1. Mathematical models in economics
1.1 Introduction
1.2 A model of the market
1.3 Market equilibrium
1.4 Excise tax
1.5 Comments
Worked examples
Main topics/Key terms, notations and formulae
Exercises
2. Mathematical terms and notations
2.1 Sets
2.2 Functions
2.3 Composite functions
2.4 Graphs and equations
Worked examples
Main topics/Key terms, notations and formulae
Exercises
3. Sequences, recurrences, limits
3.1 Sequences
3.2 The first-order recurrence
3.3 Limits
3.4 Special cases
Worked examples
Main topics/Key terms, notations and formulae
Exercises
4. The elements of finance
4.1 Interest and capital growth
4.2 Income generation
4.3 The interval of compounding
Worked examples
Main topics/Key terms, notations and formulae
Exercises
5. The cobweb model
5.1 How stable is market equilibrium
5.2 An example
5.3 The general linear case
5.4 Economic interpretation
Worked examples
Main topics/Key terms, notations and formulae
Exercises
6. Introduction to calculus
6.1 The rate of change of a function
6.2 Rules for finding the derivative
6.3 Marginal cost as a derivative
6.4 The derivative of a composite function
6.5 The derivative of an inverse function
Worked examples
Main topics/Key terms, notations and formulae
Exercises
7. Some special functions
7.1 Powers
7.2 The exponential function and its properties
7.3 Continuous compounding of interest
7.4 The logarithm function
7.5 Trigonometrical functions
Worked examples
Main topics/Key terms, notations and formulae
Exercises
8. Introduction to optimisation
8.1 Profit maximisation
8.2 Critical points
8.3 Optimisation in an interval
8.4 Infinite intervals
Worked examples
Main topics/Key terms, notations and formulae
Exercises
9. The derivative in economics--I
9.1 Elasticity of demand
9.2 Profit maximisation again
9.3 Competition versus monopoly
Worked examples
Main topics/Key terms, notations and formulae
Exercises
10. The derivative in economics--II
10.1 The efficient small firm
10.2 Startup and breakeven points
Worked examples
Main topics/Key terms, notations and formulae
Exercises
11. Partial derivatives
11.1 Functions of several variables
11.2 Partial derivatives
11.3 The chain rule
Worked examples
Main topics/Key terms, notations and formulae
Exercises
12. Applications of partial derivatives
12.1 Functions defined implicitly
12.2 The derivative of an implicit function
12.3 Contours and isoquants
12.4 Scale effects and homogeneous functions
Worked examples
Main topics/Key terms, notations and formulae
Exercises
13. Optimisation in two variables
13.1 Profit maximisation again
13.2 How prices are related to quantities
13.3 Critical points
13.4 Maxima, minima, and saddle points
13.5 Classification of critical points - introduction
13.6 The classification of critical points in general
Worked examples
Main topics/Key terms, notations and formulae
Exercises
14. Vectors, preferences and convexity
14.1 Vectors and bundles
14.2 Prices and budgets
14.3 Preferences, utility, and indifference curves
14.4 Linear and convex combinations
14.5 Choosing optimal bundles
Worked examples
Main topics/Key terms, notations and formulae
Exercises
15. Matrix algebra
15.1 What is a matrix
……
16. Linear equations--I
17. Linear equations--II
18. Inverse matrices
19. The input-output model
20. Determinants
21. Constrained optimisation
22. Lagrangeans and the consumer
23. Second-order recurrence equations
24. Macroeconomic applications
25. Areas and integrals
26. Techniques of integration
27. First-order differential equations
28. Second-order differential equations
Solutions to selected exercises
Index
This book is an introduction to calculus and linear algebra for students of disciplines such as economics, finance, business, management, and accounting. It is intended for readers who may have already encountered some differential calculus, and it will also be appropriate for those with less experience, possibly used in conjunction with one of the many more elementary texts on basic mathematics.
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