THEORY The welfare of society and economic growth Income as a measure of economic activity Is income per person a fair gauge of society’s welfare? A major caveat 12 14 The growth process 26 The growth process: an intuitive approach A more precise approach: a simple model of economic growth Introducing technical progress 26 28 49 Poverty traps 68 68 68 69 74 Introduction The bare facts Correcting a serious mistake Escaping poverty traps A production function of central importance 76 Motivation The links between the elasticity of substitution and income distribution Determining the constant elasticity of substitution production function 76 83 85 The CES production function as a general mean (in collaboration with Robert M Solow) 92 The concept of the general mean of order p, and its fundamental properties Applications to the CES production function The qualitative behaviour of the CES function as σ changes 94 96 98 Capital–labour substitution and economic growth (in collaboration with Robert M Solow) 114 Further analytics of the CES function in a growth model The elasticity of substitution at work 115 127 ix www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Frontmatter More Information x Contents Introducing technical progress Time-series and cross-section estimates The broader signiicance of the elasticity of substitution in the context of economic growth Why has the elasticity of substitution most often been observed as smaller than 1? And why is it of importance? Introduction The unsustainability of competitive equilibrium with σ > A vivid contrast: the sustainability of competitive equilibrium and its associated growth paths with σ < 155 157 162 170 172 177 183 OPTIMAL GROWTH THEORY Optimal growth theory: an introduction to the calculus of variations The Euler equation Fundamental properties of the Euler equation Particular cases of the Euler equation Functionals depending on n functions y1 (x), , yn (x) A necessary and suficient condition for y(x) to maximize the functional b F (x, y, y′ )dx a End-point and transversality conditions ∞ The case of improper integrals F (y, y′ , t )dt and transversality conditions at ininity Deriving the central equations of the calculus of variations with a single stroke of the pen A one-line derivation of the Euler equation through economic reasoning: x the case of an extremum for x0n F (x, y, y′ )dx Extending this reasoning to the derivation of the Ostrogradski equation: ∂z ∂z , ∂y )dx dy the case of an extremum for R F (x, y, z, ∂x An intuitive derivation of the Beltrami equation End-point and transversality conditions: derivations through direct reasoning Conclusions 11 155 From daily to yearly growth rates The irst moments of the long-term yearly growth rate Application to the long-term growth rates of the US economy 10 151 The long-term growth rate as a random variable, with an application to the US economy PART II 132 145 Other major tools for optimal growth theory: the Pontryagin maximum principle and the Dorfmanian The maximum principle in its simplest form The relationship between the Pontryagin maximum principle and the calculus of variations An economic derivation of the maximum principle 191 192 197 197 199 201 203 207 222 223 225 227 228 230 231 232 233 234 www.cambridge.org 414 Capital and economic growth in the coming century It is to be noted that the equality M = F + L indicates how the money in circulation was created; the forms under which this money is held are the fiat money f M and the deposits (1 − f )M held by the public Not all fiat money created by the central bank is in circulation, precisely because banks hold part of it in reserves, in the amount of r(1 − f )M The deposits not covered by reserves are equal to (1 − f )M − r(1 − f )M = (1 − r)(1 − f )M; this of course equals the loans made by the banks We can verify that the proportion of deposits not covered by bank reserves is (1 − r)(1 − f )M/[(1 − f )M] = − r In our example, typical of most economies, it is 90% These numbers set in full light the de facto privilege and responsibility conferred on central and commercial banks if they are to belie what David Ricardo wrote two centuries ago: “Experience, however, shows that neither a State nor a Bank ever have had the unrestricted power of issuing paper money without abusing that power.” 20 Feb 2017 at 17:30:10, 025 IN CONCLUSION: ON THE CONVERGENCE OF IDEAS A N D VA L U E S T H RO U G H C I V I L I Z AT I O N S We shall not be converted to the promise of the future by more knowledge, but rather by an increase of loving wisdom and reverence, for life, for the earth and for one another Richard Chartres I cannot agree more with you when you say that life is a glorious opportunity if it is used to condition us for eternity Georgy Arbatov In chapter 18, we have shown how a conjecture of tremendous import for the future of our societies, namely Ibn Khaldun’s and Adam Smith’s idea that our well-being is driven by competitive equilibrium, is vindicated today by economic theory Their conjecture came from two different worlds, four centuries apart Nevertheless, their works were linked in more ways than one William Letwin had these words to conclude his “Introduction” to Adam Smith’s magnum opus: “Far from being a hymn in praise of anarchic greed, the Wealth of Nations is a reasoned argument for justice, order, liberty and prudent plenty”.1 It would certainly be difficult to find a better way to characterize the Muquaddimah by Ibn Khaldun We can pursue the examples of the convergence of ideas and values among civilizations on the normative level Remember how Ibn Khaldun had relied on the Tâhir b al-Husayn letter, written in 821, to define what in his mind was the optimal form of government, and how its responsibilities were to be defined It turns out that Tâhir’s letter found an exact echo four centuries later, in Thomas Aquinas’ letter to Hugues II, King of Cyprus (De Regno ad Regem Cypri, 1265) We will never know if Thomas Aquinas had known of Tâhir’s letter It is most likely that he had not This convergence toward a common political and social ethic is then nothing short of remarkable William Letwin, in the Introduction of Adam Smith, op cit., p xxii See the profound analysis of Aquinas’ De Regno ad Regem Cypri (1265) by Patrick de Laubier, in Pour une civilisation de l’amour, Fayard, Paris, 1990 415 20 Feb 2017 at 17:31:18, 026 416 Convergence of ideas and values through civilizations Some of the most cherished values of Western civilization were independently formulated in the ancient Chinese philosophical writings of Mo Tzu3 (later half of the fifth century BC) Mo Tzu spent a good part of his life trying to advocate the principle of defensive wars, and condemning offensive warfare But this is not the only way he announces the Augustinian precepts His message of universal love is based upon the fundamental principle of equality among individuals, families, cities and States – they are all equal under the Heavens This principle would take thousands of years to be slowly, very imperfectly implemented in law and societal behaviour Mo Tzu announced values that we recognize today as belonging to civilization – a rich, complex concept designed to characterize the multi-faceted development of society A civilization grows in step with the degree by which individuals, being considered as equal, are respected in their persons and in their ideas Progress takes many forms; it means progress in equality of rights, in tolerance, as well as in the respect of nature The concept is intertemporal in the sense that it requires to heed the interests not only of the current, but of the future generations as well The Mo Tzu principle applies: from one generation to another, society transmits more than it has received Economic growth is just one of those facets; it is only one of the interdependent processes which make up civilization Like natural phenomena, they not follow smooth paths, and defy prediction In each of those fractal-like processes, tiny and apparently harmless events may lead to momentous, unpredictable consequences, often referred to as “accidents of history” Not only the economic development of societies, but also the evolution of ideas may experience steep, sustained downfalls marked by the strangest of ideologies, carrying down civilization with them Those downfalls were endured in China after Mo Tzu’s time, during and after Europe’s Renaissance, and throughout the French revolution; they doomed our twentieth century, in China and on the Western and the Eastern sides of the Danube alike Nevertheless, how could we not see an upward trend in the paths that are slowly shaping civilization? When we hear the voices of Mo Tzu, Tâhir b al-Husayn, Ibn Khaldun, Thomas Aquinas, Adam Smith, those voices from a distant past and at the same time so close to each of us, how could we ever doubt that civilizations will converge toward a system of common, elevated values? This is the message of hope I want to convey to you See Basic writings of Mo Tzu, Hsün Tzu and Han Fei Tzu (trans Watson 1963) I am very grateful to my colleague Patrick de Laubier for bringing to my attention Mo Tzu’s work 20 Feb 2017 at 17:31:18, 026 F U RT H E R R E A D I N G , DATA O N G ROW T H AND REFERENCES An excellent companion to this book, illustrating the difficulties and challenges of growth and development, is William Easterly, The elusive quest for growth: an economist’s adventures in the tropics, MIT Press, 2001 Readers may also want to pursue the subject of growth in two broad directions: empirical observations and theory They will find tremendous help in a website opened and maintained by Jonathan Temple of Bristol University: www.bris.ac.uk/Depts/ Economics/Growth his address is also a list of the sites which carry the most detailed and accurate data on economic growth, for a very large number of countries Those are: r r r r r r r r r Penn World Table (Summers–Heston data set) Barro–Lee (1993) growth data set Barro–Lee (2000) education data set Political instability and growth data set Sachs and Warner data sets Social Indicators of Development Trends in Developing Economies World Bank Growth Research World Bank World Tables Most economic journals publish research on growth and development; some even specialize in each of these fields: the Journal of Economic Growth, the Journal of Economic Development A wealth of recent books and papers is also available online through Jonathan Temple’s website The reader who would like to refresh his calculus, especially on subjects directly relevant to economic dynamics, has many excellent texts at his disposal We indicate four of these, which he may find particularly helpful: Chiang, A (1985) Fundamental methods of mathematical economics, 3rd edition, McGrawHill, New York Gandolfo, G (2009) Economic dynamics, 4th edition, Springer, Berlin and New York 417 20 Feb 2017 at 17:32:14, 027 418 Further reading Hammond, P J and K Sydsaeter (1995) Mathematics for economic analysis, Prentice Hall, Englewood Cliffs, NJ Takayama, A (1985) Mathematical economics, 2nd edition, Cambridge University Press, Cambridge and New York If the reader wants to enter the subject of the calculus of variations and optimal control, the following references are particularly recommended r For the calculus of variations per se: Elsgolc, L (1960) Calculus of variations, International Series of Monographs in Pure and Applied Mathematics, Pergamon Press, Reading, MA Gelfand, I and S Fomin (1961) Calculus of variations, Prentice Hall, Englewood Cliffs, NJ r For optimal control and its applications to growth, a good introduction is: Chiang, A (1992) Elements of dynamic optimization, McGraw-Hill, New York In-depth and very clear presentations can be found in: Arrow, K J (1968) “Applications of control theory to economic growth”, in G B Dantzig and A F Veinott, eds, Mathematics of the decision sciences, American Mathematical Society, Providence, RI Arrow, K J and M Kurz (1971) Public investment, the rate of return, and optimal fiscal policy, Johns Hopkins Press, Baltimore, MD The best known textbooks and collected papers in growth theory, often from very different perspectives and at different levels, are: Acemoglu, D (2009) Introduction to Modern Economic Growth, Princeton University Press Acemoglu, D., ed (2004) Recent developments in growth theory, Edward Elgar, Cheltenham, UK Aghion, P and S N Durlauf (2005) Handbook of economic growth, North-Holland, Amsterdam Aghion, P and R Griffith (2005) Competition and growth, reconciling theory and evidence, MIT Press, Cambridge, MA Aghion, P and P Howitt (1998) Endogenous growth theory, MIT Press, Cambridge, MA Barro, R J and X Sala-i-Martin (2004) Economic growth, 2nd edition, MIT Press, Boston, MA Bertola, G., R Foellmi and J Zweimüller (2006) Income distribution in macroeconomic models, Princeton University Press, Princeton, NJ Eicher, T and C García-Palosa, eds (2006) Institutions, development and economic growth, MIT Press, Cambridge, MA Eicher, T and S Turnovsky, eds (2007) Inequality and growth, theory and policy implications, MIT Press, Cambridge, MA George, D A R., L Oxley and K I Carlaw (2004) Surveys in economic growth: theory and empirics, Blackwell, Oxford Gylfason, T (1999) Principles of economic growth, Oxford University Press, Oxford Helpman, E (2004) The mystery of economic growth, Harvard University Press, Cambridge, MA Jensen, B S (1994) The dynamic systems of basic economic growth models, Kluwer Academic, Dordrecht Jones, C I (1997) An introduction to economic growth, Norton, New York and London 20 Feb 2017 at 17:32:14, 027 Further reading 419 Klundert, T van de (2001) Growth theory in historical perspective: selected essays of Theo van de Klundert (ed S Smulders), Edward Elgar, Cheltenham, UK Lucas, R E., Jr (2002) In search of prosperity: analytic narratives on economic growth, Princeton University Press, Princeton, NJ Malinvaud, E (1998) Macroeconomic theory: a textbook on macroeconomic knowledge and analysis (trans F Kirman), Elsevier, Amsterdam Parker, P M (2000) Physioeconomics: the basis for long-run economic growth, MIT Press, Cambridge, MA Rodrigo, G C (2001) Technology, economic growth and crises in East Asia, Edward Elgar, Cheltenham, UK Rodrik, D., ed (2003) In search of prosperity: analytic narratives on economic growth, Princeton University Press, Princeton, NJ Rogers, M (2003) Knowledge, technological catch-up and economic growth, Edward Elgar, Cheltenham, UK Romer, D (2001) Advanced macroeconomics, 2nd edition, McGraw-Hill, Boston, MA Ros, J (2000) Development theory and the economics of growth, University of Michigan Press Solow, R M (2000) Growth theory: an exposition, 2nd edition, Oxford University Press, Oxford Thirlwall, T (2002) The nature of economic growth: an alternative framework for understanding the performance of nations, Edward Elgar, Cheltenham, UK Mexico lectures, 2002 Weil, D N (2005) Economic growth, Pearson Addison-Wesley An excellent synthesis of the research presently conducted on the all-important environmental issues can be found in: Brock, W A and M S Taylor, “Economic growth and the environment: a review of theory and empirics”, in Aghion and Durlauf (2005), vol 1, part B, pp 1749–1821 Other references, quoted in this book Allen, R G D (1938) Mathematical analysis for economists, Macmillan, London Antràs, P (2004) “Is the US aggregate production function Cobb–Douglas? New estimates of the elasticity of substitution”, Contributions to Macroeconomics, (1), art Arrow, K J (1968) “Applications of control theory to economic growth”, in G B Dantzig and A F Veinott, eds, Mathematics of the decision sciences, American Mathematical Society, Providence, RI Arrow, K., H Chenery, B Minhas and R M Solow (1961) “Capital–labour substitution and economic efficiency”, Review of Economics and Statistics, 43 (4), 225–50 Arrow, K J and F Hahn (1971) General competitive analysis, Holden-Day, San Francisco, and Oliver and Boyd, Edinburgh Arrow, K J and M Kurz (1971) Public investment, the rate of return, and optimal fiscal policy, Johns Hopkins Press, Baltimore, MD Byström J., L E Persson and F Strömberg, www.sm.luth.se∼johanb/applmath/chap.en/part7 htm Chiang, A (1992) Elements of dynamic optimization, McGraw-Hill, New York Chirinko, R (2008) “σ : the long and short of it”, Journal of Macroeconomics, 30 (2), 671–86 Courant, R and D Hilbert (1989) Methods of mathematical physics, vol I, Interscience Publishers, Inc., New York Dorfman, R (1969) “An economic interpretation of optimal control theory”, American Economic Review, 59 (5), 817–31 Elsgolc, L (1960) Calculus of variations, International Series of Monographs in Pure and Applied Mathematics, Pergamon Press, Reading, MA 20 Feb 2017 at 17:32:14, 027 420 Further reading Feynman, R (1999) The pleasure of finding things out, Penguin Books, London and New York Fisher, I (1896) “Appreciation and interest”, Publications of the American Economic Association, New York, XI (4), 331–442 Gelfand, I and S Fomin (1961) Calculus of variations, Prentice Hall, Englewood Cliffs, NJ Goldstine, H H (1981) A history of the calculus of variations, Springer, New York Goodwin, R M (1961) “The optimal growth path for an underdeveloped economy”, The Economic Journal, 71 (284), 756–74 Hairer, E., S P Nørsett and G Wanner (2000) Solving ordinary differential equations, vol I, 2nd edition, Springer, New York Hairer, E and G Wanner (2000) L’analyse au fil de l’histoire, Springer, Berlin, Heidelberg and New York Hardy, G., J E Littlewood and G Pólya (1952) Inequalities, Cambridge University Press, Cambridge Heston, A., R Summers and B Aten (2012) Penn World Table, Version 7.1, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania Hicks, J (1932) Theory of wages, Macmillan, London Ibn Khaldun (1377) The Muqaddimah: an introduction to history (trans F Rosenthal), Routledge and Kegan Paul, London and Henley First printing, 1958; this edition, 1986 Intriligator, M D (1971) Mathematical optimization and economic theory, Prentice Hall Ivanov, A http://home.ural.ru/∼iagsoft/BrachJ2.html Johnston, L D and S H Williamson (2005) “The annual real and nominal GDP for the United States, 1790–present”, Economic History Services www.eh.net/hmit/gdp/ Johnston, L and S H Williamson (2013) “What was the US GDP then?” www measuringworth.com/datasets/usgdp/result.php Jones, R (1965) “The structure of simple general equilibrium models”, The Journal of Political Economy, 73 (6), 557–72 Kaldor, N (1957) “A model of economic growth”, The Economic Journal, 67, 591–624 Kamikigashi, T and S Roy (2006) “Dynamic optimisation with a nonsmooth, non-convex technology: the case of a linear objective function”, Journal of Economic Theory, 29, 325–40 King, R G and S T Rebelo (1993) “Transitional dynamics and economic growth in the neoclassical model”, American Economic Review, 83 (4), 908–31 Klump, R and O de La Grandville (2000) “Economic growth and the elasticity of substitution: two theorems and some suggestions”, American Economic Review, 90 (1), 282–91 Klump, R., P McAdam and A Willman (2006) “A supply-side diagnosis of growth in the euro area: factor substitution, productivity and unemployment”, Paper presented at the CES Conference, University of Frankfurt, 20–22 October 2006 Klump, R., P McAdam and A Willman (2007) “Factor substitution and factor augmenting technical progress in the US: a normalized supply-side system approach”, Review of Economics and Statistics, 89 (1), 183–92 Klump, R and H Preissler (2000) “CES production functions and economic growth”, Scandinavian Journal of Economics, 102, 41–56 La Grandville, O de (1980) “Capital theory, optimal growth and efficiency conditions with exhaustible resources”, Econometrica, 48 (7), 1763–76 (1989) “In quest of the Slutsky diamond”, American Economic Review, 79 (3), 468–81 (1992) “New Hamiltonians for high-order equations of the calculus of variations: a generalization of the Dorfman approach”, Archives des Sciences, 45 (1), 51–8 (1997) “Curvature and the elasticity of substitution: straightening it out”, Journal of Economics, 66 (1), 23–34 (1998) “The long-term expected rate of return: setting it right”, The Financial Analysts Journal, 54 (6), 75–80 20 Feb 2017 at 17:32:14, 027 Further reading 421 (2003) Bond pricing and portfolio analysis: protecting investors in the long run, MIT Press, Cambridge, MA (2006a) “Protecting investors against changes in interest rates”, in Asset and liability management (ed W Ziemba and S Zenios), Elsevier North-Holland, Amsterdam and New York, pp 69–138 (2006b) “The 1956 contribution to theory of economic growth by Robert Solow: a major landmark and some of its undiscovered riches”, Oxford Review of Economic Policy, 23 (1), 15–24 (2009) Economic growth: a unified approach, with two special contributions by Robert M Solow, 1st edition, Cambridge University Press, Cambridge (2011) “A new property of general means of order p with an application to the theory of economic growth”, The Australian Journal of Mathematical Analysis and Applications, (1), 1–5 (2012a) “A one-line derivation of the Euler and Ostrogradski equations”, The Australian Journal of Mathematical Analysis and Applications, (2), art (2012b) “How much should a nation save? A new answer”, Studies in Non-linear Dynamics and Econometrics, 16 (2), 1–35 (2014a) “End-point and transversality conditions in the calculus of variations: Derivation through direct reasoning”, The Australian Journal of Mathematical Analysis and Applications, 11 (1), art 11 (2014b) “Optimal growth theory: challenging problems and suggested solutions”, Economic Modelling, 36, 608–11 (2016a) “An alternative derivation of the Euler–Poisson equation”, The American Mathematical Monthly, Vol 123, No (October 2016), pp 821–824 (2016b) “Why is optimal economic growth theory mute? Restoring its rightful voice”, Macroeconomic Dynamics, to appear La Grandville, O de and R M Solow (2006) “A conjecture on general means”, Journal of Inequalities in Pure and Applied Mathematics, (1), art Landes, D (1998) The wealth and poverty of nations, Norton Laubier, Patrick de (1990) Pour une civilisation de l’amour, Fayard, Paris León-Ledesma, M A., P McAdam and A Willman (2010) “Identifying the elasticity of substitution with biased technical change”, American Economic Review, 100 (4), 1330–57 Leung, H M (2006), “Endogenizing the aggregate elasticity of substitution”, Paper presented at the CES Conference, University of Frankfurt, 20–22 October 2006 Malinvaud, E (2002) “Sur l’aggrégation des demandes de travail non-qualifié”, Annales d’Economie et de Statistique, 66, 41–80 Malinvaud, E (2003) “An aggregation problem”, Working Paper Pitchford, J (1960) “Growth and the elasticity of substitution”, Economic Record, 36, 491–504 Pitman, J (1993) Probability, Springer, New York Pontryagin, L S., V G Boltyanskii, R V Gamkrelidze and E F Mishchenko (1962), The mathematical theory of optimal processes (trans K N Trirogoff), Interscience, New York Ramsey, F (1928) “A mathematical theory of saving”, The Economic Journal, 38 (152), 543– 59 Rutherford, T (2003) Lecture notes on constant elasticity functions, University of Colorado Sato, R (2006) Biased technical change and economic conservation laws, Springer, New York Smith, A (1776) An inquiry into the nature and causes of the wealth of nations This edition, Dent & Sons, London and Toronto, 1975, pp 398–400 Solow, R (1956) “A contribution to the theory of economic growth”, The Quarterly Journal of Economics, 70 (1), 65–94 Srinivasan, T N (1964) “Optimal savings in a two-sector model of growth”, Econometrica, 32 (3), 358–73 20 Feb 2017 at 17:32:14, 027 422 Further reading Stoléru, L (1970) L’équilibre et la croissance économique: Principes de macroéconomie, Dunod, Paris Sussmann, H J and J C Willems (1997) “300 years of optimal control: from the brachistochrone to the maximum principle”, IEEE Control Systems, 17 (3), 32–44 Swan, T (1956) “Economic growth and capital accumulation”, Economic Record, 32, 340–61 Sydsaeter, J and P Hammond (1995) Mathematics for economic analysis, Prentice Hall Thanh, N P and M N Minh (2008) “Proof of a conjecture on general means”, Journal of Inequalities in Pure and Applied Mathematics, (3), art 86 Toynbee, A (1934), A study of history, vol III, Royal Institute of International Affairs and Oxford University Press Uzawa, H (1965) “Optimal growth in a two-sector model of capital accumulation”, Review of Economic Studies, XXXII (90), 85–104 Watson, B., trans (1963) Basic writings of Mo Tzu, Hsün Tzu and Han Fei Tzu, Columbia University Press, New York Young, L (1996) “The Tao of markets: Sima Qian and the invisible hand”, Pacific Economic Review, (2), 137–45 Yuhn, K H (1991) “Economic growth, technical change biases, and the elasticity of substitution: a test of the de La Grandville hypothesis”, The Review of Economics and Statistics, LXIII (2), 340–6 Ziemba, W and S Zenios, eds (2006), Asset and liability management, Elsevier North-Holland, Amsterdam and New York 20 Feb 2017 at 17:32:14, 027 Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information INDEX agriculture, value added of, Allen, R.G.D., 155 arbitrage, 327 see also investment Arrow, Kenneth, 48–9, 76, 84, 85, 92, 147, 155–6, 392 asset value, and Fisher equation, 319–21 asymptotic factors, in consumption per person, 373 asymptotic growth, with labour-augmenting technical progress, 134–44 banks, money creation by, 411–14 Bellman, Richard, 231–2 Beltrami equation, 227–8 Bernoulli, Johan, 192, 210–15 biosphere changes, 14–15 brachistochrome problem, 192–6, 197, 210–15 calculus of variations central equations, 222–30 optimal growth theory, 189–216, 244–9 capital as factor of production, 26–8 marginal productivity of, 33, 118 and competitive equilibrium, 361–6 optimal time path of, 166–7, 381–2 per eficient labour unit, 135 capital depreciation, and GDP (gross domestic product), 14–15 capital income, 4, 408 capital marginal product, and elasticity of substitution, 80–2 capital productivity, 35 capital share values limitation, 126–7 capital stock value, and Fisher equation, 319–21 capital valuation, 316–21 and Fisher equation, 318–21 investment total return, 317 unit evaluation, 317–18 value of dollar invested in capital good, 316–17 capital-augmenting technical progress, 49, 153, 157 capital-labour ratio, 35, 49, 51, 63, 69–74, 269 and constant elasticity of substitution, 82, 83–4, 110–11, 114, 116–18, 129–30, 133, 152, 155 capital-output ratio, 408, 410–11 and constant elasticity of substitution, 111, 165 time path of, 165, 368–9, 382 central banks, money creation by, 411–14 central limit theorem, 179–80 CES (constant elasticity of substitution), xix, 48–9, 76–91 in aggregative theory of economic growth, 114–15, 156 as boost to economy during development, 128–30 calibrated capital share in total income, 125–6 and capital marginal product, 80–2 capital share values limitation, 126–7 and capital-labour ratio, 82, 83–4, 110–11, 114, 116–18, 129–30, 133, 152, 155 and capital-output ratio, 111, 165 and competitive equilibrium, 156–7, 160, 406 concave power function, 155–6 cross-section estimates, 146–7 and curvature of isoquant, 79–80 deinition of, 78 distribution parameter, economic interpretation of, 108 as eficiency parameter, 104 and elasticity of income per person/wage rate, 82–3 and equilibrium income per person, 130–2 estimate of, 149 factor demand, 76 factors determining magnitude, 151–2 function in growth model, 115–27, 156 general mean of order p, fundamental properties, 94–6 geometrical representation of, 78–80 and growth, 115–26, 127, 151–3, 156, 159 and income distribution, 83–4 and income per person, 105–11, 118–27, 129–32, 155–6, 374–6 increase by country, 146, 151 and initial savings rate, 353–4 measurement as less than 1, 155–66 and national product production cost, 116–18 and order of the mean p, 93 Pitchford constant, 120–2, 136, 156 423 www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information 424 Index CES (constant elasticity of substitution) (cont.) production function applications, 96–8 production function constants, 87–8 production function determination, 85–8 production function as general mean, 92–113 production function isoquants, 99–105 production function special cases, 98 production function theorems, 116–18, 132, 133–4 production per person, 105–8 properties of, 80–3 qualitative behaviour of CES function, 98–111 and savings-investment rate, 116–18, 124, 125–6 and technical progress see technical progress threshold value and permanent growth, 122–6, 127 wage-rental ratio/capital-labour ratio relationship, 76–83, 114, 152, 155 Walras-Leontief production function, 97 Chenery, Hollis, 48–9, 76, 84, 85, 92, 147, 155–6 China, popular communes in, 401–3 Cobb-Douglas case, 43, 49, 106, 107 Cobb-Douglas function, xix, 60–1, 64–6, 79, 84, 152, 164–5 collective farming see planned economies commercial banks, money creation by, 411–14 competitive equilibrium, 156–7, 160, 408–10 capital-output ratio time path, 165, 368–9, 382 and concavity of utility functions, 349–57, 359, 360 and consumption lows, 297, 408–11 economy in, 410–11 and elasticity of substitution, 156–7, 160, 406 and Euler equation, 357–60, 376–7 and initial income per person growth rate, 353–4 and initial savings rate, 353–4 intertemporal optimality of, 361–6 labour share in net national income, 408–10 labour share in total income, 165–6 and marginal productivity of capital, 361–6 optimal evolution of the economy, 366–9 optimal evolution of income per person, 164–5 optimal location of economy in, 163 optimal savings rate, 165, 367–8 optimal time path of capital, 166–7, 381–2 and remuneration of labour, 163–4, 362, 365 sustainability of, 162–6, 349–60 theorem 1, 163–4 traditional approach incompatibility, 357–60 in traditional model, 337 unsustainability of, 157–62, 337 concavity of utility/production function, 155–6, 163–4, 335, 336, 347, 349–57, 359, 360, 376 see also utility functions consumers’ surplus, 18–19 consumption discounted lows, 163–4 goods and services, 3–4 measurement, 11–12 private, 4–5 public, 4–5 consumption lows, 360–1 consumption per person, asymptotic factors, 373 Contribution to the Theory of Economic Growth, 43 cost function, derivation with capital and labour-augmenting process, 153 currency valuation, 11–12 curvature of isoquant, 79–80 demographic growth factor, 394 derivatives, concept of, 52–3 descriptive growth theory, 35–6 differential equation, solutions of irst order, 57–60 discounted consumption lows, xviii–xix, 362, 408–11 disequilibrium, 127–8, 139–40 DOPRI program, xx–xxi Dorfman, Robert, xx, 231–2 Dorfmanian approach, xx, 231–42, 251, 270–1, 363–6 Dorfmanian extensions, 238–42 Easterly, William, 417 economic activity factors neglected in calculation, 13 GDP see GDP and income, 3–12 measuring approaches to, 4–5 expenditure approach, 4–5 income approach, income per person, 3–14, 15 input-output table, 5–8, 20 national income at current/constant prices, 9–12 output (value added) approach, NNP see NNP economic growth see growth economic welfare see welfare economy sectors, elasticity concept of, 52–7 and growth rates, 55–7 reading function from graph, 54–5 of substitution see CES Elsgolc, L., 210–15 equation of motion of capital-labour ratio, 71–4 of the economy, 34–9, 71–4 fundamental property, 35 equilibrium competitive see competitive equilibrium disequilibrium, 127–8, 139–40 and income per person, 118–27, 130–2 price equilibrium, 17, 297 saddle-point, 7, 282 www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information Index spot price, 297 and technical progress, 139–40, 403–5 in utility functions, 336 equilibrium instability, 69–75 equilibrium interest rates, 297, 298–300 equilibrium investment, 327, 332–4, 349–60 equilibrium point and ixed prices, 18, 23 and negative exponential, 347 equilibrium values, 49 Euler equation, 192–6, 222–5, 230, 237–8, 363–6 additional gain, 224, 226 and Beltrami equation, 227–8 and calculus of variation, 245–6 and competitive equilibrium, 357–60, 376–7 end-point conditions, 228–9 fundamental properties of, 197 and Hamiltonian, 234, 270–1 and improper integrals, 207–8 and integration constants, 207 and optimal savings rate, 336 particular equations, 197–9 transversality conditions, 206, 207–8, 228–9 and utility functions, 357–60 and welfare, 361 Euler-Lagrange equation, 199, 201–3, 231–2, 270–1 Euler-Ostrogradski equation, 225–7, 230 Euler-Poisson equation, 231–2, 238–42 Euler’s theorem, 30–4, 60, 61 expenditure growth factors, 9–12 with individuals’ consent, 12 without individuals’ consent, 12 exports, 4–5 factor demand, 76 factors of production, 26–8, 407 irst-order differential equation, 57–60 Fisher equation, 318–21, 332–3 Fisher-Solow equation, 408 ixed prices and equilibrium point, 18, 23 and supply and demand, 17–18 foreign competition, 24 fundamental equation of positive, 35–6 future price equilibrium, 297 GDP (gross domestic product) approaches to measuring, 4–5, 20 and capital depreciation, 14–15 excluded expenditures, 12–13 GDP/public debt ratio, 335 and GNP, 8–9 implicit GDP delator, 11–12 input-output table, 5–8, 20 and NNP see NNP real GDP per person, third world countries, 68–71 425 general mean, proofs of, 111–13 general mean of order p, fundamental properties, 94–6 GNP (gross national product), 8–9 Goodwin model, 343–4, 376 Goodwin, Richard, 266, 335–6, 338–43, 376 growth agreed hypotheses, 407 alternate production functions, 41–9 asymptotic growth with labour-augmenting technical progress, 134–44 demographic, 394 descriptive growth theory, 35–6 equation of motion of the economy see motion of the economy equilibrium points, 41–3 excessive taxation transgression, 397–8 factors of production, 26–8 homogenous functions, 30–4, 60 illustration of, 26–8 and institutional soundness, 398–400 investment behaviour of society hypothesis, 28–30, 34 monopolies transgression, 397, 398 optimal, 163–4 and popular communes, 384–8, 401–3 population growth hypothesis, 34 production function hypothesis, 28–34 signiicance of elasticity of substitution, 151–3 slavery transgression, 396, 398 solution of irst-order differential equation, 57–60 speed of convergence toward equilibrium, 39–41 technical progress hypothesis, 5, 34, 49–52, 115, 407 and threshold value of elasticity of substitution, 122–7 growth factors Ibn Khaldun’s, 393–400 individual proit, 394–5, 400–5 private property, 394–5 technical progress, 394, 403–5 growth model, 28–49 growth problems and planned economies, 383–90, 401–3 see also planned economies growth rate and elasticity, 55–7 long-term see long-term growth rate growth stability analysis, 41–9 Hahn, Frank, 392 Hairer, Ernst, xx–xxi, 347 Hamiltonian approach, xx, 231–2, 233–4, 236–7, 250, 270–1 Hammond, P., 271 Han Fei Tzu, 383 Harrod-Domar case, 43–6 www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information 426 Hicks, John, 114, 151–2, 155 homogenous functions, 30–4, 60, 62–3, 71 Ibn Khaldun, 1–2, 392–405, 415 and Tahir b al-Husayn, 399–400, 415 import duty, 24 import quotas, 25 imports, 4–5 income and democracy, 13–14 as measure of economic activity, 3–12, see also economic activity optimal growth rate, 368 per person, 3–14, 15, 22, 40, 43, 46–8, 51, 67, 82–3, 105–11, 118–27, 129–30, 135, 143, 164–5, 349, 355, 374–6 and society’s welfare, 12–13 income distribution, and elasticity of substitution, 83–4 individual proit growth factor, 394–5 industry, value added of, inlation, and interest rates, 298 input-output table, 5–8, 20 interest rates artiicially ixed, 299–300 and capital valuation see capital valuation continuous compounded forward rate, 301–4 continuous compounded spot rate, 304–7 continuous compounded total return, 307–11 continuous compounding, 301, 304–7 economic interpretation of e, 309–11 economic interpretation of log x, 311–15 equilibrium, 297, 298–300 forward rates, 301–4, 308, 315–16 and inlation, 298 instantaneous forward rate, 304 properties of, 315–16 real interest rate, 345 reason for existence of, 298–300 and savings rate, 353–4 spot rates, 301–2, 304–7, 308, 309, 315–16 total return, 307–11 types of, 301–16 Introduction to History, 1–2, 392–405 ive growth factors, 393–400 investment arbitrage, 327–8 equilibrium, 327, 332–4, 349–60 Fisher equation, 318–21, 332–3 investors’ behaviour, 327–8, 330 overvalued capital good/asset and arbitrageurs, 331–2 and investors’ behaviour, 332 private, 4–5 public, 4–5 risk premium, 332–4, 376–7 risk-free transactions, 327, 361 Index supply-demand curves, 327–8 uncertainty, 327 undervalued capital good/asset and arbitrageurs, 328–30 and investors’ behaviour, 330 investment goods, 3–4 investment-savings rate, 74–5 invisible hand, xviii–xix Johnston, Louis D., 183–4, 342 Jones, Ronald, 152 Kaldor, Nicholas, 164–5 King, Robert, 335–7, 338–43, 347 King/Rebelo model, 335–7, 344–6, 347, 376 Klump, R., 116–18 La Grandville, Olivier de, 111–13, 116–18, 238, 337, 347, 348, 349 labour as factor of production, 26–8, 63–4 as function of time, 408 in intensive units, 50 productivity, 63–4, 74–5 remuneration of, 163–4, 362, 365, 408–11 rising share of, 408 share in total income, 165–6 labour income, labour units, 135 Lagrange, Ludovico, 193, 199 legal institutional soundness, 398–400 Leibniz formula, 208–10 Leontief, Wassily, 7, 282 Letwin, William, 377 L’Hospital’s rule, 120–1, 315 lognormal variable, 173–7, 181 long-term growth rate, 170–85 10-year expected growth rate, 171–2 arithmetic/geometric means for discrete/ continuous random variables, 182–3 central limit theorem, 179–80 daily growth rate, 172–7 expected value and variance of, 180–1 geometric mean convergence, 182–3 lognormal variable, 173–7, 181 moment generating functions, 185 n-horizon intervals probabilities, 181 in US economy, 183–4 yearly growth rate, 171–7 irst moments, 177–83 irst moments (methods of obtaining), 178–80 Maastricht Treaty, 335 Malinvaud, Edmond, 152 Mao Tse Tung, 401–3 Markovitz, Harry, 333–4 Minh, Mach Nguyet, 113 www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information Index Minhas, Bagicha, 48–9, 76, 84, 85, 92, 147, 155–6 Mo Tzu, 416 moment generating functions, 185 money creation, by central/commercial banks, 411–14 motion of the economy see equation of motion Muqaddimah see Introduction to History net national income, 8–9, 71 net production by sector, NNP (net national product), 8–9 optimal control theory, 231 optimal growth theory Beltrami equation, 197–9, 212–13, 222–3, 227–8, 380–1 calculus of variations approach, 189–216, 244–9 central model, 267–9 concavity of production functions, 255 concavity of utility functions, 278 cusp area enlargement, 288–9 differentiating integrals, 208–10 Dorfmanian approach, xx, 231–42, 251, 270–1, 363–6 Dorfmanian extensions, 238–42 economy as steady state, 277–80 end-point conditions, 203–7 equilibrium point, 287 Euler equation see Euler functionals depending on n functions, 199–200 Goodwin model, 343–4, 376 Hamiltonian approach, xx, 231–2, 233–4, 236–7, 250, 270–1 modiied Hamiltonian see Dorfmanian improper integrals, 207–8 King/Rebelo model, 335–7, 344–6, 347, 376 Leibniz formula, 208–10 mainstream problem of, 244 optimal consumption level, 352 optimal growth paths, 272–7 optimal savings rate, xix–xx, 28–30, 34, 165, 266–89, 336–7, 338–46, 347–8, 352, 367–8, 369–76 robustness of, 369–76 optimal time paths, 272–7 optimal trajectories of the economy, 256–63 Ostrogradski equation, 222–3, 225–7, 230, 231–2, 238–42 Pontryagin maximum principle, 164, 231–42, 249–51 Ramsey equation, 245–6 derivations, 248–9 economic variations, 246–9 inite horizon, 248–9 ininite horizon, 247–8 with short time interval, 247 427 Ramsey model, 198, 199, 243, 266, 335–6, 338–43, 376 Ramsey optimal savings-investment rate, 377–81 Ramsey rule differential equations, 251–6 optimal time paths, 251–63 Ramsey utility function, 339, 341–3 real interest rate, 345 Takayama theorem, 201–3, 215–16, 245–6, 270–1, 363 traditional results, 243–63 transversality conditions, 203–7 utility functions see utility functions and welfare, 410–11 see also competitive equilibrium order of the mean p, and elasticity of substitution, 93 Ostrogradski equation, 222–3, 225–7, 230, 231–2, 238–42 Pitchford constant, 120–2, 136, 156 Pitchford, John, 120–1 planned economies black market, 388 collective farming, 384–8 common traits in poor countries, 388–90 broken growth process, 389 closed economies, 389 equality of chances, 389–90 stability of system, 390 consequences of, 384–8 ixed selling price possibilities, 385–8 and growth problems, 383–90 popular communes, 384–8 rationing consequences, 388 separation of powers, 390 state agencies, 384–8 political institutional soundness, 398–400 Pontryagin, Lev, 231–2 Pontryagin maximum principle, 164, 231–42, 249–51 popular communes, 384–8, 401–3 population growth hypothesis, 34, 74–5, 116–18, 124 positive growth theory, overview, 1–2 poverty traps, 68–75 hypotheses, 71 stability analysis hypotheses, 71 technological, 69–71 price equilibrium, 297 price indexes, 9–12 private property growth factor, 394–5 producers’ surplus, 18–19 production factors of, 26–8, 407 net by sector, production function, 28–34, 60, 62–4, 66–7, 157, 163–4 applications, 96–8 www.cambridge.org Cambridge University Press 978-1-107-11523-1 — Economic Growth 2nd Edition Index More Information 428 Index production function (cont.) constants, 87–8 determination, 85–8 as general mean, 92–113 isoquants, 99–105 special cases, 98 theorems, 116–18, 132, 133–4 proits, US inancial sector, 408–10 public debt/GDP ratio, 335 Ramsey, Frank, 198, 199, 243, 266, 335–6, 376 Ramsey model/equation see optimal growth theory Rebelo, Sergio, 335–7, 338–43, 347 rental rate equilibrium, 297 risk premium, 361, 376–7, 407 risk-free transactions, 327 savings, optimal savings rate see optimal growth theory savings rate threshold, 116 savings-investment rate, 116–18, 124, 125–6, 377–81 separation of powers, in planned economies, 390 services, value added of, Sfreddo, Claudio, xx–xxi Sharpe, William, 333–4 Smith, Adam, xviii–xix, 1–2, 377, 392–3, 395, 400–5 society’s activity, 408–11 society’s welfare see welfare Solow, Robert, xx–xxi, 43, 46–9, 76, 84, 85, 92, 111–13, 147, 155–6, 293–5, 316–21 spot price equilibrium, 297 Stoléru, L., 266 supply and demand and ixed prices, 17–18 law of, 16–17 Sydsaeter, J., 271 Tahir b al-Husayn, 399–400, 415 Takayama theorem, 201–3, 215–16, 245–6, 270–1, 363 taxation, excessive taxation and growth, 397–8 technical progress, 132–45 and capital productivity, 156 capital-augmenting, 49, 153, 157, 163–5, 349 and change in CES, 145 cross-section estimates, 145–51 equilibrium/disequilibrium in, 139–40 general speciications, 133–4 and growth, 5, 34, 49–52, 115, 394, 403–5 introduction to, 49–52 labour-augmenting, 49, 153, 163–5, 349 with asymptotic growth, 134–44 results, 133–4, 403–5 time-series estimates, 145–51 technical progress growth factor, 394 technological poverty traps, 69–71 Thanh, Nam Phan, 113 Theory of Wages, 114, 151–2 third case (Solow), 46–8, 49 time-dependent differential equations, 52 Toynbee, Arnold, 1–2 utility functions, xix–xx, 256–63, 267–9, 285, 343–4, 346–9 capital growth rate behaviour, 358 capital-output ratio behaviour, 359 concavity of, 155–6, 163–4, 335, 336, 347, 349–57, 359, 360, 376 consumption behaviour, 357 and Euler equation, 357–60 exponential utility functions, 281–9 negative exponential utility function, 286, 347 in optimal growth theory see optimal growth theory power utility function, 269–81, 347–8 Ramsey’s see optimal growth theory real income per person growth rate, 355 savings rate behaviour, 356 Walras-Leontief case, 43–6, 49, 106, 115 Walras-Leontief production function, 97 Wealth of Nations, xviii–xix, 1–2, 377 welfare and consumption, 360–1 and equal opportunity, 13 and equity, 13 and expenditure, 22 and income, 12–14 and optimal growth, 410–11 welfare lows, 360, 376–7 Williamson, Samuel H., 183–4, 342 world population, 14–15 Yuhn, Ky-Hyang, 116 www.cambridge.org ... has come to public attention Only part of the needed analytical apparatus appears in this book, but it is an important part The many calculations add measurably to the force of the analysis Any... Srinivasan Muthukrishnan, Elisabeth Paté-Cornell, Enrico Saltari, Wolfgang Stummer, Jim Sweeney, Richard Waswo, Juerg Weber and Milad ZarinNejadan, as well as to participants in seminars at Stanford,... Gundlach, Andreas Irmen, Bjarne Jensen, Mathias Jonsson, Rainer Klump, Anastasia Litina, Miguel León-Ledesma, Henri Loubergé, Peter McAdam, Bernardo Maggi, Scott Murff, Srinivasan Muthukrishnan,