Optimization Techniques for Economists

Module description


Optimising decision behaviour is at the core of most economic analysis. Whether we ask how a consumer should behave, how firms should compete in a market or how governments should decide on their monetary policy, the ability to solve optimisation problems is key to finding an answer. This module provides a thorough introduction to the techniques involved. It will treat unconstrained and constrained optimisation, basic variation calculus and optimal control. It expands on the optimisation techniques introduced in the microeconomics and macroeconomics courses in the first term and lays the foundation for many advanced economic option courses in the second term.

Additional Information: Internationalisation

Microeconomics is relevant across countries as it is based on mathematical models.


All of the resources for this module are available on the ELE (Exeter learning Environment).


This module equips students with logical thinking, numeracy and writing skills, as well as an understanding and theoretical knowledge of economic issues. These help students think like economists, a quality highly valued by employers.

Full module specification

Module title:Optimization Techniques for Economists
Module code:BEEM103
Module level:M
Academic year:2016/7
Module lecturers:
  • Professor Dieter Balkenborg - Convenor
Module credit:15
ECTS value:






Duration of module: Duration (weeks) - term 1:


Module aims

Economic problems are often expressed using mathematical models which are to be formulated, analysed and to be confronted with real-world data. The module aims to make you familiar with those mathematical tools and methods which are used frequently in most economic models and to demonstrate how they are applied.

ILO: Module-specific skills

  • 1. demonstrate the skill to differentiate functions in several variables
  • 2. solve economic optimisation problems and learn to handle the essential techniques used in linear algebra, difference and differential equations

ILO: Discipline-specific skills

  • 3. understand the important role of mathematical tools in economics and related disciplines in a global setting
  • 4. apply essential skills to analyse models from microeconomics and macroeconomics
  • 5. demonstrate familiarity with concepts of linear algebra that are essential for econometrics

ILO: Personal and key skills

  • 6. demonstrate numeracy and the ability to handle logical and structured problem analysis
  • 7. present written and quantitative data effectively
  • 8. demonstrate independent learning and time management
  • 9. demonstrate inductive and deductive reasoning

Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad

Details of learning activities and teaching methods

CategoryHours of study timeDescription
Contact hours24Lectures & Tutorials

Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
Tutorial exercisesVarious1-9Verbal

Summative assessment (% of credit)

CourseworkWritten examsPractical exams

Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Examination802 hours1-9Written
In-class test101 hour1-9Written
In-class test101 hour1-9Written

Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
Examination and in-class testsExamination (100%) 2 hours1-9Aug/Sep

Syllabus plan

Introduction, Univariate optimization
Multivariate functions, unconstrained optimization and applications Constrained optimization and applications. The Kuhn-Tucker theorem
Difference- and differential equations
The calculus of variations
Optimal control and applications

Indicative learning resources - Basic reading

Basic reading:
Sydsaeter, K., Hammond, P.J., Seierstad, A and Strøm, A. (2006) Further Mathematics for Economic
Analysis, 2nd Main textbook for the module primarily because of the many exercises and worked examples it contains.
It is not an easy textbook to find your way through, but it covers all the advanced topics.
edition, Prentice Hall
Sydsæter, K. and Hammond, P.J. (2006) Essential Mathematics for Economic Analysis, 2nd edition,
Prentice Hall
This book covers slightly less advanced material and will also occasionally be used.
Dowling, E. T. Schaum’s outlines (1980) Introduction to Mathematical Economics, McGraw Hill
Inexpensive, brief summaries and hundreds of worked out examples. We will use it for additional
exercises. Highly recommended.
The following are some alternative standard textbook covering similar topics. You may find some more
Simon, C.P. and Blume, L. (1994) Mathematics for Economists, Norton
Wainwright, K. and Chiang, A.C. (2005) Fundamental Methods of Mathematical Economics, 4th Edition,
McGraw Hill
Sundaram, R.K. (1996) A First Course in Optimization Theory, Cambridge University Press
Arrow, K.J. and Endhoven, A. (1961) Quasi-concave Programming, Econometrica, Vol 29, No 4, pp 779 –
The results in this article will form the highlight of the first half of the module.
Kamien, M.I. and Schwartz, N.L. (1991) Dynamic Optimization: The Calculus of Variations and Optimal
Control in Economics and Management, Elsevier Science; 2nd edition

Excellent textbook for the second part of the module, but out of print and it has always been very
Dixit, A.K.A brief, intuitive introduction for Economists.(1990) Optimization in Economic Theory, Oxford; 2nd edition
For preparation:
Hoffman, L.D. and Bradley, G.L. (2000) Calculus for Business, Economics and the Social and Life
Sciences, McGraw Hill, 7th Edition

My favourite introduction to calculus with lots of really good exercises and worked examples.
Bradley, T. and Patton, P. (2005) Essential Mathematics for Economics and Business, Wiley.
Renshaw, G. (2002) Maths for Economics, Oxford Ian, J. (2002) Mathematics for Economics and Business, Addison-Wesley

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