An introduction to mathematics for economics

Cover......Page 1
An Introduction to Mathematics for Economics......Page 2
Contents......Page 6
List of illustrations......Page 9
List of tables......Page 12
Preface......Page 14
Acknowledgements......Page 17
1.1 Markets......Page 18
1.2 Demand and supply schedules......Page 20
1.3 Market equilibrium......Page 22
1.4 Rest of this book......Page 24
2 Basic mathematics......Page 25
2.1 Numbers......Page 26
2.2 Fractions, decimal numbers and the use of a calculator......Page 27
2.3 Some algebraic properties of real numbers......Page 28
2.4 Equalities, inequalities and intervals......Page 29
2.5 Powers......Page 30
2.7 Factorisation: reducing polynomial expressions......Page 33
2.8 Equations......Page 36
2.9 Functions......Page 39
2.10 Simultaneous equations: the demand and supply analysis......Page 51
2.11 Logic......Page 60
2.12 Proofs......Page 64
2.13 Additional exercises......Page 70
3.1 Limits......Page 74
3.2 Summation......Page 78
3.3 A geometric series......Page 81
3.4 Compound interest......Page 82
3.5 The exponential function: how can we calculate the compound amount of the principal if interest is compounded continuously?......Page 87
3.6 Logarithms: how many years will it take for my money to double?......Page 92
3.7 Present values......Page 97
3.8 Annuities: what is the value of your home loan?......Page 99
3.9 Perpetuity......Page 103
3.10 Additional exercises......Page 104
4.1 Cost function......Page 107
4.2 The marginal cost and the average costs......Page 109
4.3 Production function......Page 112
4.4 Firm’s supply curve......Page 115
4.5 From a one-unit change to an infinitesimally small change......Page 120
4.6 The relative positions of MC, AC and AV C revisited......Page 127
4.7 Profit maximisation......Page 128
4.8 Additional exercises......Page 138
5.1 Curve sketching......Page 141
5.2 The differential......Page 151
5.3 Elasticity......Page 153
5.4 Additional exercises......Page 161
6 Multivariate calculus......Page 164
6.1 The utility function......Page 165
6.3 The marginal utility for the two-good case......Page 168
6.4 The marginal rate of substitution......Page 174
6.5 Total differentiation and implicit differentiation......Page 176
6.6 Maxima and minima revisited......Page 181
6.7 The utility maximisation problem: constrained optimisation......Page 186
6.8 The substitution method......Page 191
6.9 The Lagrange multiplier method......Page 193
6.10 The individual demand function......Page 196
6.11 Additional exercises......Page 199
7.1 An anti-derivative and the indefinite integral......Page 201
7.2 The fundamental theorem of integral calculus......Page 204
7.3 Application of integration to finance: the present value of a continuous annuity......Page 207
7.4 Demand and supply analysis revisited......Page 212
7.5 The deadweight loss of taxation......Page 223
7.6 Additional exercises......Page 231
Appendix A Matrix algebra......Page 235
A.1 Matrices and vectors......Page 236
A.2 An inverse of a matrix and the determinant: solving a system of equations......Page 245
A.3 An unconstrained optimisation problem......Page 251
B.1 The cobweb model of price adjustment......Page 260
B.2 The linear first-order autonomous difference equation......Page 265
B.3 The linear first-order autonomous differential equation......Page 272
Index......Page 279