Mathematics for Economics and Business

Citation

Jacques, I. (2018). Mathematics for Economics and Business (9th ed.). Pearson.

Chapter Summary

Introduction: Getting Started

A short guide for students on how to work with the text. It describes the mix of students on first-year economics courses, recommends studying in short sessions and attempting the problems, and shows how the chapters depend on each other. Chapter 3 can be skipped by economics students who want to reach calculus quickly.

Chapter 1: Linear Equations

Starts from elementary algebra (negative numbers, expressions, brackets, fractions, equations and inequalities), then moves to graphs of linear equations and the algebraic solution of simultaneous equations. The economic applications are supply and demand analysis and national income determination, with a section on transposition of formulae.

Chapter 2: Non-linear Equations

Quadratic functions, applied to revenue, cost and profit, then indices and logarithms and the exponential and natural logarithm functions.

Chapter 3: Mathematics of Finance

Percentages (including index numbers and inflation), compound interest, geometric series and investment appraisal. This chapter is the most relevant to business and accountancy students.

Chapter 4: Differentiation

The derivative of a function, rules of differentiation (constant, sum, difference, chain, product and quotient rules), marginal functions for revenue, cost, production, consumption and savings, elasticity, optimisation of economic functions, and the derivative of the exponential and natural logarithm functions.

Chapter 5: Partial Differentiation

Functions of several variables, partial elasticity and marginal functions, comparative statics, unconstrained optimisation, constrained optimisation, and Lagrange multipliers.

Chapter 6: Integration

Indefinite and definite integration.

Chapter 7: Matrices

Basic matrix operations, matrix inversion and Cramer's rule.

Chapter 8: Linear Programming

Graphical solution of linear programming problems and applications of linear programming.

Chapter 9: Dynamics

Difference equations and differential equations, each with applications to national income determination and to supply and demand analysis.

Back matter

Answers to problems for all nine chapters, a glossary and an index. Every section ends with Key Terms and two parallel exercise sets, and every chapter ends with a "Formal mathematics" section, multiple choice questions and examination questions.

Key Concepts

Chapters 1–3: Algebra, Equations and Finance

• Simultaneous linear equations: solving for supply-demand equilibrium and national income.
• Quadratic, exponential and logarithmic functions: the functions behind revenue, cost, profit and growth.
• Compound interest and investment appraisal: the mathematics of present value and returns.

Chapters 4–6: Calculus

• Marginal functions: derivatives interpreted as marginal revenue, cost and similar quantities.
• Elasticity: percentage responsiveness, expressed with derivatives.
• Optimisation: finding maxima and minima of economic functions, with or without constraints.
• Partial derivatives and Lagrange multipliers: tools for functions of several variables and constrained choice.
• Integration: indefinite and definite integrals.

Chapters 7–9: Matrices, Linear Programming and Dynamics

• Matrix inverse and Cramer's rule: methods for solving systems of equations.
• Linear programming: optimisation with linear objective and constraints, solved graphically.
• Difference and differential equations: models of how economic variables change over time.

Critical Analysis

Strengths

• Written for readers with little maths. The preface says the text assumes very little prerequisite knowledge and is suitable for students who have not studied mathematics for some time. Chapter 1 begins with negative numbers and brackets.
• Designed for self-study. The preface describes an informal style with many worked examples and detailed solutions, so work can be checked. Problems are interspersed in the text, and answers to every question are printed at the back.
• Two levels of exercise in every section. Each section ends with a basic exercise and a parallel starred exercise that is more challenging, and the author tells readers to use the starred exercise as a self-test of whether a section needs reading.
• Wide range. The preface says the material runs from percentages and linear equations to constrained optimisation of multivariate functions, so it can serve both lower- and higher-level quantitative methods courses.
• Assessment practice. The edition adds over 200 questions, with multiple choice questions and longer examination-style questions at the end of every chapter.

Limitations

• Applications are standard textbook models. The economic applications named in the contents are supply and demand, national income, revenue, cost and profit, and consumption and savings; the text does not aim at advanced economic theory.
• A book of techniques. The book teaches calculation methods more than formal proof, although each chapter has a "Formal mathematics" section. Students who need a proof-based course will need a different text.
• Limited scope beyond the nine chapters. Topics such as probability, statistics, optimal control or real analysis are not covered.

Where It Fits in the Course

Within the mathematical economics list this is a first-year text, comparable with Lis and Rosser's Basic Mathematics for Economists, which rebuilds arithmetic and algebra before introducing calculus, and with Sydsæter, Hammond, Strøm and Carvajal's Essential Mathematics for Economic Analysis, which goes further in calculus, optimisation and linear algebra. Chiang and Wainwright's Fundamental Methods of Mathematical Economics is the natural next step after Jacques, with a heavier use of matrix algebra and dynamic methods, and Brock and Malliaris's book on differential equations in economics is a rigorous graduate-level treatment of what Chapter 9 only introduces.

Jacques differs from its course mates in including mathematics of finance, linear programming and a dynamics chapter, which suits business as well as economics students.

How to Use This Book

The book is for first-year economics, business and management students, and for anyone returning to mathematics. Beginners can start at Chapter 1 and work in order. Students with school algebra and some calculus can test themselves on the starred exercises and skip what they know.

Read one section at a time; the author estimates between one and two hours per section. Attempt the in-text problems before reading solutions. Core chapters for most economics courses are 1, 2, 4 and 5, with Chapters 6 to 9 added as the syllabus requires; Chapter 3 is best for business and accountancy students. Use the multiple choice questions at the end of a chapter for recall, and leave the examination questions until revision. This guide covers the ninth edition; a tenth edition (2023) has since appeared.