Applied Mathematical Demography
What follows is a new edition of the second in a series of three books providing an account of the mathematical development of demography. The first, Introduction to the Mathematics of Population (Addison-Wesley, 1968), gave the mathematical background. T
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Ingram Olkin
Nathan Keyfitz
Applied Mathematical DeInography Second Edition
With 41 Illustrations
Springer Science+Business Media, LLC
Nathan Keyfitz IIASA A-2361 Laxenburg Austria
Series Advisors Stephen Fienberg Department of Statistics Carnegie-Melon University Pittsburgh, PA 15213
Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305
U.S.A.
U.S.A.
AMS Subject Classifications: 92A15, 62P99 Library of Congress Cataloging in Publication Data Keyfitz, Nathan Applied mathematical demography. (Springer texts in statistics) Bibliography: p. Includes index. 1. Demography - Mathematical models. 1. Title. II. Series. HB849.51.K49 1985 304.6'01'51 85-16430
© 1985 by Springer Science+Business Media New York Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1985 Softcover reprint ofthe hardcover 2nd edition 1985 AII rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer Science+Business Media, LLC.
Typeset by J. W. Arrowsmith Ud., Bristol, England.
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ISBN 978-1-4757-1881-2 ISBN 978-1-4757-1879-9 (eBook) DOI 10.1007/978-1-4757-1879-9
To the students at Chicago, Berkeley, and Harvard who are responsible for any merit this book may have
PREFACE TO THE SPRINGER EDITION
What follows is a new edition of the second in a series of three books providing an account of the mathematical development of demography. The first, Introduction to the Mathematics of Population (Addison-Wesley, 1968), gave the mathematical background. The second, the original of the present volume, was concerned with demography itself. The third in the sequence, Mathematics Through Problems (with John Beekman; SpringerVerlag, 1982), supplemented the first two with an ordered sequence of problems and answers. Readers interested in the mathematics may consult the earlier book, republished with revisions by Addison-Wesley in 1977 and still in print. There is no overlap in subject matter between Applied Mathematical Demography and the Introduction to the Mathematics of Population. Three new chapters have been added, dealing with matters that have come recently into the demographic limelight: multi-state calculations, family demography, and heterogeneity.
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PREFACE
This book is concerned with commonsense questions about, for instance, the effect of a lowered death rate on the proportion of old people or the effect of abortions on the birth rate. The answers that it reaches are not always commonsense, and we will meet instances in which intuition has to be adjusted to accord with what the mathematics shows to be the case. Even when the intuitive answer gives the right direction of an effect, technical analysis is still needed to estimate its amount. We may see intuitively that the drop from an increasing to a stationary population will slow the promotion for the average person in a factory or office, but nothing short of an integral equation can show that each drop of I percent in the rate of increase will delay p
