Economics Express: Quantitative Methods

269 Pages·2013·14.564 MB·English

by  Ian Jacques

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Quantitative Methods
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E
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Quantitative i
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Methods
Ian Jacques
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PEARSON EDUCATION LIMITED
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Tel: [phone]
Web: www.pearson.com/uk
First published 2013 (print)
© Pearson Education Limited 2013 (print)
© Pearson Education Limited 2013 (print and electronic)
The right(s) of Ian Jacques to be identified as author of this work has been asserted by him in accordance with
the Copyright, Designs and Patents Act 1988.
The print publication is protected by copyright. Prior to any prohibited reproduction, storage in a retrieval sys-
tem, distribution or transmission in any form or by any means, electronic, mechanical, recording or otherwise,
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ISBN: 978-0-273-77616-1 (print)
978-0-273-77618-5 (PDF)
978-0-273-78557-6 (eText)
British Library Cataloguing-in-Publication Data
A catalogue record for the print edition is available from the British Library
Library of Congress Cataloging-in-Publication Data
A catalogue record for the print edition is available from the Library of Congress
Jacques, Ian, 1957–
Economics express: quantitative methods/Ian Jacques.
pages cm
Includes index.
ISBN 978-0-273-77616-1
1. Economics–Mathematical models. 2. Economics, Mathematical. I. Title.
HG135.J318 2013
330.01′519–dc23
2013019287
10 9 8 7 6 5 4 3 2 1
17 16 15 14 13
Print edition typeset in 9.5/12.5 pt Scene std by 71
Print edition printed and bound in Great Britain by Henry Ling Ltd., at the Dorset Press, Dorchester, Dorset
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Contents
Series Introduction vii
Introduction xi
1 Foundations 1
2 Financial mathematics 25
3 Functions of one variable 43
4 Further differentiation and integration 61
5 Functions of several variables 79
6 Linear mathematics 99
7 Descriptive statistics 119
8 Probability distributions 137
9 Sampling and estimation 163
10 Hypothesis testing 183
11 Chi-squared distribution 203
12 Correlation and regression 221
And finally, before the assessment . . . 237
Glossary 243
Read to impress 249
Index 251
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Supporting Resources
➔ Understand key concepts quickly
Printable versions of the Topic maps give an overview of the subject and help
you plan your revision
Test yourself on key definitions with the online Flashcards
➔ Revise effectively
Check your understanding and practise for exams with the multiple choice
questions
➔ Improve your confidence
Attempt the Specimen Examination Questions and compare your answers with
the worked solutions provided.
All this and more can be found at www.pearsoned.co.uk/econexpress
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Introduction – Economics
Express series
From the series editor, Professor Stuart Wall
Welcome to Economics Express – a series of short books to help you to
● take exams with confidence
● prepare for assessments with ease
● understand quickly
● and revise effectively
There has never been a more exciting time to study economics, given the shock
to so many individuals, institutions and countries in 2007/8 when long established
economic certainties were suddenly brought into question. The so-called ‘credit
crunch’ overpowered both financial and non-financial organisations. Government
bail-outs of banks and businesses became the order of the day in many coun-
tries, with massive increases in government expenditures to fund these bail-outs,
quickly followed by austerity budgets aimed at restoring national debts and
budget deficits to pre-credit crunch levels. Looking forward, there is as much talk
about ‘triple-dip’ recessions as there is about recovery.
As you embark on your economic journey, this series of books will be your com-
panions. They are not intended to be a replacement for the lectures, textbooks,
seminars or further reading suggested by your lecturers. Rather, as you come to
an exam or an assessment, they will help you to revise and prepare effectively.
Whatever form your assessment takes, each book in the series will help you build
up the skills and knowledge to maximise your performance.
You can find more detail of the features contained in this book and which will
help develop your assessment skills in the ‘Guided Tour’ on page ix.
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Acknowledgements
I would like to thank my wife, Victoria, for her careful checking of the
manuscript, and her suggestions on how the text could be improved.
Ian Jacques
Series editor’s acknowledgements
I am extremely grateful to Kate Brewin and Gemma Doel at Pearson Education
for their key roles in shaping this series. I would also like to thank the many lectur-
ers and students who have so helpfully reviewed the key features of this series
and whose responses have encouraged us to believe that many others will also
benefit from the approaches we have adopted throughout this series.
Stuart Wall
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Guided tour
➔ Understand key concepts quickly
Simultaneous equations
eqLuinaetiaorns Market equilibrium
National income models
Quadratic Factorisation
equations Quadratic formula Start to plan your
revision using the
Foundations
Topic maps.
Supply and demand
Graphs of Total revenue
economic Total cost
functions Average cost
Profit
Fractional and negative powers
Indices and Rules of indices
logarithms Homogeneous production functions
Rules of logs
Equations involving powers
Grasp Key definitions
Key definition
quickly using this
The 95% confidence interval for a population mean is the range from
handy box. Use the
s s
flashcards online to x-1.96 to x+1.96 .
n n
test yourself. 2 2
➔ Revise Effectively
Prepare for upcoming
exams and tests using
Assessment question
the Assessment
Could you answer this question? Guidelines on answering the question are
presented at the end of this chapter. question at the start of
A firm’s fixed costs are 66 and the variable costs are 2 per unit. The each chapter, and the
corresponding profit function is p=aQ2+bQ+c.
Assessment advice
(a) Write down expressions for the total and average cost functions, and
sketch their graphs. throughout the chapter.
(b) Explain why c=-66.
(c) The firm makes a loss of 18 when Q = 2 and a profit of 24 when Q = 5.
(i) Write down a pair of simultaneous equations and solve them to
find a and b. Assessment advice
● Practise the elimination method for solving simultaneous equations,
especially when there are three equations. Common mistakes include
forgetting to multiply the right-hand side as well as the left-hand side
and failing to deal correctly with negative terms such as -2y-(-7y)
(which should equal 5y).
● The solution of equations (including simultaneous equations) can
always be checked by substituting the answers back into the original
equations.
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