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Tables of Contents for Basic Mathematics for Economists
Chapter/Section Title
Page #
Page Count
Preface
ix
Preface to Second Edition
xi
Acknowledgements
xii
Introduction
1
7
Why study mathematics?
1
2
Calculators and computers
3
2
Using the book
5
3
Arithmetic
8
26
Revision of basic concepts
8
1
Multiple operations
9
2
Brackets
11
1
Fractions
12
3
Elasticity of demand
15
3
Decimals
18
3
Negative numbers
21
2
Powers
23
3
Roots and fractional powers
26
3
Logarithms
29
5
Introduction to algebra
34
29
Representation
34
2
Evaluation
36
2
Simplification: addition and subtraction
38
2
Simplification: multiplication
40
5
Simplification: factorizing
45
4
Simplification: division
49
2
Solving simple equations
51
5
The summation sign Σ
56
3
Inequality signs
59
4
Graphs and functions
63
46
Functions
63
2
Inverse functions
65
3
Graphs of linear functions
68
5
Fitting linear functions
73
3
Slope
76
5
Budget constraints
81
5
Non-linear functions
86
4
Composite functions
90
5
Using Excel to plot functions
95
4
Functions with two independent variables
99
5
Summing functions horizontally
104
5
Linear equations
109
59
Simultaneous linear equation systems
109
1
Solving simultaneous linear equations
110
1
Graphical solution
110
2
Equating to same variable
112
3
Substitution
115
1
Row operations
116
2
More than two unknowns
118
3
Which method?
121
5
Comparative statics and the reduced form of an economic model
126
9
Price discrimination
135
6
Multiplant monopoly
141
27
Appendix: linear programming
148
20
Quadratic equations
168
21
Solving quadratic equations
168
1
Graphical solution
169
4
Factorization
173
3
The quadratic formula
176
2
Quadratic simultaneous equations
178
4
Polynomials
182
7
Financial mathematics: series, time and investment
189
58
Discrete and continuous growth
189
2
Interest
191
5
Part year investment and the annual equivalent rate
196
6
Time periods, initial amounts and interest rates
202
5
Investment appraisal: net present value
207
11
The internal rate of return
218
6
Geometric series and annuities
224
6
Perpetual annuities
230
4
Loan repayments
234
6
Other applications of growth and decline
240
7
Introduction to calculus
247
25
The differential calculus
247
2
Rules for differentiation
249
3
Marginal revenue and total revenue
252
6
Marginal cost and total cost
258
3
Profit maximization
261
2
Respecifying functions
263
2
Point elasticity of demand
265
2
Tax yield
267
2
The Keynesian multiplier
269
3
Unconstrained optimization
272
19
First-order conditions for a maximum
272
1
Second-order condition for a maximum
273
3
Second-order condition for a minimum
276
1
Summary of second-order conditions
277
3
Profit maximization
280
2
Inventory control
282
3
Comparative static effects of taxes
285
6
Partial differentiation
291
43
Partial differentiation and the marginal product
291
5
Further applications of partial differentiation
296
11
Second-order partial derivatives
307
5
Unconstrained optimization: functions with two variables
312
13
Total differentials and total derivatives
325
9
Constrained optimization
334
30
Constrained optimization and resource allocation
334
1
Constrained optimization by substitution
334
8
The Lagrange multiplier: constrained maximization with two variables
342
6
The Lagrange multiplier: second-order conditions
348
2
Constrained minimization using the Lagrange multiplier
350
5
Constrained optimization with more than two variables
355
9
Further topics in calculus
364
31
Overview
364
1
The chain rule
364
8
The product rule
372
5
The quotient rule
377
4
Individual labour supply
381
3
Integration
384
4
Definite integrals
388
7
Dynamics and difference equations
395
37
Dynamic economic analysis
395
1
The cobweb: iterative solutions
396
9
The cobweb: difference equation solutions
405
9
The lagged Keynesian macroeconomic model
414
12
Duopoly price adjustment
426
6
Exponential functions, continuous growth and differential equations
432
33
Continuous growth and the exponential function
432
2
Accumulated final values after continuous growth
434
3
Continuous growth rates and initial amounts
437
3
Natural logarithms
440
6
Differentiation of logarithmic functions
446
1
Continuous time and differential equations
447
1
Solution of homogeneous differential equations
448
4
Solution of non-homogeneous differential equations
452
4
Continuous adjustment of market price
456
5
Continuous adjustment in a Keynesian macroeconomic model
461
4
Matrix algebra
465
45
Introduction to matrices and vectors
465
4
Basic principles of matrix multiplication
469
3
Matrix multiplication -- the general case
472
6
The matrix inverse and the solution of simultaneous equations
478
3
Determinants
481
3
Minors, cofactors and the Laplace expansion
484
3
The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula
487
5
Application of the matrix inverse to the solution of linear simultaneous equations
492
5
Cramer's rule
497
2
Second-order conditions and the Hessian matrix
499
6
Constrained optimization and the bordered Hessian
505
5
Answers
510
13
Symbols and terminology
523
2
Index
525