An Introduction to Mathematics for Economics

Cambridge University Press 978-1-107-00760-4 - An Introduction to Mathematics for Economics Akihito Asano Frontmatter More information

An Introduction to Mathematics for Economics

An Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a background in economics is not essential, as it aims to help students appreciate that learning mathematics is relevant to their overall understanding of the subject. Economic and financial applications are explained in detail before students learn how mathematics can be used, enabling students to learn how to put mathematics into practice. Starting with a revision of basic mathematical principles the second half of the book introduces calculus, emphasising economic applications throughout. Appendices on matrix algebra and difference/differential equations are included for the benefit of more advanced students. Other features, including worked examples and exercises, help to underpin the readers' knowledge and learning. Akihito Asano has drawn upon his own extensive teaching experience to create an unintimidating yet rigorous textbook.

Akihito Asano is Associate Professor of Economics at the Faculty of Liberal Arts, Sophia University, Tokyo. He has previously held positions at the University of Melbourne and the Australian National University (ANU). In 2008 he received the Award for Teaching Excellence from the College of Business and Economics at the ANU. He currently teaches introductory and intermediate microeconomics, international trade and introduction to game theory to undergraduate students, and mathematical techniques in economics to graduate students.

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Cambridge University Press 978-1-107-00760-4 - An Introduction to Mathematics for Economics Akihito Asano Frontmatter More information

? in this web service Cambridge University Press



Cambridge University Press 978-1-107-00760-4 - An Introduction to Mathematics for Economics Akihito Asano Frontmatter More information

An Introduction to Mathematics for Economics

AKIHITO ASANO

? in this web service Cambridge University Press



Cambridge University Press 978-1-107-00760-4 - An Introduction to Mathematics for Economics Akihito Asano Frontmatter More information

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sa~o Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York Information on this title: 9780521189460 C Akihito Asano 2013 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 2013 Printed and Bound in Great Britain by the MPG Books Group A catalogue record for this publication is available from the British Library ISBN 978-1-107-00760-4 Hardback ISBN 978-0-521-18946-0 Paperback

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Cambridge University Press 978-1-107-00760-4 - An Introduction to Mathematics for Economics Akihito Asano Frontmatter More information

Contents

List of illustrations List of tables Preface Acknowledgements

page viii xi

xiii xvi

1 Demand and supply in competitive markets

1

1.1 Markets

1

1.2 Demand and supply schedules

3

1.3 Market equilibrium

5

1.4 Rest of this book

7

2 Basic mathematics

8

2.1 Numbers

9

2.2 Fractions, decimal numbers and the use of a calculator

10

2.3 Some algebraic properties of real numbers

11

2.4 Equalities, inequalities and intervals

12

2.5 Powers

13

2.6 An imaginary number and complex numbers

16

2.7 Factorisation: reducing polynomial expressions

16

2.8 Equations

19

2.9 Functions

22

2.10 Simultaneous equations: the demand and supply analysis

34

2.11 Logic

43

2.12 Proofs

47

2.13 Additional exercises

53

3 Financial mathematics

57

3.1 Limits

57

3.2 Summation

61

3.3 A geometric series

64

3.4 Compound interest

65

3.5 The exponential function: how can we calculate the compound amount of

the principal if interest is compounded continuously?

70

3.6 Logarithms: how many years will it take for my money to double?

75

3.7 Present values

80

3.8 Annuities: what is the value of your home loan?

82

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