Pre Mba

PreMBA Analytical Primer

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PreMBA Analytical Primer
Essential Quantitative Concepts for Business Math

Regina Treviño

PREMBA ANALYTICAL PRIMER

Copyright © Regina Treviño, 2008. All rights reserved. First published in 2008 by PALGRAVE MACMILLAN® in the United States—a division of St. Martin’s Press LLC, 175 Fifth Avenue, New York, NY 10010. Wherethis book is distributed in the UK, Europe and the rest of the world, this is by Palgrave Macmillan, a division of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Palgrave® and Macmillan®are registered trademarks in the United States, the United Kingdom, Europe and other countries. ISBN-13: 978–0–230–60912–9 (hardcover) ISBN-10: 0–230–60912–0 (hardcover) ISBN-13: 978–0–230–60913–6 (paperback) ISBN-10: 0–230–60913–9 (paperback) Library of Congress Cataloging-in-Publication Data Trevino, Regina. PreMBA analytical primer : essential quantitative concepts for business math / ReginaTrevino. p. cm. Includes bibliographical references and index. ISBN 0–230–60913–9 1. Business mathematics. 2. Investments—Mathematics. I. Title. HF5691.T74 2008 650.01 513—dc22 2008006209

A catalogue record of the book is available from the British Library. Design by Newgen Imaging Systems (P) Ltd., Chennai, India. First edition: October 2008 10 9 8 7 6 5 4 3 2 1 Printed in the United States ofAmerica.

a mi esposo Paul

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C o n te n ts

Preface Mathematical Symbols and Abbreviations 1 Business Math: Functions and Graphs 1.1 Functions Application 1.1 The Revenue Function 1.1.1 Multivariate Functions Application 1.2 The Demand and Supply Functions 1.2 Graphing Functions Application 1.3 The Demand Curve 1.3 Equations 1.4 Linear Functions 1.4.1Solving Linear Equations Application 1.4 Linear Demand Curves 1.4.2 Solving Linear Inequalities 1.5 Slopes and Intercepts of Linear Equations 1.5.1 Slope-Intercept Form of a Line Application 1.5 Graphing a Linear Demand Curve 1.5.2 Finding the Equation of a Line 1.5.3 General Linear Form of a Line Application 1.6 The Consumer’s Budget Constraint 1.5.4 Horizontal and Vertical Lines 1.6 SolvingTwo-Variable Systems of Linear Equations Application 1.7 Market Equilibrium 1.7 Properties of Functions Application 1.8 Kinked Budget Constraints 1.8 Exponents Application 1.9 Cobb-Douglas Production Function 1.8.1 Radicals and Fractional Exponents 1.8.2 Homogenous Functions Application 1.10 Constant Returns to Scale 1.9 Changes and Growth Rates 1.9.1 Growth Rate Formulas Application 1.11 The Sources ofEconomic Growth

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CONTENTS

1.9.2 Index Numbers Application 1.12 Consumer Price Index and Inflation Practice Exercises 2 Business Math: Optimization 2.1 Nonlinear Functions 2.2 The Concept of a Derivative 2.2.1 Notation of Derivatives 2.2.2 Rules of Differentiation Application 2.1 MarginalFunctions 2.3 Graphical Interpretation of Derivatives Application 2.2 Marginal Product of Labor 2.4 Additional Topics on Derivatives 2.5 Second Derivatives Application 2.3 Diminishing Marginal Utility 2.6 Partial Derivatives Application 2.4 Partial Derivatives and the Ceteris Paribus Assumption Application 2.5 Income Elasticity of Demand 2.7 Optimization 2.7.1 Unconstrained Optimization Application 2.6Profit Maximization 2.7.2 Constrained Optimization Application 2.7 Consumer’s Utility Maximization Problem 2.8 Exponential and Logarithmic Functions Application 2.8 Continuously Compounded Interest Rate 2.8.1 Logarithmic Functions 2.8.2 The Natural Logarithm Application 2.9 Doubling Time for an Investment 2.8.3 Differentiation of e and ln 2.9 Measuring Areas under Linear Functions Application...