Essential Mathematics for Economics and Business

Until 2012, Teresa Bradley lectured in mathematics and statistics at Limerick Institute of Technology, and has been involved for many years with the University of London on the external Diploma in Economics as well as the BSc in Economics, Business and Management. Teresa Bradley is also author of Essential Statistics for Economics, Business and Management, published by John Wiley & Sons, Ltd.

Introduction xiii

Chapter 1

Mathematical Preliminaries 1

1.1 Some Mathematical Preliminaries 2

1.2 Arithmetic Operations 3

1.3 Fractions 6

1.4 Solving Equations 11

1.5 Currency Conversions 14

1.6 Simple Inequalities 18

1.7 Calculating Percentages 21

1.8 The Calculator. Evaluation and Transposition of Formulae 24

1.9 Introducing Excel 28

Chapter 2

The Straight Line and Applications 37

2.1 The Straight Line 38

2.2 Mathematical Modelling 54

2.3 Applications: Demand, Supply, Cost, Revenue 59

2.4 More Mathematics on the Straight Line 76

2.5 Translations of Linear Functions 82

2.6 Elasticity of Demand, Supply and Income 83

2.7 Budget and Cost Constraints 91

2.8 Excel for Linear Functions 92

2.9 Summary 97

Chapter 3

Simultaneous Equations 101

3.1 Solving Simultaneous Linear Equations 102

3.2 Equilibrium and Break-even 111

3.3 Consumer and Producer Surplus 128

3.4 The National Income Model and the IS-LM Model 133

3.5 Excel for Simultaneous Linear Equations 137

3.6 Summary 142

Appendix 143

Chapter 4

Non-linear Functions and Applications 147

4.1 Quadratic, Cubic and Other Polynomial Functions 148

4.2 Exponential Functions 170

4.3 Logarithmic Functions 184

4.4 Hyperbolic (Rational) Functions of the Form a/(bx + c) 197

4.5 Excel for Non-linear Functions 202

4.6 Summary 205

Chapter 5

Financial Mathematics 209

5.1 Arithmetic and Geometric Sequences and Series 210

5.2 Simple Interest, Compound Interest and Annual Percentage Rates 218

5.3 Depreciation 228

5.4 Net Present Value and Internal Rate of Return 230

5.5 Annuities, Debt Repayments, Sinking Funds 236

5.6 The Relationship between Interest Rates and the Price of Bonds 248

5.7 Excel for Financial Mathematics 251

5.8 Summary 254

Appendix 256

Chapter 6

Differentiation and Applications 259

6.1 Slope of a Curve and Differentiation 260

6.2 Applications of Differentiation, Marginal Functions, Average Functions 270

6.3 Optimisation for Functions of One Variable 286

6.4 Economic Applications of Maximum and Minimum Points 304

6.5 Curvature and Other Applications 320

6.6 Further Differentiation and Applications 334

6.7 Elasticity and the Derivative 347

6.8 Summary 357

Chapter 7

Functions of Several Variables 361

7.1 Partial Differentiation 362

7.2 Applications of Partial Differentiation 380

7.3 Unconstrained Optimisation 400

7.4 Constrained Optimisation and Lagrange Multipliers 410

7.5 Summary 422

Chapter 8

Integration and Applications 427

8.1 Integration as the Reverse of Differentiation 428

8.2 The Power Rule for Integration 429

8.3 Integration of the Natural Exponential Function 435

8.4 Integration by Algebraic Substitution 436

8.5 The Definite Integral and the Area under a Curve 441

8.6 Consumer and Producer Surplus 448

8.7 First-order Differential Equations and Applications 456

8.8 Differential Equations for Limited and Unlimited Growth 468

8.9 Integration by Substitution and Integration by Parts website only

8.10 Summary 474

Chapter 9

Linear Algebra and Applications 477

9.1 Linear Programming 478

9.2 Matrices 488

9.3 Solution of Equations: Elimination Methods 498

9.4 Determinants 504

9.5 The Inverse Matrix and Input/Output Analysis 518

9.6 Excel for Linear Algebra 531

9.7 Summary 534

Chapter 10

Difference Equations 539

10.1 Introduction to Difference Equations 540

10.2 Solution of Difference Equations (First-order) 542

10.3 Applications of Difference Equations (First-order) 554

10.4 Summary 564

Solutions to Progress Exercises 567

Worked Examples 653

Index 659