Mathematics for Economics and Business, Ninth Edition
Contents:
Preface xi
INTRODUCTION: Getting Started 1
Notes for students: how to use this text 1
Chapter 1 Linear Equations 5
1.1 Introduction to algebra 6
1.1.1 Negative numbers 7
1.1.2 Expressions 9
1.1.3 Brackets 12
Key Terms 17
Exercise 1.1 18
Exercise 1.1* 20
1.2 Further algebra 22
1.2.1 Fractions 22
1.2.2 Equations 29
1.2.3 Inequalities 33
Key Terms 36
Exercise 1.2 36
Exercise 1.2* 38
1.3 Graphs of linear equations 40
Key Terms 51
Exercise 1.3 52
Exercise 1.3* 53
1.4 Algebraic solution of simultaneous linear equations 55
Key Term 65
Exercise 1.4 65
Exercise 1.4* 66
1.5 Supply and demand analysis 67
Key Terms 80
Exercise 1.5 80
Exercise 1.5* 82
1.6 Transposition of formulae 84
Key Terms 91
Exercise 1.6 91
Exercise 1.6* 92
1.7 National income determination 93
Key Terms 105
Exercise 1.7 105
Exercise 1.7* 106
Formal mathematics 109
Multiple choice questions 112
Examination questions 116
Chapter 2 Non-linear Equations 121
2.1 Quadratic functions 122
Key Terms 136
Exercise 2.1 137
Exercise 2.1* 138
2.2 Revenue, cost and profit 140
Key Terms 148
Exercise 2.2 148
Exercise 2.2* 150
2.3 Indices and logarithms 151
2.3.1 Index notation 151
2.3.2 Rules of indices 155
2.3.3 Logarithms 161
2.3.4 Summary 167
Key Terms 168
Exercise 2.3 168
Exercise 2.3* 170
2.4 The exponential and natural logarithm functions 172
Key Terms 182
Exercise 2.4 182
Exercise 2.4* 183
Formal mathematics 186
Multiple choice questions 189
Examination questions 193
Chapter 3 Mathematics of Finance 197
3.1 Percentages 198
3.1.1 Index numbers 204
3.1.2 Inflation 208
Key Terms 210
Exercise 3.1 210
Exercise 3.1* 213
3.2 Compound interest 216
Key Terms 226
Exercise 3.2 226
Exercise 3.2* 228
3.3 Geometric series 230
Key Terms 238
Exercise 3.3 238
Exercise 3.3* 239
3.4 Investment appraisal 241
Key Terms 253
Exercise 3.4 253
Exercise 3.4* 255
Formal mathematics 257
Multiple choice questions 259
Examination questions 263
Chapter 4 Differentiation 267
4.1 The derivative of a function 268
Key Terms 277
Exercise 4.1 277
Exercise 4.1* 278
4.2 Rules of differentiation 279
Rule 1 The constant rule 279
Rule 2 The sum rule 280
Rule 3 The difference rule 281
Key Terms 286
Exercise 4.2 286
Exercise 4.2* 288
4.3 Marginal functions 290
4.3.1 Revenue and cost 290
4.3.2 Production 297
4.3.3 Consumption and savings 299
Key Terms 301
Exercise 4.3 301
Exercise 4.3* 302
4.4 Further rules of differentiation 304
Rule 4 The chain rule 305
Rule 5 The product rule 307
Rule 6 The quotient rule 310
Exercise 4.4 312
Exercise 4.4* 313
4.5 Elasticity 314
Key Terms 326
Exercise 4.5 326
Exercise 4.5* 327
4.6 Optimisation of economic functions 329
Key Terms 345
Exercise 4.6 345
Exercise 4.6* 347
4.7 Further optimisation of economic functions 348
Key Term 359
Exercise 4.7* 359
4.8 The derivative of the exponential and natural logarithm functions 361
Exercise 4.8 370
Exercise 4.8* 371
Formal mathematics 373
Multiple choice questions 376
Examination questions 382
Chapter 5 Partial Differentiation 389
5.1 Functions of several variables 390
Key Terms 400
Exercise 5.1 401
Exercise 5.1* 402
5.2 Partial elasticity and marginal functions 404
5.2.1 Elasticity of demand 404
5.2.2 Utility 407
5.2.3 Production 413
Key Terms 415
Exercise 5.2 416
Exercise 5.2* 418
5.3 Comparative statics 420
Key Terms 429
Exercise 5.3* 429
5.4 Unconstrained optimisation 433
Key Terms 444
Exercise 5.4 444
Exercise 5.4* 445
5.5 Constrained optimisation 447
Key Terms 456
Exercise 5.5 457
Exercise 5.5* 458
5.6 Lagrange multipliers 460
Key Terms 468
Exercise 5.6 469
Exercise 5.6* 470
Formal mathematics 472
Multiple choice questions 474
Examination questions 477
Chapter 6 Integration 483
6.1 Indefinite integration 484
Key Terms 495
Exercise 6.1 496
Exercise 6.1* 497
6.2 Definite integration 499
6.2.1 Consumer’s surplus 503
6.2.2 Producer’s surplus 504
6.2.3 Investment flow 506
6.2.4 Discounting 508
Key Terms 509
Exercise 6.2 509
Exercise 6.2* 510
Formal mathematics 513
Multiple choice questions 515
Examination questions 518
Chapter 7 Matrices 523
7.1 Basic matrix operations 524
7.1.1 Transposition 526
7.1.2 A ddition and subtraction 527
7.1.3 Scalar multiplication 530
7.1.4 Matrix multiplication 531
7.1.5 Summary 539
Key Terms 539
Exercise 7.1 540
Exercise 7.1* 542
7.2 Matrix inversion 545
Key Terms 560
Exercise 7.2 560
Exercise 7.2* 561
7.3 Cramer’s rule 564
Key Term 572
Exercise 7.3 572
Exercise 7.3* 573
Formal mathematics 576
Multiple choice questions 577
Examination questions 581
Chapter 8 Linear Programming 585
8.1 Graphical solution of linear programming problems 586
Key Terms 600
Exercise 8.1 601
Exercise 8.1* 602
8.2 Applications of linear programming 604
Key Terms 612
Exercise 8.2 612
Exercise 8.2* 614
Formal mathematics 617
Multiple choice questions 618
Examination questions 623
Chapter 9 Dynamics 627
9.1 Difference equations 628
9.1.1 National income determination 634
9.1.2 Supply and demand analysis 636
Key Terms 639
Exercise 9.1 639
Exercise 9.1* 640
9.2 Differential equations 643
9.2.1 National income determination 649
9.2.2 Supply and demand analysis 651
Key Terms 653
Exercise 9.2 654
Exercise 9.2* 655
Formal mathematics 658
Multiple choice questions 659
Examination questions 662
Answers to Problems 664
Chapter 1 664
Chapter 2 674
Chapter 3 683
Chapter 4 687
Chapter 5 698
Chapter 6 705
Chapter 7 709
Chapter 8 715
Chapter 9 719
Glossary 723
Index 730
Preface:
This text is intended primarily for students on economics, business studies and management courses. It assumes very little prerequisite knowledge, so it can be read by students who have not undertaken a mathematics course for some time. The style is informal, and the text contains a large number of worked examples. Students are encouraged to tackle problems for themselves as they read through each section. Detailed solutions are provided so that all answers can be checked. Consequently, it should be possible to work through this text on a self-study basis. The material is wide ranging and varies from elementary topics such as percentages and linear equations to more sophisticated topics such as constrained optimisation of multivariate functions. The text should therefore be suitable for use on both low- and high-level quantitative methods courses.
This text was first published in 1991. The prime motivation for writing it then was to try to produce a text that students could actually read and understand for themselves. This remains the guiding principle when writing this ninth edition. One of the main improvements is the inclusion of over 200 additional questions. Each chapter now ends with both multiple choice questions and a selection of longer examination-style questions.
Students usually enjoy tackling multiple choice questions since they provide a quick way of testing recall of the material covered in each chapter. Several universities include multiple choice as part of their assessment. The final section in each chapter entitled “Examination Questions” contains longer problems which require knowledge and understanding of more than one topic. Although these have been conveniently placed at the end of each chapter it may be best to leave these until the end of the academic year so that they can be used during the revision period just before the examinations.