Studies in Contemporary Economics

Transcription

1 Studies in Contemporary Economics Philosophy of Economics. Proceedings, Edited by W StegmOller, W Balzer and W Spohn. VIII, 306 pages B. Hamminga, Neoclassical Theory Structure and Theory Development. IX, 174 pages J. Dermine, Pricing Policies of Financial Intermediaries.VII, 174 pages Economic Consequences of Population Change in Industrialized Countries. Proceedings Edited by G. Steinmann. X, 415 pages Problems of Advanced Economies. Proceedings, Edited by N. Miyawaki. VI, 319 pages Studies in Labor Market Dynamics. Proceedings, Edited by G. R. Neumann and N. C. Westergard-Nielsen. X, 285 pages The Economics ofthe Shadow Economy. Proceedings, Edited by W Gaertner and A. Wenig. XlV, 214 pages A. Pfingsten, The Measurement of Tax Progression. VI, 131 pages T. M. Devinney, Rationing in a Theory of the Banking Firm. VI, 102 pages Causes of Contemporary Stagnation. Proceedings, Edited by H. Frisch and B. Gahlen. IX, 216 pages K E. Schenk, New Institutional Dimensions of Economics. IX, 196 pages O. Raaten, The Economics of Multispecies Harvesting. VII, 162 pages D. Laussel, W Marois, A. Soubeyran, (Eds.), Monetary Theory and Policy. Proceedings, XVIII, 383 pages G. RObel, Factors Determining External Debt. VI, 264 pages B. C. J. van Velthoven, The Endogenization of Government Behaviour in Macroeconomic Models. XI, 367 pages A. Wenig, K F. Zimmermann (Eds.), Demographic Change and Economic Development. XII, 325 pages D. Suhr, The Capitalistic Cost-Benefit Structure of Money. X, 136 pages J. K Brunner, Theory of Equitable Taxation. VIII, 217 pages p. S. A. Renaud, Applied Political Economic Modelling. XII, 242 pages, E. van Imhoff, Optimal Economic Growth and Non-Stable Population. IX, 218 pages

2 Studies in Contemporary Economics Evert van Imhoff Optimal Economic Growth and Non-Stable Population Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong

3 Dr. LENNART BENGTSSON, European Centre for Medium Range Weather Forecasts, Shlnfield Park, Reading, Berkshire RG2 9AX 1 England Sir JAMES LIGHTHILL, University College London Gower Street, London WClE 6BT 1 England Series Editors: Professor Dr. MICHAEL GHIL Courant Institute of Mathematical Sciences, New York University 251 Mercer Street, New York, NY USA Professor Dr. JORGEN SONDERMANN Universitiit Hamburg, Institut fur Meereskunde Heimhuder StraBe 71, 2000 Hamburg 13 1 FRG Professor Dr. ROBERT SADOURNY Laboratoire de Meteorologie Dynarnique, Ecole Normale Superieure 24 rue Lhomond, Paris Cedex 05 1 France ISBN-13: e- ISBN-i3 : DOl: / Library of Congress Cataloging in Publication Data. Main entry under title: Intense atmospheric vortices. (Topics in atmospheric and oceanographic sciences) Symposium sponsored by the International Union oftheoreticai and Applied Mechanics and the International Union of Geodesy and Geophysics, and held at the European Centre for Medium Range Weather Forecasts. Bibliography: p. 1. Vortex-motion--Congresses. 2. Tropics-Cyc!ones--Congresses. 3. Tornadoes--Congresses.l. Bengtsson, Lennart. II. Lighthill, M. J., Sir. III. International Union of Theoretical and Applied Mechanics. IV. International Union of Geodesy and Geophysics. V. Series. QC880.4:V6I ' This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law, wheroe copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. by Springer-Verlag, Berlin Heidelberg The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2132/

4 PREFACE AND ACKNOWLEDGEMENTS When I joined the Erasmus University of Rotterdam, in January 1985, Jo Ritzen did not waste much time in rousing my interest for growth theory and population economics. It was he who suggested the subject for the research reported in this book (which is a slightly revised version of my Ph.D. dissertation), thereby sending me on an adventurous journey into the unknown. This journey has not been an easy one, with ups and downs changing places at regular intervals. Especially during those downs, having Jo Ritzen as my supervisor proved to be a wonderful experience. I am deeply indebted to him for his never wavering encouragement and assistance. Several people made valuable comments on earlier drafts of (parts of) the manuscript. They are Harry van Dalen, Onno van Hilten, Miriam King, Joop Odink and Ton Vorst. Chapter 4.2, "A model with exogenous embodied technical change", was written in the summer of 1987 during a stay at the International Institute for Applied Systems Analysis in Laxenburg, Austria. I am grateful for the opportunities it provided me with. Mrs. Amy Gons-Daugherty agreed to teach me one final lesson in English and corrected my errors with an almost frustrating eye for even the smallest detail. She has been a great help. Finally, I have to thank those who contributed to the necessary atmosphere which enabled me to finish this work. At the university, the pleasant surroundings were created by my colleagues at the Department of Public Finance and Fiscal Law. At home, most of the burden was taken by Annelies. Without her, life would have been much more difficult and much less interesting.

5 TABLE OF CONTENTS 1 Introduction 1.1 Growth theory and demographic change 1.2 Optimal economic growth 1.3 Population dynamics and economic development 1.4 Research goals and outline of the book Optimal economic growth in the simple one-sector growth model 2.1 The simple one-sector growth model Population and labour Production and investment Social welfare 2.2 The Non-Stationary Golden Rule 2.3 Comparative statics and the Golden Rule 2.4 Optimal population growth 2.5 The non-stationary optimal growth path 2.6 Summary Technical change and economic growth 3.1 On the concept of technical change 3.2 Classifications of technical change Exogenous vs. endogenous technical change Neutral vs. biased technical change Embodied vs. disembodied technical change 3.3 Technical change in one-sector growth models Optimal economic growth under conditions of technical change 4.1 A model with exogenous disembodied technical change The Generalized Golden Rule Comparative statics The non-stationary optimal growth path Summary

6 VI Contents A model with exogenous embodied technical change The fixed-coefficients capital vintage model Optimal economic growth Comparative statics Stability of steady states Second-order conditions The non-stationary optimal growth path Summary A model with endogenous technical change The Golden Rule of Research Comparative statics The non-stationary optimal growth path Summary Appendix to Chapter Education and economic growth 5.1 Economics and education 5.2 Education as a production process Educational outputs Educational inputs Functional form 5.3 Selection of models Optimal economic growth and investment in education 6.1 A model with homogeneous human capital Homogeneous human capital in a model of overlapping generations Optimal investment in education Comparative statics The non-stationary optimal growth path Summary 6.2 A model with heterogeneous human capital Optimal control with integral state equations and bounded controls The model with two types of labour Optimal economic growth Comparative statics Dynamics Summary

7 Contents VII 7 Optimal educational policy under conditions of technical change 7.1 Education and exogenous disembodied technical change Optimal investment in education Comparative statics Summary 7.2 A model with education as transmitter of technical change Education and labour-embodied technical progress Optimal economic growth Comparative statics The non-stationary optimal growth path Summary Simulations for the Netherlands 8.1 Demographic data 8.2 Simulation for the model with homogeneous human capital 8.3 Simulations for the model with heterogeneous human capital Summary and evaluation 9.1 Summary 9.2 Evaluation References Author index

8 LIST OF TABLES 2.1 Comparative-statics results for the simple one-sector 24 growth model 2.2 Characteristics of the non-stationary optimal growth path Parameters used for illustrations in Figures 2.2 and Classifications of technical change in one-sector growth models Comparative-statics results for the one-sector model 64 with exogenous disembodied labour-augmenting technical change Selected numerical steady-state values Comparative-statics effects Parameters used in the simulation The simulated non-stationary optimal economic growth path Comparative-statics results for the one-sector model with endogenous disembodied labour-augmenting technical change Parameters used for illustrations in Figures and Optimal economic growth path with gb falling Optimal economic growth path with gb rising Comparative-statics results for the one-sector model 132 with homogeneous human capital Parameters used for illustrations in Figures and Optimal economic growth path with gb falling Optimal economic growth path with gb rising Selected numerical steady-state values Comparative-statics results for the one-sector model 151 with heterogeneous human capital Selected numerical steady-state values for the 168 optimal age-training profile Selected numerical steady-state values Comparative-statics results for the one-sector model with labour-embodied technical change Optimal economic growth path with gb falling Age-specific survival schedule Demographic time series Parameters used with model Parameters used with model Values of the social welfare function 198

9 LIST OF FIGURES 1.1 The age-composition of the population in the Netherlands 2.1 Phase diagram in (k,~)-space 2.2 Optimal economic growth with gb falling 2.3 Optimal economic growth with gb rising The effect of labour-augmentation on the long-run optimal consumption path The double integral before changing the order of integration The double integral after changing the order of integration The simulated non-stationary optimal economic growth path Optimal economic growth path with gb falling Optimal economic growth path with gb rising 4.3.Al Phase diagram for s-l - case A2 Phase diagram for s~l - case A3 Uzawa's phase diagram for s-l 4.3.A4 Phase diagram for s=o Optimal economic growth path with gb falling Optimal economic growth path with gb rising 8.1 Growth rates of births and total population Case study with model 7.1 factor prices and ratio Case study with model 7.1 age-training profiles Case study with model 7.1 age-ability profiles Case study with model 7.1 human capital and labour force Case study with model 7.1 savings rate and consumption Case studies with model 6.2 the enrollment rate Case studies with model 6.2 the savings rate Case studies with model 6.2 the unskilled/skilled labour ratio Case studies with model 6.2 the capital/skilled-labour ratio Case studies with model 6.2 consumption per capita