EEn
Basic Mathematics for Economists, Second Edition
Back Cover
Copyright Info
TOC
Preface
Preface to Second Edition
Acknowledgements
Chapter 1: Introduction
Learning objective
1.1 Why study mathematics?
Quantification
Simplification
Scarcity and choice
Economic statistics and estimating relationships
Mathematics and business
1.2 Calculators and computers
Rubbish in, rubbish out
Algebra
Rounding errors
When should you use calculators and computers?
1.3 Using the book
Practise, practise
Group working
Don’t give up!
Chapter 2: Arithmetic
Learning objectives
2.1 Revision of basic concepts
Example 2.1
Test Yourself, Exercise 2.1
2.2 Multiple operations
Example 2.2
Example 2.3
Example 2.4
Example 2.5
Test Yourself, Exercise 2.2
2.3 Brackets
Example 2.6
Example 2.7
Test Yourself, Exercise 2.3
2.4 Fractions
Example 2.8
Example 2.9
Example 2.10
Example 2.11
Example 2.12
Example 2.13
Example 2.14
Example 2.15
Example 2.16
Example 2.17
Test Yourself, Exercise 2.4
2.5 Elasticity of demand
Example 2.18
Example 2.19
Test Yourself, Exercise 2.5
2.6 Decimals
Addition and subtraction
Example 2.20
Multiplication
Example 2.21
Division
Example 2.22
Example 2.23
Example 2.24
Test Yourself, Exercise 2.6
2.7 Negative numbers
Example 2.25
Example 2.26
Example 2.27
Example 2.28
Test Yourself, Exercise 2.7
2.8 Powers
Example 2.29
Example 2.30
Example 2.31
Example 2.32
Example 2.33
Example 2.34
Example 2.35
Example 2.36
Example 2.37
Example 2.38
Example 2.39
Example 2.40
Example 2.41
Test Yourself, Exercise 2.8
2.9 Roots and fractional powers
Example 2.42
Example 2.43
Example 2.44
Example 2.45
Example 2.46
Example 2.47
Example 2.48
Example 2.49
Test Yourself, Exercise 2.9
2.10 Logarithms
Example 2.50
Example 2.51
Example 2.52
Example 2.53
Example 2.54
Test Yourself, Exercise 2.10
Chapter 3: Introduction to algebra
Learning objectives
3.1 Representation
Example 3.1
Test Yourself, Exercise 3.1
3.2 Evaluation
Example 3.2
Example 3.3
Example 3.4
Example 3.5
Test Yourself, Exercise 3.2
3.3 Simplification: addition and subtraction
Example 3.6
Example 3.7
Example 3.8
Example 3.9
Example 3.10
Test Yourself, Exercise 3.3
3.4 Simplification: multiplication
Example 3.11
Example 3.12
Example 3.13
Example 3.14
Example 3.15
Example 3.16
Example 3.17
Example 3.18
Example 3.19
Test Yourself, Exercise 3.4
3.5 Simplification: factorizing
Example 3.20
Example 3.21
Example 3.22
Example 3.23
Example 3.24
Example 3.25
Example 3.26
Example 3.27
Test Yourself, Exercise 3.5
3.6 Simplification: division
Example 3.28
Example 3.29
Example 3.30
Example 3.31
Example 3.32
Example 3.33
Example 3.34
Example 3.35
Test Yourself, Exercise 3.6
3.7 Solving simple equations
Example 3.36
Example 3.37
Example 3.38
Example 3.39
Example 3.40
Example 3.41
Example 3.42
Test Yourself, Exercise 3.7
3.8 The summation sign Sigma
Example 3.43
Example 3.44
Example 3.45
Example 3.46
Test Yourself, Exercise 3.8
3.9 Inequality signs
Example 3.47
Example 3.48
Example 3.49
Example 3.50
Example 3.51
Example 3.52
Example 3.53
Example 3.54
Test Yourself, Exercise 3.9
Chapter 4: Graphs and functions
Learning objectives
4.1 Functions
Test Yourself, Exercise 4.1
4.2 Inverse functions
Example 4.1
Example 4.2
Example 4.3
Test Yourself, Exercise 4.2
4.3 Graphs of linear functions
Example 4.4
Example 4.5
Test Yourself, Exercise 4.3
4.4 Fitting linear functions
Example 4.6
Test Yourself, Exercise 4.4
4.5 Slope
Example 4.7
Example 4.8
Example 4.9
Test Yourself, Exercise 4.5
4.6 Budget constraints
Example 4.10
Example 4.11
Test Yourself, Exercise 4.6
4.7 Non-linear functions
Example 4.12
Test Yourself, Exercise 4.7
4.8 Composite functions
Example 4.13
Example 4.14
Slope of non-linear functions
Example 4.15
Example 4.16
Test Yourself, Exercise 4.8
4.9 Using Excel to plot functions
Example 4.17
Plotting a graph using Excel
Test Yourself, Exercise 4.9
4.10 Functions with two independent variables
Example 4.18
Example 4.19
The Cobb–Douglas production function
Example 4.20
Test Yourself, Exercise 4.10
4.11 Summing functions horizontally
Example 4.21
Example 4.22
Test Yourself, Exercise 4.11
Chapter 5: Linear equations
Learning objectives
5.1 Simultaneous linear equation systems
5.2 Solving simultaneous linear equations
5.3 Graphical solution
Example 5.1
Example 5.2
Test Yourself, Exercise 5.1
5.4 Equating to same variable
Example 5.3
Example 5.4
Example 5.5
Test Yourself, Exercise 5.2
5.5 Substitution
Example 5.6
Example 5.7
Test Yourself, Exercise 5.3
5.6 Row operations
Example 5.8
Example 5.9
Test Yourself, Exercise 5.4
5.7 More than two unknowns
Example 5.10
Example 5.11
Test Yourself, Exercise 5.5
5.8 Which method?
Example 5.12
Example 5.13
Example 5.14
Test Yourself, Exercise 5.6
5.9 Comparative statics and the reduced form of an economic model
Equilibrium and comparative statics
Reduced form
Example 5.15
Reduced form and comparative static analysis of monopoly
Example 5.16
The effect of a proportional sales tax
Example 5.17
The reduced form of a Keynesian macroeconomic model
Reduced forms in models with more than one independent variable
Test Yourself, Exercise 5.7
5.10 Price discrimination
Example 5.18
Example 5.19
Test Yourself, Exercise 5.8
5.11 Multiplant monopoly
Example 5.20
Example 5.21
Price discrimination with multiplant monopoly
Example 5.22
Test Yourself, Exercise 5.9
Appendix: linear programming
Constrained maximization
Example 5.A1
Example 5.A2
Example 5.A3
Example 5.A4
Test Yourself, Exercise 5.A1
Constrained minimization
Example 5.A5
Example 5.A6
Test Yourself, Exercise 5.A2
Mixed constraints
Example 5.A7
Test Yourself, Exercise 5.A3
More than two variables
Chapter 6: Quadratic equations
Learning objectives
6.1 Solving quadratic equations
6.2 Graphical solution
Example 6.1
Example 6.2
Plotting quadratic functions with Excel
6.3 Factorization
Example 6.3
Example 6.4
Test Yourself, Exercise 6.1
6.4 The quadratic formula
Example 6.5
Example 6.6
Test Yourself, Exercise 6.2
6.5 Quadratic simultaneous equations
Example 6.7
Example 6.8
Test Yourself, Exercise 6.3
6.6 Polynomials
Example 6.9
Example 6.10
Example 6.11
Test Yourself, Exercise 6.4
Chapter 7: Financial mathematics
Learning objectives
7.1 Discrete and continuous growth
7.2 Interest
Example 7.1
Example 7.2
Example 7.3
Example 7.4
Calculating the final value of an investment
Example 7.3 (reworked)
Example 7.4 (reworked)
Example 7.5
Example 7.6
Changes in interest rates
Example 7.7
Example 7.8
Test Yourself, Exercise 7.1
7.3 Part year investment and the annual equivalent rate
Nominal annual interest rates
Example 7.9
The Annual Equivalent Rate (AER) and Annual Percentage Rate (APR)
Example 7.10
Example 7.11
Example 7.12
Interest rates on Treasury Bills
Example 7.13
Test Yourself, Exercise 7.2
7.4 Time periods, initial amounts and interest rates
Initial amount
Example 7.14
Time period
Example 7.15
Example 7.16
Example 7.17
Interest rates
Example 7.18
Example 7.19
Example 7.20
Test Yourself, Exercise 7.3
7.5 Investment appraisal: net present value
Example 7.21
Example 7.22
Example 7.23
Example 7.24
Example 7.25
Investment appraisal using a spreadsheet
Example 7.26
Example 7.27
Test Yourself, Exercise 7.4
7.6 The internal rate of return
Example 7.28
Example 7.29
Deficiencies of the IRR method
Example 7.30
Example 7.31
Test Yourself, Exercise 7.5
7.7 Geometric series and annuities
Geometric series
Example 7.32
Example 7.33
Sum of a geometric series
Example 7.34
Example 7.35
Example 7.36
Example 7.37
Example 7.38
Example 7.39
Test Yourself, Exercise 7.6
7.8 Perpetual annuities
Example 7.40
Example 7.41
Example 7.42
Test Yourself, Exercise 7.7
7.9 Loan repayments
Example 7.43
Example 7.44
Example 7.45
Example 7.46
Example 7.47
Example 7.48
Test Yourself, Exercise 7.8
7.10 Other applications of growth and decline
Example 7.49
Example 7.50
Example 7.51
Example 7.52
Example 7.53
Example 7.54
Test Yourself, Exercise 7.9
Chapter 8: Introduction to calculus
Learning objectives
8.1 The differential calculus
Example 8.1
Example 8.2
Example 8.3
Test Yourself, Exercise 8.1
8.2 Rules for differentiation
Example 8.4
Example 8.5
Example 8.6
Example 8.7
Example 8.8
Example 8.9
Example 8.10
Example 8.11
Example 8.12
Example 8.13
Test Yourself, Exercise 8.2
8.3 Marginal revenue and total revenue
Example 8.14
Example 8.15
Example 8.16
Example 8.17
Test Yourself, Exercise 8.3
8.4 Marginal cost and total cost
Example 8.18
Example 8.19
Example 8.20
Test Yourself, Exercise 8.4
8.5 Profit maximization
Example 8.21
Example 8.22
Test Yourself, Exercise 8.5
8.6 Respecifying functions
Example 8.23
Example 8.24
Test Yourself, Exercise 8.6
8.7 Point elasticity of demand
Example 8.25
Example 8.26
Test Yourself, Exercise 8.7
8.8 Tax yield
Example 8.27
Test Yourself, Exercise 8.8
8.9 The Keynesian multiplier
Example 8.28
Test Yourself, Exercise 8.9
Chapter 9: Unconstrained optimization
Learning objectives
9.1 First-order conditions for a maximum
Test Yourself, Exercise 9.1
9.2 Second-order condition for a maximum
Example 9.1
Example 9.2
Test Yourself, Exercise 9.2
9.3 Second-order condition for a minimum
Example 9.3
Test Yourself, Exercise 9.3
9.4 Summary of second-order conditions
Example 9.4
End-point solutions
Test Yourself, Exercise 9.4
9.5 Profit maximization
Example 9.5
Test Yourself, Exercise 9.5
9.6 Inventory control
Example 9.6
Test Yourself, Exercise 9.6
9.7 Comparative static effects of taxes
(a) Per-unit sales tax
(b) A lump sum tax
(c) A percentage profits tax
Test Yourself, Exercise 9.7
Chapter 10: Partial differentiation
Learning objectives
10.1 Partial differentiation and the marginal product
Example 10.1
Example 10.2
Example 10.3
Example 10.4
Example 10.5
Test Yourself, Exercise 10.1
10.2 Further applications of partial differentiation
Elasticity
Example 10.6
Consumer utility functions
Example 10.7
Example 10.8
The Keynesian multiplier
Example 10.9
Cost and revenue functions
Example 10.10
Example 10.11
Test Yourself, Exercise 10.2
10.3 Second-order partial derivatives
Example 10.12
Example 10.13
Example 10.14
Example 10.15
Test Yourself, Exercise 10.3
10.4 Unconstrained optimization: functions with two variables
Example 10.16
Example 10.17
Example 10.18
Example 10.19
Example 10.20
Example 10.21
Test Yourself, Exercise 10.4
10.5 Total differentials and total derivatives
Example 10.22
Total differentials
Example 10.23
Euler’s theorem
Example 10.24
Total derivatives
Example 10.25
Test Yourself, Exercise 10.5
Chapter 11: Constrained optimization
Learning objectives
11.1 Constrained optimization and resource allocation
11.2 Constrained optimization by substitution
Example 11.1
Example 11.1 (reworked)
Example 11.2
Example 11.3
Example 11.4
Example 11.5
Test Yourself, Exercise 11.1
11.3 The Lagrange multiplier: constrained maximization with two variables
Example 11.6
Example 11.7
Test Yourself, Exercise 11.2
11.4 The Lagrange multiplier: second-order conditions
11.5 Constrained minimization using the Lagrange multiplier
Example 11.8
Example 11.9
Example 11.10
Test Yourself, Exercise 11.3
11.6 Constrained optimization with more than two variables
Example 11.11
Example 11.12
Example 11.13
Example 11.14
Example 11.15
Test Yourself, Exercise 11.4
Chapter 12: Further topics in calculus
Learning objectives
12.1 Overview
12.2 The chain rule
Example 12.1
Example 12.2
The marginal revenue productivity theory of the demand for labour
Example 12.3
Example 12.4
Point elasticity of demand
Example 12.5
Example 12.6
Test Yourself, Exercise 12.1
12.3 The product rule
Example 12.7
Example 12.8
Example 12.9
Example 12.10
Test Yourself, Exercise 12.2
12.4 The quotient rule
Example 12.11
Example 12.12
Example 12.13
Minimum average cost
12.5 Individual labour supply
Example 12.14
Test Yourself, Exercise 12.3
12.6 Integration
Example 12.15
Example 12.16
Example 12.17
Example 12.18
Example 12.19
Test Yourself, Exercise 12.4
12.7 Definite integrals
Example 12.20
Definite integrals of marginal cost functions
Definite integrals of marginal revenue functions
Integration and consumer surplus
Example 12.21
Test Yourself, Exercise 12.5
Chapter 13: Dynamics and difference equations
Learning objectives
13.1 Dynamic economic analysis
13.2 The cobweb: iterative solutions
Example 13.1
Example 13.2
Example 13.3
Test Yourself, Exercise 13.1
13.3 The cobweb: difference equation solutions
Example 13.4
Example 13.5
Example 13.6
Test Yourself, Exercise 13.2
13.4 The lagged Keynesian macroeconomic model
Example 13.7
Difference equation solution
Example 13.8
Example 13.9
Example 13.10
Test Yourself, Exercise 13.3
13.5 Duopoly price adjustment
Example 13.11
Example 13.12
Test Yourself, Exercise 13.4
Chapter 14: Exponential functions, continuous growth and differential equations
Learning objectives
14.1 Continuous growth and the exponential function
Example 14.1
The natural exponential function
14.2 Accumulated final values after continuous growth
Example 14.2
Example 14.3
Example 14.4
Continuous and discrete growth rates compared
Test Yourself, Exercise 14.1
14.3 Continuous growth rates and initial amounts
Derivation of continuous rates of growth
Example 14.5
Initial amounts
Example 14.6
Example 14.7
Test Yourself, Exercise 14.2
14.4 Natural logarithms
Example 14.8
Determination of continuous growth rates using natural logarithms
Example 14.9
Example 14.10
Example 14.11
Example 14.12
Comparison of discrete and continuous growth
Example 14.13
Test Yourself, Exercise 14.3
14.5 Differentiation of logarithmic functions
14.6 Continuous time and differential equations
14.7 Solution of homogeneous differential equations
Example 14.14
Differential equation solutions and growth rates
Test Yourself, Exercise 14.4
14.8 Solution of non-homogeneous differential equations
Example 14.15
Example 14.16
Convergence and stability
Checking differential equation solutions with Excel
Test Yourself, Exercise 14.5
14.9 Continuous adjustment of market price
Example 14.17
Example 14.18
Test Yourself, Exercise 14.6
14.10 Continuous adjustment in a Keynesian macroeconomic model
Example 14.19
Example 14.20
Test Yourself, Exercise 14.7
Chapter 15: Matrix algebra
Learning objectives
15.1 Introduction to matrices and vectors
Matrix addition and subtraction
Example 15.1
Example 15.2
Scalar multiplication
Example 15.3
Example 15.4
Test Yourself, Exercise 15.1
15.2 Basic principles of matrix multiplication
Example 15.5
Test Yourself, Exercise 15.2
15.3 Matrix multiplication – the general case
Example 15.6
Using Excel for matrix multiplication
Example 15.7
Example 15.8
Vectors of coefficients
Example 15.9
Test Yourself, Exercise 15.3
15.4 The matrix inverse and the solution of simultaneous equations
Conditions for the existence of the matrix inverse
Test Yourself, Exercise 15.4
15.5 Determinants
Example 15.10
The determinant of a 3rd order matrix
Example 15.11
Example 15.11 (reworked)
Test Yourself, Exercise 15.5
15.6 Minors, cofactors and the Laplace expansion
Minors
Example 15.12
Cofactors
Example 15.13
The Laplace expansion
Example 15.14
Using Excel to evaluate determinants
Test Yourself, Exercise 15.6
15.7 The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula
The transpose of a matrix
The cofactor matrix
The adjoint matrix
The inverse matrix
Example 15.15
Example 15.16
Derivation of the matrix inverse formula
Using Excel for matrix inversion
Test Yourself, Exercise 15.7
15.8 Application of the matrix inverse to the solution of linear simultaneous equations
Example 15.17
Using Excel to solve simultaneous equations
Example 15.18
Estimating the parameters of an economic model
Test Yourself, Exercise 15.8
15.9 Cramer’s rule
Example 15.19
Test Yourself, Exercise 15.9
15.10 Second-order conditions and the Hessian matrix
The Hessian matrix
Example 15.20
3rd order Hessians
Example 15.21
Higher order Hessians
Test Yourself, Exercise 15.10
15.11 Constrained optimization and the bordered Hessian
Maximization
Minimization
Example 15.22
Example 15.23
Constrained optimization with any number of variables and constraints
Test Yourself, Exercise 15.11
Answers
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Symbols and terminology
