Bradley, Teresa () - Essential of Mathematics for Economics and Business (3rd Ed.,) (20161001)

Essential Mathematics for Economics and Business

Teresa Bradley Limerick Institute of Technology  Third Edition

John Wiley & Sons, Ltd

CONTENTS

Introduction

xi

CHAPTER 1 Mathematical Preliminaries 1.1 Some Mathematical Preliminaries 1.2 Arithmetic Operations 1.3 Fractions 1.4 Solving Equations 1.5 Currency Conversions 1.6 Simple Inequalities 1.7 Calculating Percentages 1.8 The Calculator: Evaluation and Transposition of Formulae 1.9 Introducing Excel

1 2 2 5 8 10 15 18 21 27

CHAPTER 2 The Straight Line and Applications 2.1 The Straight Line 2.2 Mathematical Modelling 2.3 Applications: Demand, Supply, Cost, Revenue 2.4 More Mathematics on the Straight Line 2.5 Translations of Linear Functions (on the website) 2.6 Elasticity of Demand, Supply and Income 2.7 Budget and Cost Constraints (on the website) 2.8 Excel for Linear Functions 2.9 Summary

CHAPTER 3 Simultaneous Equations 3.1 Solving Simultaneous Linear Equations 3.2 Equilibrium and Break-even 3.3 Consumer and Producer Surplus 3.4 The National Income Model and the IS-LM Model 3.5 Excel for Simultaneous Linear Equations 3.6 Summary Appendix

37 38 55 60 76 82 83 91 92 97

101 102 111 127 132 137 142 143

[viil] CONTENTS

CHAPTER 4 Non-linear Functions and Applications 4.1 Quadratic, Cubic and Other Polynomial Functions 4.2 Exponential Functions 4.3 Logarithmic Functions 4.4 Hyperbolic Functions of the Form a/(bx + c) 4-5 Excel for Non-linear Functions 4.6 Summary

147 148 170 184 196 202 204

CHAPTER 5 Financial Mathematics 5.1 Arithmetic and Geometric Sequences and Series 5.2 Simple Interest, Compound Interest and Annual Percentage Rates 5.3 Depreciation 5.4 Net Present Value and Internal Rate of Return 5.5 Annuities, Debt Repayments, Sinking Funds 5.6 The Relationship between Interest Rates and the Price of Bonds 5.7 Excel for Financial Mathematics 5.8 Summary Appendix

207 208 216 226 228 234 246 249 252 254

CHAPTER 6 Differentiation and Applications 6.1 Slope of a Curve and Differentiation 6.2 Applications of Differentiation, Marginal Functions, Average Functions 6.3 Optimisation for Functions of One Variable 6.4 Economic Applications of Maximum and Minimum Points 6.5 Curvature and Other Applications 6.6 Further Differentiation and Applications 6.7 Elasticity and the Derivative 6.8 Summary

257 258 268 284 301 317 331 344 354

CHAPTER 7 Functions of Several Variables 7.1 Partial Differentiation 7.2 Applications of Partial Differentiation 7.3 Unconstrained Optimisation 7.4 Constrained Optimisation and Lagrange Multipliers 7.5 Summary

359 360 378 398 408 420

CHAPTER 8 Integration and Applications 8.1 Integration as the Reverse of Differentiation 8.2 The Power Rule for Integration 8.3 Integration of the Natural Exponential Function 8.4 Integration by Algebraic Substitution 8.5 The Definite Integral and the Area under a Curve

425 426 427 433 434 439

[ix]

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CONTENTS

8.6 8.7 8.8 8.9

Consumer and Producer Surplus First-order Differential Equations and Applications Differential Equations for Limited and Unlimited Growth Summary

446 454 466 471

CHAPTER 9 Linear Algebra and Applications 9.1 Linear Programming 9.2 Matrices 9.3 Solution of Equations: Elimination Methods 9.4 Determinants 9.5 The Inverse Matrix and Input/Output Analysis 9.6 Excel for Linear Algebra 9.7 Summary

475 476 486 496 502 516 529 532

CHAPTER 10 Difference Equations 10.1 Introduction to Difference Equations 10.2 Solution of Difference Equations (First-order) 10.3 Applications of Difference Equations (First-order) 10.4 Summary

537 538 540 552 562

Solutions to Progress Exercises

565

Bibliography

651

List of Worked Examples

653

Index

659