Basic Mathematics for Economists

Citation

Lis, P., & Rosser, M. (2025). Basic Mathematics for Economists (4th ed.). Routledge.

Chapter Summary

The fourth edition has sixteen chapters in about 570 pages of text; the contents also list answers and, in the front matter, a list of symbols and terminology. Routledge describes the book as suitable both for students with only a basic mathematics background and for those who have studied more mathematics but want clear explanations of the fundamentals. It starts by revising arithmetic and algebra and works up to calculus, comparative statics, dynamic analysis and matrix algebra, explaining each topic through applications in economics, finance and business. The new edition adds and updates real-world applications and gives fuller treatment to savings and pension schemes and to asset valuation. The page ranges below show how the weight is distributed.

Chapters 1–3: Introduction; Arithmetic; Introduction to algebra

A short introduction (about seven pages) is followed by two chapters that rebuild the basics from the ground up: arithmetic (about 25 pages) and an introduction to algebra (about 30 pages). These are the chapters for readers whose school mathematics is rusty.

Chapters 4–5: Graphs and functions; Simultaneous linear equations

Two substantial chapters (about 45 and 40 pages) on representing economic relationships as functions and graphs, and on solving systems of linear equations, the tool behind market equilibrium and other simple economic models.

Chapters 6–7: Linear programming; Quadratic equations

Linear programming (about 20 pages) introduces optimisation subject to linear constraints before any calculus is used; quadratic equations (about 20 pages) extend the algebra to non-linear functions.

Chapter 8: Financial mathematics – series, time and investment

At more than 80 pages, the longest chapter in the book. It covers series and the time value of money for investment decisions; the publisher highlights the fuller analysis of savings and pension schemes and asset valuation techniques in this edition, and the chapter includes sections on asset valuation and the valuation of shares.

Chapters 9–11: Introduction to calculus; Unconstrained optimization; Partial differentiation

The calculus core: an introduction to calculus (about 25 pages), unconstrained optimisation (about 20 pages, placed before the treatment of several variables), and partial differentiation for functions of several variables (about 45 pages).

Chapter 12: Constrained optimization

About 30 pages on optimising subject to constraints, the standard setting for consumer and producer choice problems.

Chapter 13: Further topics in differentiation and integration

About 40 pages extending the calculus toolkit and introducing integration.

Chapters 14–15: Dynamics and difference equations; Exponential functions, continuous growth and differential equations

The dynamic analysis promised in the description: difference equations for variables that change over discrete periods (about 40 pages), then exponential functions, continuous growth and differential equations (about 35 pages).

Chapter 16: Matrix algebra

The final and second-longest chapter (about 60 pages) introduces matrix methods.

Key Concepts

Terms that recur in the book, such as arc elasticity, budget constraint, cobweb model, isoquant, annuity and yield to maturity, show the kinds of economic and financial applications it uses.

Chapters 1–7: Algebraic Foundations

• Functions and graphs: expressing economic relationships such as demand and cost as functions and plotting them.
• Simultaneous linear equations: solving several equations together, for example to find equilibrium values.
• Linear programming: maximising or minimising a linear objective subject to linear constraints.

Chapter 8: Financial Mathematics

• Series and the time value of money: the arithmetic of interest, discounting, savings plans, loans and pensions.
• Asset valuation: pricing shares and other assets from the future payments they generate.

Chapters 9–13: Calculus and Optimisation

• Unconstrained optimization: finding stationary points and checking second-order conditions.
• Partial differentiation: rates of change of functions of several variables, used in comparative statics.
• Constrained optimization: optimising subject to constraints such as a budget.

Chapters 14–16: Dynamics and Matrices

• Difference and differential equations: describing how variables evolve over time in discrete and continuous models.
• Matrix algebra: compact methods for linear systems.

Critical Analysis

Strengths

• Starts genuinely from the beginning. Three chapters on arithmetic and algebra, about 60 pages in all, precede the main material, which suits students who did not take mathematics to an advanced level at school.
• Applications throughout. The publisher stresses that all topics are explained in the context of applications in economics, finance and business, and recurring terms such as elasticities, isoquants, profit maximisation, price discrimination and cobweb models confirm the economic focus.
• Strong financial mathematics. Chapter 8 is by far the longest, and the fourth edition expands savings, pensions and asset valuation; students in finance or business programmes will find more here than in many economics-only mathematics books.
• Self-study support. The book includes answers and digital supplements for students and lecturers; a reviewer quoted by Routledge, Gloria L. Bernal (Pontificia Universidad Javeriana), uses it as the main support for the mathematics in an intermediate microeconomics course.

Limitations

• Introductory by design. The publisher presents the book as covering the basic tenets needed to understand mathematics and its use in economics; students heading for more theoretical economics will need a more formal treatment of calculus, optimisation and linear algebra later.
• Matrix algebra comes last. Linear algebra is held back to the final chapter, so courses that want matrices early, or that use them for multi-market models, will need to reorder the reading.
• Long for its level. At about 600 pages the book is substantial; a one-semester course will normally use only part of it.

Where It Fits in the Course

Within this course list, Lis and Rosser is the most elementary of the mathematics-for-economics texts and the natural first book for students whose algebra needs rebuilding. Sydsæter, Hammond, Strøm and Carvajal's Essential Mathematics for Economic Analysis covers a similar range with more mathematical precision and is a good next step or alternative for students who are already comfortable with school algebra. Ian Jacques's Mathematics for Economics and Business is another text written for business and economics students.

Chiang and Wainwright's Fundamental Methods of Mathematical Economics goes further into equilibrium analysis, matrix algebra, optimisation and dynamics applied to economic models, suitable for the courses that follow this book. Brock and Malliaris's Differential Equations, Stability, and Chaos in Dynamic Economics is a graduate-level specialist text on dynamics, far beyond the scope of Chapters 14–15 here.

How to Use This Book

The book is aimed at first-year students of economics, finance and business, especially those without advanced school mathematics, and at stronger students who want clear explanations of fundamentals. Basic arithmetic is enough to start.

• Diagnose first: students with weak algebra should work through Chapters 2–3 carefully; others can skim them and start at Chapter 4.
• Core for a first course: Chapters 4–5, 7, 9–12, which cover functions, equations and optimisation with and without constraints.
• Finance and business students: add Chapter 8 early; it is long but self-contained in its topic.
• Second-term or later topics: Chapters 13–16 (integration, dynamics, matrices), together with Chapter 6 if linear programming is on the syllabus.

Do the exercises and check them against the answers provided; spreadsheets recur among the book's tools, so it is worth reproducing financial calculations such as loan repayments and pension savings in a spreadsheet alongside Chapter 8.